Sven Koenig

AIJ Journal 2026 Journal Article

Approximate multi-objective search

• Han Zhang
• Oren Salzman
• T. K. Satish Kumar
• Ariel Felner
• Carlos Hernández Ulloa
• Sven Koenig

JAAMAS Journal 2026 Journal Article

Confidence-Based curricula for multi-agent path finding via reinforcement learning

• Thomy Phan
• Joseph Driscoll
• Sven Koenig

Abstract A wide range of real-world applications can be formulated as Multi-Agent Path Finding (MAPF) problem, where the goal is to find collision-free paths for multiple agents with individual start and goal locations. State-of-the-art MAPF solvers are mainly centralized and rely on global information, which limits their scalability and flexibility when facing changes or new maps that require expensive replanning. Multi-agent reinforcement learning (MARL) offers an alternative approach to addressing MAPF problems by learning decentralized policies that generalize across a variety of maps. While there exist some prior works that attempt to connect both areas, the proposed techniques are heavily engineered and very complex due to the integration of many mechanisms that limit generality and are expensive to use. We argue that much simpler and more general approaches are needed to enable decentralized MAPF in a sustainable manner at significantly lower cost. In this paper, we propose Confidence-based Auto-Curriculum for Team Update Stability (CACTUS) as a lightweight MARL approach to decentralized MAPF. CACTUS defines a simple reverse curriculum scheme, where the goal of each agent is randomly placed within an allocation radius around the agent’s start location. The allocation radius increases gradually as all agents improve, which is assessed by a confidence-based measure. In addition, we propose an extension called Confidence- and Conflict-Based Curriculum Learning with Allocation Radius Adaptation (C \(^3\) LARA), using weighted sampling of goal locations to improve conflict resolution in scenarios of high agent density. We provide a theoretical analysis of the strengths and limitations of CACTUS regarding exploration efficiency, optimality, and multi-agent coordination. We evaluate CACTUS and C \(^3\) LARA across various maps of different sizes, obstacle densities, and numbers of agents. Our experiments demonstrate better performance and generalization capabilities than state-of-the-art MARL approaches with less than 600, 000 trainable parameters, which is less than 5% of the neural network size of current MARL approaches to decentralized MAPF.

AAAI Conference 2026 Conference Paper

Deeper Treatment of the Bi-objective Search Framework

• Shawn Skyler
• Dor Atzmon
• Ariel Felner
• Oren Salzman
• Carlos Hernández Ulloa
• Sven Koenig

In Bi-Objective Search (BOS), the task is to compute the Pareto-optimal frontier of paths in a graph with two cost values per edge. Recent work introduced a general BOS framework that classifies search nodes and studies how ordering functions affect expansion order. In this paper, we continue this line of research. We further refine the classes of nodes and show that many nodes that were added to the open list and are classified as never-expand nodes still need to be extracted and further examined. Additionally, we introduce a method that enables constant-time dominance checks for the MIN and MAX ordering functions. This allows a practical usage of these ordering functions, as we demonstrate in our experimental section.

AAAI Conference 2026 Conference Paper

Discrete-Guided Diffusion for Scalable and Safe Multi-Robot Motion Planning

• Jinhao Liang
• Sven Koenig
• Ferdinando Fioretto

Multi-Robot Motion Planning (MRMP) involves generating collision-free trajectories for multiple robots operating in a shared continuous workspace. While discrete multi-agent path finding (MAPF) methods are broadly adopted due to their scalability, their coarse discretization severely limits trajectory quality. In contrast, continuous optimization-based planners offer higher-quality paths but suffer from the curse of dimensionality, resulting in poor scalability with respect to the number of robots. This paper tackles the limitations of these two approaches by introducing a novel framework that integrates discrete MAPF solvers with constrained generative diffusion models. The resulting framework, called Discrete-Guided Diffusion (DGD), has three key characteristics: (1) it decomposes the original nonconvex MRMP problem into tractable subproblems with convex configuration spaces, (2) it combines discrete MAPF solutions with constrained optimization techniques to guide diffusion models capture complex spatiotemporal dependencies among robots, and (3) it incorporates a lightweight constraint repair mechanism to ensure trajectory feasibility. The proposed method sets a new state-of-the-art performance in large-scale, complex environments, scaling to 100 robots while achieving planning efficiency and high success rates.

AAAI Conference 2026 Conference Paper

Multi-Objective Search: Algorithms, Applications, and Emerging Directions

• Oren Salzman
• Carlos Hernández Ulloa
• Ariel Felner
• Sven Koenig

Multi-objective search (MOS) has emerged as a unifying framework for planning and decision-making problems where multiple, often conflicting, criteria must be balanced. While the problem has been studied for decades, recent years have seen renewed interest in the topic across AI applications such as robotics, transportation, and operations research, eflecting the reality that real-world systems rarely optimize a single measure. This paper surveys developments in MOS while highlighting cross-disciplinary opportunities, and outlines open challenges that define the emerging frontier of MOS research.

AAAI Conference 2026 Conference Paper

Spatially Grouped Curriculum Learning for Multi-Agent Path Finding

• Thomy Phan
• Sven Koenig

Multi-agent path finding (MAPF) is the challenging problem of finding conflict-free paths with minimal costs for multiple agents. While traditional MAPF solvers are centralized using heuristic search, reinforcement learning (RL) is becoming increasingly popular due to its potential to learn decentralized and generalizing policies. RL-based MAPF must cope with spatial coordination, which is often addressed by combining independent training with ad hoc measures like replanning and communication. Such ad hoc measures often complicate the approach and require knowledge beyond the actual accessible information in RL, such as the full map occupation or broadcast communication channels, which limits generalizability, effectiveness, and sample efficiency. In this paper, we propose Partitioned Attention-based Reverse Curricula for Enhanced Learning (PARCEL), considering a bounding region for each agent. PARCEL trains all agents with overlapping regions jointly via self-attention to avoid potential conflicts. By employing a reverse curriculum, where the bounding regions grow as the policies improve, all agents will eventually merge into a single coordinated group. We evaluate PARCEL in two simple coordination tasks and four MAPF benchmark maps. Compared with state-of-the-art RL-based MAPF methods, PARCEL demonstrates better effectiveness and sample efficiency without ad hoc measures.

AAAI Conference 2026 Conference Paper

Truncated Counterfactual Learning for Anytime Multi-Agent Path Finding

• Thomy Phan
• Shao-Hung Chan
• Sven Koenig

Anytime multi-agent path finding (MAPF) is a promising approach to scalable and collision-free path optimization in multi-agent systems. MAPF-LNS, based on Large Neighborhood Search (LNS), is the current state-of-the-art approach where a fast initial solution is iteratively optimized by destroying and repairing selected paths, i.e., a neighborhood, of the solution. Delay-based MAPF-LNS has demonstrated particular effectiveness in generating promising neighborhoods via seed agents, according to their delays. Seed agents are selected using handcrafted strategies or online learning, where the former relies on human intuition about underlying structures, while the latter conducts black-box optimization, ignoring any structure. In this paper, we propose Truncated Adaptive Counterfactual K-ranked LEarning (TACKLE) to select seed agents via informed online learning by leveraging handcrafted strategies as human intuition. We show theoretically that TACKLE dominates its handcrafted and black-box learning counterparts in the limit. Our experiments demonstrate cost improvements of at least 60% in instances with one thousand agents, compared with state-of-the-art anytime solvers.

IROS Conference 2025 Conference Paper

Accelerating Focal Search in Multi-Agent Path Finding with Tighter Lower Bounds

• Yimin Tang
• Zhenghong Yu
• Jiaoyang Li 0001
• Sven Koenig

Multi-Agent Path Finding (MAPF) involves finding collision-free paths for multiple agents while minimizing a cost function—an NP-hard problem. Bounded suboptimal methods like Enhanced Conflict-Based Search (ECBS) and Explicit Estimation CBS (EECBS) balance solution quality with computational efficiency using focal search mechanisms. While effective, traditional focal search faces a limitation: the lower bound (LB) value determining which nodes enter the FOCAL list often increases slowly in early search stages, resulting in a constrained search space that delays finding valid solutions. In this paper, we propose a novel bounded suboptimal algorithm, double-ECBS (DECBS), to address this issue by first determining the maximum LB value and then employing a best-first search guided by this LB to find a collision-free path. Experimental results demonstrate that DECBS outperforms ECBS in most test cases and is compatible with existing optimization techniques. DECBS can reduce nearly 30% high-level Constraint Tree (CT) nodes and 50% low-level focal search nodes. When agent density is high, DECBS achieves a 23. 5% average runtime improvement over ECBS with identical suboptimality bounds and optimizations.

IROS Conference 2025 Conference Paper

An Anytime, Scalable and Complete Algorithm for Embedding a Manufacturing Procedure in a Smart Factory

• Christopher Leet
• Aidan Sciortino
• Sven Koenig

Modern automated factories increasingly run manufacturing procedures using a matrix of programmable machines, such as 3D printers, interconnected by a programmable transport system, such as a fleet of tabletop robots. To embed a manufacturing procedure into a smart factory, an operator must: (a) assign each of its processes to a machine and (b) specify how agents should transport parts between machines. The problem of embedding a manufacturing process into a smart factory is termed the Smart Factory Embedding (SFE) problem. State-of-the-art SFE solvers can only scale to factories containing a couple dozen machines. Modern smart factories, however, may contain hundreds of machines. We fill this hole by introducing the first highly scalable solution to the SFE, TSACES, the Traffic System based Anytime Cyclic Embedding Solver. We show that TS-ACES is complete and can scale to SFE instances based on real industrial scenarios with more than a hundred machines.

AAAI Conference 2025 Conference Paper

Anytime Multi-Agent Path Finding with an Adaptive Delay-Based Heuristic

• Thomy Phan
• Benran Zhang
• Shao-Hung Chan
• Sven Koenig

Anytime multi-agent path finding (MAPF) is a promising approach to scalable and collision-free path optimization in multi-agent systems. MAPF-LNS, based on Large Neighborhood Search (LNS), is the current state-of-the-art approach where a fast initial solution is iteratively optimized by destroying and repairing selected paths of the solution. Current MAPF-LNS variants commonly use an adaptive selection mechanism to choose among multiple destroy heuristics. However, to determine promising destroy heuristics, MAPF-LNS requires a considerable amount of exploration time. As common destroy heuristics are stationary, i.e., non-adaptive, any performance bottleneck caused by them cannot be overcome by adaptive heuristic selection alone, thus limiting the overall effectiveness of MAPF-LNS. In this paper, we propose Adaptive Delay-based Destroy-and-Repair Enhanced with Success-based Self-learning (ADDRESS) as a single-destroy-heuristic variant of MAPF-LNS. ADDRESS applies restricted Thompson Sampling to the top-K set of the most delayed agents to select a seed agent for adaptive LNS neighborhood generation. We evaluate ADDRESS in multiple maps from the MAPF benchmark set and demonstrate cost improvements by at least 50% in large-scale scenarios with up to a thousand agents, compared with the original MAPF-LNS and other state-of-the-art methods.

AAAI Conference 2025 Conference Paper

Counterfactual Online Learning for Open-Loop Monte-Carlo Planning

• Thomy Phan
• Shao-Hung Chan
• Sven Koenig

Monte-Carlo Tree Search (MCTS) is a popular approach to online planning under uncertainty. While MCTS uses statistical sampling via multi-armed bandits to avoid exhaustive search in complex domains, common closed-loop approaches typically construct enormous search trees to consider a large number of potential observations and actions. On the other hand, open-loop approaches offer better memory efficiency by ignoring observations but are generally not competitive with closed-loop MCTS in terms of performance - even with commonly integrated human knowledge. In this paper, we propose Counterfactual Open-loop Reasoning with Ad hoc Learning (CORAL) for open-loop MCTS, using a causal multi-armed bandit approach with unobserved confounders (MABUC). CORAL consists of two online learning phases that are conducted during the open-loop search. In the first phase, observational values are learned based on preferred actions. In the second phase, counterfactual values are learned with MABUCs to make a decision via an intent policy obtained from the observational values. We evaluate CORAL in four POMDP benchmark scenarios and compare it with closed-loop and open-loop alternatives. In contrast to standard open-loop MCTS, CORAL achieves competitive performance compared with closed-loop algorithms while constructing significantly smaller search trees.

AIJ Journal 2025 Journal Article

EMOA*: A framework for search-based multi-objective path planning

• Zhongqiang Ren
• Carlos Hernández
• Maxim Likhachev
• Ariel Felner
• Sven Koenig
• Oren Salzman
• Sivakumar Rathinam
• Howie Choset

AAMAS Conference 2025 Conference Paper

Empirical Hardness in Multi-Agent Pathfinding: Research Challenges and Opportunities

• Jingyao Ren
• Eric Ewing
• T. K. Satish Kumar
• Sven Koenig
• Nora Ayanian

Multi-agent pathfinding (MAPF) is the problem of finding collisionfree paths for a team of agents on a map. Although MAPF is NPhard, the hardness of solving individual instances varies significantly, revealing a gap between theoretical complexity and actual hardness. This paper outlines three key research challenges in MAPF empirical hardness to understand such phenomena. The first challenge, known as algorithm selection, is determining the bestperforming algorithms for a given instance. The second challenge is understanding the key instance features that affect MAPF empirical hardness, such as structural properties like phase transition and backbone/backdoor. The third challenge is how to leverage our knowledge of MAPF empirical hardness to effectively generate hard MAPF instances or diverse benchmark datasets. This work establishes a foundation for future empirical hardness research and encourages deeper investigation into these promising and underexplored areas.

JAIR Journal 2025 Journal Article

Generative Curricula for Multi-Agent Path Finding via Unsupervised and Reinforcement Learning

• Thomy Phan
• Timy Phan
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the challenging problem of finding collision-free paths for multiple agents, which has a wide range of applications, such as automated warehouses, smart manufacturing, and traffic management. Recently, machine learning-based approaches have become popular in addressing MAPF problems in a decentralized and potentially generalizing way. Most learning-based MAPF approaches use reinforcement and imitation learning to train agent policies for decentralized execution under partial observability. However, current state-of-the-art approaches suffer from a prevalent bias to micro-aspects of particular MAPF problems, such as congestions in corridors and potential delays caused by single agents, leading to tight specializations through extensive engineering via oversized models, reward shaping, path finding algorithms, and communication. These specializations are generally detrimental to the sample efficiency, i.e., the learning progress given a certain amount of experience, and generalization to previously unseen scenarios. In contrast, curriculum learning offers an elegant and much simpler way of training agent policies in a step-by-step manner to master all aspects implicitly without extensive engineering. In this paper, we propose a generative curriculum approach to learning-based MAPF using Variational Autoencoder Utilized Learning of Terrains (VAULT). We introduce a two-stage framework to (I) train the VAULT via unsupervised learning to obtain a latent space representation of maps and (II) use the VAULT to generate curricula in order to improve sample efficiency and generalization of learning-based MAPF methods. For the second stage, we propose a bi-level curriculum scheme by combining our VAULT curriculum with a low-level curriculum method to improve sample efficiency further. Our framework is designed in a modular and general way, where each proposed component serves its purpose in a black-box manner without considering specific micro-aspects of the underlying problem. We empirically evaluate our approach in maps of the public MAPF benchmark set as well as novel artificial maps generated with the VAULT. Our results demonstrate the effectiveness of the VAULT as a map generator and our VAULT curriculum in improving sample efficiency and generalization of learning-based MAPF methods compared to alternative approaches. We also demonstrate how data pruning can further reduce the dependence on available maps without affecting the generalization potential of our approach.

ICRA Conference 2025 Conference Paper

Jointly Assigning Processes to Machines and Generating Plans for Autonomous Mobile Robots in a Smart Factory

• Christopher Leet
• Aidan Sciortino
• Sven Koenig

A modern smart factory runs a manufacturing procedure using a collection of programmable machines. Typically, materials are ferried between these machines using a team of mobile robots. To embed a manufacturing procedure in a smart factory, a factory operator must a) assign its processes to the smart factory's machines and b) determine how agents should carry materials between machines. A good embedding maximizes the smart factory's throughput; the rate at which it outputs products. Existing smart factory management systems solve the aforementioned problems sequentially, limiting the throughput that they can achieve. In this paper we introduce ACES, the Anytime Cyclic Embedding Solver, the first solver which jointly optimizes the assignment of processes to machines and the assignment of paths to agents. We evaluate ACES and show that it can scale to real industrial scenarios.

IROS Conference 2025 Conference Paper

RAILGUN: A Unified Convolutional Policy for Multi-Agent Path Finding Across Different Environments and Tasks

• Yimin Tang
• Xiao Xiong
• Jingyi Xi
• Jiaoyang Li 0001
• Erdem Biyik
• Sven Koenig

Multi-Agent Path Finding (MAPF), which focuses on finding collision-free paths for multiple robots, is crucial for applications ranging from aerial swarms to warehouse automation. Solving MAPF is NP-hard so learning-based approaches for MAPF have gained attention, particularly those leveraging deep neural networks. Nonetheless, despite the community’s continued efforts, all learning-based MAPF planners still rely on decentralized planning due to variability in the number of agents and map sizes. We have developed the first centralized learning-based policy for MAPF problem called RAILGUN. RAILGUN is not an agent-based policy but a map-based policy. By leveraging a CNN-based architecture, RAILGUN can generalize across different maps and handle any number of agents. We collect trajectories from rule-based methods to train our model in a supervised way. In experiments, RAILGUN outperforms most baseline methods and demonstrates great zero-shot generalization capabilities on various tasks, maps and agent numbers that were not seen in the training dataset.

ICML Conference 2025 Conference Paper

Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models

• Jinhao Liang
• Jacob K. Christopher
• Sven Koenig
• Ferdinando Fioretto

Recent advances in diffusion models hold significant potential in robotics, enabling the generation of diverse and smooth trajectories directly from raw representations of the environment. Despite this promise, applying diffusion models to motion planning remains challenging due to their difficulty in enforcing critical constraints, such as collision avoidance and kinematic feasibility. These limitations become even more pronounced in Multi-Robot Motion Planning (MRMP), where multiple robots must coordinate in shared spaces. To address these challenges, this work proposes S imultaneous M RMP D iffusion (SMD), a novel approach integrating constrained optimization into the diffusion sampling process to produce collision-free, kinematically feasible trajectories. Additionally, the paper introduces a comprehensive MRMP benchmark to evaluate trajectory planning algorithms across scenarios with varying robot densities, obstacle complexities, and motion constraints. Experimental results show SMD consistently outperforms classical and other learning-based motion planners, achieving higher success rates and efficiency in complex multi-robot environments. The code and implementation are available at https: //github. com/RAISELab-atUVA/Diffusion-MRMP.

TMLR Journal 2025 Journal Article

Solving Multi-agent Path Finding as an LLM Benchmark: How, How Good and Why

• Weizhe Chen
• Sven Koenig
• Bistra Dilkina

The rapid success of large language models (LLMs) has spurred extensive research into their ability to solve a wide range of tasks. However, their potential in multi-agent planning remains underexplored. Multi-agent planning presents unique challenges due to the combined complexity of coordination and long-horizon reasoning, often making it difficult to leverage external tools for assistance. In this paper, we introduce Multi-Agent Path Finding (MAPF), also known as multi-robot route planning, as a novel benchmark for evaluating the reasoning capabilities of LLMs. We first describe how the MAPF benchmark can be adapted for LLM-based evaluation, including dataset curation and an agentic workflow for LLMs. We show the motivating success of single-agent planning and multi-agent pathfinding in an empty room map without obstacles, then the failure to plan on the harder room map and maze map of the standard MAPF benchmark. We present our position on why directly solving MAPF with LLMs has not been successful yet, and we use various experiments to support our hypothesis. Based on our results, we discussed how researchers with different backgrounds could help with this problem from different perspectives.

SoCS Conference 2024 Conference Paper

A-A*pex: Efficient Anytime Approximate Multi-Objective Search

• Han Zhang 0018
• Oren Salzman
• Ariel Felner
• Carlos Hernández Ulloa
• Sven Koenig

In the multi-objective search problem, a typical task is to compute the Pareto frontier, i. e. , the set of all undominated solutions. However, computing the entire Pareto frontier can be very time-consuming, and in practice, we often have limited deliberation time. Therefore, this paper focuses on solving the multi-objective search problem with anytime algorithms, which compute an initial approximate frontier quickly and then work to find more solutions until eventually finding the entire Pareto frontier. Existing work has investigated such anytime algorithms for problem instances with only two objectives. In this paper, we propose Anytime A*pex (A-A*pex), which works with any number of objectives. In each iteration of A-A*pex, it runs A*pex, a state-of-the-art approximate multi-objective search algorithm, to compute more solutions. From one iteration to the next, A-A*pex can either reuse its previous search effort or restart from scratch. Our experimental results show that an A-A*pex variant that mixes reusing its search effort and restarting from scratch yields the best runtime performance. We also show that A-A*pex often computes solutions that collectively approximate the Pareto frontier much better than the solutions found by state-of-the-art multi-objective search algorithms for short deliberation times.

AAAI Conference 2024 Conference Paper

Adaptive Anytime Multi-Agent Path Finding Using Bandit-Based Large Neighborhood Search

• Thomy Phan
• Taoan Huang
• Bistra Dilkina
• Sven Koenig

Anytime multi-agent path finding (MAPF) is a promising approach to scalable path optimization in large-scale multi-agent systems. State-of-the-art anytime MAPF is based on Large Neighborhood Search (LNS), where a fast initial solution is iteratively optimized by destroying and repairing a fixed number of parts, i.e., the neighborhood of the solution, using randomized destroy heuristics and prioritized planning. Despite their recent success in various MAPF instances, current LNS-based approaches lack exploration and flexibility due to greedy optimization with a fixed neighborhood size which can lead to low-quality solutions in general. So far, these limitations have been addressed with extensive prior effort in tuning or offline machine learning beyond actual planning. In this paper, we focus on online learning in LNS and propose Bandit-based Adaptive LArge Neighborhood search Combined with Exploration (BALANCE). BALANCE uses a bi-level multi-armed bandit scheme to adapt the selection of destroy heuristics and neighborhood sizes on the fly during search. We evaluate BALANCE on multiple maps from the MAPF benchmark set and empirically demonstrate performance improvements of at least 50% compared to state-of-the-art anytime MAPF in large-scale scenarios. We find that Thompson Sampling performs particularly well compared to alternative multi-armed bandit algorithms.

AAMAS Conference 2024 Conference Paper

Anytime Multi-Agent Path Finding using Operation Parallelism in Large Neighborhood Search

• Shao-Hung Chan
• Zhe Chen
• Dian-Lun Lin
• Yue Zhang
• Daniel Harabor
• Sven Koenig
• Tsung-Wei Huang
• Thomy Phan

Multi-Agent Path Finding (MAPF) is the problem of finding a set of collision-free paths for multiple agents in a shared environment while improving the solution quality. The state-of-the-art anytime MAPF algorithm is based on Large Neighborhood Search (MAPF- LNS), which is a combinatorial search algorithm that iteratively destroys and repairs a subset of collision-free paths. In this paper, we propose Destroy-Repair Operation Parallelism for MAPF-LNS (DROP-LNS), a parallel framework that performs multiple destroy and repair operations concurrently to explore more regions of the search space and improve the solution quality. Unlike MAPF-LNS, DROP-LNS is able to exploit multiple threads during the search. The results show that DROP-LNS outperforms the state-of-the-art anytime MAPF algorithms, namely MAPF-LNS and LaCAM*, with respect to solution quality when terminated at the same runtime.

ICRA Conference 2024 Conference Paper

Benchmarking Multi-Robot Coordination in Realistic, Unstructured Human-Shared Environments

• Lukas Heuer
• Luigi Palmieri
• Anna Mannucci
• Sven Koenig
• Martin Magnusson 0002

Coordinating a fleet of robots in unstructured, human-shared environments is challenging. Human behavior is hard to predict, and its uncertainty impacts the performance of the robotic fleet. Various multi-robot planning and coordination algorithms have been proposed, including Multi-Agent Path Finding (MAPF) methods to precedence-based algorithms. However, it is still unclear how human presence impacts different coordination strategies in both simulated environments and the real world. With the goal of studying and further improving multi-robot planning capabilities in those settings, we propose a method to develop and benchmark different multi-robot coordination algorithms in realistic, unstructured and human-shared environments. To this end, we introduce a multi-robot benchmark framework that is based on state-of-the-art open-source navigation and simulation frameworks and can use different types of robots, environments and human motion models. We show a possible application of the benchmark framework with two different environments and three centralized coordination methods (two MAPF algorithms and a loosely-coupled coordination method based on precedence constraints). We evaluate each environment for different human densities to investigate its impact on each coordination method. We also present preliminary results that show how informing each coordination method about human presence can help the coordination method to find faster paths for the robots.

ICAPS Conference 2024 Conference Paper

Bounded-Suboptimal Weight-Constrained Shortest-Path Search via Efficient Representation of Paths

• Han Zhang 0018
• Oren Salzman
• Ariel Felner
• T. K. Satish Kumar
• Sven Koenig

In the Weight-Constrained Shortest-Path (WCSP) problem, given a graph in which each edge is annotated with a cost and a weight, a start state, and a goal state, the task is to compute a minimum-cost path from the start state to the goal state with weight no larger than a given weight limit. While most existing works have focused on solving the WCSP problem optimally, many real-world situations admit a trade-off between efficiency and a suboptimality bound for the path cost. In this paper, we propose the bounded-suboptimal WCSP algorithm WC-A*pex, which is built on the state-of-the-art approximate bi-objective search algorithm A*pex. WC-A*pex uses an approximate representation of paths with similar costs and weights to compute a (1+ε)-suboptimal path, for a given ε. During its search, WC-A*pex avoids storing all paths explicitly and thereby reduces the search effort while still retaining its (1 + ε)-suboptimality bound. On benchmark road networks, our experimental results show that WC-A*pex with ε = 0. 01 (i. e. , with a guaranteed suboptimality of at most 1%) achieves a speed-up of up to an order of magnitude over WC-A*, a state-of-the-art WCSP algorithm, and its bounded-suboptimal variant.

AAMAS Conference 2024 Conference Paper

Confidence-Based Curriculum Learning for Multi-Agent Path Finding

• Thomy Phan
• Joseph Driscoll
• Justin Romberg
• Sven Koenig

A wide range of real-world applications can be formulated as Multi- Agent Path Finding (MAPF) problem, where the goal is to find collision-free paths for multiple agents with individual start and goal locations. State-of-the-art MAPF solvers are mainly centralized and depend on global information, which limits their scalability and flexibility regarding changes or new maps that would require expensive replanning. Multi-agent reinforcement learning (MARL) offers an alternative way by learning decentralized policies that can generalize over a variety of maps. While there exist some prior works that attempt to connect both areas, the proposed techniques are heavily engineered and very complex due to the integration of many mechanisms that limit generality and are expensive to use. We argue that much simpler and general approaches are needed to bring the areas of MARL and MAPF closer together with significantly lower costs. In this paper, we propose Confidence-based Auto-Curriculum for Team Update Stability (CACTUS) as a lightweight MARL approach to MAPF. CACTUS defines a simple reverse curriculum scheme, where the goal of each agent is randomly placed within an allocation radius around the agent’s start location. The allocation radius increases gradually as all agents improve, which is assessed by a confidence-based measure. We evaluate CACTUS in various maps of different sizes, obstacle densities, and numbers of agents. Our experiments demonstrate better performance and generalization capabilities than state-of-the-art MARL approaches with less than 600, 000 trainable parameters, which is less than 5% of the neural network size of current MARL approaches to MAPF.

