Aneta Neumann

IJCAI Conference 2025 Conference Paper

Theoretical Analysis of Evolutionary Algorithms with Quality Diversity for a Classical Path Planning Problem

• Duc-Cuong Dang
• Aneta Neumann
• Frank Neumann
• Andre Opris
• Dirk Sudholt

Quality diversity (QD) algorithms, an extension of evolutionary algorithms, excel at generating diverse sets of high-quality solutions for complex problems in robotics, games, and combinatorial optimisation. Despite their success, the underlying mechanisms remain poorly understood due to a lack of a theoretical foundation. We address this gap by analysing QD algorithms on the all-pairs-shortest-paths (APSP) problem, a classical planning task that naturally seeks multiple solutions. Using Map-Elites, a prominent QD approach, we leverage its ability to evolve solutions across distinct regions of a behavioural space, which for APSP corresponds to all pairs of nodes in the graph. Our analysis rigorously demonstrates that evolutionary algorithms using Map-Elites efficiently compute shortest paths for all node pairs in parallel by exploiting synergies in the behavioural space. By appending edges to an existing shortest path, mutation can create optimal solutions in other regions of the behavioural space. Crossover is particularly effective, as it can combine optimal paths from two regions to produce an optimal path for a third region simply by concatenating two shortest paths. Finally, refining the parent selection to facilitate successful crossovers exhibits significant speed-ups compared to standard QD approaches.

AAAI Conference 2024 Conference Paper

Limited Query Graph Connectivity Test

• Mingyu Guo
• Jialiang Li
• Aneta Neumann
• Frank Neumann
• Hung Nguyen

We propose a combinatorial optimisation model called Limited Query Graph Connectivity Test. We consider a graph whose edges have two possible states (On/Off). The edges' states are hidden initially. We could query an edge to reveal its state. Given a source s and a destination t, we aim to test s−t connectivity by identifying either a path (consisting of only On edges) or a cut (consisting of only Off edges). We are limited to B queries, after which we stop regardless of whether graph connectivity is established. We aim to design a query policy that minimizes the expected number of queries. Our model is mainly motivated by a cyber security use case where we need to establish whether attack paths exist in a given network, between a source (i.e., a compromised user node) and a destination (i.e., a high-privilege admin node). Edge query is resolved by manual effort from the IT admin, which is the motivation behind query minimization. Our model is highly related to Stochastic Boolean Function Evaluation (SBFE). There are two existing exact algorithms for SBFE that are prohibitively expensive. We propose a signifcantly more scalable exact algorithm. While previous exact algorithms only scale for trivial graphs (i.e., past works experimented on at most 20 edges), we empirically demonstrate that our algorithm is scalable for a wide range of much larger practical graphs (i.e., graphs representing Windows domain networks with tens of thousands of edges). We also propose three heuristics. Our best-performing heuristic is via limiting the planning horizon of the exact algorithm. The other two are via reinforcement learning (RL) and Monte Carlo tree search (MCTS). We also derive an algorithm for computing the performance lower bound. Experimentally, we show that all our heuristics are near optimal. The heuristic building on the exact algorithm outperforms all other heuristics, surpassing RL, MCTS and eight existing heuristics ported from SBFE and related literature.

IJCAI Conference 2023 Conference Paper

Diverse Approximations for Monotone Submodular Maximization Problems with a Matroid Constraint

• Anh Viet Do
• Mingyu Guo
• Aneta Neumann
• Frank Neumann

Finding diverse solutions to optimization problems has been of practical interest for several decades, and recently enjoyed increasing attention in research. While submodular optimization has been rigorously studied in many fields, its diverse solutions extension has not. In this study, we consider the most basic variants of submodular optimization, and propose two simple greedy algorithms, which are known to be effective at maximizing monotone submodular functions. These are equipped with parameters that control the trade-off between objective and diversity. Our theoretical contribution shows their approximation guarantees in both objective value and diversity, as functions of their respective parameters. Our experimental investigation with maximum vertex coverage instances demonstrates their empirical differences in terms of objective-diversity trade-offs.

