Author name cluster

Quentin Cappart

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

11 papers

2 author rows

JAIR Journal 2025 Journal Article

Combining Constraint Programming and Machine Learning: From Current Progress to Future Opportunities

Quentin Cappart
Tias Guns
Michele Lombardi
Gilles Pesant
Dimos Tsouros

The integration of constraint programming (CP) together with machine learning (ML) has emerged as a promising direction for tackling complex decision-making and combinatorial optimization problems. While CP offers expressive modeling capabilities and formal guarantees, ML provides adaptive methods for learning from data and generalizing across instances. This survey presents a comprehensive overview of recent advances in combining CP and ML. We first show how ML has been used to improve the CP toolbox, both in modeling and in the efficiency of solving. Then, we examine how CP can support ML, particularly in providing structure, guarantees, and symbolic reasoning capabilities. Finally, we identify key open challenges inherent to such hybrid approaches and outline promising directions for future research. This survey provides a first conceptual and structured review of recent advancements in this emerging field, aiming to serve as a resource for practitioners and researchers in both the CP and ML communities. To keep the progress up to date, a curated list of references is hosted on an accompanying repository (https://github.com/corail-research/CPML-paper-list) and is open to community contributions.

PDF Details DOI

AAAI Conference 2025 Conference Paper

Learning Valid Dual Bounds in Constraint Programming: Boosted Lagrangian Decomposition with Self-Supervised Learning

Swann Bessa
Darius Dabert
Max Bourgeat
Louis-Martin Rousseau
Quentin Cappart

Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the search space effectively.In brief, a vector of Lagrangian multipliers is associated with each sub-problem, and an iterative procedure (e.g., a sub-gradient optimization) adjusts these multipliers to find the tightest bound. Initially applied to integer programming, Lagrangian decomposition also had success in constraint programming due to its versatility and the fact that global constraints provide natural sub-problems. However, the non-linear and combinatorial nature of sub-problems in constraint programming makes it computationally intensive to optimize the Lagrangian multipliers with sub-gradient methods at each node of the tree search. This currently limits the practicality of LD as a general bounding mechanism for constraint programming. To address this challenge, we propose a self-supervised learning approach that leverages neural networks to generate multipliers directly, yielding tight bounds. This approach significantly reduces the number of sub-gradient optimization steps required, enhancing the pruning efficiency and reducing the execution time of constraint programming solvers. This contribution is one of the few that leverage learning to enhance bounding mechanisms on the dual side, a critical element in the design of combinatorial solvers. This work presents a generic method for learning valid dual bounds in constraint programming. We validate our approach on two challenging combinatorial problems: The multi-dimensional knapsack problem and the shift scheduling problem. The results show that our approach can solve more instances than the standard application of LD to constraint programming, reduce execution time by more than half, and has promising generalization ability through fine-tuning.

PDF Details DOI

TMLR Journal 2025 Journal Article

The BrowserGym Ecosystem for Web Agent Research

Thibault Le Sellier de Chezelles
Maxime Gasse
Alexandre Lacoste
Massimo Caccia
Alexandre Drouin
Léo Boisvert
Megh Thakkar
Tom Marty

The BrowserGym ecosystem addresses the growing need for efficient evaluation and benchmarking of web agents, particularly those leveraging automation and Large Language Models (LLMs) for web interaction tasks. Many existing benchmarks suffer from fragmentation and inconsistent evaluation methodologies, making it challenging to achieve reliable comparisons and reproducible results. In an earlier work, Drouin et al. (2024) introduced BrowserGym which aims to solve this by providing a unified, gym-like environment with well-defined observation and actionspaces, facilitating standardized evaluation across diverse benchmarks. We propose an extended BrowserGym-based ecosystem for web agent research, which unifies existing benchmarks from the literature and includes AgentLab, a complementary framework that aids in agent creation, testing, and analysis. Our proposed ecosystem offers flexibility for integrating new benchmarks while ensuring consistent evaluation and comprehensive experiment management. This standardized approach seeks to reduce the time and complexity of developing web agents, supporting more reliable comparisons and facilitating in-depth analysis of agent behaviors, and could result in more adaptable, capable agents, ultimately accelerating innovation in LLM-driven automation. As a supporting evidence, we conduct the first large-scale, multi-benchmark web agent experiment and compare the performance of 6 state-of-the-art LLMs across 6 popular web agent benchmarks made available in BrowserGym. Among other findings, our results highlight a large discrepancy between OpenAI and Anthropic’s latests models, with Claude-3.5-Sonnet leading the way on almost all benchmarks, except on vision-related tasks where GPT-4o is superior. Despite these advancements, our results emphasize that building robust and efficient web agents remains a significant challenge, due to the inherent complexity of real-world web environments and the limitations of current models.