ICAPS Conference 2024 Conference Paper

Efficient Approximate Search for Multi-Objective Multi-Agent Path Finding

• Fangji Wang
• Han Zhang 0018
• Sven Koenig
• Jiaoyang Li 0001

The Multi-Objective Multi-Agent Path Finding (MO-MAPF) problem is the problem of computing collision-free paths for a team of agents while minimizing multiple cost metrics. Most existing MO-MAPF algorithms aim to compute the Pareto frontier. However, the Pareto frontier can be time-consuming to compute. Our first main contribution is BB-MO-CBS-pex, an approximate MO-MAPF algorithm that computes an approximate frontier for a user-specific approximation factor. BB-MO-CBS-pex builds upon BB-MO-CBS, a state-of-the-art MO-MAPF algorithm, and leverages A*pex, a state-of-the-art single-agent multi-objective search algorithm, to speed up different parts of BB-MO-CBS. We also provide two speed-up techniques for BB-MO-CBS-pex. Our second main contribution is BB-MO-CBS-k, which builds upon BB-MO-CBS-pex and computes up to k solutions for a user-provided k-value. BB-MO-CBS-k is useful when it is unclear how to determine an appropriate approximation factor. Our experimental results show that both BB-MO-CBS-pex and BB-MO-CBS-k solved significantly more instances than BB-MO-CBS for different approximation factors and k-values, respectively. Additionally, we compare BB-MO-CBS-pex with an approximate baseline algorithm derived from BB-MO-CBS and show that BB-MO-CBS-pex achieved speed-ups up to two orders of magnitude.

SoCS Conference 2024 Conference Paper

Efficient Set Dominance Checks in Multi-Objective Shortest-Path Algorithms via Vectorized Operations

• Carlos Hernández Ulloa
• Han Zhang 0018
• Sven Koenig
• Ariel Felner
• Oren Salzman

In the multi-objective shortest-path problem (MOSP) we are interested in finding paths between two vertices of a graph while considering multiple objectives. A key procedure, which dominates the running time of many state-of-the-art (SOTA) algorithms for MOSP is set dominance checks (SDC). In SDC, we are given a set X of N-dimensional tuples and a new N-dimensional tuple p and we need to determine whether there exists a tuple q in X such that q dominates p (i. e. , if every element in q is lower or equal than the corresponding element in p). In this work, we offer a simple-yet-effective approach to perform SDC in a parallel manner, an approach that can be seamlessly integrated with most SOTA MOSP algorithms. Specifically, by storing states in memory dimension-wise and not state-wise, we can exploit vectorized operations offered by ``Single Instruction/Multiple Data

SoCS Conference 2024 Conference Paper

Fools Rush in Where Angels Fear to Tread in Multi-Goal CBS

• Grigorios Mouratidis
• Bernhard Nebel
• Sven Koenig

Research on multi-agent pathfinding (MAPF) has recently shifted towards problem variants that are closer to actual applications. Such variants often include the assignment of multiple goals to agents. To solve them, researchers have extended the Conflict Based Search (CBS) algorithm to multiple goals. This extension might look straightforward at first sight but it is tricky and this has already led to the development of algorithms that despite claiming to be optimal, return suboptimal solutions for some MAPF instances. In this paper, we provide a detailed analysis of the issue to raise awareness among the search community so that this mistake will not be perpetuated. Furthermore, a first evaluation against an optimal implementation is conducted which shows why this issue might have been difficult to spot. In only one of the randomly generated instances, the suboptimal behavior emerged.

SoCS Conference 2024 Conference Paper

ITA-ECBS: A Bounded-Suboptimal Algorithm for Combined Target-Assignment and Path-Finding Problem

• Yimin Tang
• Sven Koenig
• Jiaoyang Li 0001

Multi-Agent Path Finding (MAPF), i. e. , finding collision-free paths for multiple robots, plays a critical role in many applications. Sometimes, assigning a target to each agent also presents a challenge. The Combined Target-Assignment and Path-Finding (TAPF) problem, a variant of MAPF, requires one to simultaneously assign targets to agents and plan collision-free paths for agents. Several algorithms, including CBM, CBS-TA, and ITA-CBS, optimally solve the TAPF problem, with ITA-CBS being the leading algorithm for minimizing flowtime. However, the only existing bounded-suboptimal algorithm ECBS-TA is derived from CBS-TA rather than ITA-CBS. So, it faces the same issues as CBS-TA, such as searching through multiple constraint trees and spending too much time on finding the next-best target assignment. We introduce ITA-ECBS, the first bounded-suboptimal variant of ITA-CBS. Transforming ITA-CBS to its bounded-suboptimal variant is challenging because different constraint tree nodes can have different assignments of targets to agents. ITA-ECBS uses focal search to achieve efficiency and determines target assignments based on a new lower bound matrix. We show that it runs faster than ECBS-TA in 87. 42% of 54, 033 test cases.

ICAPS Conference 2024 Conference Paper

Map Connectivity and Empirical Hardness of Grid-based Multi-Agent Pathfinding Problem

• Jingyao Ren
• Eric Ewing
• T. K. Satish Kumar
• Sven Koenig
• Nora Ayanian

We present an empirical study of the relationship between map connectivity and the empirical hardness of the multi-agent pathfinding (MAPF) problem. By analyzing the second smallest eigenvalue (commonly known as lambda2) of the normalized Laplacian matrix of different maps, our initial study indicates that maps with smaller lambda2 tend to create more challenging instances when agents are generated uniformly randomly. Additionally, we introduce a map generator based on Quality Diversity (QD) that is capable of producing maps with specified lambda2 ranges, offering a possible way for generating challenging MAPF instances. Despite the absence of a strict monotonic correlation with lambda2 and the empirical hardness of MAPF, this study serves as a valuable initial investigation for gaining a deeper understanding of what makes a MAPF instance hard to solve.

SoCS Conference 2024 Conference Paper

Solving Facility Location Problems via FastMap and Locality Sensitive Hashing

• Ang Li
• Peter J. Stuckey
• Sven Koenig
• T. K. Satish Kumar

Facility Location Problems (FLPs) arise while serving multiple customers in a shared environment, minimizing transportation and other costs. Hence, they involve the optimal placement of facilities. They are defined on graphs as well as in Euclidean spaces with or without obstacles; and they are typically NP-hard to solve optimally. There are many heuristic algorithms tailored to different kinds of FLPs. However, FLPs defined in Euclidean spaces without obstacles are the most amenable to efficient and effective heuristic algorithms. This motivates the idea of quickly reformulating FLPs on graphs and in Euclidean spaces with obstacles to FLPs in Euclidean spaces without obstacles. Towards this end, we propose a new approach that uses FastMap and Locality Sensitive Hashing. FastMap is a near-linear-time algorithm that embeds the vertices of a graph in a Euclidean space while approximately preserving graph-based distances as Euclidean distances for all pairs of vertices. Through extensive experiments, we show that our approach significantly outperforms other state-of-the-art competing algorithms on a variety of FLPs: the Multi-Agent Meeting, Vertex K-Median (VKM), Weighted VKM, and the Capacitated VKM problems.

SoCS Conference 2024 Conference Paper

Speeding Up Dominance Checks in Multi-Objective Search: New Techniques and Data Structures

• Han Zhang 0018
• Oren Salzman
• Ariel Felner
• T. K. Satish Kumar
• Carlos Hernández Ulloa
• Sven Koenig

In multi-objective search, given a directed graph where each edge is annotated with multiple cost metrics, a start state, and a goal state. We are interested in computing the Pareto frontier, i. e. , the set of all undominated paths from the start state to the goal state. Almost all multi-objective search algorithms use dominance checks to determine if a search node can be pruned. Since dominance checks are performed in the inner loop of the multi-objective search, they are the most time-consuming part of it. In this paper, we propose (1) two novel techniques to reduce duplicate dominance checks and (2) a simple data structure that enables more efficient dominance checks. Our experimental results show that combining our proposed techniques and data structure speeds up LTMOA*, a state-of-the-art multi-objective search algorithm, by up to an order of magnitude on road network instances.

IJCAI Conference 2024 Conference Paper

Theoretical Study on Multi-objective Heuristic Search

• Shawn Skyler
• Shahaf Shperberg
• Dor Atzmon
• Ariel Felner
• Oren Salzman
• Shao-Hung Chan
• Han Zhang
• Sven Koenig

This paper provides a theoretical study on Multi-Objective Heuristic Search. We first classify states in the state space into must-expand, maybe-expand, and never-expand states and then transfer these definitions to nodes in the search tree. We then formalize a framework that generalizes A* to Multi-Objective Search. We study different ways to order nodes under this framework and their relation to traditional tie-breaking policies and provide theoretical findings. Finally, we study and empirically compare different ordering functions.

ICRA Conference 2023 Conference Paper

A Benchmark for Multi-Robot Planning in Realistic, Complex and Cluttered Environments

• Simon Schaefer
• Luigi Palmieri
• Lukas Heuer
• Rüdiger Dillmann
• Sven Koenig
• Alexander Kleiner

Several successful approaches exist for solving the complex problem of multi-robot planning and coordination. Due to the lack of adequate benchmarking tools, comparing these approaches and judging their suitability for use in realistic scenarios is currently difficult. Therefore, we propose an open-source benchmark suite that aims to close this gap. Unlike existing benchmarks, our approach uses full-stack multi-robot navigation systems in realistic 3D simulated environments from the intralogistic and household domains. Using the open-source frameworks ROS 2, Gazebo and RMF allows the user to add other robot platforms easily. The framework provides easy-to-use abstractions, typical metrics and interfaces to several established planning libraries for multi-robot systems. With all these features, our framework successfully aids practitioners and researchers in comparing multi-robot planning and coordination systems to the state of the art. Our experiments show how the proposed benchmark simplifies gaining insights on relevant close to real-life robotics use cases.

ICAPS Conference 2023 Conference Paper

Binary Branching Multi-Objective Conflict-Based Search for Multi-Agent Path Finding

• Zhongqiang Ren
• Jiaoyang Li 0001
• Han Zhang 0018
• Sven Koenig
• Sivakumar Rathinam
• Howie Choset

This paper considers a multi-agent multi-objective path-finding problem that requires not only finding collision-free paths for multiple agents from their respective start locations to their respective goal locations but also optimizing multiple objectives simultaneously. In general, there is no single solution that optimizes all the objectives simultaneously, and the problem is thus to find the so-called Pareto-optimal frontier. To solve this problem, an algorithm called Multi-Objective Conflict-Based Search (MO-CBS) was recently developed and is guaranteed to find the exact Pareto-optimal frontier. However, MO-CBS does not scale well with the number of agents due to the large branching factor of the search, which leads to a lot of duplicated effort in agent-agent collision resolution. This paper therefore develops a new algorithm called Binary Branching MO-CBS (BB-MO-CBS) that reduces the branching factor as well as the duplicated collision resolution during the search, which expedites the search as a result. Our experimental results show that BB-MO-CBS reduces the number of conflicts by up to two orders of magnitude and often doubles or triples the success rates of MO-CBS on various maps given a runtime limit.

AIJ Journal 2023 Journal Article

Conflict-tolerant and conflict-free multi-agent meeting

• Dor Atzmon
• Ariel Felner
• Jiaoyang Li
• Shahaf Shperberg
• Nathan Sturtevant
• Sven Koenig

ICAPS Conference 2023 Conference Paper

Cost Splitting for Multi-Objective Conflict-Based Search

• Cheng Ge
• Han Zhang 0018
• Jiaoyang Li 0001
• Sven Koenig

The Multi-Objective Multi-Agent Path Finding (MO-MAPF) problem is the problem of finding the Pareto-optimal frontier of collision-free paths for a team of agents while minimizing multiple cost metrics. Examples of such cost metrics include arrival times, travel distances, and energy consumption. In this paper, we focus on the Multi-Objective Conflict-Based Search (MO-CBS) algorithm, a state-of-the-art MO-MAPF algorithm. We show that the standard splitting strategy used by MO-CBS can lead to duplicate search nodes and hence can duplicate the search effort of MO-CBS. To address this issue, we propose two new splitting strategies for MO-CBS, namely cost splitting and disjoint cost splitting. Our theoretical results show that, when using either splitting strategy, MO-CBS maintains its completeness and optimality guarantees. Our experimental results show that disjoint cost splitting, our best splitting strategy, speeds up MO-CBS by up to two orders of magnitude and substantially improves its success rates in various settings.

ICAPS Conference 2023 Conference Paper

Deadline-Aware Multi-Agent Tour Planning

• Taoan Huang
• Vikas Shivashankar
• Michael Caldara
• Joseph W. Durham
• Jiaoyang Li 0001
• Bistra Dilkina
• Sven Koenig

The increasing demand for same-day delivery and the commitment of e-commerce companies to this service raise a number of challenges in logistics. One of these challenges for fulfillment centers is to coordinate hundreds of mobile robots in their automated warehouses efficiently to allow for the retrieval and packing of thousands of ordered items within the promised delivery deadlines. We formulate this challenge as the new problem of deadline-aware multi-agent tour planning, where the objective is to coordinate robots to visit multiple picking stations in congested warehouses to allow as many orders to be packed on time as possible. To solve it, we propose LaRge NeighbOrhood Search for DEadline-Aware MulTi-Agent Tour PlAnning (ROSETTA). We conduct extensive experiments to evaluate ROSETTA with up to 350 robots in simulated warehouses inspired by KIVA systems. We show that it increases the number of orders completed on time by up to 38% compared to several baseline algorithms and also significantly outperforms them in terms of throughput and station utilization.

ICAPS Conference 2023 Conference Paper

Efficient Multi-Query Bi-Objective Search via Contraction Hierarchies

• Han Zhang 0018
• Oren Salzman
• Ariel Felner
• T. K. Satish Kumar
• Carlos Hernández Ulloa
• Sven Koenig

Contraction Hierarchies (CHs) have been successfully used as a preprocessing technique in single-objective graph search for finding shortest paths. However, only a few existing works on utilizing CHs for bi-objective search exist, and none of them uses CHs to compute Pareto frontiers. This paper proposes an CH-based approach capable of efficiently computing Pareto frontiers for bi-objective search along with several speedup techniques. Specifically, we propose a new preprocessing approach that computes CHs with fewer edges than the existing preprocessing approach, which reduces both the preprocessing times (up to 3x in our experiments) and the query times. Furthermore, we propose a partial-expansion technique, which dramatically speeds up the query times. We demonstrate the advantages of our approach on road networks with 1 to 14 million states. The longest preprocessing time is less than 6 hours, and the average speedup in query times is roughly two orders of magnitude compared to BOA*, a state-of-the-art single-query bi-objective search algorithm.

SoCS Conference 2023 Conference Paper

Greedy Priority-Based Search for Suboptimal Multi-Agent Path Finding

• Shao-Hung Chan
• Roni Stern
• Ariel Felner
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths, one for each agent, in a shared environment, while minimizing their sum of travel times. Since solving MAPF optimally is NP-hard, researchers have explored algorithms that solve MAPF suboptimally but efficiently. Priority-Based Search (PBS) is the leading algorithm for this purpose. It finds paths for individual agents, one at a time, and resolves collisions by assigning priorities to the colliding agents and replanning their paths during its search. However, PBS becomes ineffective for MAPF instances with high densities of agents and obstacles. Therefore, we introduce Greedy PBS (GPBS), which uses greedy strategies to speed up PBS by minimizing the number of collisions between agents. We then propose techniques that speed up GPBS further, namely partial expansions, target reasoning, induced constraints, and soft restarts. We show that GPBS with all these improvements has a higher success rate than the state-of-the-art suboptimal algorithm for a 1-minute runtime limit, especially for MAPF instances with small maps and dense obstacles.

IJCAI Conference 2023 Conference Paper

Heuristic-Search Approaches for the Multi-Objective Shortest-Path Problem: Progress and Research Opportunities

• Oren Salzman
• Ariel Felner
• Carlos Hernández
• Han Zhang
• Shao-Hung Chan
• Sven Koenig

In the multi-objective shortest-path problem we are interested in computing a path, or a set of paths that simultaneously balance multiple cost functions. This problem is important for a diverse range of applications such as transporting hazardous materials considering travel distance and risk. This family of problems is not new with results dating back to the 1970's. Nevertheless, the significant progress made in the field of heuristic search resulted in a new and growing interest in the sub-field of multi-objective search. Consequently, in this paper we review the fundamental problems and techniques common to most algorithms and provide a general overview of the field. We then continue to describe recent work with an emphasis on new challenges that emerged and the resulting research opportunities.

AAAI Conference 2023 Conference Paper

Intersection Coordination with Priority-Based Search for Autonomous Vehicles

• Jiaoyang Li
• The Anh Hoang
• Eugene Lin
• Hai L. Vu
• Sven Koenig

The development of connected and autonomous vehicles opens an opportunity to manage intersections without signals. One promising approach is to use a central autonomous intersection manager to optimize the movement of the vehicles in the intersection. Existing work uses Mixed Integer Linear Programming (MILP) to find optimal solutions for this problem but is time-consuming and cannot be applied in real-time. On the other hand, the coordination of the vehicles is essentially a Multi-Agent Path Finding (MAPF) problem, for which dozens of efficient algorithms have been proposed in recent years. Inspired by these MAPF algorithms, we propose a three-level algorithm called PSL to solve the intersection coordination problem. Theoretically, PSL is complete and polynomial-time in the number of vehicles. Empirically, PSL runs significantly faster with only a slight compromise in the solution quality than the optimal MILP method. It also generates significantly better solutions with a slightly larger runtime than the traditional First-Come-First-Served strategy.

IJCAI Conference 2023 Conference Paper

Multi-objective Search via Lazy and Efficient Dominance Checks

• Carlos Hernández
• William Yeoh
• Jorge A. Baier
• Ariel Felner
• Oren Salzman
• Han Zhang
• Shao-Hung Chan
• Sven Koenig

Multi-objective search can be used to model many real-world problems that require finding Pareto optimal paths from a specified start state to a specified goal state, while considering different costmetrics such as distance, time, and fuel. The performance of multi-objective search can be improved by making dominance checking—an operation necessary to determine whether or not a path dominates another—more efficient. This was shown in practice by BOA*, a state-of-the-art bi-objective search algorithm, which outperforms previously existing bi-objective search algorithms in part because it adopts a lazy approach towards dominance checking. EMOA*, a recent multi-objective search algorithm, generalizes BOA* to more-than-two objectives using AVL trees for dominance checking. In this paper, we first propose Linear-Time Multi-Objective A* (LTMOA*), an multi-objective search algorithm that implements a more efficient dominance checking than EMOA* using simple data structures like arrays. We then propose an even lazier approach towards dominance checking, and the resulting algorithm, LazyLTMOA*, distinguishes from EMOA* and LTMOA* by removing the dominance checking during node generation. Our experimental results show that LazyLTMOA* outperforms EMOA* by up to an order of magnitude in terms of runtime.

SoCS Conference 2023 Conference Paper

Must-Expand Nodes in Multi-Objective Search [Extended Abstract]

• Shawn Skyler
• Shahaf S. Shperberg
• Dor Atzmon
• Ariel Felner
• Oren Salzman
• Shao-Hung Chan
• Han Zhang 0018
• Sven Koenig

This extended abstract presents a theoretical analysis of node expansions in Multi-Objective Search. We define three categories of nodes, Must-Expand Nodes, Maybe-Expand Nodes, and Never-Expand Nodes. Our analysis establishes that regardless of the Ordering Function or Multi-Objective Search algorithm used, any Multi-Objective Search algorithm must expand all Must-Expand Nodes, some or none of Maybe-Expand Nodes, and none of Never-Expand Nodes. In addition, we conduct experimental evaluations of various Ordering Functions, revealing that they all expand the same number of nodes and compare their efficiency at finding solutions at various stages of the search.

ICAPS Conference 2023 Conference Paper

Priority-Based Search for the Virtual Network Embedding Problem

• Yi Zheng 0010
• Hang Ma 0001
• Sven Koenig
• Erik Kline
• T. K. Satish Kumar

The Virtual Network Embedding (VNE) problem is a constrained optimization problem. It arises in the context of allocating resources on heterogeneous physical networks to provide end-to-end computing services. In this paper, we introduce a new solver, called VNE-PBS, that uses priority-based search (PBS) for solving the VNE problem. VNE-PBS uses a prioritized heuristic search algorithm that explores the space of all possible priority orderings using a systematic depth-first search. The solver is inspired by the success of PBS for the Multi-Agent Path Finding (MAPF) problem and the similarities between the VNE and MAPF problems. We show that VNE-PBS significantly outperforms competing methods on various benchmark instances for both the offline and online versions of the VNE problem.

AIJ Journal 2023 Journal Article

Simple and efficient bi-objective search algorithms via fast dominance checks

• Carlos Hernández
• William Yeoh
• Jorge A. Baier
• Han Zhang
• Luis Suazo
• Sven Koenig
• Oren Salzman

IROS Conference 2023 Conference Paper

Task Assignment, Scheduling, and Motion Planning for Automated Warehouses for Million Product Workloads

• Christopher Leet
• Chanwook Oh
• Michele Lora
• Sven Koenig
• Pierluigi Nuzzo 0002

We address the Warehouse Servicing Problem (WSP) in automated warehouses, which use teams of mobile robots to move products from shelves to packaging stations. Given a list of products, the WSP amounts to finding a motion plan which brings every product on the list from a shelf to a packaging station within a given time limit. The WSP consists of four subproblems, namely, deciding where to source and deposit a product (task formulation), who should transport each product (task assignment) and when (scheduling) and how (motion planning). These problems are NP-Hard individually and made more challenging by their interdependence. The difficulty of the WSP is compounded by the scale of automated warehouses, which use teams of hundreds of agents to transport thousands of products. In this paper, we present Contract-based Cyclic Motion Planning (CCMP), a novel contract-based methodology for solving the WSP at scale. CCMP decomposes a warehouse into a set of traffic system components. By assigning each component a contract which describes the traffic flows it can support, CCMP can generate a traffic flow which satisfies a given WSP instance. CCMP then uses a novel motion planner to transform this traffic flow into a motion plan for a team of robots. Evaluation shows that CCMP can solve WSP instances taken from real industrial scenarios with up to 1 million products while outperforming other methodologies for solving the WSP by up to 2. 9×.

TMLR Journal 2023 Journal Article

The (Un)Scalability of Informed Heuristic Function Estimation in NP-Hard Search Problems

• Sumedh Pendurkar
• Taoan Huang
• Brendan Juba
• Jiapeng Zhang
• Sven Koenig
• Guni Sharon

The A* algorithm is commonly used to solve NP-hard combinatorial optimization problems. When provided with a completely informed heuristic function, A* can solve such problems in time complexity that is polynomial in the solution cost and branching factor. In light of this fact, we examine a line of recent publications that propose fitting deep neural networks to the completely informed heuristic function. We assert that these works suffer from inherent scalability limitations since --- under the assumption of NP $\not \subseteq$ P/poly --- such approaches result in either (a) network sizes that scale super-polynomially in the instance sizes or (b) the accuracy of the fitted deep neural networks scales inversely with the instance sizes. Complementing our theoretical claims, we provide experimental results for three representative NP-hard search problems. The results suggest that fitting deep neural networks to informed heuristic functions requires network sizes that grow quickly with the problem instance size. We conclude by suggesting that the research community should focus on scalable methods for integrating heuristic search with machine learning, as opposed to methods relying on informed heuristic estimation.

SoCS Conference 2023 Conference Paper

Towards Effective Multi-Valued Heuristics for Bi-objective Shortest-Path Algorithms via Differential Heuristics

• Han Zhang 0018
• Oren Salzman
• Ariel Felner
• T. K. Satish Kumar
• Shawn Skyler
• Carlos Hernández Ulloa
• Sven Koenig

In bi-objective graph search, each edge is annotated with a cost pair, where each cost corresponds to an objective to optimize. We are interested in finding all undominated paths from a given start state to a given goal state (called the Pareto front). Almost all existing works of bi-objective search use single-valued heuristics, which use one number for each objective, to estimate the cost between any given state and the goal state. However, single-valued heuristics cannot reflect the trade-offs between the two costs. On the other hand, multi-valued heuristics use a set of pairs to estimate the Pareto front between any given state and the goal state and are more informed than single-valued heuristics. However, they are rarely studied and have yet to be investigated in explicit state spaces by any existing work. In this paper, we are interested in using multi-valued heuristics to improve bi-objective search algorithms in explicit state spaces. More specifically, we generalize Differential Heuristics (DHs), a class of memory-based heuristics for single-objective search, to bi-objective search, resulting in Bi-objective Differential Heuristics (BO-DHs). We propose several techniques to reduce the memory usage and computational overhead of BO-DHs significantly. Our experimental results show that, with suggested improvement and tuned parameters, BO-DHs can reduce the node expansion and runtime of a bi-objective search algorithm by up to an order of magnitude, paving the way for more effective multi-valued heuristics.

SoCS Conference 2022 Conference Paper

A Discussion on the Scalability of Heuristic Approximators (Extended Abstract)

• Sumedh Pendurkar
• Taoan Huang
• Sven Koenig
• Guni Sharon

In this work, we examine a line of recent publications that propose to use deep neural networks to approximate the goal distances of states for heuristic search. We present a first step toward showing that this work suffers from inherent scalability limitations since --- under the assumption that P≠NP --- such approaches require network sizes that scale exponentially in the number of states to achieve the necessary (high) approximation accuracy.

ICAPS Conference 2022 Conference Paper

A*pex: Efficient Approximate Multi-Objective Search on Graphs

• Han Zhang 0018
• Oren Salzman
• T. K. Satish Kumar
• Ariel Felner
• Carlos Hernández Ulloa
• Sven Koenig

In multi-objective search, edges are annotated with cost vectors consisting of multiple cost components. A path dominates another path with the same start and goal vertices iff the component-wise sum of the cost vectors of the edges of the former path is ``less than'' the component-wise sum of the cost vectors of the edges of the latter path. The Pareto-optimal solution set is the set of all undominated paths from a given start vertex to a given goal vertex. Its size can be exponential in the size of the graph being searched, which makes multi-objective search time-consuming. In this paper, we therefore study how to find an approximate Pareto-optimal solution set for a user-provided vector of approximation factors. The size of such a solution set can be significantly smaller than the size of the Pareto-optimal solution set, which enables the design of approximate multi-objective search algorithms that are efficient and produce small solution sets. We present such an algorithm in this paper which we call A*pex and which builds on PP-A*, a state-of-the-art approximate bi-objective search algorithm (where there are only two cost components) but (1) makes PP-A* more efficient for bi-objective search and (2) generalizes it to multi-objective search for any number of cost components. We first analyze the correctness of A*pex and then experimentally demonstrate its efficiency advantage over existing approximate algorithms for bi- and tri-objective search.