NeurIPS Conference 2023 Conference Paper

Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems

• Anh Viet Do
• Aneta Neumann
• Frank Neumann
• Andrew Sutton

We study the multi-objective minimum weight base problem, an abstraction of classical NP-hard combinatorial problems such as the multi-objective minimum spanning tree problem. We prove some important properties of the convex hull of the non-dominated front, such as its approximation quality and an upper bound on the number of extreme points. Using these properties, we give the first run-time analysis of the MOEA/D algorithm for this problem, an evolutionary algorithm that effectively optimizes by decomposing the objectives into single-objective components. We show that the MOEA/D, given an appropriate decomposition setting, finds all extreme points within expected fixed-parameter polynomial time, in the oracle model. Experiments are conducted on random bi-objective minimum spanning tree instances, and the results agree with our theoretical findings. Furthermore, compared with a previously studied evolutionary algorithm for the problem GSEMO, MOEA/D finds all extreme points much faster across all instances.

AAAI Conference 2023 Conference Paper

Scalable Edge Blocking Algorithms for Defending Active Directory Style Attack Graphs

• Mingyu Guo
• Max Ward
• Aneta Neumann
• Frank Neumann
• Hung Nguyen

Active Directory (AD) is the default security management system for Windows domain networks. An AD environment naturally describes an attack graph where nodes represent computers/accounts/security groups, and edges represent existing accesses/known exploits that allow the attacker to gain access from one node to another. Motivated by practical AD use cases, we study a Stackelberg game between one attacker and one defender. There are multiple entry nodes for the attacker to choose from and there is a single target (Domain Admin). Every edge has a failure rate. The attacker chooses the attack path with the maximum success rate. The defender can block a limited number of edges (i.e., revoke accesses) from a set of blockable edges, limited by budget. The defender's aim is to minimize the attacker's success rate. We exploit the tree-likeness of practical AD graphs to design scalable algorithms. We propose two novel methods that combine theoretical fixed parameter analysis and practical optimisation techniques. For graphs with small tree widths, we propose a tree decomposition based dynamic program. We then propose a general method for converting tree decomposition based dynamic programs to reinforcement learning environments, which leads to an anytime algorithm that scales better, but loses the optimality guarantee. For graphs with small numbers of non-splitting paths (a parameter we invent specifically for AD graphs), we propose a kernelization technique that significantly downsizes the model, which is then solved via mixed-integer programming. Experimentally, our algorithms scale to handle synthetic AD graphs with tens of thousands of nodes.

AIJ Journal 2022 Journal Article

Pareto optimization for subset selection with dynamic cost constraints

• Vahid Roostapour
• Aneta Neumann
• Frank Neumann
• Tobias Friedrich

AAAI Conference 2022 Conference Paper

Practical Fixed-Parameter Algorithms for Defending Active Directory Style Attack Graphs

• Mingyu Guo
• Jialiang Li
• Aneta Neumann
• Frank Neumann
• Hung Nguyen

Active Directory is the default security management system for Windows domain networks. We study the shortest path edge interdiction problem for defending Active Directory style attack graphs. The problem is formulated as a Stackelberg game between one defender and one attacker. The attack graph contains one destination node and multiple entry nodes. The attacker’s entry node is chosen by nature. The defender chooses to block a set of edges limited by his budget. The attacker then picks the shortest unblocked attack path. The defender aims to maximize the expected shortest path length for the attacker, where the expectation is taken over entry nodes. We observe that practical Active Directory attack graphs have small maximum attack path lengths and are structurally close to trees. We first show that even if the maximum attack path length is a constant, the problem is still W[1]-hard with respect to the defender’s budget. Having a small maximum attack path length and a small budget is not enough to design fixed-parameter algorithms. If we further assume that the number of entry nodes is small, then we derive a fixedparameter tractable algorithm. We then propose two other fixed-parameter algorithms by exploiting the tree-like features. One is based on tree decomposition and requires a small tree width. The other assumes a small number of splitting nodes (nodes with multiple outgoing edges). Finally, the last algorithm is converted into a graph convolutional neural network based heuristic, which scales to larger graphs with more splitting nodes.