PDF Details

IJCAI Conference 2024 Conference Paper

MARCO: A Memory-Augmented Reinforcement Framework for Combinatorial Optimization

Andoni I. Garmendia
Quentin Cappart
Josu Ceberio
Alexander Mendiburu

Neural Combinatorial Optimization (NCO) is an emerging domain where deep learning techniques are employed to address combinatorial optimization problems as a standalone solver. Despite their potential, existing NCO methods often suffer from inefficient search space exploration, frequently leading to local optima entrapment or redundant exploration of previously visited states. This paper introduces a versatile framework, referred to as Memory-Augmented Reinforcement for Combinatorial Optimization (MARCO), that can be used to enhance both constructive and improvement methods in NCO through an innovative memory module. MARCO stores data collected throughout the optimization trajectory and retrieves contextually relevant information at each state. This way, the search is guided by two competing criteria: making the best decision in terms of the quality of the solution and avoiding revisiting already explored solutions. This approach promotes a more efficient use of the available optimization budget. Moreover, thanks to the parallel nature of NCO models, several search threads can run simultaneously, all sharing the same memory module, enabling an efficient collaborative exploration. Empirical evaluations, carried out on the maximum cut, maximum independent set and travelling salesman problems, reveal that the memory module effectively increases the exploration, enabling the model to discover diverse, higher-quality solutions. MARCO achieves good performance in a low computational cost, establishing a promising new direction in the field of NCO.

PDF Details DOI

ECAI Conference 2024 Conference Paper

Winning the 2023 CityLearn Challenge: A Community-Based Hierarchical Energy Systems Coordination Algorithm

Andoni I. Garmendia
Francesco Morri
Quentin Cappart
Hélène Le Cadre

The effective management and control of building energy systems are crucial for reducing the energy consumption peak loads, CO2 emissions, and ensuring the stability of the power grid, while maintaining optimal comfort levels within buildings. The difficulty to accommodate this trade-off is amplified by dynamic environmental conditions and the need for scalable solutions that can adapt across various building types and geographic locations. Acknowledging the importance of this problem, NeurIPS conference hosted since 2020 the CityLearn control challenge to foster the design of innovative solutions in building energy management. Participants were tasked with developing strategies that not only enhance energy efficiency but also prioritize sustainability and occupant comfort. This paper introduces the Community-based Hierarchical Energy Systems Coordination Algorithm (CHESCA), the winning approach of the 2023 edition. We rely on a hierarchical approach adaptable to an arbitrary number of buildings, first optimizing building-level metrics individually, and later refining these through a central community-level controller to improve grid-related metrics. Compared to the other high-ranked competitors, our approach demonstrated fast inference capabilities like learning-based methods, while offering a better interpretability and a superior generalization capabilities with minimal data requirements. This paper details our approach, supported by comprehensive experimental results and ablation studies.