AIJ Journal 2022 Journal Article

AI Journal Special Issue on Ethics for Autonomous Systems

• Michael Fisher
• Sven Koenig
• Marija Slavkovik

SoCS Conference 2022 Conference Paper

Anytime Approximate Bi-Objective Search

• Han Zhang 0018
• Oren Salzman
• T. K. Satish Kumar
• Ariel Felner
• Carlos Hernández Ulloa
• Sven Koenig

The Pareto-optimal frontier for a bi-objective search problem instance consists of all solutions that are not worse than any other solution in both objectives. The size of the Pareto-optimal frontier can be exponential in the size of the input graph, and hence finding it can be hard. Some existing works leverage a user-specified approximation factor epsilon to compute an approximate Pareto-optimal frontier that can be significantly smaller than the Pareto-optimal frontier. In this paper, we propose an anytime approximate bi-objective search algorithm, called Anytime Bi-Objective A*-epsilon (A-BOA*). A-BOA* is useful when deliberation time is limited. It first finds an approximate Pareto-optimal frontier quickly, iteratively improves it while time allows, and eventually finds the Pareto-optimal frontier. It efficiently reuses the search effort from previous iterations and makes use of a novel pruning technique. Our experimental results show that A-BOA* substantially outperforms baseline algorithms that do not reuse previous search effort, both in terms of runtime and number of node expansions. In fact, the most advanced variant of A-BOA* even slightly outperforms BOA*, a state-of-the-art bi-objective search algorithm, for finding the Pareto-optimal frontier. Moreover, given only a limited amount of deliberation time, A-BOA* finds solutions that collectively approximate the Pareto-optimal frontier much better than the solutions found by BOA*.

AAAI Conference 2022 Conference Paper

Anytime Multi-Agent Path Finding via Machine Learning-Guided Large Neighborhood Search

• Taoan Huang
• Jiaoyang Li
• Sven Koenig
• Bistra Dilkina

Multi-Agent Path Finding (MAPF) is the problem of finding a set of collision-free paths for a team of agents in a common environment. MAPF is NP-hard to solve optimally and, in some cases, also bounded-suboptimally. It is thus timeconsuming for (bounded-sub)optimal solvers to solve large MAPF instanc¡es. Anytime algorithms find solutions quickly for large instances and then improve them to close-to-optimal ones over time. In this paper, we improve the current state-ofthe-art anytime solver MAPF-LNS, that first finds an initial solution fast and then repeatedly replans the paths of subsets of agents via Large Neighborhood Search (LNS). It generates the subsets of agents for replanning by randomized destroy heuristics, but not all of them increase the solution quality substantially. We propose to use machine learning to learn how to select a subset of agents from a collection of subsets, such that replanning increases the solution quality more. We show experimentally that our solver, MAPF-ML-LNS, significantly outperforms MAPF-LNS on the standard MAPF benchmark set in terms of both the speed of improving the solution and the final solution quality.

SoCS Conference 2022 Conference Paper

Bounded-Cost Bi-Objective Heuristic Search

• Shawn Skyler
• Dor Atzmon
• Ariel Felner
• Oren Salzman
• Han Zhang 0018
• Sven Koenig
• William Yeoh 0001
• Carlos Hernández Ulloa

There are many settings that extend the basic shortest path search problem. In Bounded-Cost Search, we are given a constant bound and the task is to find a solution within the bound. In Bi-Objective Search, each edge is associated with two costs (objectives) and the task is to minimize both objectives. In this paper, we combine both these settings into a new setting of Bounded-Cost Bi-Objective Search. We are given two bounds, one for each objective and the task is to find a solution within these bounds. We provide a scheme for normalizing the two objectives. We then introduce several algorithms for this new setting and compare them experimentally.

ICAPS Conference 2022 Conference Paper

Conflict-Based Search for the Virtual Network Embedding Problem

• Yi Zheng 0010
• Srivatsan Ravi
• Erik Kline
• Sven Koenig
• T. K. Satish Kumar

In emerging network virtualization architectures, service providers will be able to create many heterogeneous virtual networks and offer customized end-to-end services by leasing shared resources from infrastructure providers. The Virtual Network Embedding (VNE) problem is central to such technology. It involves the proper allocation of CPU and bandwidth resources available in a physical substrate network to meet the demands of multiple virtual networks. Combinatorially, the VNE problem is a problem in resource management that is NP-hard to solve. In this paper, we present a novel version of the Conflict-Based Search (CBS) algorithm for solving the VNE problem. Our approach, called VNE-CBS, is inspired by the success of the CBS framework in the Multi-Agent Path Finding domain. We successfully address the unique challenges in applying the CBS framework to the VNE problem, and, in doing so, we pave the way for overcoming a crucial issue in Internet ossification via heuristic search methods. On the theoretical front, we show that, unlike many existing algorithms, our algorithm is complete and optimal. On the experimental front, we show that our algorithm significantly outperforms other state-of-the-art methods on various benchmark instances for both the offline and online versions of the VNE problem.

AAAI Conference 2022 Conference Paper

Flex Distribution for Bounded-Suboptimal Multi-Agent Path Finding

• Shao-Hung Chan
• Jiaoyang Li
• Graeme Gange
• Daniel Harabor
• Peter J. Stuckey
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents that minimize the sum of path costs. EECBS is a leading two-level algorithm that solves MAPF bounded-suboptimally, that is, within some factor w of the minimum sum of path costs C∗. It uses focal search to find bounded-suboptimal paths on the low level and Explicit Estimation Search (EES) to resolve collisions on the high level. EES keeps track of a lower bound LB on C∗ to find paths whose sum of path costs is at most w · LB in order to solve MAPF bounded-suboptimally. However, the costs of many paths are often much smaller than w times their minimum path costs, meaning that the sum of path costs is much smaller than w ·C∗. In this paper, we therefore propose Flexible EECBS (FEECBS), which uses a flex(ible) distribution of the path costs (that relaxes the requirement to find bounded-suboptimal paths on the low level) in order to reduce the number of collisions that need to be resolved on the high level while still guaranteeing to solve MAPF bounded suboptimally. We address the drawbacks of flex distribution via techniques such as restrictions on the flex distribution, restarts of the high-level search with EECBS, and low-level focal-A* search. Our empirical evaluation shows that FEECBS substantially improves the efficiency of EECBS on MAPF instances with large maps and large numbers of agents.

SoCS Conference 2022 Conference Paper

Learning a Priority Ordering for Prioritized Planning in Multi-Agent Path Finding

• Shuyang Zhang
• Jiaoyang Li 0001
• Taoan Huang
• Sven Koenig
• Bistra Dilkina

Prioritized Planning (PP) is a fast and popular framework for solving Multi-Agent Path Finding, but its solution quality depends heavily on the predetermined priority ordering of the agents. Current PP algorithms use either greedy policies or random assignments to determine a total priority ordering, but none of them dominates the others in terms of the success rate and solution quality (measured by the sum-of-costs). We propose a machine-learning (ML) framework to learn a good priority ordering for PP. We develop two models, namely ML-T, which is trained on a total priority ordering, and ML-P, which is trained on a partial priority ordering. We propose to boost the effectiveness of PP by further applying stochastic ranking and random restarts. The results show that our ML-guided PP algorithms outperform the existing PP algorithms in success rate, runtime, and solution quality on small maps in most cases and are competitive with them on large maps despite the difficulty of collecting training data on these maps.

AAAI Conference 2022 Conference Paper

MAPF-LNS2: Fast Repairing for Multi-Agent Path Finding via Large Neighborhood Search

• Jiaoyang Li
• Zhe Chen
• Daniel Harabor
• Peter J. Stuckey
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the problem of planning collision-free paths for multiple agents in a shared environment. In this paper, we propose a novel algorithm MAPF- LNS2 based on large neighborhood search for solving MAPF efficiently. Starting from a set of paths that contain collisions, MAPF-LNS2 repeatedly selects a subset of colliding agents and replans their paths to reduce the number of collisions until the paths become collision-free. We compare MAPF- LNS2 against a variety of state-of-the-art MAPF algorithms, including Prioritized Planning with random restarts, EECBS, and PPS, and show that MAPF-LNS2 runs significantly faster than them while still providing near-optimal solutions in most cases. MAPF-LNS2 solves 80% of the random-scenario instances with the largest number of agents from the MAPF benchmark suite with a runtime limit of just 5 minutes, which, to our knowledge, has not been achieved by any existing algorithms.

AAMAS Conference 2022 Conference Paper

Multi-Agent Path Finding for Precedence-Constrained Goal Sequences

• Han Zhang
• Jingkai Chen
• Jiaoyang Li
• Brian C. Williams
• Sven Koenig

With the rising demand for deploying robot teams in autonomous warehouses and factories, the Multi-Agent Path Finding (MAPF) problem has drawn more and more attention. The classical MAPF problem and most of its variants focus on navigating agent teams to goal locations while avoiding collisions. However, they do not take into account any precedence constraints that agents should respect when reaching their goal locations. Planning with precedence constraints is important for real-world multi-agent systems. For example, a mobile robot can only pick up a package at a station after it has been delivered by another robot. In this paper, we study the Multi-Agent Path Finding with Precedence Constraints (MAPF-PC) problem, in which agents need to visit sequences of goal locations while satisfying precedence constraints between the goal locations. We propose two algorithms for solving this problem systematically: Conflict-Based Search with Precedence Constraints (CBS-PC) is complete and optimal, and Priority-Based Search with Precedence Constraints (PBS-PC) is incomplete but more efficient in finding near-optimal solutions in practice. Our experimental results show that CBS-PC scales to dozens of agents and hundreds of goal locations and precedence constraints, and PBS-PC scales to hundreds of agents, around one thousand goal locations, and hundreds of precedence constraints.

AIJ Journal 2022 Journal Article

Multi-agent path finding with mutex propagation

• Han Zhang
• Jiaoyang Li
• Pavel Surynek
• T.K. Satish Kumar
• Sven Koenig

IROS Conference 2022 Conference Paper

Multi-Goal Multi-Agent Pickup and Delivery

• Qinghong Xu
• Jiaoyang Li 0001
• Sven Koenig
• Hang Ma 0001

In this work, we consider the Multi-Agent Pickup-and-Delivery (MAPD) problem, where agents constantly engage with new tasks and need to plan collision-free paths to execute them. To execute a task, an agent needs to visit a pair of goal locations, consisting of a pickup location and a delivery location. We propose two variants of an algorithm that assigns a sequence of tasks to each agent using the anytime algorithm Large Neighborhood Search (LNS) and plans paths using the Multi-Agent Path Finding (MAPF) algorithm Priority-Based Search (PBS). LNS-PBS is complete for well-formed MAPD instances, a realistic subclass of MAPD instances, and empirically more effective than the existing complete MAPD algorithm CENTRAL. LNS-wPBS provides no completeness guarantee but is empirically more efficient and stable than LNS-PBS. It scales to thousands of agents and thousands of tasks in a large warehouse and is empirically more effective than the existing scalable MAPD algorithm HBH+MLA*. LNS-PBS and LNS-wPBS also apply to a more general variant of MAPD, namely the Multi-Goal MAPD (MG-MAPD) problem, where tasks can have different numbers of goal locations.

SoCS Conference 2022 Conference Paper

Multi-Train Path Finding Revisited

• Zhe Chen 0016
• Jiaoyang Li 0001
• Daniel Harabor
• Peter J. Stuckey
• Sven Koenig

Multi-Train Path Finding (MTPF) is a coordination problem that asks us to plan collision-free paths for a team of moving agents, where each agent occupies a sequence of locations at any given time. MTPF is useful for planning a range of real-world vehicles, including rail trains and road convoys. MTPF is closely related to another coordination problem known as k-Robust Multi-Agent Path Finding (kR-MAPF). Although similar in principle, the performance of optimal MTPF algorithms in practice lags far behind that of optimal kR-MAPF algorithms. In this work, we revisit the connection between them and reduce the performance gap. First, we show that, in many cases, a valid kR-MAPF plan is also a valid MTPF plan, which leads to a new and faster approach for collision resolution. We also show that many recently introduced improvements for kR-MAPF, such as lower-bounding heuristics and symmetry reasoning, can be extended to MTPF. Finally, we explore a new type of pairwise symmetry specific to MTPF. Our experiments show that these improvements yield large efficiency gains for optimal MTPF.

SoCS Conference 2022 Conference Paper

Mutex Propagation in Multi-Agent Path Finding for Large Agents

• Han Zhang 0018
• Yutong Li
• Jiaoyang Li 0001
• T. K. Satish Kumar
• Sven Koenig

Mutex propagation and its concomitant symmetry-breaking techniques have proven useful in Multi-Agent Path Finding (MAPF) with point agents. In this paper, we show that they can be easily generalized to richer MAPF problems. In particular, we demonstrate their application to MAPF with ``Large

SoCS Conference 2022 Conference Paper

On Merging Agents in Multi-Agent Pathfinding Algorithms

• Eli Boyarski
• Shao-Hung Chan
• Dor Atzmon
• Ariel Felner
• Sven Koenig

In Multi-Agent Pathfinding (MAPF), the task is to find non-colliding paths for a set of agents. This paper focuses on search-based MAPF algorithms from the Conflict-Based Framework, which is introduced here. A common technique in such algorithms is to merge a group of dependent agents into a meta-agent and plan non-colliding paths for the meta-agent using a low-level MAPF sub-solver. We analyze the patterns that emerge when agents are merged in an arbitrary order. We then introduce policies for choosing which agents or meta-agents to merge to achieve improved efficiency in three algorithms: Independence Detection (ID) and Improved Conflict-Based Search (ICBS), which are optimal, and Priority-Based Search (PBS), which is a fast suboptimal algorithm. Experimental results show a significant improvement in efficiency

ICRA Conference 2022 Conference Paper

Optimal and Bounded-Suboptimal Multi-Goal Task Assignment and Path Finding

• Xinyi Zhong
• Jiaoyang Li 0001
• Sven Koenig
• Hang Ma 0001

We formalize and study the multi-goal task assignment and path finding (MG-TAPF) problem from theoretical and algorithmic perspectives. The MG-TAPF problem is to compute an assignment of tasks to agents, where each task consists of a sequence of goal locations, and collision-free paths for the agents that visit all goal locations of their assigned tasks in sequence. Theoretically, we prove that the MG-TAPF problem is NP-hard to solve optimally. We present algorithms that build upon algorithmic techniques for the multi-agent path finding problem and solve the MG-TAPF problem optimally and bounded-suboptimally. We experimentally compare these algorithms on a variety of different benchmark domains.

AAAI Conference 2022 Conference Paper

Shard Systems: Scalable, Robust and Persistent Multi-Agent Path Finding with Performance Guarantees

• Christopher Leet
• Jiaoyang Li
• Sven Koenig

Modern multi-agent robotic systems increasingly require scalable, robust and persistent Multi-Agent Path Finding (MAPF) with performance guarantees. While many MAPF solvers that provide some of these properties exist, none provides them all. To fill this need, we propose a new MAPF framework, the shard system. A shard system partitions the workspace into geographic regions, called shards, linked by a novel system of buffers. Agents are routed optimally within a shard by a local controller to local goals set by a global controller. The buffer system novelly allows shards to plan with perfect parallelism, providing scalability. A novel global controller algorithm can rapidly generate an inter-shard routing plan for thousands of agents while minimizing the traffic routed through any shard. A novel workspace partitioning algorithm produces shards small enough to replan rapidly. These innovations allow a shard system to adjust its routing plan in real time if an agent is delayed or assigned a new goal, enabling robust, persistent MAPF. A shard system’s local optimality and optimized inter-shard routing bring the sum-ofcosts of its solutions to single-shot MAPF problems to between 25% and 70% of optimal on a diversity of workspaces. Its scalability allows it to plan paths for thousands of agents in seconds. If any of their goals change or move actions fails, a shard system can replan in under a second.

SoCS Conference 2022 Conference Paper

Which MAPF Model Works Best for Automated Warehousing?

• Sumanth Varambally
• Jiaoyang Li 0001
• Sven Koenig

Multi-Agent Path Finding (MAPF) algorithms and their variants can find high-quality collision-free plans for automated warehousing under simplified assumptions about the robot dynamics. However, these simplifying assumptions pose challenging implementational issues as the robots cannot follow the plans precisely. Various robust execution frameworks, such as the Action Dependency Graph (ADG) framework, have been proposed to enable the real-world execution of MAPF plans. Under such a framework, it is unclear how the simplifying assumptions affect the performance of the robots. In this work, we first argue that the ADG framework provides the same robustness guarantees as the single-agent framework (where plans are generated independently for each robot and collisions are avoided through a reservation table), which is widely used in industry. We then improve the efficiency of the ADG framework by integrating it with the Rolling-Horizon Collision-Resolution framework to solve MAPF problems with a persistent stream of online tasks. Using the integrated framework, we compare the standard MAPF model with many of its more complex variants, such as MAPF with rotation, k-robust MAPF, and continuous-time MAPF (taking robot dynamics into account). We examine their effectiveness in improving throughput through realistic simulations of warehouse settings with the Gazebo simulator.

SoCS Conference 2021 Conference Paper

A Hierarchical Approach to Multi-Agent Path Finding

• Han Zhang 0018
• Mingze Yao
• Ziang Liu 0002
• Jiaoyang Li 0001
• Lucas Terr
• Shao-Hung Chan
• T. K. Satish Kumar
• Sven Koenig

Solving Multi-Agent Path Finding (MAPF) instances optimally is NP-hard, and existing optimal and bounded suboptimal MAPF solvers thus usually do not scale to large MAPF instances. Greedy MAPF solvers scale to large MAPF instances, but their solution qualities are often bad. In this paper, we therefore propose a novel MAPF solver, Hierarchical Multi-Agent Path Planner (HMAPP), which creates a spatial hierarchy by partitioning the environment into multiple regions and decomposes a MAPF instance into smaller MAPF sub-instances for each region. For each sub-instance, it uses a bounded-suboptimal MAPF solver to solve it with good solution quality. Our experimental results show that HMAPP is able to solve as large MAPF instances as greedy MAPF solvers while achieving better solution qualities on various maps.

IJCAI Conference 2021 Conference Paper

Anytime Multi-Agent Path Finding via Large Neighborhood Search

• Jiaoyang Li
• Zhe Chen
• Daniel Harabor
• Peter J. Stuckey
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the challenging problem of computing collision-free paths for multiple agents. Algorithms for solving MAPF can be categorized on a spectrum. At one end are (bounded-sub)optimal algorithms that can find high-quality solutions for small problems. At the other end are unbounded-suboptimal algorithms that can solve large problems but usually find low-quality solutions. In this paper, we consider a third approach that combines the best of both worlds: anytime algorithms that quickly find an initial solution using efficient MAPF algorithms from the literature, even for large problems, and that subsequently improve the solution quality to near-optimal as time progresses by replanning subgroups of agents using Large Neighborhood Search. We compare our algorithm MAPF-LNS against a range of existing work and report significant gains in scalability, runtime to the initial solution, and speed of improving the solution.

AAMAS Conference 2021 Conference Paper

Anytime Multi-Agent Path Finding via Large Neighborhood Search

• Jiaoyang Li
• Zhe Chen
• Daniel Harabor
• Peter J. Stuckey
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the challenging problem of computing collision-free paths for a cooperative team of moving agents. Algorithms for solving MAPF can be categorized on a spectrum. At one end are (bounded-sub)optimal algorithms that can find high-quality solutions for small problems. At the other end are unbounded-suboptimal algorithms (including prioritized and rule-based algorithms) that can solve very large practical problems but usually find low-quality solutions. In this paper, we consider a third approach that combines both advantages: anytime algorithms that quickly find an initial solution, including for large problems, and that subsequently improve the solution to near-optimal as time progresses. To improve the solution, we replan subsets of agents using Large Neighborhood Search, a popular meta-heuristic often applied in combinatorial optimization. Empirically, we compare our algorithm MAPF-LNS to the state-of-the-art anytime MAPF algorithm anytime BCBS and report significant gains in scalability, runtime to the first solution, and speed of improving solutions.

SoCS Conference 2021 Conference Paper

ECBS with Flex Distribution for Bounded-Suboptimal Multi-Agent Path Finding

• Shao-Hung Chan
• Jiaoyang Li 0001
• Graeme Gange
• Daniel Harabor
• Peter J. Stuckey
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the problem of finding collision-free paths for multiple agents. CBS is a leading optimal two-level MAPF solver whose low level plans optimal paths for single agents and whose high level runs a best-first search on a Constraint Tree (CT) to resolve the collisions between the paths. ECBS, a bounded-suboptimal variant of CBS, speeds up CBS by reducing the number of collisions that need to be resolved on the high level. It achieves this by generating bounded-suboptimal paths with fewer collisions with the paths of the other agents on the low level and expanding bounded-suboptimal CT nodes that contain fewer collisions on the high level. In this paper, we propose Flexible ECBS (FECBS) that further reduces the number of collisions that need to be resolved on the high level by using looser suboptimal bounds on the low level while still providing bounded-suboptimal solutions. Instead of requiring the cost of each path to be bounded-suboptimal, FECBS requires only the overall cost of the paths to be bounded-suboptimal, which gives us the freedom to distribute the cost leeway among different agents according to their needs. Our empirical results show that FECBS can solve more MAPF instances than state-of-the-art ECBS variants within 5 minutes.

AAAI Conference 2021 Conference Paper

EECBS: A Bounded-Suboptimal Search for Multi-Agent Path Finding

• Jiaoyang Li
• Wheeler Ruml
• Sven Koenig

Multi-Agent Path Finding (MAPF), i. e. , finding collision-free paths for multiple robots, is important for many applications where small runtimes are necessary, including the kind of automated warehouses operated by Amazon. CBS is a leading two-level search algorithm for solving MAPF optimally. ECBS is a bounded-suboptimal variant of CBS that uses focal search to speed up CBS by sacrificing optimality and instead guaranteeing that the costs of its solutions are within a given factor of optimal. In this paper, we study how to decrease its runtime even further using inadmissible heuristics. Motivated by Explicit Estimation Search (EES), we propose Explicit Estimation CBS (EECBS), a new bounded-suboptimal variant of CBS, that uses online learning to obtain inadmissible estimates of the cost of the solution of each high-level node and uses EES to choose which high-level node to expand next. We also investigate recent improvements of CBS and adapt them to EECBS. We find that EECBS with the improvements runs significantly faster than the state-of-the-art bounded-suboptimal MAPF algorithms ECBS, BCP-7, and eMDD-SAT on a variety of MAPF instances. We hope that the scalability of EECBS enables additional applications for bounded-suboptimal MAPF algorithms.

AAAI Conference 2021 Conference Paper

f-Aware Conflict Prioritization & Improved Heuristics For Conflict-Based Search

• Eli Boyarski
• Ariel Felner
• Pierre Le Bodic
• Daniel D. Harabor
• Peter J. Stuckey
• Sven Koenig

Conflict-Based Search (CBS) is a leading two-level algorithm for optimal Multi-Agent Path Finding (MAPF). The main step of CBS is to expand nodes by resolving conflicts (where two agents collide). Choosing the ‘right’ conflict to resolve can greatly speed up the search. CBS first resolves conflicts where the costs (g-values) of the resulting child nodes are larger than the cost of the node to be split. However, the recent addition of high-level heuristics to CBS and expanding nodes according to f = g + h reduces the relevance of this conflict prioritization method. Therefore, we introduce an expanded categorization of conflicts, which first resolves conflicts where the f-values of the child nodes are larger than the f-value of the node to be split, and present a method for identifying such conflicts. We also enhance all known heuristics for CBS by using information about the cost of resolving certain conflicts with only a small computational overhead. Finally, we experimentally demonstrate that both the expanded categorization of conflicts and the improved heuristics contribute to making CBS even more efficient.

SoCS Conference 2021 Conference Paper

Further Improved Heuristics For Conflict-Based Search

• Eli Boyarski
• Ariel Felner
• Pierre Le Bodic
• Daniel Harabor
• Peter J. Stuckey
• Sven Koenig

Conflict-Based Search (CBS) is a leading two-level algorithm for optimal Multi-Agent Path Finding (MAPF). At its high level, CBS expands nodes by resolving conflicts. In recent years, admissible heuristics were added to the high level of CBS. We enhance all known heuristic functions for CBS by using information about the cost of resolving certain conflicts, with only a small computational overhead. We experimentally demonstrate that the improved heuristics contribute to making CBS even more efficient.

AAMAS Conference 2021 Conference Paper

Learning Node-Selection Strategies in Bounded-Suboptimal Conflict-Based Search for Multi-Agent Path Finding

• Taoan Huang
• Bistra Dilkina
• Sven Koenig

Multi-Agent Path Finding (MAPF) is an NP-hard problem that has important applications for distribution centers, traffic management and computer games, and it is still difficult for current solvers to solve large instances optimally. Bounded suboptimal solvers, such as Enhanced Conflict-Based Search (ECBS) and its variants, are more efficient than optimal solvers in finding a solution with suboptimality guarantees. ECBS is a tree search algorithm that expands the search tree by repeatedly selecting search tree nodes from a focal list. In this work, we propose to use machine learning (ML) to learn a node-selection strategy to speed up ECBS. In the first phase of our framework, we use imitation learning and curriculum learning to learn node-selection strategies iteratively for different numbers of agents from training instances. In the second phase, we deploy the learned models in ECBS and test their solving performance on unseen instances drawn from the same distribution as the training instances. We demonstrate that our solver, ECBS+ML, shows substantial improvement in terms of the success rates and runtimes over ECBS on five different types of grid maps from the MAPF benchmark.

AAAI Conference 2021 Conference Paper

Learning to Resolve Conflicts for Multi-Agent Path Finding with Conflict-Based Search

• Taoan Huang
• Sven Koenig
• Bistra Dilkina

Conflict-Based Search (CBS) is a state-of-the-art algorithm for multi-agent path finding. On the high level, CBS repeatedly detects conflicts and resolves one of them by splitting the current problem into two subproblems. Previous work chooses the conflict to resolve by categorizing conflicts into three classes and always picking one from the highest-priority class. In this work, we propose an oracle for conflict selection that results in smaller search tree sizes than the one used in previous work. However, the computation of the oracle is slow. Thus, we propose a machine-learning (ML) framework for conflict selection that observes the decisions made by the oracle and learns a conflict-selection strategy represented by a linear ranking function that imitates the oracle’s decisions accurately and quickly. Experiments on benchmark maps indicate that our approach, ML-guided CBS, significantly improves the success rates, search tree sizes and runtimes of the current state-of-the-art CBS solver.