TCS Journal 2022 Journal Article

Single- and multi-objective evolutionary algorithms for the knapsack problem with dynamically changing constraints

• Vahid Roostapour
• Aneta Neumann
• Frank Neumann

ECAI Conference 2020 Conference Paper

Evolutionary Bi-Objective Optimization for the Dynamic Chance-Constrained Knapsack Problem Based on Tail Bound Objectives

• Hirad Assimi
• Oscar Harper
• Yue Xie
• Aneta Neumann
• Frank Neumann 0001

Real-world combinatorial optimization problems are often stochastic and dynamic. Therefore, it is essential to make optimal and reliable decisions with a holistic approach. In this paper, we consider the dynamic chance-constrained knapsack problem where the weight of each item is stochastic, the capacity constraint changes dynamically over time, and the objective is to maximize the total profit subject to the probability that total weight exceeds the capacity. We make use of prominent tail inequalities such as Chebyshev’s inequality, and Chernoff bound to approximate the probabilistic constraint. Our key contribution is to introduce an additional objective which estimates the minimal capacity bound for a given stochastic solution that still meets the chance constraint. This objective helps to cater for dynamic changes to the stochastic problem. We apply single- and multi-objective evolutionary algorithms to the problem and show how bi-objective optimization can help to deal with dynamic chance-constrained problems.

ECAI Conference 2020 Conference Paper

Non-Monotone Submodular Maximization with Multiple Knapsacks in Static and Dynamic Settings

• Vanja Doskoc
• Tobias Friedrich 0001
• Andreas Göbel 0001
• Aneta Neumann
• Frank Neumann 0001
• Francesco Quinzan

We study the problem of maximizing a non-monotone submodular function under multiple knapsack constraints. We propose a simple discrete greedy algorithm to approach this problem, and prove that it yields strong approximation guarantees for functions with bounded curvature. In contrast to other heuristics, this does not require problem relaxation to continuous domains and it maintains a constant-factor approximation guarantee in the problem size. In the case of a single knapsack, our analysis suggests that the standard greedy can be used in non-monotone settings. Additionally, we study this problem in a dynamic setting, in which knapsacks change during the optimization process. We modify our greedy algorithm to avoid a complete restart at each constraint update. This modification retains the approximation guarantees of the static case. We evaluate our results experimentally on a video summarization and sensor placement task. We show that our proposed algorithm competes with the state-of-the-art in static settings. Furthermore, we show that in dynamic settings with tight computational time budget, our modified greedy yields significant improvements over starting the greedy from scratch, in terms of the solution quality achieved.

AAAI Conference 2020 Conference Paper

Optimization of Chance-Constrained Submodular Functions

• Benjamin Doerr
• Carola Doerr
• Aneta Neumann
• Frank Neumann
• Andrew Sutton

Submodular optimization plays a key role in many real-world problems. In many real-world scenarios, it is also necessary to handle uncertainty, and potentially disruptive events that violate constraints in stochastic settings need to be avoided. In this paper, we investigate submodular optimization problems with chance constraints. We provide a first analysis on the approximation behavior of popular greedy algorithms for submodular problems with chance constraints. Our results show that these algorithms are highly effective when using surrogate functions that estimate constraint violations based on Chernoff bounds. Furthermore, we investigate the behavior of the algorithms on popular social network problems and show that high quality solutions can still be obtained even if there are strong restrictions imposed by the chance constraint.

AAAI Conference 2019 Conference Paper

Pareto Optimization for Subset Selection with Dynamic Cost Constraints

• Vahid Roostapour
• Aneta Neumann
• Frank Neumann
• Tobias Friedrich

In this paper, we consider the subset selection problem for function f with constraint bound B which changes over time. We point out that adaptive variants of greedy approaches commonly used in the area of submodular optimization are not able to maintain their approximation quality. Investigating the recently introduced POMC Pareto optimization approach, we show that this algorithm efficiently computes a φ = (αf /2)(1 − 1 e αf )-approximation, where αf is the submodularity ratio of f, for each possible constraint bound b ≤ B. Furthermore, we show that POMC is able to adapt its set of solutions quickly in the case that B increases. Our experimental investigations for the influence maximization in social networks show the advantage of POMC over generalized greedy algorithms.