AAAI Conference 2021 Conference Paper

Lifelong Multi-Agent Path Finding in Large-Scale Warehouses

• Jiaoyang Li
• Andrew Tinka
• Scott Kiesel
• Joseph W. Durham
• T. K. Satish Kumar
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the problem of moving a team of agents to their goal locations without collisions. In this paper, we study the lifelong variant of MAPF, where agents are constantly engaged with new goal locations, such as in large-scale automated warehouses. We propose a new framework Rolling-Horizon Collision Resolution (RHCR) for solving lifelong MAPF by decomposing the problem into a sequence of Windowed MAPF instances, where a Windowed MAPF solver resolves collisions among the paths of the agents only within a bounded time horizon and ignores collisions beyond it. RHCR is particularly well suited to generating pliable plans that adapt to continually arriving new goal locations. We empirically evaluate RHCR with a variety of MAPF solvers and show that it can produce high-quality solutions for up to 1, 000 agents (= 38. 9% of the empty cells on the map) for simulated warehouse instances, significantly outperforming existing work.

AIJ Journal 2021 Journal Article

Pairwise symmetry reasoning for multi-agent path finding search

• Jiaoyang Li
• Daniel Harabor
• Peter J. Stuckey
• Hang Ma
• Graeme Gange
• Sven Koenig

AIJ Journal 2021 Journal Article

Path-length analysis for grid-based path planning

• James P. Bailey
• Alex Nash
• Craig A. Tovey
• Sven Koenig

ICAPS Conference 2021 Conference Paper

Scalable Rail Planning and Replanning: Winning the 2020 Flatland Challenge

• Jiaoyang Li 0001
• Zhe Chen 0016
• Yi Zheng 0010
• Shao-Hung Chan
• Daniel Harabor
• Peter J. Stuckey
• Hang Ma 0001
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the combinatorial problem of finding collision-free paths for multiple agents on a graph. This paper describes MAPF-based software for solving train planning and replanning problems on large-scale rail networks under uncertainty. The software recently won the 2020 Flatland Challenge, a NeurIPS competition trying to determine how to efficiently manage dense traffic on rail networks. The software incorporates many state-of-the-art MAPF or, in general, optimization technologies, such as prioritized planning, large neighborhood search, safe interval path planning, minimum communication policies, parallel computing, and simulated annealing. It can plan collision-free paths for thousands of trains within a few minutes and deliver deadlock-free actions in real-time during execution.

SoCS Conference 2021 Conference Paper

Scalable Rail Planning and Replanning: Winning the 2020 Flatland Challenge

• Jiaoyang Li 0001
• Zhe Chen 0016
• Yi Zheng 0010
• Shao-Hung Chan
• Daniel Harabor
• Peter J. Stuckey
• Hang Ma 0001
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the combinatorial problem of finding collision-free paths for multiple agents on a graph. This paper describes MAPF-based software for solving train planning and replanning problems on large-scale railway networks under uncertainty. The software recently won the 2020 Flatland Challenge, a NeurIPS competition trying to determine how to efficiently manage dense traffic on rail networks. The software incorporates many state-of-the-art MAPF, or in general, optimization technologies, such as prioritized planning, large neighborhood search, safe interval path planning, minimum communication policies, parallel computing, and simulated annealing. It can plan collision-free paths for thousands of trains within a few minutes and deliver deadlock-free actions in real-time during execution.

ICAPS Conference 2021 Conference Paper

Temporal Reasoning with Kinodynamic Networks

• Han Zhang 0018
• Neelesh Tiruviluamala
• Sven Koenig
• T. K. Satish Kumar

Temporal reasoning is central to Artificial Intelligence (AI) and many of its applications. However, the existing algorithmic frameworks for temporal reasoning are not expressive enough to be applicable to robots with complex kinodynamic constraints typically described using differential equations. For example, while minimum and maximum velocity constraints can be encoded in Simple Temporal Networks (STNs), higher-order kinodynamic constraints cannot be represented in existing frameworks. In this paper, we present a novel framework for temporal reasoning called Kinodynamic Networks (KDNs). KDNs combine elements of existing temporal reasoning frameworks with the idea of Bernstein polynomials. The velocity profiles of robots are represented using Bernstein polynomials; and dynamic constraints on these velocity profiles can be converted to linear constraints on the to-be-determined coefficients of their Bernstein polynomials. We study KDNs for their attractive theoretical properties and apply them to the Multi-Agent Path Finding (MAPF) problem with higher-order kinodynamic constraints. We show that our approach is not only scalable but also yields smooth velocity profiles for all robots that can be executed by their controllers.

SoCS Conference 2020 Conference Paper

A Simple and Fast Bi-Objective Search Algorithm

• Carlos Hernández Ulloa
• William Yeoh 0001
• Jorge A. Baier
• Luis Suazo
• Han Zhang 0018
• Sven Koenig

Many interesting search problems can be formulated as bi-objective search problems; for example, transportation problems where both travel distance and time need to be minimized. Multi-objective best-first search algorithms need to maintain the set of undominated paths from the start state to each state to compute a set of paths from a given start state to a given goal state (the Pareto-optimal solutions) such that no path in the set is dominated by another path in the set. Each time they find a new path to a state n, they perform a dominance check to determine whether such a path dominates any of the previously found paths to n. Existing algorithms do not perform these checks efficiently, requiring at least a full iteration over the Open list per check. In this paper, we present the first multi-objective algorithm that performs these checks efficiently. Indeed, Bi-Objective A* (BOA*)—our algorithm—requires constant time to check for dominance. Our experimental evaluation shows that BOA*is orders-of-magnitude faster than state-of-the-art search algorithms, such as NAMOA*, Bi-Objective Dijkstra, and Bidirectional Bi-Objective Dijkstra.

ICAPS Conference 2020 Conference Paper

A Simple and Fast Bi-Objective Search Algorithm

• Carlos Hernández Ulloa
• William Yeoh 0001
• Jorge A. Baier
• Han Zhang 0018
• Luis Suazo
• Sven Koenig

Many interesting search problems can be formulated as bi-objective search problems, that is, search problems where two kinds of costs have to be minimized, for example, travel distance and time for transportation problems. Bi-objective search algorithms have to maintain the set of undominated paths from the start state to each state to compute the set of paths from the start state to the goal state that are not dominated by some other path from the start state to the goal state (called the Pareto-optimal solution set). Each time they find a new path to a state s, they perform a dominance check to determine whether this path dominates any of the previously found paths to s or whether any of the previously found paths to s dominates this path. Existing algorithms do not perform these checks efficiently. On the other hand, our Bi-Objective A* (BOA*) algorithm requires only constant time per check. In our experimental evaluation, we show that BOA* can run an order of magnitude (or more) faster than state-of-the-art bi-objective search algorithms, such as NAMOA*, NAMOA*dr, Bi-Objective Dijkstra, and Bidirectional Bi-Objective Dijkstra.

SoCS Conference 2020 Conference Paper

Decision Tree Learning-Inspired Dynamic Variable Ordering for the Weighted CSP

• Hong Xu 0003
• Kexuan Sun 0002
• Sven Koenig
• T. K. Satish Kumar

The weighted constraint satisfaction problem (WCSP) is a powerful mathematical framework for combinatorial optimization. The branch and bound search paradigm is very successful in solving the WCSP but critically depends on the ordering in which variables are instantiated. In this paper, we introduce a new framework for dynamic variable ordering for solving the WCSP. This framework is inspired by regression decision tree learning. Variables are ordered dynamically based on samples of random assignments of values to variables as well as their corresponding total weights. Within this framework, we propose four variable ordering heuristics (sdr, inv-sdr, rr and inv-rr). We compare them with many other state-of-the-art dynamic variable ordering heuristics, and show that sdr and rr outperform them on many real-world and random benchmark instances.

SoCS Conference 2020 Conference Paper

Embedding Directed Graphs in Potential Fields Using FastMap-D

• Sriram Gopalakrishnan
• Liron Cohen 0002
• Sven Koenig
• T. K. Satish Kumar

Embedding undirected graphs in a Euclidean space has many computational benefits. FastMap is an efficient embedding algorithm that facilitates a geometric interpretation of problems posed on undirected graphs. However, Euclidean distances are inherently symmetric and, thus, Euclidean embeddings cannot be used for directed graphs. In this paper, we present FastMap-D, an efficient generalization of FastMap to directed graphs. FastMap-D embeds vertices using a potential field to capture the asymmetry between the to-and-fro pairwise distances in directed graphs. FastMap-D learns a potential function to define the potential field using a machine learning module. In experiments on various kinds of directed graphs, we demonstrate the advantage of FastMap-D over other approaches.

SoCS Conference 2020 Conference Paper

From Multi-Agent Pathfinding to 3D Pipe Routing

• Gleb Belov
• Wenbo Du 0004
• Maria Garcia de la Banda
• Daniel Harabor
• Sven Koenig
• Xinrui Wei

The 2D Multi-Agent Path Finding (MAPF) problem aims at finding collision-free paths for a number of agents, from a set of start locations to a set of goal positions in a known 2D environment. MAPF has been studied in theoretical computer science, robotics, and artificial intelligence over several decades, due to its importance for robot navigation. It is currently experiencing significant scientific progress due to its relevance in automated warehousing (such as those operated by Amazon) and in other contemporary application areas. In this paper, we demonstrate that some recently developed MAPF algorithms apply more broadly than currently believed in the MAPF research community. In particular, we describe the 3D Pipe Routing (PR) problem, which aims at placing collision-free pipes from given start locations to given goal locations in a known 3D environment. The MAPF and PR problems are similar: a solution to a MAPF instance is a set of blocked cells in x-y-t space, while a solution to the corresponding PR instance is a set of blocked cells in x-y-z space. We show how to use this similarity to apply several recently developed MAPF algorithms to the PR problem, and discuss their performance on real-world PR instances. This opens up a new direction of industrial relevance for the MAPF research community.

AAAI Conference 2020 Conference Paper

Idle Time Optimization for Target Assignment and Path Finding in Sortation Centers

• Ngai Meng Kou
• Cheng Peng
• Hang Ma
• T. K. Satish Kumar
• Sven Koenig

In this paper, we study the one-shot and lifelong versions of the Target Assignment and Path Finding problem in automated sortation centers, where each agent needs to constantly assign itself a sorting station, move to its assigned station without colliding with obstacles or other agents, wait in the queue of that station to obtain a parcel for delivery, and then deliver the parcel to a sorting bin. The throughput of such centers is largely determined by the total idle time of all stations since their queues can frequently become empty. To address this problem, we first formalize and study the oneshot version that assigns stations to a set of agents and finds collision-free paths for the agents to their assigned stations. We present efficient algorithms for this task based on a novel min-cost max-flow formulation that minimizes the total idle time of all stations in a fixed time window. We then demonstrate how our algorithms for solving the one-shot problem can be applied to solving the lifelong problem as well. Experimentally, we believe to be the first researchers to consider real-world automated sortation centers using an industrial simulator with realistic data and a kinodynamic model of real robots. On this simulator, we showcase the benefits of our algorithms by demonstrating their efficiency and effectiveness for up to 350 agents.

IJCAI Conference 2020 Conference Paper

Iterative-Deepening Conflict-Based Search

• Eli Boyarski
• Ariel Felner
• Daniel Harabor
• Peter J. Stuckey
• Liron Cohen
• Jiaoyang Li
• Sven Koenig

Conflict-Based Search (CBS) is a leading algorithm for optimal Multi-Agent Path Finding (MAPF). CBS variants typically compute MAPF solutions using some form of A* search. However, they often do so under strict time limits so as to avoid exhausting the available memory. In this paper, we present IDCBS, an iterative-deepening variant of CBS which can be executed without exhausting the memory and without strict time limits. IDCBS can be substantially faster than CBS due to incremental methods that it uses when processing CBS nodes.

SoCS Conference 2020 Conference Paper

Moving Agents in Formation in Congested Environments

• Jiaoyang Li 0001
• Kexuan Sun 0002
• Hang Ma 0001
• Ariel Felner
• T. K. Satish Kumar
• Sven Koenig

In this paper, we formalize and study the Moving Agents in Formation (MAiF) problem, that combines the tasks of finding short collision-free paths for multiple agents and keeping them in close adherence to a desired formation. Previous work includes controller-based algorithms, swarm-based algorithms, and potential-field-based algorithms. They usually focus on only one or the other of these tasks, solve the problem greedily without systematic search, and thus generate costly solutions or even fail to find solutions in congested environment. In this paper, we develop a two-phase search algorithm, called SWARM-MAPF, whose first phase is inspired by swarm-based algorithms (in open regions) and whose second phase is inspired by multi-agent path-finding (MAPF) algorithms (in congested regions). In the first phase, SWARM-MAPF selects a leader among the agents and finds a path for it that is sufficiently far away from the obstacles so that the other agents can preserve the desired formation around it. It also identifies the critical segments of the leader

ICAPS Conference 2020 Conference Paper

Multi-Agent Path Finding with Mutex Propagation

• Han Zhang 0018
• Jiaoyang Li 0001
• Pavel Surynek
• Sven Koenig
• T. K. Satish Kumar

Mutex propagation is a form of efficient constraint propagation popularly used in AI planning to tightly approximate the reachable states from a given state. We utilize this idea in the context of Multi-Agent Path Finding (MAPF). When adapted to MAPF, mutex propagation provides stronger constraints for conflict resolution in Conflict-Based Search (CBS), a popular optimal MAPF algorithm, and provides it with the ability to identify and reason with symmetries in MAPF. While existing work identifies a limited form of symmetries using rectangle reasoning and requires the manual design of symmetry-breaking constraints, mutex propagation is more general and allows for the automated design of symmetry-breaking constraints. Our experimental results show that CBS with mutex propagation is capable of outperforming CBSH with rectangle reasoning, a state-of-the-art variant of CBS, with respect to runtime and success rate.

IJCAI Conference 2020 Conference Paper

Multi-Directional Heuristic Search

• Dor Atzmon
• Jiaoyang Li
• Ariel Felner
• Eliran Nachmani
• Shahaf Shperberg
• Nathan Sturtevant
• Sven Koenig

In the Multi-Agent Meeting problem (MAM), the task is to find a meeting location for multiple agents, as well as a path for each agent to that location. In this paper, we introduce MM*, a Multi-Directional Heuristic Search algorithm that finds the optimal meeting location under different cost functions. MM* generalizes the Meet in the Middle (MM) bidirectional search algorithm to the case of finding an optimal meeting location for multiple agents. Several admissible heuristics are proposed, and experiments demonstrate the benefits of MM*.

SoCS Conference 2020 Conference Paper

Multi-Directional Search

• Dor Atzmon
• Jiaoyang Li 0001
• Ariel Felner
• Eliran Nachmani
• Shahaf S. Shperberg
• Nathan R. Sturtevant
• Sven Koenig

In the Multi-Agent Meeting (MAM) problem, the task is to find a meeting location for multiple agents, as well as a path for each agent to that location. In this paper, we introduce MM*, a Multi-Directional Search algorithm that finds the optimal meeting location under different cost functions. MM* generalizes the Meet in the Middle (MM) bidirectional search algorithm to the case of finding optimal meeting locations for multiple agents. A number of admissible heuristics are proposed and experiments demonstrate the benefits of MM*.

ICAPS Conference 2020 Conference Paper

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding

• Jiaoyang Li 0001
• Graeme Gange
• Daniel Harabor
• Peter J. Stuckey
• Hang Ma 0001
• Sven Koenig

We consider two new classes of pairwise path symmetries which appear in the context of Multi-Agent Path Finding (MAPF). The first of them, corridor symmetry, arises when two agents attempt to pass through the same narrow passage in opposite directions. The second, target symmetry, arises when the shortest path of one agent passes through the target location of a second agent after the second agent has already arrived at it. These symmetries can produce an exponential explosion in the space of possible collision resolutions, leading to unacceptable runtimes even for state-of-the-art MAPF algorithms such as Conflict-Based Search (CBS). We propose to break these symmetries using new reasoning techniques that: (1) detect each class of symmetry and (2) resolve them by introducing specialized constraints. We experimentally show that our techniques can, in some cases, more than double the success rate of CBS and improve its runtime by one order of magnitude.

SoCS Conference 2020 Conference Paper

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding

• Jiaoyang Li 0001
• Graeme Gange
• Daniel Harabor
• Peter J. Stuckey
• Hang Ma 0001
• Sven Koenig

We consider two new types of pairwise path symmetries which appear in the context of Multi-Agent Path Finding (MAPF). The first of them, corridor symmetry, arises when two agents attempt to pass through the same narrow passage but in opposite directions. The second, target symmetry, arises when the shortest path of one agent requires the target location of a second agent after the second agent has already arrived. These symmetries can produce an exponential blowup in the space of possible collision resolutions, leading to timeout failure even for state-of-the-art algorithms such as Conflict-Based Search. We propose to break symmetries using new reasoning techniques that: (1) detect each type of situation and, (2) resolve them by introducing specialized constraints. We implement our ideas in the context of Conflict-Based Search where, in a range of experiments, we report up to an order-of-magnitude improvement in runtime performance and, in some cases, more than a doubling in success rate.

ICAPS Conference 2020 Conference Paper

Probabilistic Robust Multi-Agent Path Finding

• Dor Atzmon
• Roni Stern
• Ariel Felner
• Nathan R. Sturtevant
• Sven Koenig

In a multi-agent path finding (MAPF) problem, the task is to move a set of agents to their goal locations without conflicts. In the real world, unexpected events may delay some of the agents. In this paper, we therefore study the problem of finding a p-robust solution to a given MAPF problem, which is a solution that succeeds with probability at least p, even though unexpected delays may occur. We propose two methods for verifying that given solutions are p-robust. We also introduce an optimal CBS-based algorithm, called pR-CBS, and a fast suboptimal algorithm, called pR-GCBS, for finding such solutions. Our experiments show that a p-robust solution reduces the number of conflicts compared to optimal, non-robust solutions.

SoCS Conference 2020 Conference Paper

Toward a String-Pulling Approach to Path Smoothing on Grid Graphs

• Jihee Han
• Tansel Uras
• Sven Koenig

Paths found on grid graphs are often unrealistic looking in the continuous environment that the grid graph represents and often need to be smoothed after a search. The well-known algorithm for path smoothing is greedy in nature and does not necessarily eliminate all heading changes in freespace. We present a new path-smoothing algorithm based on “string pulling” and show experimentally that it consistently finds shorter paths than the greedy algorithm and produces paths with no heading changes in freespace.

SoCS Conference 2019 Conference Paper

A Learning-Based Framework for Memory-Bounded Heuristic Search: First Results

• Carlos Hernández Ulloa
• Jorge A. Baier
• William Yeoh 0001
• Vadim Bulitko
• Sven Koenig

Many existing boundedly-suboptimal heuristic search algorithms are variants of best-first search. Due to memory limitations, these algorithms are unable to solve problems with extremely large search spaces. In this paper, we present a framework that allows best-first search algorithms to solve problems with such large search spaces given a (reasonable) memory bound while also preserving optimality guarantees in tree-structured search spaces. In our framework, a given algorithm is run several times. In each search episode, the algorithm expands up to a user-defined number of states. After each episode, unless the goal has been found, the heuristic values of the generated states are updated using a linear-time algorithm that preserves consistency in tree-structured search spaces. In subsequent search episodes, only the heuristic values of the states generated in the previous episode need to be kept in memory. We present experimental results where we plug A*, GBFS, and wA* into our framework to solve traveling salesman problems and compare them against benchmark linear-memory algorithms like DFBnB and wDFBnB.

AAMAS Conference 2019 Conference Paper

A New Constraint Satisfaction Perspective on Multi-Agent Path Finding: Preliminary Results

• Jiangxing Wang
• Jiaoyang Li
• Hang Ma
• Sven Koenig
• T. K. Satish Kumar

In this paper, we adopt a new perspective on the Multi-Agent Path Finding (MAPF) problem and view it as a Constraint Satisfaction Problem (CSP). A variable corresponds to an agent, its domain is the set of all paths from the start vertex to the goal vertex of the agent, and the constraints allow only conflict-free paths for each pair of agents. Although the domains and constraints are only implicitly defined, this new CSP perspective allows us to use successful techniques from CSP search. With the concomitant idea of using matrix computations for calculating the size of the reduced domain of an uninstantiated variable, we apply Dynamic Variable Ordering and Rapid Random Restarts to the MAPF problem. In our experiments, the resulting simple polynomial-time MAPF solver, called Matrix MAPF solver, either outperforms or matches the performance of many state-of-the-art solvers for the MAPF problem and its variants.

ICAPS Conference 2019 Conference Paper

Disjoint Splitting for Multi-Agent Path Finding with Conflict-Based Search

• Jiaoyang Li 0001
• Daniel Harabor
• Peter J. Stuckey
• Hang Ma 0001
• Sven Koenig

Multi-Agent Path Finding (MAPF) is the planning problem of finding collision-free paths for a team of agents. We focus on Conflict-Based Search (CBS), a two-level tree-search state-of-the-art MAPF algorithm. The standard splitting strategy used by CBS is not disjoint, i. e. , when it splits a problem into two subproblems, some solutions are shared by both subproblems, which can create duplication of search effort. In this paper, we demonstrate how to improve CBS with disjoint splitting and how to modify the low-level search of CBS to take maximal advantage of it. Experiments show that disjoint splitting increases the success rates and speeds of CBS and its variants by up to 2 orders of magnitude.

SoCS Conference 2019 Conference Paper

Extended Abstract: Lifelong Path Planning with Kinematic Constraintsfor Multi-Agent Pickup and Delivery

• Hang Ma 0001
• Wolfgang Hönig
• T. K. Satish Kumar
• Nora Ayanian
• Sven Koenig

The Multi-Agent Pickup and Delivery (MAPD) problem models applications where a large number of agents attend to a stream of incoming pickup-and-delivery tasks. Token Passing (TP) is a recent MAPD algorithm that is efficient and effective. We make TP even more efficient and effective by using a novel combinatorial search algorithm, called Safe Interval Path Planning with Reservation Table (SIPPwRT), for single-agent path planning. SIPPwRT uses an advanced data structure that allows for fast updates and lookups of the current paths of all agents in an online setting. The resulting MAPD algorithm TP-SIPPwRT takes kinematic constraints of real robots into account directly during planning, computes continuous agent movements with given velocities that work on non-holonomic robots rather than discrete agent movements with uniform velocity, and is complete for well-formed MAPD instances. We demonstrate its benefits for automated warehouses using both an agent simulator and a standard robot simulator. For example, we demonstrate that it can compute paths for hundreds of agents and thousands of tasks in seconds and is more efficient and effective than existing MAPD algorithms that use a post-processing step to adapt their paths to continuous agent movements with given velocities. This paper was published at AAAI 2019.

SoCS Conference 2019 Conference Paper

Extended Abstract: Searching with Consistent Prioritization for Multi-Agent Path Finding

• Hang Ma 0001
• Daniel Harabor
• Peter J. Stuckey
• Jiaoyang Li 0001
• Sven Koenig

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-driven combinatorial search framework. In a variety of empirical comparisons, we demonstrate state-of-the-art solution qualities and success rates, often with similar runtimes to existing algorithms. We also develop new theoretical results that explore the limitations of prioritized planning, in terms of completeness and optimality, for the first time. This paper was published at AAAI 2019.

IJCAI Conference 2019 Conference Paper

Improved Heuristics for Multi-Agent Path Finding with Conflict-Based Search

• Jiaoyang Li
• Ariel Felner
• Eli Boyarski
• Hang Ma
• Sven Koenig

Conflict-Based Search (CBS) and its enhancements are among the strongest algorithms for Multi-Agent Path Finding. Recent work introduced an admissible heuristic to guide the high-level search of CBS. In this work, we prove the limitation of this heuristic, as it is based on cardinal conflicts only. We then introduce two new admissible heuristics by reasoning about the pairwise dependencies between agents. Empirically, CBS with either new heuristic significantly improves the success rate over CBS with the recent heuristic and reduces the number of expanded nodes and runtime by up to a factor of 50.

SoCS Conference 2019 Conference Paper

Improved Heuristics for Multi-Agent Path Finding with Conflict-Based Search: Preliminary Results

• Jiaoyang Li 0001
• Eli Boyarski
• Ariel Felner
• Hang Ma 0001
• Sven Koenig

Conflict-Based Search (CBS) and its enhancements are among the strongest algorithms for Multi-Agent Pathfinding. Recent work introduced an admissible heuristic to guide the high-level search of CBS. In this work, we prove the limitation of this heuristic, as it is based on cardinal conflicts only. We then introduce two new admissible heuristics by reasoning about the pairwise dependency between agents. Empirically, CBS with both new heuristics significantly improves the success rate over CBS with the recent heuristic and reduces the number of expanded nodes and runtime by up to a factor of 50, yielding a new state-of-the-art CBS-based algorithm.

AAAI Conference 2019 Conference Paper

Lifelong Path Planning with Kinematic Constraints for Multi-Agent Pickup and Delivery

• Hang Ma
• Wolfgang Hönig
• T. K. Satish Kumar
• Nora Ayanian
• Sven Koenig

The Multi-Agent Pickup and Delivery (MAPD) problem models applications where a large number of agents attend to a stream of incoming pickup-and-delivery tasks. Token Passing (TP) is a recent MAPD algorithm that is efficient and effective. We make TP even more efficient and effective by using a novel combinatorial search algorithm, called Safe Interval Path Planning with Reservation Table (SIPPwRT), for single-agent path planning. SIPPwRT uses an advanced data structure that allows for fast updates and lookups of the current paths of all agents in an online setting. The resulting MAPD algorithm TP-SIPPwRT takes kinematic constraints of real robots into account directly during planning, computes continuous agent movements with given velocities that work on non-holonomic robots rather than discrete agent movements with uniform velocity, and is complete for wellformed MAPD instances. We demonstrate its benefits for automated warehouses using both an agent simulator and a standard robot simulator. For example, we demonstrate that it can compute paths for hundreds of agents and thousands of tasks in seconds and is more efficient and effective than existing MAPD algorithms that use a post-processing step to adapt their paths to continuous agent movements with given velocities.

AAAI Conference 2019 Conference Paper

Multi-Agent Path Finding for Large Agents

• Jiaoyang Li
• Pavel Surynek
• Ariel Felner
• Hang Ma
• T. K. Satish Kumar
• Sven Koenig

Multi-Agent Path Finding (MAPF) has been widely studied in the AI community. For example, Conflict-Based Search (CBS) is a state-of-the-art MAPF algorithm based on a twolevel tree-search. However, previous MAPF algorithms assume that an agent occupies only a single location at any given time, e. g. , a single cell in a grid. This limits their applicability in many real-world domains that have geometric agents in lieu of point agents. Geometric agents are referred to as “large” agents because they can occupy multiple points at the same time. In this paper, we formalize and study LA- MAPF, i. e. , MAPF for large agents. We first show how CBS can be adapted to solve LA-MAPF. We then present a generalized version of CBS, called Multi-Constraint CBS (MC- CBS), that adds multiple constraints (instead of one constraint) for an agent when it generates a high-level search node. We introduce three different approaches to choose such constraints as well as an approach to compute admissible heuristics for the high-level search. Experimental results show that all MC-CBS variants outperform CBS by up to three orders of magnitude in terms of runtime. The best variant also outperforms EPEA* (a state-of-the-art A*-based MAPF solver) in all cases and MDD-SAT (a state-of-the-art reduction-based MAPF solver) in some cases.

SoCS Conference 2019 Conference Paper

Multi-Agent Path Finding for Large Agents

• Jiaoyang Li 0001
• Pavel Surynek
• Ariel Felner
• Hang Ma 0001
• T. K. Satish Kumar
• Sven Koenig

Multi-Agent Path Finding (MAPF) has been widely studied in the AI community. For example, Conflict-Based Search (CBS) is a state-of-the-art MAPF algorithm based on a two-level tree-search. However, previous MAPF algorithms assume that an agent occupies only a single location at any given time, e. g. , a single cell in a grid. This limits their applicability in many real-world domains that have geometric agents in lieu of point agents. Geometric agents are referred to as “large” agents because they can occupy multiple points at the same time. In this paper, we formalize and study LAMAPF, i. e. , MAPF for large agents. We first show how CBS can be adapted to solve LA-MAPF. We then present a generalized version of CBS, called Multi-Constraint CBS (MC-CBS), that adds multiple constraints (instead of one constraint) for an agent when it generates a high-level search node. We introduce three different approaches to choose such constraints as well as an approach to compute admissible heuristics for the high-level search. Experimental results show that all MC-CBS variants outperform CBS by up to three orders of magnitude in terms of runtime. The best variant also outperforms EPEA* (a state-of-the-art A*-based MAPF solver) in all cases and MDD-SAT (a state-of-the-art reduction-based MAPF solver) in some cases.

SoCS Conference 2019 Conference Paper

Multi-Agent Pathfinding: Definitions, Variants, and Benchmarks

• Roni Stern
• Nathan R. Sturtevant
• Ariel Felner
• Sven Koenig
• Hang Ma 0001
• Thayne T. Walker
• Jiaoyang Li 0001
• Dor Atzmon

The multi-agent pathfinding problem (MAPF) is the fundamental problem of planning paths for multiple agents, where the key constraint is that the agents will be able to follow these paths concurrently without colliding with each other. Applications of MAPF include automated warehouses, autonomous vehicles, and robotics. Research on MAPF has been flourishing in the past couple of years. Different MAPF research papers assume different sets of assumptions, e. g. , whether agents can traverse the same road at the same time, and have different objective functions, e. g. , minimize makespan or sum of agents

SoCS Conference 2019 Conference Paper

Optimal and Bounded-Suboptimal Multi-Agent Motion Planning

• Liron Cohen 0002
• Tansel Uras
• T. K. Satish Kumar
• Sven Koenig

Multi-Agent Motion Planning (MAMP) is the task of finding conflict-free kinodynamically feasible plans for agents from start to goal states. While MAMP is of significant practical importance, existing solvers are either incomplete, inefficient or rely on simplifying assumptions. For example, Multi-Agent Path Finding (MAPF) solvers conventionally assume discrete timesteps and rectilinear movement of agents between neighboring vertices of a graph. In this paper, we develop MAMP solvers that obviate these simplifying assumptions and yet generalize the core ideas of state-of-the-art MAPF solvers. Specifically, since different motions may take arbitrarily different durations, MAMP solvers need to efficiently reason with continuous time and arbitrary wait durations. To do so, we adapt (Enhanced) Conflict-Based Search to continuous time and develop a novel bounded-suboptimal extension of Safe Interval Path Planning, called Soft Conflict Interval Path Planning. On the theoretical side, we justify the completeness, optimality and bounded-suboptimality of our MAMP solvers. On the experimental side, we show that our MAMP solvers scale well with increasing suboptimality bounds.

IJCAI Conference 2019 Conference Paper

Regarding Jump Point Search and Subgoal Graphs

• Daniel D. Harabor
• Tansel Uras
• Peter J. Stuckey
• Sven Koenig

In this paper, we define Jump Point Graphs (JP), a preprocessing-based path-planning technique similar to Subgoal Graphs (SG). JP allows for the first time the combination of Jump Point Search style pruning in the context of abstraction-based speedup techniques, such as Contraction Hierarchies. We compare JP with SG and its variants and report new state-of-the-art results for grid-based pathfinding.

AAAI Conference 2019 Conference Paper

Searching with Consistent Prioritization for Multi-Agent Path Finding

• Hang Ma
• Daniel Harabor
• Peter J. Stuckey
• Jiaoyang Li
• Sven Koenig

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-driven combinatorial search framework. In a variety of empirical comparisons, we demonstrate state-of-the-art solution qualities and success rates, often with similar runtimes to existing algorithms. We also develop new theoretical results that explore the limitations of prioritized planning, in terms of completeness and optimality, for the first time.

AAAI Conference 2019 Conference Paper

Symmetry-Breaking Constraints for Grid-Based Multi-Agent Path Finding

• Jiaoyang Li
• Daniel Harabor
• Peter J. Stuckey
• Hang Ma
• Sven Koenig

We describe a new way of reasoning about symmetric collisions for Multi-Agent Path Finding (MAPF) on 4-neighbor grids. We also introduce a symmetry-breaking constraint to resolve these conflicts. This specialized technique allows us to identify and eliminate, in a single step, all permutations of two currently assigned but incompatible paths. Each such permutation has exactly the same cost as a current path, and each one results in a new collision between the same two agents. We show that the addition of symmetry-breaking techniques can lead to an exponential reduction in the size of the search space of CBS, a popular framework for MAPF, and report significant improvements in both runtime and success rate versus CBSH and EPEA* – two recent and state-of-the-art MAPF algorithms.

SoCS Conference 2019 Conference Paper

Symmetry-Breaking Constraints for Grid-Based Multi-Agent Path Finding

• Jiaoyang Li 0001
• Daniel Harabor
• Peter J. Stuckey
• Hang Ma 0001
• Sven Koenig

We describe a new way of reasoning about symmetric collisions for Multi-Agent Path Finding (MAPF) on 4-neighbor grids. We also introduce a symmetry-breaking constraint to resolve these conflicts. This specialized technique allows us to identify and eliminate, in a single step, all permutations of two currently assigned but incompatible paths. Each such permutation has exactly the same cost as a current path, and each one results in a new collision between the same two agents. We show that the addition of symmetry-breaking techniques can lead to an exponential reduction in the size of the search space of CBS, a popular framework for MAPF, and report significant improvements in both runtime and success rate versus CBSH and EPEA* – two recent and state-of-the-art MAPF algorithms.

AAMAS Conference 2019 Conference Paper

Task and Path Planning for Multi-Agent Pickup and Delivery

• Minghua Liu
• Hang Ma
• Jiaoyang Li
• Sven Koenig

We study the offline Multi-Agent Pickup-and-Delivery (MAPD) problem, where a team of agents has to execute a batch of tasks with release times in a known environment. To execute a task, an agent has to move first from its current location to the pickup location of the task and then to the delivery location of the task. The MAPD problem is to assign tasks to agents and plan collision-free paths for them to execute their tasks. Online MAPD algorithms can be applied to the offline MAPD problem, but do not utilize all of the available information and may thus not be effective. Therefore, we present two novel offline MAPD algorithms that improve a state-of-the-art online MAPD algorithm with respect to task planning, path planning, and deadlock avoidance for the offline MAPD problem. Our MAPD algorithms first compute one task sequence for each agent by solving a special traveling salesman problem and then plan paths according to these task sequences. We also introduce an effective deadlock avoidance method, called “reserving dummy paths. ” Theoretically, our MAPD algorithms are complete for well-formed MAPD instances, a realistic subclass of all MAPD instances. Experimentally, they produce solutions of smaller makespans and scale better than the online MAPD algorithm in simulated warehouses with hundreds of robots and thousands of tasks.

ICAPS Conference 2019 Conference Paper

Using FastMap to Solve Graph Problems in a Euclidean Space

• Jiaoyang Li 0001
• Ariel Felner
• Sven Koenig
• T. K. Satish Kumar

It is well known that many graph problems, like the Traveling Salesman Problem, are easier to solve in a Euclidean space. This motivates the idea of quickly preprocessing a given graph by embedding it in a Euclidean space to solve graph problems efficiently. In this paper, we study a nearlinear time algorithm, called FastMap, that embeds a given non-negative edge-weighted undirected graph in a Euclidean space and approximately preserves the pairwise shortest path distances between vertices. The Euclidean space can then be used either for heuristic guidance of A* (as suggested previously) or for geometric interpretations that facilitate the application of techniques from analytical geometry. We present a new variant of FastMap and compare it with the original variant theoretically and empirically. We demonstrate its usefulness for solving a path-finding and a multi-agent meeting problem.

ICAPS Conference 2018 Conference Paper

Adding Heuristics to Conflict-Based Search for Multi-Agent Path Finding

• Ariel Felner
• Jiaoyang Li 0001
• Eli Boyarski
• Hang Ma 0001
• Liron Cohen 0002
• T. K. Satish Kumar
• Sven Koenig

Conflict-Based Search (CBS) and its enhancements are among the strongest algorithms for the multi-agent path-finding problem. However, existing variants of CBS do not use any heuristics that estimate future work. In this paper, we introduce different admissible heuristics for CBS by aggregating cardinal conflicts among agents. In our experiments, CBS with these heuristics outperforms previous state-of-the-art CBS variants by up to a factor of five.

IJCAI Conference 2018 Conference Paper

Anytime Focal Search with Applications

• Liron Cohen
• Matias Greco
• Hang Ma
• Carlos Hernandez
• Ariel Felner
• T. K. Satish Kumar
• Sven Koenig

Focal search (FS) is a bounded-suboptimal search (BSS) variant of A*. Like A*, it uses an open list whose states are sorted in increasing order of their f-values. Unlike A*, it also uses a focal list containing all states from the open list whose f-values are no larger than a suboptimality factor times the smallest f-value in the open list. In this paper, we develop an anytime version of FS, called anytime FS (AFS), that is useful when deliberation time is limited. AFS finds a "good" solution quickly and refines it to better and better solutions if time allows. It does this refinement efficiently by reusing previous search efforts. On the theoretical side, we show that AFS is bounded suboptimal and that anytime potential search (ATPS/ANA*), a state-of-the-art anytime bounded-cost search (BCS) variant of A*, is a special case of AFS. In doing so, we bridge the gap between anytime search algorithms based on BSS and BCS. We also identify different properties of priority functions, used to sort the focal list, that may allow for efficient reuse of previous search efforts. On the experimental side, we demonstrate the usefulness of AFS for solving hard combinatorial problems, such as the generalized covering traveling salesman problem and the multi-agent pathfinding problem.

SoCS Conference 2018 Conference Paper

Fast Near-Optimal Path Planning on State Lattices with Subgoal Graphs

• Tansel Uras
• Sven Koenig

Subgoal graphs can be constructed on top of graphs during a preprocessing phase to speed-up shortest path queries. They have an undominated query-time/memory trade-off in the Grid-Based Path Planning Competitions. While grids are useful for path planning, other kinds of graphs, such as state lattices, have to be used for motion planning. While state lattices are regular graphs like grids, subgoal graphs improve query times by a much smaller factor on state lattices than on grids. In this paper, we present a new version of subgoal graphs that forfeits its optimality guarantee for smaller query times. It guarantees completeness, and our experimental results on state lattices suggest that it can find paths that are close to optimal.

ICRA Conference 2018 Conference Paper

Gradient-Informed Path Smoothing for Wheeled Mobile Robots

• Eric Heiden
• Luigi Palmieri
• Sven Koenig
• Kai O. Arras
• Gaurav S. Sukhatme

Planning smooth trajectories is important for the safe, efficient and comfortable operation of mobile robots, such as wheeled robots moving in crowded environments or cars moving at high speed. Asymptotically optimal sampling-based motion planners can be used to generate such trajectories. However, to achieve the necessary efficiency for the realtime operation of robots, one often uses their initial feasible trajectories or the trajectories of non-optimal motion planners instead, typically after a post-smoothing step. We propose a gradient-informed post-smoothing algorithm, called GRIPS, that deforms given trajectories by locally optimizing the placement of vertices while satisfying the system's kinodynamic constraints. We show experimentally that GRIPS typically produces trajectories of significantly smaller length and higher smoothness than several existing post-smoothing algorithms.

SoCS Conference 2018 Conference Paper

Message Passing Algorithms for Semiring-Based and Valued Constraint Satisfaction Problems

• Hong Xu 0003
• Cheng Cheng 0001
• Sven Koenig
• T. K. Satish Kumar

Local consistency algorithms, like arc consistency (AC) algorithms, are polynomial-time algorithms that prune the search space of constraint satisfaction problems (CSPs). In this paper, we present connections between message passing algorithms and AC for semiring-based CSPs (SCSPs) and valued CSPs (VCSPs), two well-established frameworks that generalize CSPs. Message passing algorithms are well known distributed search algorithms for solving many combinatorial problems in artificial intelligence, probabilistic reasoning, and information theory. However, the relationship between message passing algorithms and SCSPs or VCSPs still remains understudied. Towards this end, we propose the best-O message passing (BOMP) algorithm for SCSPs and VCSPs. We prove that, unlike other standard message passing algorithms which are in general not guaranteed to converge, the BOMP algorithm guarantees convergence for SCSPs and specific subclasses of VCSPs. We also theoretically study the relationship between the BOMP algorithm and AC on SCSPs, and empirically study the quality of the solutions produced by the BOMP algorithm for VCSPs.

IJCAI Conference 2018 Conference Paper

Multi-Agent Path Finding with Deadlines

• Hang Ma
• Glenn Wagner
• Ariel Felner
• Jiaoyang Li
• T. K. Satish Kumar
• Sven Koenig

We formalize Multi-Agent Path Finding with Deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within the deadline, without colliding with each other. We first show that MAPF-DL is NP-hard to solve optimally. We then present two classes of optimal algorithms, one based on a reduction of MAPF-DL to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network and the other one based on novel combinatorial search algorithms. Our empirical results demonstrate that these MAPF-DL solvers scale well and each one dominates the other ones in different scenarios.

AAMAS Conference 2018 Conference Paper

Multi-Agent Path Finding with Deadlines: Preliminary Results

• Hang Ma
• Glenn Wagner
• Ariel Felner
• Jiaoyang Li
• T. K. Satish Kumar
• Sven Koenig

We formalize the problem of multi-agent path finding with deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within a given deadline, without colliding with each other. We first show that the MAPF-DL problem is NP-hard to solve optimally. We then present an optimal MAPF-DL algorithm based on a reduction of the MAPF-DL problem to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network.

SoCS Conference 2018 Conference Paper

Rapid Randomized Restarts for Multi-Agent Path Finding Solvers

• Liron Cohen 0002
• Glenn Wagner
• David M. Chan
• Howie Choset
• Nathan R. Sturtevant
• Sven Koenig
• T. K. Satish Kumar

Multi-Agent Path Finding (MAPF) is an NP-hard problem that has been well studied in artificial intelligence and robotics. Recently, randomized MAPF solvers have been shown to exhibit heavy-tailed distributions of runtimes, which can be exploited to boost their success rate for a given runtime limit. In this paper, we discuss different ways of randomizing MAPF solvers and evaluate simple rapid randomized restart strategies for state-of-the-art MAPF solvers such as iECBS, M* with highways and CBS-CL.

AAMAS Conference 2018 Conference Paper

Rapid Randomized Restarts for Multi-Agent Path Finding: Preliminary Results

• Liron Cohen
• Sven Koenig
• T. K. Satish Kumar
• Glenn Wagner
• Howie Choset
• David Chan
• Nathan Sturtevant

Multi-Agent Path Finding (MAPF) is an NP-hard problem with many real-world applications. However, existing MAPF solvers are deterministic and perform poorly on MAPF instances where many agents interfere with each other in a small region of space. In this paper, we enhance MAPF solvers with randomization and observe that their runtimes can exhibit heavy-tailed distributions. This insight leads us to develop simple Rapid Randomized Restart (RRR) strategies with the intuition that multiple short runs will have a better chance of solving such MAPF instances than one long run with the same runtime limit. Our contribution is to show experimentally that the same RRR strategy indeed boosts the performance of two state-of-the-art MAPF solvers, namely M* and ECBS.

ICAPS Conference 2018 Conference Paper

The Factored Shortest Path Problem and Its Applications in Robotics

• Zhi Wang 0013
• Liron Cohen 0002
• Sven Koenig
• T. K. Satish Kumar

Many real-world combinatorial problems exhibit structure in the way in which their variables interact. Such structure can be exploited in the form of "factors" for representational as well as computational benefits. Factored representations are extensively used in probabilistic reasoning, constraint satisfaction, planning, and decision theory. In this paper, we formulate the factored shortest path problem (FSPP) on a collection of constraints interpreted as factors of a high-dimensional map. We show that the FSPP is not only a generalization of the regular shortest path problem but also particularly relevant to robotics. We develop factored-space heuristics for A* and prove that they are admissible and consistent. We provide experimental results on both random and handcrafted instances as well as on an example robotics domain to show that A* with factored-space heuristics outperforms A* with the Manhattan Distance heuristic in many cases.

IJCAI Conference 2018 Conference Paper

The FastMap Algorithm for Shortest Path Computations

• Liron Cohen
• Tansel Uras
• Shiva Jahangiri
• Aliyah Arunasalam
• Sven Koenig
• T. K. Satish Kumar

We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph. Later, at runtime, a shortest path between any two nodes can be computed with an A* search using the Euclidean distances as heuristic. Our preprocessing algorithm, called FastMap, is inspired by the data-mining algorithm of the same name and runs in near-linear time. Hence, FastMap is orders of magnitude faster than competing approaches that produce a Euclidean embedding using Semidefinite Programming. FastMap also produces admissible and consistent heuristics and therefore guarantees the generation of shortest paths. Moreover, FastMap applies to general undirected graphs for which many traditional heuristics, such as the Manhattan Distance heuristic, are not well defined. Empirically, we demonstrate that A* search using the FastMap heuristic is competitive with A* search using other state-of-the-art heuristics, such as the Differential heuristic.

IJCAI Conference 2018 Conference Paper

Understanding Subgoal Graphs by Augmenting Contraction Hierarchies

• Tansel Uras
• Sven Koenig

Contraction hierarchies and (N-level) subgoal graphs are two preprocessing-based path-planning algorithms that have so far only been compared experimentally through the grid-based path-planning competitions, where both algorithms had undominated runtime/memory trade-offs. Subgoal graphs can be considered as a framework that can be customized to different domains through the choice of a reachability relation R that identifies pairs of nodes on a graph between which it is easy to find shortest paths. Subgoal graphs can exploit R in various ways to speed-up query times and reduce memory requirements. In this paper, we break down the differences between N-level subgoal graphs and contraction hierarchies, and augment contraction hierarchies with ideas from subgoal graphs to exploit R. We propose three different modifications, analyze their runtime/memory trade-offs, and provide experimental results on grids using canonical-freespace-reachability as R, which show that both N-level subgoal graphs and contraction hierarchies are dominated in terms of the runtime/memory trade-off by some of our new variants.

SoCS Conference 2017 Conference Paper

A Linear-Time and Linear-Space Algorithm for the Minimum Vertex Cover Problem on Giant Graphs

• Hong Xu 0003
• T. K. Satish Kumar
• Sven Koenig

In this paper, we develop the message passing based linear-time and linear-space MVC algorithm (MVC-MPL) for solving the minimum vertex cover (MVC) problem. MVC-MPL is based on heuristics derived from a theoretical analysis of message passing algorithms in the context of belief propagation. We show that MVC-MPL produces smaller vertex covers than other linear-time and linear-space algorithms.

SoCS Conference 2017 Conference Paper

Feasibility Study: Subgoal Graphs on State Lattices

• Tansel Uras
• Sven Koenig

Search using subgoal graphs is a recent preprocessing-based path-planning algorithm that can find shortest paths on 8-neighbor grids several orders of magnitude faster than A*, while requiring little preprocessing time and memory overhead. In this paper, we first generalize the ideas behind subgoal graphs to a framework that can be specialized to different types of environments (represented as weighted directed graphs) through the choice of a reachability relation. Intuitively, a reachability relation identifies pairs of vertices for which a shortest path can be found quickly. A subgoal graph can then be constructed as an overlay graph that is guaranteed to have edges only between vertices that satisfy the reachability relation, which allows one to find shortest paths on the original graph quickly. In the context of this general framework, subgoal graphs on grids use freespace-reachability (originally called h-reachability) as the reachability relation, which holds for pairs of vertices if and only if their distance on the grid with blocked cells is equal to their distance on the grid without blocked cells (freespace assumption). We apply this framework to state lattices by using variants of freespace-reachability as the reachability relation. We provide preliminary results on (x, y, theta)-state lattices, which shows that subgoal graphs can be used to speed up path planning on state lattices as well, although the speed-up is not as significant as it is on grids.

AAMAS Conference 2017 Conference Paper

Lifelong Multi-Agent Path Finding for Online Pickup and Delivery Tasks

• Hang Ma
• Jiaoyang Li
• T. K. Satish Kumar
• Sven Koenig

The multi-agent path-finding (MAPF) problem has recently received a lot of attention. However, it does not capture important characteristics of many real-world domains, such as automated warehouses, where agents are constantly engaged with new tasks. In this paper, we therefore study a lifelong version of the MAPF problem, called the multiagent pickup and delivery (MAPD) problem. In the MAPD problem, agents have to attend to a stream of delivery tasks in an online setting. One agent has to be assigned to each delivery task. This agent has to first move to a given pickup location and then to a given delivery location while avoiding collisions with other agents. We present two decoupled MAPD algorithms, Token Passing (TP) and Token Passing with Task Swaps (TPTS). Theoretically, we show that they solve all well-formed MAPD instances, a realistic subclass of MAPD instances. Experimentally, we compare them against a centralized strawman MAPD algorithm without this guarantee in a simulated warehouse system. TP can easily be extended to a fully distributed MAPD algorithm and is the best choice when real-time computation is of primary concern since it remains efficient for MAPD instances with hundreds of agents and tasks. TPTS requires limited communication among agents and balances well between TP and the centralized MAPD algorithm.

AAAI Conference 2017 Conference Paper

Multi-Agent Path Finding with Delay Probabilities

• Hang Ma
• T. K. Satish Kumar
• Sven Koenig

Several recently developed Multi-Agent Path Finding (MAPF) solvers scale to large MAPF instances by searching for MAPF plans on 2 levels: The high-level search resolves collisions between agents, and the low-level search plans paths for single agents under the constraints imposed by the high-level search. We make the following contributions to solve the MAPF problem with imperfect plan execution with small average makespans: First, we formalize the MAPF Problem with Delay Probabilities (MAPF-DP), define valid MAPF-DP plans and propose the use of robust plan-execution policies for valid MAPF-DP plans to control how each agent proceeds along its path. Second, we discuss 2 classes of decentralized robust plan-execution policies (called Fully Synchronized Policies and Minimal Communication Policies) that prevent collisions during plan execution for valid MAPF-DP plans. Third, we present a 2-level MAPF-DP solver (called Approximate Minimization in Expectation) that generates valid MAPF-DP plans.

IS Journal 2017 Journal Article

Overview: A Hierarchical Framework for Plan Generation and Execution in Multirobot Systems

• Hang Ma
• Wolfgang Hönig
• Liron Cohen
• Tansel Uras
• Hong Xu
• T.K. Satish Kumar
• Nora Ayanian
• Sven Koenig

The authors present an overview of a hierarchical framework for coordinating task- and motion-level operations in multirobot systems. Their framework is based on the idea of using simple temporal networks to simultaneously reason about precedence/causal constraints required for task-level coordination and simple temporal constraints required to take some kinematic constraints of robots into account. In the plan-generation phase, the framework provides a computationally scalable method for generating plans that achieve high-level tasks for groups of robots and take some of their kinematic constraints into account. In the plan-execution phase, the framework provides a method for absorbing an imperfect plan execution to avoid time-consuming re-planning in many cases. The authors use the multirobot path-planning problem as a case study to present the key ideas behind their framework for the long-term autonomy of multirobot systems.

IJCAI Conference 2017 Conference Paper

Summary: Multi-Agent Path Finding with Kinematic Constraints

• Wolfgang Hönig
• T. K. Satish Kumar
• Liron Cohen
• Hang Ma
• Hong Xu
• Nora Ayanian
• Sven Koenig

Multi-Agent Path Finding (MAPF) is well studied in both AI and robotics. Given a discretized environment and agents with assigned start and goal locations, MAPF solvers from AI find collision-free paths for hundreds of agents with user-provided sub-optimality guarantees. However, they ignore that actual robots are subject to kinematic constraints (such as velocity limits) and suffer from imperfect plan-execution capabilities. We therefore introduce MAPF-POST to postprocess the output of a MAPF solver in polynomial time to create a plan-execution schedule that can be executed on robots. This schedule works on non-holonomic robots, considers kinematic constraints, provides a guaranteed safety distance between robots, and exploits slack to avoid time-intensive replanning in many cases. We evaluate MAPF-POST in simulation and on differential-drive robots, showcasing the practicality of our approach.

IJCAI Conference 2016 Conference Paper

Bounded Suboptimal Multi-Agent Path Finding Using Highways

• Liron Cohen
• Sven Koenig

The multi-agent path finding (MAPF) problem is defined as follows: Given a graph and a set of agents with unique start and goal vertices, find collision-free paths for all agents from their respective start vertices to their respective goal vertices. Our objective is to minimize the the total arrival time. MAPF has many applications such as video games, traffic control and robotics.

IROS Conference 2016 Conference Paper

Formation change for robot groups in occluded environments

• Wolfgang Hönig
• T. K. Satish Kumar
• Hang Ma 0001
• Sven Koenig
• Nora Ayanian

We study formation change for robot groups in known environments. We are given a team of robots partitioned into groups, where robots in the same group are interchangeable with each other. A formation specifies the locations occupied by each group. The objective is to find collision-free paths that move all robots from a given start formation to a given goal formation. Our algorithm TAPF* has the following features: (a) it incorporates kinematic constraints of robots in form of velocity limits; (b) it maintains a user-specified safety distance between robots; (c) it attempts to minimize the makespan; and (d) it runs efficiently for hundreds of robots and dozens of groups even in dense 3D environments with narrow corridors and other occlusions. We demonstrate the efficiency and effectiveness of TAPF* in simulation and on robots.

IJCAI Conference 2016 Conference Paper

Improved Solvers for Bounded-Suboptimal Multi-Agent Path Finding

• Liron Cohen
• Tansel Uras
• T. K. Satish Kumar
• Hong Xu
• Nora Ayanian
• Sven Koenig

Multi-Agent Path Finding (MAPF) with the objective to minimize the sum of the travel times of the agents along their paths is a hard combinatorial problem. Recent work has shown that bounded-suboptimal MAPF solvers, such as Enhanced Conflict-Based Search or ECBS(w1) for short, run often faster than optimal MAPF solvers at the cost of incurring a suboptimality factor w1, that is due to using focal search. Other recent work has used experience graphs to guide the search of ECBS(w1) and speed it up, at the cost of incurring a separate suboptimality factor w2, that is due to inflating the heuristic values. Thus, the combination has suboptimality factor w1w2. In this first feasibility study, we develop a bounded-suboptimal MAPF solver, Improved-ECBS or iECBS(w1) for short, that has sub optimality factor w1 rather than w1w2 (because it uses experience graphs to guide its search without inflating the heuristic values) and can run faster than ECBS(w1). We also develop two first approaches for automatically generating experience graphs for a given MAPF instance. Finally, we observe heavy-tailed behavior in the runtimes of these MAPF solvers and develop a simple rapid randomized restart strategy that can increase the success rate of iECBS(w1) within a given runtime limit.

AAMAS Conference 2016 Conference Paper

Local Search on Trees and a Framework for Automated Construction Using Multiple Identical Robots (Extended Abstract)

• Trevor Cai
• David Y. Zhang
• T. K. Satish Kumar
• Sven Koenig
• Nora Ayanian

We present an algorithmic framework for automated construction using multiple identical robots. Our approach is based on the principle of tree-based dynamic programming and a concomitant idea of local search on trees to improve the quality of the generated plans. Inspired by the TER- MES project of Harvard University, robots in this domain are required to gather construction blocks from a reservoir and coordinate with each other in building user-specified structures much larger than themselves. While the robots are roughly of the same size as the blocks, they can scale greater heights by using temporarily constructed ramps in the substructures. Our algorithm employs an inner loop in which the planning problem is solved by performing dynamic programming on a tree that spans the footprint of the user-specified structure. The outer loop of the algorithm furnishes a good tree for the inner loop. We show how we can search for a good tree in the outer loop using local search methods that yield significant improvements in plan quality. Synchronization rules are then applied to parallelize the execution of the generated plan for multiple identical robots. General Terms Algorithms, Performance, Experimentation

ICAPS Conference 2016 Conference Paper

Multi-Agent Path Finding with Kinematic Constraints

• Wolfgang Hönig
• T. K. Satish Kumar
• Liron Cohen 0002
• Hang Ma 0001
• Hong Xu 0003
• Nora Ayanian
• Sven Koenig

Multi-Agent Path Finding (MAPF) is well studied in both AI and robotics. Given a discretized environment and agents with assigned start and goal locations, MAPF solvers from AI find collision-free paths for hundreds of agents with user-provided sub-optimality guarantees. However, they ignore that actual robots are subject to kinematic constraints (such as finite maximum velocity limits) and suffer from imperfect plan-execution capabilities. We therefore introduce MAPF-POST, a novel approach that makes use of a simple temporal network to postprocess the output of a MAPF solver in polynomial time to create a plan-execution schedule that can be executed on robots. This schedule works on non-holonomic robots, takes their maximum translational and rotational velocities into account, provides a guaranteed safety distance between them, and exploits slack to absorb imperfect plan executions and avoid time-intensive replanning in many cases. We evaluate MAPF-POST in simulation and on differential-drive robots, showcasing the practicality of our approach.

AAAI Conference 2016 Conference Paper

Multi-Agent Path Finding with Payload Transfers and the Package-Exchange Robot-Routing Problem

• Hang Ma
• Craig Tovey
• Guni Sharon
• T. K. Kumar
• Sven Koenig

We study transportation problems where robots have to deliver packages and can transfer the packages among each other. Specifically, we study the package-exchange robotrouting problem (PERR), where each robot carries one package, any two robots in adjacent locations can exchange their packages, and each package needs to be delivered to a given destination. We prove that exchange operations make all PERR instances solvable. Yet, we also show that PERR is NP-hard to approximate within any factor less than 4/3 for makespan minimization and is NP-hard to solve for flowtime minimization, even when there are only two types of packages. Our proof techniques also generate new insights into other transportation problems, for example, into the hardness of approximating optimal solutions to the standard multiagent path-finding problem (MAPF). Finally, we present optimal and suboptimal PERR solvers that are inspired by MAPF solvers, namely a flow-based ILP formulation and an adaptation of conflict-based search. Our empirical results demonstrate that these solvers scale well and that PERR instances often have smaller makespans and flowtimes than the corresponding MAPF instances.

AAMAS Conference 2016 Conference Paper

Optimal Target Assignment and Path Finding for Teams of Agents

• Hang Ma
• Sven Koenig

We study the TAPF (combined target-assignment and path- finding) problem for teams of agents in known terrain, which generalizes both the anonymous and non-anonymous multiagent path-finding problems. Each of the teams is given the same number of targets as there are agents in the team. Each agent has to move to exactly one target given to its team such that all targets are visited. The TAPF problem is to first assign agents to targets and then plan collisionfree paths for the agents to their targets in a way such that the makespan is minimized. We present the CBM (Conflict- Based Min-Cost-Flow) algorithm, a hierarchical algorithm that solves TAPF instances optimally by combining ideas from anonymous and non-anonymous multi-agent path- finding algorithms. On the low level, CBM uses a mincost max-flow algorithm on a time-expanded network to assign all agents in a single team to targets and plan their paths. On the high level, CBM uses conflict-based search to resolve collisions among agents in different teams. Theoretically, we prove that CBM is correct, complete and optimal. Experimentally, we show the scalability of CBM to TAPF instances with dozens of teams and hundreds of agents and adapt it to a simulated warehouse system.

ICRA Conference 2016 Conference Paper

RRT-based nonholonomic motion planning using any-angle path biasing

• Luigi Palmieri
• Sven Koenig
• Kai O. Arras

RRT and RRT* have become popular planning techniques, in particular for high-dimensional systems such as wheeled robots with complex nonholonomic constraints. Their planning times, however, can scale poorly for such robots, which has motivated researchers to study hierarchical techniques that grow the RRT trees in more focused ways. Along this line, we introduce Theta*-RRT that hierarchically combines (discrete) any-angle search with (continuous) RRT motion planning for nonholonomic wheeled robots. Theta*-RRT is a variant of RRT that generates a trajectory by expanding a tree of geodesics toward sampled states whose distribution summarizes geometric information of the any-angle path. We show experimentally, for both a differential drive system and a high-dimensional truck-and-trailer system, that Theta*-RRT finds shorter trajectories significantly faster than four baseline planners (RRT, A*-RRT, RRT*, A*-RRT*) without loss of smoothness, while A*-RRT* and RRT* (and thus also Informed RRT*) fail to generate a first trajectory sufficiently fast in environments with complex nonholonomic constraints. We also prove that Theta*-RRT retains the probabilistic completeness of RRT for all small-time controllable systems that use an analytical steer function.

SoCS Conference 2015 Conference Paper

An Empirical Comparison of Any-Angle Path-Planning Algorithms

• Tansel Uras
• Sven Koenig

We compare five any-angle path-planning algorithms, Theta*, Block A*, Field D*, ANYA, and Any-Angle Subgoal Graphs in terms of solution quality and runtime. Any-angle path-planning is a fairly new research area, and no direct comparison exists between these algorithms. We implement each algorithm from scratch and use similar implementations to provide a fair comparison.

SoCS Conference 2015 Conference Paper

Feasibility Study: Using Highways for Bounded-Suboptimal Multi-Agent Path Finding

• Liron Cohen 0002
• Tansel Uras
• Sven Koenig

Multi-agent path-finding (MAPF) is important for applications such as the kind of warehousing done by Kiva systems. Solving the problem optimally is NP-hard, yet finding low-cost solutions is important. Bounded-suboptimal MAPF algorithms, such as enhanced conflict-based search (ECBS), often do not perform well in warehousing domains with many agents. We therefore develop bounded-suboptimal MAPF algorithms, called CBS+HWY and ECBS+HWY, that exploit the problem structure of a given MAPF instance by finding paths for the agents that include edges from user-provided highways, which encourages a global behavior of the agents that avoids collisions. On the theoretical side, we develop a simple approach that uses highways for MAPF and provides suboptimality guarantees. On the experimental side, we demonstrate that ECBS+HWY can decrease the runtimes and solution costs of ECBS in Kiva-like domains with many agents if the highways capture the problem structures well.

ICAPS Conference 2015 Conference Paper

Speeding-Up Any-Angle Path-Planning on Grids

• Tansel Uras
• Sven Koenig

Simple Subgoal Graphs are constructed from grids by placing subgoals at the corners of obstacles and connecting them. They are analogous to visibility graphs for continuous terrain but have fewer edges and can be used to quickly find shortest paths on grids. The vertices of a Simple Subgoal Graph can be partitioned into different levels to create N-Level Subgoal Graphs, which can be used to find shortest paths on grids even more quickly by ignoring subgoals that are not relevant for the search, which significantly reduces the size of the graph being searched. Search using Two-Level Subgoal Graphs was a non-dominated entry in the Grid-Based Path Planning Competitions 2012 and 2013. In this paper, we take advantage of the similarities between Subgoal Graphs and visibility graphs to show that Subgoal Graphs can be used, with small modifications, to quickly find “any-angle” paths, thus extending their applicability. Any-angle paths are usually shorter and more realistic looking than grid paths since the movement along any-angle paths is not constrained to grid edges. Our algorithm has the advantage that it is a simple extension of searching Subgoal Graphs and is up to two orders of magnitude faster than Theta* and up to an order of magnitude faster than Block A* (using 5 × 5 blocks), two of the most well-known any-angle pathplanning algorithms, while still finding any-angle paths of comparable lengths.

SoCS Conference 2015 Invited Paper

The Grid-Based Path Planning Competition: 2014 Entries and Results

• Nathan R. Sturtevant
• Jason M. Traish
• James R. Tulip
• Tansel Uras
• Sven Koenig
• Ben Strasser
• Adi Botea
• Daniel Harabor

The Grid-Based Path Planning Competition has just completed its third iteration. The entriesused in the competition have improved significantly during this time, changing the view ofthe state of the art of grid-based pathfinding. Furthermore, the entries from the competition have beenmade publicly available, improving the ability of researchers to compare their work. Thispaper summarizes the entries to the 2014 competition, presents the 2014 competition results, and talks about what has been learned and where there is room for improvement.

IROS Conference 2014 Conference Paper

A lattice-based approach to multi-robot motion planning for non-holonomic vehicles

• Marcello Cirillo
• Tansel Uras
• Sven Koenig

Coordinating fleets of autonomous, non-holonomic vehicles is paramount to many industrial applications. While there exists solutions to efficiently calculate trajectories for individual vehicles, an effective methodology to coordinate their motions and to avoid deadlocks is still missing. Decoupled approaches, where motions are calculated independently for each vehicle and then centrally coordinated for execution, have the means to identify deadlocks, but not to solve all of them. We present a novel approach that overcomes this limitation and that can be used to complement the deficiencies of decoupled solutions with centralized coordination. Here, we formally define an extension of the framework of lattice-based motion planning to multi-robot systems and we validate it experimentally. Our approach can jointly plan for multiple vehicles and it generates kinematically feasible and deadlock-free motions.

AAAI Conference 2014 Conference Paper

A Simple Polynomial-Time Randomized Distributed Algorithm for Connected Row Convex Constraints

• T. K. Satish Kumar
• Duc Thien Nguyen
• William Yeoh
• Sven Koenig

In this paper, we describe a simple randomized algorithm that runs in polynomial time and solves connected row convex (CRC) constraints in distributed settings. CRC constraints generalize many known tractable classes of constraints like 2- SAT and implicational constraints. They can model problems in many domains including temporal reasoning and geometric reasoning, and generally speaking, play the role of “Gaussians” in the logical world. Our simple randomized algorithm for solving them in distributed settings, therefore, has a number of important applications. We support our claims through a theoretical analysis and empirical results.

ICAPS Conference 2014 Conference Paper

A Tree-Based Algorithm for Construction Robots

• T. K. Satish Kumar
• Sangmook Johnny Jung
• Sven Koenig

In this paper, we present a tree-based algorithm for construction robots. Inspired by the TERMES project of Harvard University, robots in this domain are required to gather construction blocks from a reservoir and build user-specified structures much larger than themselves. While the robots are of roughly the same size as the blocks, they can scale greater heights by using temporarily constructed ramps in the substructures. In this paper, we consider the problem of minimizing the number of pickup and drop-off operations performed on blocks in order to build user-specified structures. Our polynomial-time algorithm heuristically solves this problem and is based on the idea of performing dynamic programming on a spanning tree in the inner loop and searching for a good tree to do so in the outer loop. Our algorithm performs very well in simulation and scales easily to large problem instances. For planning problems of this nature that are akin to construction domains, we believe that valuable lessons can be learned from comparing the success of our algorithm with the failure of off-the-shelf planning technologies.

AAAI Conference 2014 Conference Paper

Identifying Hierarchies for Fast Optimal Search

• Tansel Uras
• Sven Koenig

Search with Subgoal Graphs (Uras, Koenig, and Hernández 2013) was a non-dominated optimal path-planning algorithm in the Grid-Based Path Planning Competitions 2012 and 2013. During a preprocessing phase, it computes a Simple Subgoal Graph from a given grid, which is analogous to a visibility graph for continuous terrain, and then partitions the vertices into global and local subgoals to obtain a Two-Level Subgoal Graph. During the path-planning phase, it performs an A* search that ignores local subgoals that are not relevant to the search, which significantly reduces the size of the graph being searched. In this paper, we generalize this partitioning process to any undirected graph and show that it can be recursively applied to generate more than two levels, which reduces the size of the graph being searched even further. We distinguish between basic partitioning, which only partitions the vertices into different levels, and advanced partitioning, which can also add new edges. We show that the construction of Simple- Subgoal Graphs from grids and the construction of Two- Level Subgoal Graphs from Simple Subgoal Graphs are instances of generalized partitioning. We then report on experiments on Subgoal Graphs that demonstrate the effects of different types and levels of partitioning. We also report on experiments that demonstrate that our new N-Level Subgoal Graphs achieve a speed up of 1. 6 compared to Two-Level Subgoal graphs from (Uras, Koenig, and Hernández 2013) on maps from the video games StarCraft and Dragon Age: Origins.

SoCS Conference 2014 Conference Paper

Identifying Hierarchies for Fast Optimal Search

• Tansel Uras
• Sven Koenig

For some search problems, the graph is known beforehand and there is time to preprocess the graph to make the search faster. One such example is video games, where one can often preprocess maps before a game is released or while a map is loaded into memory. The data produced by preprocessing should use only a small amount of memory, and, in case they are generated during runtime, preprocessing should be fast. Search with Subgoal Graphs (Uras, Koenig, and Hernandez 2013) was a non-dominated optimal path-planning algorithm in the Grid-Based Path Planning Competitions 2012 and 2013. During a preprocessing phase, it computes a Simple Subgoal Graph from a given grid, which is analogous to a visibility graph for continuous terrain, and then partitions the vertices into global and local subgoals to obtain a Two-Level Subgoal Graph. During the path-planning phase, it performs an A* search over the subgoal graph that ignores local subgoals that are not relevant to the search, which significantly reduces the size of the graph being searched. This paper is an abstract of (Uras and Koenig 2014), which generalizes this partitioning process to any undirected graph and shows that it can be recursively applied to generate more than two levels, which reduces the size of the graph being searched even further. We call these graphs N-Level Graphs.

ICAPS Conference 2014 Conference Paper

Integrated Motion Planning and Coordination for Industrial Vehicles

• Marcello Cirillo
• Federico Pecora
• Henrik Andreasson
• Tansel Uras
• Sven Koenig

A growing interest in the industrial sector for autonomous ground vehicles has prompted significant investment in fleet management systems. Such systems need to accommodate on-line externally imposed temporal and spatial requirements, and to adhere to them even in the presence of contingencies. Moreover, a fleet management system should ensure correctness, i. e. , refuse to commit to requirements that cannot be satisfied. We present an approach to obtain sets of alternative execution patterns (called trajectory envelopes) which provide these guarantees. The approach relies on a constraint-based representation shared among multiple solvers, each of which progressively refines trajectory envelopes following a least commitment principle.

SoCS Conference 2014 Conference Paper

Invited Talks

• Sven Koenig
• Alexander Reinefeld

Abstracts of the invited talks presented at SoCS 2014.

ICAPS Conference 2014 Conference Paper

PA*SE: Parallel A* for Slow Expansions

• Mike Phillips
• Maxim Likhachev
• Sven Koenig

Planners need to become faster as we seek to tackle increasingly complicated problems. Much of the recent improvements in computer speed is due to multi-core processors. For planners to take advantage of these types of architectures, we must adapt algorithms for parallel processing. There are a number of planning domains where state expansions are slow. One example is robot motion planning, where most of the time is devoted to collision checking. In this work, we present PA*SE, a novel, parallel version of A* (and weighted A*) which parallelizes state expansions by taking advantage of this property. While getting close to a linear speedup in the number of cores, we still preserve completeness and optimality of A* (bounded sub-optimality of weighted A*). PA*SE applies to any planning problem in which significant time is spent on generating successor states and computing transition costs. We present experimental results on a robot navigation domain (x, y, heading) which requires expensive 3D collision checking for the PR2 robot. We also provide an in-depth analysis of the algorithm’s performance on a 2D navigation problem as we vary the number of cores (up to 32) as well as the time it takes to collision check successors during state expansions.

AAAI Conference 2013 Conference Paper

Simple Temporal Problems with Taboo Regions

• T. K. Kumar
• Marcello Cirillo
• Sven Koenig

In this paper, we define and study the general framework of Simple Temporal Problems with Taboo regions (STPTs) and show how these problems capture metric temporal reasoning aspects which are common to many real-world applications. STPTs encode simple temporal constraints between events and user-defined taboo regions on the timeline, during which no event is allowed to take place. We discuss two different variants of STPTs. The first one deals with (instantaneous) events, while the second one allows for (durative) processes. We also provide polynomial-time algorithms for solving them. If all events or processes cannot be scheduled outside of the taboo regions, one needs to define and reason about “soft” STPTs. We show that even “soft” STPTs can be solved in polynomial time, using reductions to max-flow problems. The resulting algorithms allow for incremental computations, which is important for the successful application of our approach in realtime domains.

ICAPS Conference 2013 Conference Paper

Subgoal Graphs for Optimal Pathfinding in Eight-Neighbor Grids

• Tansel Uras
• Sven Koenig
• Carlos Hernández Ulloa

Grids are often used to represent maps in video games. In this paper, we propose a method for preprocessing eightneighbor grids to generate subgoal graphs and show how subgoal graphs can be used to find shortest paths fast. We place subgoals at the corners of obstacles (similar to visibility graphs) and add those edges between subgoals that are necessary for finding shortest paths, while ensuring that each edge connects only subgoals that are easily reachable from one another. We describe a method for finding shortest paths by first finding high-level paths through subgoals and then shortest low-level paths between consecutive subgoals on the highlevel path. Our method was one of ten entries in the Grid-Based Path Planning Competition 2012. Among all optimal path planners, ours was the fastest to find complete paths and required the least amount of memory.

ICAPS Conference 2012 Conference Paper

Incremental ARA*: An Incremental Anytime Search Algorithm for Moving-Target Search

• Xiaoxun Sun
• Tansel Uras
• Sven Koenig
• William Yeoh 0001

Moving-target search, where a hunter has to catch a moving target, is an important problem for video game developers. In our case, the hunter repeatedly moves towards the target and thus has to solve similar search problems repeatedly. We develop Incremental ARA* (I-ARA*) for this purpose, the first incremental anytime search algorithm for moving-target search in known terrain. We provide an error bound on the lengths of the paths found by I-ARA* and show experimentally in known four-neighbor gridworlds that I-ARA* can be used with smaller time limits between moves of the hunter than competing state-of-the-art moving-target search algorithms, namely repeated A*, G-FRA*, FRA*, and sometimes repeated ARA*. The hunter tends to make more moves with I-ARA* than repeated A*, G-FRA* or FRA*, which find shortest paths for the hunter, but fewer moves with I-ARA* than repeated ARA*, which finds suboptimal paths for the hunter like I-ARA*. Also, the error bounds on the lengths of the paths of the hunter tend to be smaller with I-ARA* than repeated ARA*.

SoCS Conference 2012 Conference Paper

Paper Summary: Time-Bounded Adaptive A

• Carlos Hernández Ulloa
• Jorge A. Baier
• Tansel Uras
• Sven Koenig

This paper summarizes our AAMAS 2012 paper on "Time-Bounded Adaptive A*, " which introduces the game time model to evaluate search algorithms in real-time settings, such as video games. It then extends the existing real-time search algorithm TBA* to path planning with the freespace assumption in initially partially or completely unknown terrain, resulting in Time-Bounded Adaptive A* (TBAA*). TBAA* needs fewer time intervals in the game time model than several state-of-the-art complete and real-time search algorithms and about the same number of time intervals as the best compared complete search algorithm, even though it has the advantage over complete search algorithms that the agent starts to move right away.

SoCS Conference 2012 Conference Paper

Position Paper: Incremental Search Algorithms Considered Poorly Understood

• Carlos Hernández Ulloa
• Jorge A. Baier
• Tansel Uras
• Sven Koenig

Incremental search algorithms, such as D* Lite, reuse information from previous searches to speed up the current search and can thus solve sequences of similar search problems faster than Repeated A*, which performs repeated A* searches. In this position paper, we study goal-directed navigation in initially unknown terrain and point out that it is currently not well understood when D* Lite runs faster than Repeated A*. In general, it appears that Repeated A* runs faster than D* Lite for easy navigation problems (where the agent reaches the goal with only a small number of searches), which means that it runs faster than D* Lite quite often in practice. We draw two conclusions, namely that incremental search algorithms need to be evaluated in more diverse testbeds to improve our understanding of their properties and that they can be improved to be more competitive for easy navigation problems.

SoCS Conference 2012 Conference Paper

Subgoal Graphs for Eight-Neighbor Gridworlds

• Tansel Uras
• Sven Koenig
• Carlos Hernández Ulloa

We propose a method for preprocessing an eight-neighbor gridworld to generate a subgoal graph and a method for using this subgoal graph to find shortest paths faster than A*, by first finding high-level paths through subgoals and then shortest low-level paths between consecutive subgoals on the high-level path.

AAMAS Conference 2012 Conference Paper

Time Bounded Adaptive A*

• Carlos Hern
• aacute; ndez
• Jorge Baier
• Tansel Uras
• Sven Koenig

n this paper, we investigate real-time path planning in static terrain, as needed in video games. We introduce the game time model, where time is partitioned into uniform time intervals, an agent can execute one movement during each time interval, and search and movements are done in parallel. The objective is to move the agent from its start location to its goal location in as few time intervals as possible. For known terrain, we show experimentally that Time-Bounded A* (TBA*), an existing real-time search algorithm for undirected terrain, needs fewer time intervals than two state-of-the-art real-time search algorithms and about the same number of time intervals as A*. TBA*, however, cannot be used when the terrain is not known initially. For initially partially or completely unknown terrain, we thus propose a new search algorithm. Our Time-Bounded Adaptive A* (TBAA*) extends TBA* to on-line path planning with the freespace assumption by combining it with Adaptive A*. We prove that TBAA* either moves the agent from its start location to its goal location or detects that this is impossible - an important property since many existing realtime search algorithms are not able to detect efficiently that no path exists. Furthermore, TBAA* can eventually move the agent on a cost-minimal path from its start location to its goal location if it resets the agent into its start location whenever it reaches its goal location. We then show experimentally in initially partially or completely unknown terrain that TBAA* needs fewer time intervals than several state-of-the-art complete and real-time search algorithms and about the same number of time intervals as the best compared complete search algorithm, even though it has the advantage over complete search algorithms that the agent starts to move right away.

IJCAI Conference 2011 Conference Paper

Generalized Reaction Functions for Solving Complex-Task Allocation Problems

• Xiaoming Zheng
• Sven Koenig

We study distributed task-allocation problems wherecooperative agents need to perform some tasks simultaneously. Examples are multi-agent routing problems where several agents need to visit some targets simultaneously, for example, to move obstacles out of the way cooperatively. In this paper, we first generalize the concept of reaction functions proposed in the literature to characterize the agent costs of performing multiple complex tasks. Second, we show how agents can construct and approximate reaction functions in a distributed way. Third, we show how reaction functions can be used by an auction-like algorithm to allocate tasks to agents. Finally, we show empirically that the team costs of our algorithms are substantially smaller than those of an existing state-of-the-art allocation algorithm for complex tasks.

AAMAS Conference 2011 Conference Paper

Incremental DCOP Search Algorithms for Solving Dynamic DCOPs

• William Yeoh
• Pradeep Varakantham
• Xiaoxun Sun
• Sven Koenig

Distributed constraint optimization problems (DCOPs) are well-suited for modeling multi-agent coordination problems. However, most research has focused on developing algorithms for solving static DCOPs. In this paper, we model dynamic DCOPs as sequences of (static) DCOPs with changes from one DCOP to the next one in the sequence. We introduce the ReuseBounds procedure, which can be used by any-space ADOPT and any-space BnB-ADOPT to find cost-minimal solutions for all DCOPs in the sequence faster than by solving each DCOP individually. This procedure allows those agents that are guaranteed to remain unaffected by a change to reuse their lower and upper bounds from the previous DCOP when solving the next one in the sequence. Our experimental results show that the speedup gained from this procedure increases with the amount of memory the agents have available.

AAMAS Conference 2011 Conference Paper

Tree Adaptive A*

• Carlos Hern
• aacute; ndez
• Xiaoxun Sun
• Sven Koenig
• Pedro Meseguer

Incremental heuristic search algorithms can solve sequences of similar search problems potentially faster than heuristic search algorithms that solve each search problem from scratch. So far, there existed incremental heuristic search algorithms (such as Adaptive A*) that make the h-values of the current A* search more informed, which can speed up future A* searches, and incremental heuristic search algorithms (such as D* Lite) that change the search tree of the current A* search to the search tree of the next A* search, which can be faster than constructing it from scratch. In this paper, we present Tree Adaptive A*, which applies to goal-directed navigation in unknown terrain and builds on Adaptive A* but combines both classes of incremental heuristic search algorithms in a novel way. We demonstrate experimentally that it can run faster than Adaptive A*, Path Adaptive A* and D* Lite, the top incremental heuristic search algorithms in the context of goal-directed navigation in unknown grids.

AAMAS Conference 2010 Conference Paper

ESP: Pursuit Evasion on Series-Parallel Graphs

• Kenny Daniel
• Richard Borie
• Sven Koenig
• Craig Tovey

We develop a heuristic approach, called ESP, that solves large pursuit-evasionproblems on series-parallel (that is, treewidth-2) graphs quickly and withsmall costs. It exploits their topology by performing dynamic programming ontheir decomposition graphs. We show that ESP scales up to much larger graphsthan a strawman approach based on previous results from the literature.

AAMAS Conference 2010 Conference Paper

Generalized Fringe-Retrieving A*: Faster Moving Target Search on State Lattices

• Xiaoxun Sun
• William Yeoh
• Sven Koenig

Moving target search is important for robotics applicationswhere unmanned ground vehicles (UGVs) have to followother friendly or hostile UGVs. Artificial intelligence researchers have recently used incremental search to speedup the computation of a simple strategy for the hunter. The fastest incremental search algorithm, Fringe-RetrievingA*, solves moving target search problems only on two-dimensional grids, which are rather unrealistic models forrobotics applications. We therefore generalize it to Generalized Fringe-Retrieving A*, which solves moving target searchproblems on arbitrary graphs, including the state latticesused for UGV navigation.

SoCS Conference 2010 Conference Paper

Lazy Theta*: Any-Angle Path Planning and Path Length Analysis in 3D

• Alex Nash
• Sven Koenig
• Craig A. Tovey

Grids with blocked and unblocked cells are often used to represent continuous 2D and 3D environments in robotics and video games. The shortest paths formed by the edges of 8-neighbor 2D grids can be up to ≈ 8% longer than the shortest paths in the continuous environment. Theta* typically finds much shorter paths than that by propagating information along graph edges (to achieve short runtimes) without constraining paths to be formed by graph edges (to find short "any-angle" paths). We show in this paper that the shortest paths formed by the edges of 26-neighbor 3D grids can be ≈ 13% longer than the shortest paths in the continuous environment, which highlights the need for smart path planning algorithms in 3D. Theta* can be applied to 3D grids in a straight-forward manner, but it performs a line-of-sight check for each unexpanded visible neighbor of each expanded vertex and thus it performs many more line-of-sight checks per expanded vertex on a 26-neighbor 3D grid than on an 8-neighbor 2D grid. We therefore introduce Lazy Theta*, a variant of Theta* which uses lazy evaluation to perform only one line-of-sight check per expanded vertex (but with slightly more expanded vertices). We show experimentally that Lazy Theta* finds paths faster than Theta* on 26-neighbor 3D grids, with one order of magnitude fewer line-of-sight checks and without an increase in path length.

AAAI Conference 2010 Conference Paper

Lazy Theta*: Any-Angle Path Planning and Path Length Analysis in 3D

• Alex Nash
• Sven Koenig
• Craig Tovey

Grids with blocked and unblocked cells are often used to represent continuous 2D and 3D environments in robotics and video games. The shortest paths formed by the edges of 8neighbor 2D grids can be up to ≈ 8% longer than the shortest paths in the continuous environment. Theta* typically finds much shorter paths than that by propagating information along graph edges (to achieve short runtimes) without constraining paths to be formed by graph edges (to find short “any-angle” paths). We show in this paper that the shortest paths formed by the edges of 26-neighbor 3D grids can be ≈ 13% longer than the shortest paths in the continuous environment, which highlights the need for smart path planning algorithms in 3D. Theta* can be applied to 3D grids in a straight-forward manner, but it performs a line-of-sight check for each unexpanded visible neighbor of each expanded vertex and thus it performs many more line-of-sight checks per expanded vertex on a 26-neighbor 3D grid than on an 8-neighbor 2D grid. We therefore introduce Lazy Theta*, a variant of Theta* which uses lazy evaluation to perform only one line-of-sight check per expanded vertex (but with slightly more expanded vertices). We show experimentally that Lazy Theta* finds paths faster than Theta* on 26-neighbor 3D grids, with one order of magnitude fewer line-of-sight checks and without an increase in path length.

AAAI Conference 2010 Conference Paper

Market-Based Algorithms for Allocating Complex Tasks

• Xiaoming Zheng
• Sven Koenig

AAAI Conference 2010 Conference Paper

Model AI Assignments

• Todd Neller
• John DeNero
• Dan Klein
• Sven Koenig
• William Yeoh
• Xiaoming Zheng
• Kenny Daniel
• Alex Nash

AAMAS Conference 2010 Conference Paper

Moving Target D* Lite

• Xiaoxun Sun
• William Yeoh
• Sven Koenig

Incremental search algorithms, such as Generalized Fringe-Retrieving A* and D* Lite, reuse search trees from previous searches to speed up the current search and thus oftenfind cost-minimal paths for series of similar search problemsfaster than by solving each search problem from scratch. However, existing incremental search algorithms have limitations. For example, D* Lite is slow on moving targetsearch problems, where both the start and goal states canchange over time. In this paper, we therefore introduceMoving Target D* Lite, an extension of D* Lite that usesthe principle behind Generalized Fringe-Retrieving A* to repeatedly calculate a cost-minimal path from the hunter tothe target in environments whose blockages can change overtime. We demonstrate experimentally that Moving TargetD* Lite is four to five times faster than Generalized AdaptiveA*, which so far was believed to be the fastest incrementalsearch algorithm for solving moving target search problemsin dynamic environments.

AAAI Conference 2010 Conference Paper

Progress on Agent Coordination with Cooperative Auctions

• Sven Koenig
• Pinar Keskinocak
• Craig Tovey

Auctions are promising decentralized methods for teams of agents to allocate and re-allocate tasks among themselves in dynamic, partially known and time-constrained domains with positive or negative synergies among tasks. Auctionbased coordination systems are easy to understand, simple to implement and broadly applicable. They promise to be efficient both in communication (since agents communicate only essential summary information) and in computation (since agents compute their bids in parallel). Artificial intelligence research has explored auction-based coordination systems since the early work on contract networks (Smith 1980), mostly from an experimental perspective. This overview paper describes our recent progress towards creating a framework for the design and analysis of cooperative auctions for agent coordination.

AAAI Conference 2010 Conference Paper

Sequential Incremental-Value Auctions

• Xiaoming Zheng
• Sven Koenig

We study the distributed allocation of tasks to cooperating robots in real time, where each task has to be assigned to exactly one robot so that the sum of the latencies of all tasks is as small as possible. We propose a new auction-like algorithm, called Sequential Incremental-Value (SIV) auction, which assigns tasks to robots in multiple rounds. The idea behind SIV auctions is to assign as many tasks per round to robots as possible as long as their individual costs for performing these tasks are at most a given bound, which increases exponentially from round to round. Our theoretical results show that the team costs of SIV auctions are at most a constant factor larger than minimal.

AAAI Conference 2010 Conference Paper

Teaching Artificial Intelligence and Robotics Via Games

• Daniel Wong
• Ryan Zink
• Sven Koenig

The Department of Computer Science at the University of Southern California recently created two new degree programs, namely a Bachelor’s Program in Computer Science (Games) and a Master’s Program in Computer Science (Game Development). In this paper, we discuss two projects that use games as motivator. First, the Computer Games in the Classroom Project develops stand-alone projects on standard artificial intelligence topics that use video-game technology to motivate the students but do not require the students to use game engines. Second, the Pinball Project develops the necessary hardware and software to enable students to learn concepts from robotics by developing games on actual pinball machines.

IJCAI Conference 2009 Conference Paper

• William Yeoh
• Xiaoxun Sun
• Sven Koenig

Distributed Constraint Optimization (DCOP) is a key technique for solving agent coordination problems. Because finding cost-minimal DCOP solutions is NP-hard, it is important to develop mechanisms for DCOP search algorithms that trade off their solution costs for smaller runtimes. However, existing tradeoff mechanisms do not provide relative error bounds. In this paper, we introduce three tradeoff mechanisms that provide such bounds, namely the Relative Error Mechanism, the Uniformly Weighted Heuristics Mechanism and the Non-Uniformly Weighted Heuristics Mechanism, for two DCOP algorithms, namely ADOPT and BnB-ADOPT. Our experimental results show that the Relative Error Mechanism generally dominates the other two tradeoff mechanisms for ADOPT and the Uniformly Weighted Heuristics Mechanism generally dominates the other two tradeoff mechanisms for BnB-ADOPT.

IJCAI Conference 2009 Conference Paper

• Xiaoxun Sun
• William Yeoh
• Sven Koenig

Incremental search algorithms reuse information from previous searches to speed up the current search and are thus often able to find shortest paths for series of similar search problems faster than by solving each search problem independently from scratch. However, they do poorly on moving target search problems, where both the start and goal cells change over time. In this paper, we thus develop Fringe-Retrieving A* (FRA*), an incremental version of A* that repeatedly finds shortest paths for moving target search in known gridworlds. We demonstrate experimentally that it runs up to one order of magnitude faster than a variety of state-of-the-art incremental search algorithms applied to moving target search in known gridworlds.

IJCAI Conference 2009 Conference Paper

• Alex Nash
• Sven Koenig
• Maxim Likhachev

We study path planning on grids with blocked and unblocked cells. Any-angle path-planning algorithms find short paths fast because they propagate information along grid edges without constraining the resulting paths to grid edges. Incremental pathplanning algorithms solve a series of similar pathplanning problems faster than repeated single-shot searches because they reuse information from the previous search to speed up the next one. In this paper, we combine these ideas by making the anyangle path-planning algorithm Basic Theta* incremental. This is non-trivial because Basic Theta* does not fit the standard assumption that the parent of a vertex in the search tree must also be its neighbor. We present Incremental Phi* and show experimentally that it can speed up Basic Theta* by about one order of magnitude for path planning with the freespace assumption.

IJCAI Conference 2009 Conference Paper

• Richard Borie
• Craig Tovey
• Sven Koenig

We study pursuit-evasion problems where a number of pursuers have to clear a given graph. We study when polynomial-time algorithms exist to determine how many pursuers are needed to clear a given graph and how a given number of pursuers should move on the graph to clear it with either a minimum sum of their travel distances or minimum task-completion time. We generalize prior work to both unit-width arbitrary-length and unitlength arbitrary-width graphs and derive both algorithms and complexity results for a variety of graph topologies. In this context, we describe a polynomial-time algorithm, called CLEARTHETREE, that is much shorter and algorithmically simpler than the state-of-the-art algorithm for the minimum pursuer problem on trees. Our theoretical research lays a firm theoretical foundation for pursuit evasion on graphs and informs practitioners about which problems are easy and which ones are hard.

IJCAI Conference 2009 Conference Paper

• Xiaoming Zheng
• Sven Koenig

In this paper, we study distributed algorithms for cooperative agents that allow them to exchange their assigned tasks in order to reduce their team cost. We define a new type of contract, called K-swaps, that describes multiple task exchanges among multiple agents at a time, which generalizes the concept of single task exchanges. We design a distributed algorithm that constructs all possible K-swaps that reduce the team cost of a given task allocation and show that each agent typically only needs to communicate a small part of its local computation results to the other agents. We then demonstrate empirically that K-swaps can reduce the team costs of several existing task-allocation algorithms significantly even if K is small.

AAMAS Conference 2009 Conference Paper

Caching Schemes for DCOP Search Algorithms

• Willliam Yeoh
• Pradeep Varakantham
• Sven Koenig

Distributed Constraint Optimization (DCOP) is useful for solving agent-coordination problems. Any-space DCOP search algorithms require only a small amount of memory but can be sped up by caching information. However, their current caching schemes do not exploit the cached information when deciding which information to preempt from the cache when a new piece of information needs to be cached. Our contributions are three-fold: (1) We frame the problem as an optimization problem. (2) We introduce three new caching schemes (MaxPriority, MaxEffort and MaxUtility) that exploit the cached information in a DCOP-specific way. (3) We evaluate how the resulting speed up depends on the search strategy of the DCOP search algorithm. Our experimental results show that, on all tested DCOP problem classes, our MaxEffort and MaxUtility schemes speed up ADOPT (which uses best-first search) more than the other tested caching schemes, while our MaxPriority scheme speeds up BnB-ADOPT (which uses depth-first branch-andbound search) at least as much as the other tested caching schemes.

AAMAS Conference 2009 Conference Paper

Dynamic Fringe-Saving A*

• Xiaoxun Sun
• William Yeoh
• Sven Koenig

Fringe-Saving A* is an incremental version of A* that repeatedly finds shortest paths from a fixed start cell to a fixed goal cell in a known gridworld in case the traversability of cells changes over time. It restores the content of the OPEN and CLOSED lists of A* at the point in time when an A* search for the current search problem could deviate from the A* search for the previous search problem. Thus, Fringe- Saving A* reuses the beginning of the previous A* search that is identical to the current A* search. In this paper, we generalize the correctness proof of Fringe-Saving A* to cover the case where the goal cell changes over time in addition to the traversability of cells. We then apply Fringe-Saving A* to the problem of moving an agent along a shortest path from its current cell to a fixed destination cell in a known gridworld, where the shortest path is replanned whenever the traversability of cells changes. Our experimental results show that the resulting Dynamic Fringe-Saving A* algorithm can outperform both repeated A* searches and D* Lite (a state-of-the-art incremental version of A*) in highly dynamic gridworlds, with runtime savings of up to a factor of about 2. 5.

ICRA Conference 2009 Conference Paper

Multi-robot routing with linear decreasing rewards over time

• Ali Ekici
• Pinar Keskinocak
• Sven Koenig

We study multi-robot routing problems (MR-LDR) where a team of robots has to visit a set of given targets with linear decreasing rewards over time, such as required for the delivery of goods to rescue sites after disasters. The objective of MR-LDR is to find an assignment of targets to robots and a path for each robot that maximizes the surplus, which is defined to be the total reward collected by the team minus its total travel cost. We develop a mixed integer program that solves MR-LDR optimally with a flow-type formulation and can be solved faster than the standard TSP-type formulations but also show that solving MR-LDR optimally is NP-hard. We then develop an auction-based algorithm and demonstrate that it solves MR-LDR in seconds and with a surplus that is comparable to the surplus found by the mixed integer program with a 12 hour time limit.

IROS Conference 2009 Conference Paper

Negotiation with reaction functions for solving complex task allocation problems

• Xiaoming Zheng
• Sven Koenig

We study task-allocation problems where cooperative robots need to perform tasks simultaneously. We develop a distributed negotiation procedure that allows robots to find all task exchanges that reduce the team cost of a given task allocation, without robots having to know how other robots compute their robot costs. Finally, we demonstrate empirically that our negotiation procedure can substantially reduce the team costs of task allocations resulting from existing task-allocation procedures, including sequential single-item auctions.

ICAPS Conference 2009 Conference Paper

Path-Adaptive A* for Incremental Heuristic Search in Unknown Terrain

• Carlos Hernández Ulloa
• Pedro Meseguer
• Xiaoxun Sun
• Sven Koenig

Adaptive A* is an incremental version of A* that updates the h-values of the previous A* search to make them more informed and thus future A* searches more focused. In this paper, we show how the A* searches performed by Adaptive A* can reuse part of the path of the previous search and terminate before they expand a goal state, resulting in Path-Adaptive A*. We demonstrate experimentally that Path-Adaptive A* expands fewer states per search and runs faster than Adaptive A* when solving path-planning problems in initially unknown terrain.

AAMAS Conference 2009 Conference Paper

Simple Optimization Techniques for A*-Based Search

• Xiaoxun Sun
• William Yeoh
• Po-An Chen
• Sven Koenig

In this paper, we present two simple optimizations that can reduce the number of priority queue operations for A* and its extensions. Basically, when the optimized search algorithms expand a state, they check whether they will expand a successor of the state next. If so, they do not first insert it into the priority queue and then immediately remove it again. These changes might appear to be trivial but are well suited for Generalized Adaptive A*, an extension of A*. Our experimental results indeed show that they speed up Generalized Adaptive A* by up to 30 percent if its priority queue is implemented as a binary heap.

AAAI Conference 2008 Conference Paper

Agent Coordination with Regret Clearing

• Sven Koenig
• Richard Borie
• Vangelis Markakis

Sequential single-item auctions can be used for the distributed allocation of tasks to cooperating agents. We study how to improve the team performance of sequential singleitem auctions while still controlling the agents in real time. Our idea is to assign that task to agents during the current round whose regret is large, where the regret of a task is defined as the difference of the second-smallest and smallest team costs resulting from assigning the task to the secondbest and best agent, respectively. Our experimental results show that sequential single-item auctions with regret clearing indeed result in smaller team costs than standard sequential single-item auctions for three out of four combinations of two different team objectives and two different capacity constraints (including no capacity constraints).

AAMAS Conference 2008 Conference Paper

An Exact Algorithm for Solving MDPs under Risk-Sensitive Objective with One-Switch Utility Functions

• Yaxin Liu
• Sven Koenig

One-switch utility functions are an important class of nonlinear utility functions that can model human beings whose decisions change with their wealth level. We study how to maximize the expected utility for Markov decision problems with given one-switch utility functions. We first utilize the fact that one-switch utility functions are weighted sums of linear and exponential utility functions to prove that there exists an optimal policy that is both stationary and deterministic as the wealth level approaches negative infinity. We then develop a solution method, the backward-induction method, that starts with this policy and augments it for higher and higher wealth levels. Our backward-induction method determines maximal expected utilities in finite time, different from the previous functional value iteration method, that typically determines only approximately maximal expected utilities.

AAMAS Conference 2008 Conference Paper

BnB-ADOPT: An Asynchronous Branch-and-Bound DCOP Algorithm

• William Yeoh
• Ariel Felner
• Sven Koenig

Distributed constraint optimization (DCOP) problems are a popular way of formulating and solving agent-coordination problems. It is often desirable to solve DCOP problems optimally with memory-bounded and asynchronous algorithms. We introduce Branch-and-Bound ADOPT (BnB- ADOPT), a memory-bounded asynchronous DCOP algorithm that uses the message passing and communication framework of ADOPT, a well known memory-bounded asynchronous DCOP algorithm, but changes the search strategy of ADOPT from best-first search to depth-first branch-andbound search. Our experimental results show that BnB- ADOPT is up to one order of magnitude faster than ADOPT on a variety of large DCOP problems and faster than NCBB, a memory-bounded synchronous DCOP algorithm, on most of these DCOP problems.

JAAMAS Journal 2008 Journal Article

Comparing real-time and incremental heuristic search for real-time situated agents

• Sven Koenig
• Xiaoxun Sun

Abstract Real-time situated agents, such as characters in real-time computer games, often do not know the terrain in advance but automatically observe it within a certain range around themselves. They have to interleave searches with action executions to make the searches tractable when moving autonomously to user-specified coordinates. The searches face real-time requirements since it is important that the agents be responsive to the commands of the users and move smoothly. In this article, we compare two classes of fast heuristic search methods for these navigation tasks that speed up A* searches in different ways, namely real-time heuristic search and incremental heuristic search, to understand their advantages and disadvantages and make recommendations about when each one should be used. We first develop a competitive real-time heuristic search method. LSS-LRTA* is a version of Learning Real-Time A* that uses A* to determine its local search spaces and learns quickly. We analyze the properties of LSS-LRTA* and then compare it experimentally against the state-of-the-art incremental heuristic search method D* Lite on our navigation tasks, for which D* Lite was specifically developed, resulting in the first comparison of real-time and incremental heuristic search in the literature. We characterize when to choose each one of the two heuristic search methods, depending on the search objective and the kind of terrain. Our experimental results show that LSS-LRTA* can outperform D* Lite under the right conditions, namely when there is time pressure or the user-supplied h-values are generally not misleading.

AAMAS Conference 2008 Conference Paper

Generalized Adaptive A*

• Xiaoxun Sun
• Sven Koenig
• William Yeoh

Agents often have to solve series of similar search problems. Adaptive A* is a recent incremental heuristic search algorithm that solves series of similar search problems faster than A* because it updates the h-values using information from previous searches. It basically transforms consistent hvalues into more informed consistent h-values. This allows it to find shortest paths in state spaces where the action costs can increase over time since consistent h-values remain consistent after action cost increases. However, it is not guaranteed to find shortest paths in state spaces where the action costs can decrease over time because consistent h-values do not necessarily remain consistent after action cost decreases. Thus, the h-values need to get corrected after action cost decreases. In this paper, we show how to do that, resulting in Generalized Adaptive A* (GAA*) that finds shortest paths in state spaces where the action costs can increase or decrease over time. Our experiments demonstrate that Generalized Adaptive A* outperforms breadth-first search, A* and D* Lite for moving-target search, where D* Lite is an alternative state-of-the-art incremental heuristic search algorithm that finds shortest paths in state spaces where the action costs can increase or decrease over time.

AAMAS Conference 2008 Conference Paper

Reaction Functions for Task Allocation to Cooperative Agents

• Xiaoming Zheng
• Sven Koenig

In this paper, we present ARF, our initial effort at solving taskallocation problems where cooperative agents need to perform tasks simultaneously. An example is multi-agent routing problems where several agents need to visit targets simultaneously, for example, to move obstacles out of the way cooperatively. First, we propose reaction functions as a novel way of characterizing the costs of agents in a distributed way. Second, we show how to approximate reaction functions so that their computation and communication times are polynomial. Third, we show how reaction functions can be used by a central planner to allocate tasks to agents. Finally, we show experimentally that the resulting task allocations are better than those of other greedy methods that do not use reaction functions.

AAMAS Conference 2008 Conference Paper

Trading Off Solution Quality for Faster Computation in DCOP Search Algorithms

• William Yeoh
• Sven Koenig
• Xiaoxun Sun

Distributed Constraint Optimization (DCOP) is a key technique for solving multiagent coordination problems. Unfortunately, finding minimal-cost DCOP solutions is NP-hard. We therefore propose two mechanisms that trade off the solution costs of two DCOP search algorithms (ADOPT and BnB-ADOPT) for smaller runtimes, namely the Inadmissible Heuristics Mechanism and the Relative Error Mechanism. The solution costs that result from these mechanisms are bounded by a more meaningful quantity than the solution costs that result from the existing Absolute Error Mechanism since they both result in solution costs that are larger than minimal by at most a user-specified percentage. Furthermore, the Inadmissible Heuristics Mechanism experimentally dominates both the Absolute Error Mechanism and the Relative Error Mechanism for BnB-ADOPT and is generally no worse than them for ADOPT.

IJCAI Conference 2007 Conference Paper

• Xiaoxun Sun
• Sven Koenig

In this paper, we develop Fringe-Saving A* (FSA*), an incremental version of A* that repeatedly finds shortest paths in a known gridworld from a given start cell to a given goal cell while the traversability costs of cells increase or decrease. The first search of FSA* is the same as that of A*. However, FSA* is able to find shortest paths during the subsequent searches faster than A* because it reuses the beginning of the immediately preceeding A* search tree that is identical to the current A* search tree. FSA* does this by restoring the content of the OPEN list of A* at the point in time when an A* search for the current search problem could deviate from the A* search for the immediately preceeding search problem. We present first experimental results that demonstrate that FSA* can have a runtime advantage over A* and Lifelong Planning A* (LPA*), an alternative incremental version of A*.

IJCAI Conference 2007 Conference Paper

• Janusz Marecki
• Sven Koenig
• Milind Tambe

Agents often have to construct plans that obey deadlines or, more generally, resource limits for real-valued resources whose consumption can only be characterized by probability distributions, such as execution time or battery power. These planning problems can be modeled with continuous state Markov decision processes (MDPs) but existing solution methods are either inefficient or provide no guarantee on the quality of the resulting policy. We therefore present CPH, a novel solution method that solves the planning problems by first approximating with any desired accuracy the probability distributions over the resource consumptions with phase-type distributions, which use exponential distributions as building blocks. It then uses value iteration to solve the resulting MDPs by exploiting properties of exponential distributions to calculate the necessary convolutions accurately and efficiently while providing strong guarantees on the quality of the resulting policy. Our experimental feasibility study in a Mars rover domain demonstrates a substantial speedup over Lazy Approximation, which is currently the leading algorithm for solving continuous state MDPs with quality guarantees.

IJCAI Conference 2007 Conference Paper

• Sven Koenig
• Craig Tovey
• Xiaoming Zheng
• Ilgaz Sungur

We study auction-like algorithms for the distributed allocation of tasks to cooperating agents. To reduce the team cost of sequential single-item auction algorithms, we generalize them to assign more than one additional task during each round, which increases their similarity to combinatorial auction algorithms. We show that, for a given number of additional tasks to be assigned during each round, every agent needs to submit only a constant number of bids per round and the runtime of winner determination is linear in the number of agents. The communication and winner determination costs do not depend on the number of tasks and thus scale to a large number of tasks for small bundle sizes. We then demonstrate empirically that the team cost of sequential bundle-bid single-sale (= single-item) auction algorithms can be substantially smaller than that without bundles for multi-agent routing problems with capacity constraints.

IROS Conference 2007 Conference Paper

Multi-robot routing with rewards and disjoint time windows

• Justin Melvin
• Pinar Keskinocak
• Sven Koenig
• Craig A. Tovey
• Banu Yuksel Ozkaya

Multiple robots are often faster and more fault- tolerant than single robots for applications such as planetary exploration and search and rescue. We study applications where robots move in two-dimensional terrain and have to visit targets of given priorities during given time windows that do not overlap. We analyze the complexity of these coordination tasks and, where possible, use techniques from operations research to develop coordination methods that are efficient and optimize the team performance. We then develop auction-based coordination methods that build on these results and show experimentally that they run in seconds and achieve good team performance for NP-hard coordination tasks.

IROS Conference 2007 Conference Paper

Robot coverage of terrain with non-uniform traversability

• Xiaoming Zheng
• Sven Koenig

In this paper, we study how multiple robots can cover known terrain quickly. We extend Multi-Robot Forest Coverage, a state-of-the-art multi-robot coverage algorithm, from terrain with uniform traversability to terrain with nonuniform traversability, which is nontrivial. We prove that its cover times are at most about sixteen times larger than minimal and demonstrate experimentally that they are significantly smaller than those of an alternative multi-robot coverage algorithm.

AAMAS Conference 2007 Conference Paper

Speeding up Moving-Target Search

• Sven Koenig
• Maxim Likhachev
• Xiaoxun Sun

In this paper, we study moving-target search, where an agent (=hunter) has to catch a moving target (=prey). The agent does not necessarily know the terrain initially but can observe it within a certain sensor range around itself. It uses the strategy to always move on a shortest presumed unblocked path toward the target, which is a reasonable strategy for computer-controlled characters in video games. We study how the agent can find such paths faster by exploiting the fact that it performs A * searches repeatedly. To this end, we extend Adaptive A *, an incremental heuristic search method, to moving-target search and demonstrate experimentally that the resulting MT-Adaptive A * is faster than isolated A * searches and, in many situations, also D * Lite, a state-of-the-art incremental heuristic search method. In particular, it is faster than D * Lite by about one order of magnitude for moving-target search in known and initially unknown mazes if both search methods use the same informed heuristics.

AAAI Conference 2007 Conference Paper

Theta*: Any-Angle Path Planning on Grids

• Alex Nash
• Sven Koenig

Grids with blocked and unblocked cells are often used to represent terrain in computer games and robotics. However, paths formed by grid edges can be sub-optimal and unrealistic looking, since the possible headings are artificially constrained. We present Theta*, a variant of A*, that propagates information along grid edges without constraining the paths to grid edges. Theta* is simple, fast and finds short and realistic looking paths. We compare Theta* against both Field D*, the only other variant of A* that propagates information along grid edges without constraining the paths to grid edges, and A* with post-smoothed paths. Although neither path planning method is guaranteed to find shortest paths, we show experimentally that Theta* finds shorter and more realistic looking paths than either of these existing techniques.

SODA Conference 2006 Conference Paper

A near-tight approximation lower bound and algorithm for the kidnapped robot problem

• Sven Koenig
• Apurva Mudgal
• Craig A. Tovey

ICAPS Conference 2006 Conference Paper

A New Principle for Incremental Heuristic Search: Theoretical Results

• Sven Koenig
• Maxim Likhachev

Planning is often not a one-shot task because either the world or the agent's knowledge of the world changes. In this paper, we introduce a new principle that can be used to solve a series of similar search tasks faster with heuristic search methods than running individual searches in isolation, by updating the heuristics over time to make them more informed and thus future searches more focused. This principle is simple and easy to integrate into heuristic search methods, and it is easy to prove the correctness of the resulting heuristic search methods.

IROS Conference 2006 Conference Paper

Improving Sequential Single-Item Auctions

• Xiaoming Zheng
• Sven Koenig
• Craig A. Tovey

We study how to improve sequential single-item auctions that assign targets to robots for exploration tasks such as environmental clean-up, space-exploration, and search and rescue missions. We exploit the insight that the resulting travel distances are small if the bidding and winner-determination rules are designed to result in hillclimbing, namely to assign an additional target to a robot in each round of the sequential single-item auction so that the team cost increases the least. We study the impact of increasing the lookahead of hillclimbing and using roll-outs to improve the evaluation of partial target assignments. We describe the bidding and winner-determination rules of the resulting sequential single-item auctions and evaluate them experimentally, with surprising results: larger lookaheads do not improve sequential single-item auctions reliably while only a small number of roll-outs in early rounds already improve them substantially

ICAPS Conference 2006 Conference Paper

Probabilistic Planning with Nonlinear Utility Functions

• Yaxin Liu
• Sven Koenig

Researchers often express probabilistic planning problems as Markov decision process models and then maximize the expected total reward. However, it is often rational to maximize the expected utility of the total reward for a given nonlinear utility function, for example, to model attitudes towards risk in high-stake decision situations. In this paper, we give an overview of basic techniques for probabilistic planning with nonlinear utility functions, including functional value iteration and a backward induction method for one-switch utility functions.

AAMAS Conference 2006 Conference Paper

Real-Time Adaptive A*

• Sven Koenig
• Maxim Likhachev

AAAI Conference 2006 Conference Paper

The Power of Sequential Single-Item Auctions for Agent Coordination

• Sven Koenig
• M. Lagoudakis
• D. Kempe
• A. Kleywegt

Teams of robots are more fault tolerant than single robots, and auctions appear to be promising means for coordinating them. In a recent paper at “Robotics: Science and Systems 2005, ” we analyzed a coordination system based on sequential single-item auctions. We showed that the coordination system is simple to implement and computation and communication efficient, and that the resulting sum of all travel distances in known terrain is guaranteed to be only a constant factor away from optimum. In this paper, we put these results in perspective by comparing our coordination system against those based on either parallel single-item auctions or combinatorial auctions, demonstrating that it combines the advantages of both.

ICAPS Conference 2005 Conference Paper

A Generalized Framework for Lifelong Planning A* Search

• Maxim Likhachev
• Sven Koenig

We present a graph-based planning and replanning algorithm able to produce bounded suboptimal solutions in an anytime fashion. Our algorithm tunes the quality of its solution based on available search time, at every step reusing previous search efforts. When updated information regarding the underlying graph is received, the algorithm incrementally repairs its previous solution. The result is an approach that combines the benefits of anytime and incremental planners to provide efficient solutions to complex, dynamic search problems. We present theoretical analysis of the algorithm, experimental results on a simulated robot kinematic arm, and two current applications in dynamic path planning for outdoor mobile robots.

AAMAS Conference 2005 Conference Paper

Adaptive A*

• Sven Koenig
• Maxim Likhachev

UAI Conference 2005 Conference Paper

Existence and Finiteness Conditions for Risk-Sensitive Planning: Results and Conjectures

• Yaxin Liu
• Sven Koenig

Decision-theoretic planning with risk-sensitive planning objectives is important for building autonomous agents or decision-support systems for real-world applications. However, this line of research has been largely ignored in the artificial intelligence and operations research communities since planning with risk-sensitive planning objectives is more complicated than planning with risk-neutral planning objectives. To remedy this situation, we derive conditions that guarantee that the optimal expected utilities of the total plan-execution reward exist and are finite for fully observable Markov decision process models with non-linear utility functions. In case of Markov decision process models with both positive and negative rewards, most of our results hold for stationary policies only, but we conjecture that they can be generalized to non stationary policies.

IROS Conference 2005 Conference Paper

Multi-robot forest coverage

• Xiaoming Zheng
• Sonal Jain
• Sven Koenig
• David Kempe 0001

One of the main applications of mobile robots is terrain coverage: visiting each location in known terrain. Terrain coverage is crucial for lawn mowing, cleaning, harvesting, search-and-rescue, intrusion detection and mine clearing. Naturally, coverage can be sped up with multiple robots. In this paper, we describe multi-robot forest coverage, a new multi-robot coverage algorithm based on an algorithm by Even et al. (2004) for finding a tree cover with trees of balanced weights. The cover time of multi-robot forest coverage is at most eight times larger than optimal, and our experiments show it to perform significantly better than existing multi-robot coverage algorithms.

AAMAS Conference 2004 Conference Paper

A Comparison of Fast Search Methods for Real-Time Situated Agents

• Sven Koenig

AIJ Journal 2004 Journal Article

Lifelong Planning A∗

• Sven Koenig
• Maxim Likhachev
• David Furcy

IROS Conference 2004 Conference Paper

PDRRTs: integrating graph-based and cell-based planning

• Ananth Ranganathan
• Sven Koenig

Motion-planning problems can be solved by discretizing the continuous configuration space, for example with graph-based or cell-based techniques. We study rapidly exploring random trees (RRTs) as an example of graph-based techniques and the parti-game method as an example of cell-based techniques. We then propose parti-game directed RRTs (PDRRTs) as a novel technique that combines them. PDRRTs are based on the parti-game method but use RRTs as local controllers rather than the simplistic controllers used by the parti-game method. Our experimental results show that PDRRTs plan faster and solve more motion-planning problems than RRTs and plan faster and with less memory than the parti-game method.

IROS Conference 2004 Conference Paper

Simple auctions with performance guarantees for multi-robot task allocation

• Michail G. Lagoudakis
• Marc Berhault
• Sven Koenig
• Pinar Keskinocak
• Anton J. Kleywegt

We consider the problem of allocating a number of exploration tasks to a team of mobile robots. Each task consists of a target location that needs to be visited by a robot. The objective of the allocation is to minimize the total cost, that is, the sum of the travel costs of all robots for visiting all targets. We show that finding an optimal allocation is an NP-hard problem, even in known environments. The main contribution of this paper is PRIM ALLOCATION, a simple and fast approximate algorithm for allocating targets to robots which provably computes allocations whose total cost is at most twice as large as the optimal total cost. We then cast PRIM ALLOCATION in terms of a multi-round single-item auction where robots bid on targets, which allow for a decentralized implementation. To the best of our knowledge, PRIM ALLOCATION is the first auction-based allocation algorithm that provides a guarantee on the quality of its allocations. Our experimental results in a multi-robot simulator demonstrate that PRIM ALLOCATION is fast and results in close-to-optimal allocations despite its simplicity and decentralized nature. In particular, it needs an order of magnitude fewer bids than a computationally intensive allocation algorithm based on combinatorial auctions, yet its allocations are at least as good.

IROS Conference 2003 Conference Paper

A reactive robot architecture with planning on demand

• Ananth Ranganathan
• Sven Koenig

In this paper, we describe a reactive robot architecture that uses fast replanning methods to avoid the shortcomings of reactive navigation, such as getting stuck in box canyons or in front of small openings. Our robot architecture differs from other robot architectures in that it gives planning progressively greater control of the robot if reactive navigation continues to fail, until planning controls the robot directly. Our first experiments on a Nomad robot and in simulation demonstrate that our robot architecture promises to simplify the programming of reactive robot architectures and results in robust navigation, smooth trajectories, and reasonably good navigation performance.

AIJ Journal 2003 Journal Article

Editorial

• Craig Boutilier
• Tom Dean
• Sven Koenig

ICRA Conference 2003 Conference Paper

Improved analysis of D

• Craig A. Tovey
• Sam Greenberg
• Sven Koenig

D* is a planning method that always routes a robot in initially unknown terrain from its current location to a given goal location along a shortest presumed unblocked path. The robot moves along the path until it discovers new obstacles and then repeats the procedure. D* has been used on a large number of robots. It is therefore important to analyze the resulting travel distance. Previously, there has been only one analysis of D*, and it has two shortcomings. First, to prove the lower bound, it uses a physically unrealistic example graph which has distances that do not correspond to distances on a real map. We show that the lower bound is not smaller for grids, the kind of map-based graph on which D* is usually used. Second, there is a large gap between the upper and lower bounds on the travel distance. We considerably reduce this gap by decreasing the upper bound on arbitrary graphs, including grids. To summarize, we provide new, substantially tighter bounds on the travel distance of D* on grids, thus providing a realistic analysis for the way D* is actually used.

IROS Conference 2003 Conference Paper

Improved analysis of greedy mapping

• Craig A. Tovey
• Sven Koenig

We analyze greedy mapping, a simple mapping method that has successfully been used on mobile robots. Greedy mapping moves the robot from its current location on a shortest path towards a closest unvisited, unscanned or informative location, until the terrain is mapped. Previous work has resulted in upper and lower bounds on its worst-case travel distance but there was a large gap between the bounds. In this paper, we reduce the gap substantially by decreasing the upper bound from /spl Oscr/; (|V|/sup 3/2/) to /spl Oscr/; (|V|ln|V|) edge traversals, where |V| is the number of vertices of the graph. This upper bound demonstrates that the travel distance of greedy mapping is guaranteed to be small and thus suggests that greedy mapping is indeed a reasonable mapping method. The guaranteed good performance of greedy mapping is robust in that it holds for different versions of greedy mapping, regardless of sensor type and sensor range.

AIJ Journal 2003 Journal Article

Performance bounds for planning in unknown terrain

• Sven Koenig
• Craig Tovey
• Yuri Smirnov

AAMAS Conference 2003 Conference Paper

Risk-Averse Auction Agents

• Yaxin Liu
• Richard Goodwin
• Sven Koenig

IROS Conference 2003 Conference Paper

Robot exploration with combinatorial auctions

• Marc Berhault
• H. Huang
• Pinar Keskinocak
• Sven Koenig
• Wedad Elmaghraby
• Paul M. Griffin
• Anton J. Kleywegt

We study how to coordinate a team of mobile robots to visit a number of given targets in a partially unknown terrain. Robotics researchers have studied single-item auctions to perform this exploration task but these do not make synergies between the targets into account. We therefore design combinatorial auctions, propose different combinatorial bidding strategies and compare their performance with each other, as well as to single item auctions and an optimal centralized mechanism. Our computational results in teambots, a multi-robot simulator, indicate that combinatorial auctions generally lead to significantly superior team performance than single-item auctions, and generate very good results compared to an optimal centralized mechanism.

ICRA Conference 2003 Conference Paper

Trail-Laying Robots for Robust Terrain Coverage

• Jonas Svennebring
• Sven Koenig

Robotics researchers have studied robots that can follow the trails laid by other robots. We, on the other hand, study robots that leave trails in the terrain to cover closed terrain once or repeatedly. How to design such ant robots has so far been studied only theoretically for gross robot simplifications. In this paper, we describe for the first time how to build physical ant robots that cover terrain. We show that a modified version of node counting can model the behavior of the ant robots and report on first experiments that we performed to understand their behavior better. These experiments confirm that our ant robots indeed cover terrain robustly even if the trails are of uneven quality, the ant robots are moved without realizing this, or some trails are destroyed. Finally, we report the results of a large-scale experiment where ten simulated ant robots covered a factory floor of 25 by 25 meters repeatedly over 85 hours without any ant robots getting stuck.

AAAI Conference 2002 Conference Paper

D*Lite

• Sven Koenig

Incremental heuristic search methods use heuristics to focus their search and reuse information from previous searches to find solutions to series of similar search tasks much faster than is possible by solving each search task from scratch. In this paper, we apply Lifelong Planning A* to robot navigation in unknown terrain, including goal-directed navigation in unknown terrain and mapping of unknown terrain. The resulting D* Lite algorithm is easy to understand and analyze. It implements the same behavior as Stentz’ Focussed Dynamic A* but is algorithmically different. We prove properties about D* Lite and demonstrate experimentally the advantages of combining incremental and heuristic search for the applications studied. We believe that these results provide a strong foundation for further research on fast replanning methods in artificial intelligence and robotics.

ICAPS Conference 2002 Conference Paper

Heuristic Search-Based Replanning

• Sven Koenig
• David Furcy
• Colin Bauer

Many real-world planning problems require one to solve a series of similar planning tasks. In this case, replanning can be much faster than planning from scratch. In this paper, we introduce a novel replanning method for symbolic planning with heuristic search-based planners, currently the most popular planners. Our SHERPA replanner is not only the first heuristic search-based replanner but, different from previous replanners for other planning paradigms, it also guarantees that the quality of its plans is as good as that achieved by planning from scratch. We provide an experimental feasibility study that demonstrates the promise of SHERPA for heuristic search-based replanning.

ICRA Conference 2002 Conference Paper

Improved Fast Replanning for Robot Navigation in Unknown Terrain

• Sven Koenig
• Maxim Likhachev

Mobile robots often operate in domains that are only incompletely known, for example, when they have to move from given start coordinates to given goal coordinates in unknown terrain. In this case, they need to be able to replan quickly as their knowledge of the terrain changes. Stentz' Focussed Dynamic A* is a heuristic search method that repeatedly determines a shortest path from the current robot coordinates to the goal coordinates while the robot moves along the path. It is able to replan one to two orders of magnitudes faster than planning from scratch since it modifies previous search results locally. Consequently, it has been extensively used in mobile robotics. In this paper, we introduce an alternative to Focussed Dynamic A* that implements the same navigation strategy but is algorithmically different. Focussed Dynamic A* Lite is simpler, easier to understand, easier to analyze and easier to extend than Focussed Dynamic A*, yet is more efficient. We believe that our results will make D*-like replanning algorithms even more popular and enable robotics researchers to adapt them to additional applications.

IROS Conference 2002 Conference Paper

Incremental replanning for mapping

• Maxim Likhachev
• Sven Koenig

Incremental heuristic search methods can often replan paths much faster than incremental or heuristic search methods individually, yet are simple to use. So far, they have only been used in mobile robotics to move a robot to given goal coordinates in unknown terrain. As far as we know, incremental heuristic search methods have not yet been applied to the problem of mapping unknown terrain. In this paper we therefore describe how to apply our incremental heuristic search method D* Lite, that combines ideas from Lifelong Planning A* and Focussed D*, to mapping unknown terrain, which is rather nontrivial. We then compare its runtime against that of incremental search and heuristic search alone, demonstrating the computational benefits of their combination. By demonstrating the versatility and computational benefits of incremental heuristic search, we hope that this underexploited technique will be used more often in mobile robotics.

NeurIPS Conference 2002 Conference Paper

Speeding up the Parti-Game Algorithm

• Maxim Likhachev
• Sven Koenig

In this paper, we introduce an efficient replanning algorithm for nonde- terministic domains, namely what we believe to be the first incremental heuristic minimax search algorithm. We apply it to the dynamic dis- cretization of continuous domains, resulting in an efficient implemen- tation of the parti-game reinforcement-learning algorithm for control in high-dimensional domains.

IROS Conference 2001 Conference Paper

Greedy localization

• Craig A. Tovey
• Sven Koenig

We show that finding localization plans with optimal worst-case execution time for localization tasks with short-range sensors in discretized domains is NP-hard, even within a logarithmic factor. This strongly suggests that finding and executing localization plans with optimal or even near-optimal worst-case execution time cannot be done in polynomial time. Greedy localization methods interleave planning and execution and keep the amount of planning performed between moves small. We analyze one such greedy localization method, the delayed planning architecture, and show that it can find and execute localization plans in polynomial time and thus substantially reduce the sum of planning and execution time compared to localization methods that find localization plans with optimal or near-optimal execution time. We also characterize how suboptimal the execution time of its localization plans can be. These results provide a first step towards analyzing other greedy localization methods.

ICRA Conference 2001 Conference Paper

Greedy Mapping of Terrain

• Sven Koenig
• Craig A. Tovey
• William Halliburton

We study a greedy mapping method that always moves the robot from its current location to the closest location that it has not visited (or observed) yet, until the terrain is mapped. Although one does not expect such a simple mapping method to minimize the travel distance of the robot, we present analytical results that show (perhaps surprisingly) that the travel distance of the robot is reasonably small. This is interesting because greedy mapping has a number of desirable properties. It is simple to implement and integrate into complete robot architectures. It does not need to have control of the rebut at all times, takes advantage of prior knowledge about parts of the terrain (if available), and can be used by several robots cooperatively.

AIJ Journal 2001 Journal Article

Minimax real-time heuristic search

• Sven Koenig

ICAPS Conference 2000 Conference Paper

Representations of Decision-Theoretic Planning Tasks

• Sven Koenig
• Yaxin Liu

Goal-directed Markov Decision Process models (GDMDPs) are good models for many decision-theoretic planning tasks. They have been used in conjunction with two different reward structures, namely the goal-reward representation and the action-penalty representation. We apply GDMDPs to planning tasks in the presence of traps such as steep slopes for outdoor robots or staircases for indoor robots, and study the differences between the two reward structures. In these situations, achieving the goal is often the primary objective while minimizing the travel time is only of secondary importance. We show that the action-penalty representation without discounting guarantees that the optimal plan achieves the goal for sure (if this is possible) but neither the actionpenalty representation with discounting nor the goal-reward representation with discounting have this property. We then show exactly when this trapping phenomenon occurs, using a novel interpretation for discounting, namely that it models agents that use convex exponential utility functions and thus are optimistic in the face of uncertainty. Finally, we show how the trapping phenomenon can be eliminated with our Selective State-Deletion Method.

AAAI Conference 1999 Conference Paper

Value-Update Rules for Real-Time Search

• Sven Koenig
• Georgia Institute of Technology
• Boleslaw Szymanski
• Rensselaer Polytechnic Institute

Real-time search methods have successfully been used to solve a large variety of search problems but their properties are largely unknown. In this paper, we study how existing real-time search methods scale up. We compare two real-time search methods that differ only in the update rules of their values and have been used successfully in the literature: Node Counting, a real-time search method that always moves to the successor state that it has visited the least number of times so far, and Learning Real-Time A*, a subtly different real-time search method. Both real-time search methods seemed to perform equally well in standard domains from artificial intelligence and robotics. Our formal analysis is therefore very surprising. We show that the performance of Node Counting can be exponential in the number of states even in undirected domains. This solves an open problem from the literature and shows that the two real-time search methods do not always perform similarly in undirected domains since the performance of Learning Real-Time A* is known to be polynomial in the number of states at worst.

NeurIPS Conference 1998 Conference Paper

Exploring Unknown Environments with Real-Time Search or Reinforcement Learning

• Sven Koenig

Learning Real-Time A* (LRTA*) is a popular control method that interleaves plan(cid: 173) ning and plan execution and has been shown to solve search problems in known environments efficiently. In this paper, we apply LRTA * to the problem of getting to a given goal location in an initially unknown environment. Uninformed LRTA * with maximal lookahead always moves on a shortest path to the closest unvisited state, that is, to the closest potential goal state. This was believed to be a good exploration heuristic, but we show that it does not minimize the worst-case plan-execution time compared to other uninformed exploration methods. This result is also of interest to reinforcement-learning researchers since many reinforcement learning methods use asynchronous dynamic programming, interleave planning and plan execution, and exhibit optimism in the face of uncertainty, just like LRTA *.

ICAPS Conference 1998 Conference Paper

Solving Robot Navigation Problems with Initial Pose Uncertainty Using Real-Time Heuristic Search

• Sven Koenig
• Reid G. Simmons

Westudy goal-directednavigationtasks in mazes, wherethe robots knowthe mazebut donot knowtheir initial pose(position and orientation). Thesesearch tasks canbe modeled as planningtasks in large non-deterministicdomainswhose states are sets of poses. Theycan be solvedefficiently by interleaving planningand plan execution, whichcan reduce the sumof planningand plan-executiontime becauseit allowsthe robots to gather informationearly. Weshowhow Min-Max LRTA*, a real-time heuristic search method, can solve these and other planningtasks in non-deterministic domainsefficiently. It allowsfor fine-grainedcontrol over howmuchplanning to do betweenplan executions, uses heuristic knowledge to guideplanning, and improves its planexecutiontimeas it solvessimilarplanningtasks, until its plan-executiontimeis at least worst-caseoptimal. Wealso showthat Min-Max LRTA* solves the goal-directed navigation tasks fast, converges quickly, andrequiresonlya small amountof memory.

ICRA Conference 1997 Conference Paper

Sensor-based planning with the freespace assumption

• Sven Koenig
• Yury V. Smirnov

A popular technique for getting to a goal location in unknown terrain is planning with the freespace assumption. The robot assumes that the terrain is clear unless it knows otherwise. It always plans a shortest path to the goal location and re-plans whenever it detects an obstacle that blocks its path or, more generally, when it detects that its current path is no longer optimal. It has been unknown whether this sensor-based planning approach is worst-case optimal, given the lack of initial knowledge about the terrain. We demonstrate that planning with the freespace assumption can make good performance guarantees on some restricted graph topologies (such as grids) but is not worst-case optimal in general. For situations in which its performance guarantee is insufficient, we also describe an algorithm, called Basic-VECA, that exhibits good average-case performance and provides performance guarantees that are optimal up to a constant (user-defined) factor.

AAAI Conference 1996 Short Paper

Agent-Centered Search: Situated Search with Small Look-Ahead

• Sven Koenig

Situated search is the process of achieving a goal in the world. Traditional single-agent search algorithms (such as the A* algorithm) usually assume completely known, stationary domains with deterministic actions. These assumptions favor search approaches that first determine open-loop plans (sequences of actions) that can then be executed blindly in the world. Consequently, single-agent search in AI is often performed in a mental model of the world (state space): states are represented as memory images and search is a process inside the computer (search-in-memory).

AAAI Conference 1996 Conference Paper

Easy and Hard Testbeds for Real-Time Search Algorithms

• Sven Koenig

Although researchers have studied which factors influence the behavior of traditional search algorithms, currently not much is known about how domain properties influence the performance of real-time search algorithms. In this paper we demonstrate, both theoretically and experimentally, that Eulerian state spaces (a superset of undirected state spaces) are very easy for some existing real-time search algorithms to solve: even real-time search algorithms that can be intractable, in general, are efficient for Eulerian state spaces. Because traditional real-time search testbeds (such as the eight puzzle and gridworlds) are Eulerian, they cannot be used to distinguish between efficient and inefficient real-time search algorithms. It follows that one has to use non-Eulerian domains to demonstrate the general superiority of a given algorithm. To this end, we present two classes of hard-to-search state spaces and demonstrate the performance of various real-time search algorithms on them.

ICML Conference 1996 Conference Paper

Passive Distance Learning for Robot Navigation

• Sven Koenig
• Reid G. Simmons

ICRA Conference 1996 Conference Paper

Unsupervised learning of probabilistic models for robot navigation

• Sven Koenig
• Reid G. Simmons

Navigation methods for office delivery robots need to take various sources of uncertainty into account in order to get robust performance. In previous work, we developed a reliable navigation technique that uses partially observable Markov models to represent metric, actuator and sensor uncertainties. This paper describes an algorithm that adjusts the probabilities of the initial Markov model by passively observing the robot's interactions with its environment. The learned probabilities more accurately reflect the actual uncertainties in the environment, which ultimately leads to improved navigation performance. The algorithm, an extension of the Baum-Welch algorithm, learns without a teacher and addresses the issues of limited memory and the cost of collecting training data. Empirical results show that the algorithm learns good Markov models with a small amount of training data.

IROS Conference 1995 Conference Paper

Experience with rover navigation for lunar-like terrains

• Reid G. Simmons
• Eric Krotkov
• Lonnie Chrisman
• Fábio Gagliardi Cozman
• Richard Goodwin
• Martial Hebert
• Lalitesh Katragadda
• Sven Koenig

Reliable navigation is critical for a lunar rover, both for autonomous traverses and safeguarded remote teleoperation. This paper describes an implemented system that has autonomously driven a prototype wheeled lunar rover over a kilometer in natural, outdoor terrain. The navigation system uses stereo terrain maps to perform local obstacle avoidance, and arbitrates steering recommendations from both the user and the rover. The paper describes the system architecture, each of the major components, and the experimental results to date.

IJCAI Conference 1995 Conference Paper

Probabilistic Robot Navigation in Partially Observable Environments

• Reid Simmons
• Sven Koenig

IJCAI Conference 1995 Conference Paper

Real-Time Search in Non-Deterministic Domains

• Sven Koenig
• Reid G Simmons

ICAPS Conference 1994 Conference Paper

How to Make Probabilistic Planners Risk-sensitive (Without Altering Anything)

• Sven Koenig
• Reid G. Simmons

Probabilistic planners can have various planning objectives: usually they either maximize the probability of goal achievement or minimize the expected execution cost of the plan. Researchers have largely ignored the problem how to incorporate risk-sensitive attitudes into their planning mechanisms. We discuss a risk-sensitive planning approach that is based on utility theory. Our key result is that this approach can, at least for risk-seeking attitudes, be implemented with any reactive planner that maximizes (or satisfices) the probability of goal achievement. First, the risk-sensitive planning problem is transformed into a different planning problem, that is then solved by the planner. The larger the probability of goal achievement of the resulting plan, the better its expected utility is for the original (risk-sensitive) planning problem. This approach extends the functionality of reactive planners that maximize the probability of goal achievement, since it allows one to use them (unchanged) for risk-sensitive planning.

AAAI Conference 1993 Conference Paper

Complexity Analysis of Real-Time Reinforcement Learning

• Sven Koenig