Details

NeurIPS Conference 2024 Conference Paper

WorkArena++: Towards Compositional Planning and Reasoning-based Common Knowledge Work Tasks

Léo Boisvert
Megh Thakkar
Maxime Gasse
Massimo Caccia
Thibault L. De Chezelles
Quentin Cappart
Nicolas Chapados
Alexandre Lacoste

The ability of large language models (LLMs) to mimic human-like intelligence has led to a surge in LLM-based autonomous agents. Though recent LLMs seem capable of planning and reasoning given user instructions, their effectiveness in applying these capabilities for autonomous task solving remains underexplored. This is especially true in enterprise settings, where automated agents hold the promise of a high impact. To fill this gap, we propose WorkArena++, a novel benchmark consisting of 682 tasks corresponding to realistic workflows routinely performed by knowledge workers. WorkArena++ is designed to evaluate the planning, problem-solving, logical/arithmetic reasoning, retrieval, and contextual understanding abilities of web agents. Our empirical studies across state-of-the-art LLMs and vision-language models (VLMs), as well as human workers, reveal several challenges for such models to serve as useful assistants in the workplace. In addition to the benchmark, we provide a mechanism to effortlessly generate thousands of ground-truth observation/action traces, which can be used for fine-tuning existing models. Overall, we expect this work to serve as a useful resource to help the community progress towards capable autonomous agents. The benchmark can be found at https: //github. com/ServiceNow/WorkArena.

PDF Details DOI

JMLR Journal 2023 Journal Article

Combinatorial Optimization and Reasoning with Graph Neural Networks

Quentin Cappart
Didier Chételat
Elias B. Khalil
Andrea Lodi
Christopher Morris
Petar Veličković

Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning, especially graph neural networks, as a key building block for combinatorial tasks, either directly as solvers or by enhancing exact solvers. The inductive bias of GNNs effectively encodes combinatorial and relational input due to their invariance to permutations and awareness of input sparsity. This paper presents a conceptual review of recent key advancements in this emerging field, aiming at optimization and machine learning researchers. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

PDF Details

JAIR Journal 2023 Journal Article

Improved Peel-and-Bound: Methods for Generating Dual Bounds with Multivalued Decision Diagrams

Isaac Rudich
Quentin Cappart
Louis-Martin Rousseau

Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional solvers have had decades to build. We drew inspiration from the warm-start technique used in conventional solvers to address one of the major challenges faced by decision diagram based methods. Decision diagrams become more useful the wider they are allowed to be, but also become more costly to generate, especially with large numbers of variables. In the original version of this paper, we presented a method of peeling off a sub-graph of previously constructed diagrams and using it as the initial diagram for subsequent iterations that we call peel-and-bound. We tested the method on the sequence ordering problem, and our results indicate that our peel-and-bound scheme generates stronger bounds than a branch-and-bound scheme using the same propagators, and at significantly less computational cost. In this extended version of the paper, we also propose new methods for using relaxed decision diagrams to improve the solutions found using restricted decision diagrams, discuss the heuristic decisions involved with the parallelization of peel-and-bound, and discuss how peel-and-bound can be hyper-optimized for sequencing problems. Furthermore, we test the new methods on the sequence ordering problem and the traveling salesman problem with time-windows (TSPTW), and include an updated and generalized implementation of the algorithm capable of handling any discrete optimization problem. The new results show that peel-and-bound outperforms ddo (a decision diagram based branch-and-bound solver) on the TSPTW. We also close 15 open benchmark instances of the TSPTW.

PDF Details DOI

IJCAI Conference 2021 Conference Paper

Combinatorial Optimization and Reasoning with Graph Neural Networks

Quentin Cappart
Didier Chételat
Elias B. Khalil
Andrea Lodi
Christopher Morris
Petar Veličković

Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have mostly focused on solving problem instances in isolation, ignoring the fact that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning, especially graph neural networks, as a key building block for combinatorial tasks, either directly as solvers or by enhancing the former. This paper presents a conceptual review of recent key advancements in this emerging field, aiming at researchers in both optimization and machine learning.

PDF Details DOI

AAAI Conference 2021 Conference Paper

Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization

Quentin Cappart
Thierry Moisan
Louis-Martin Rousseau
Isabeau Prémont-Schwarz
Andre A. Cire

Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces with combinatorial optimization is the state-space explosion problem: the number of possibilities grows exponentially with the problem size, which makes solving intractable for large problems. In the last years, deep reinforcement learning (DRL) has shown its promise for designing good heuristics dedicated to solve NP-hard combinatorial optimization problems. However, current approaches have an important shortcoming: they only provide an approximate solution with no systematic ways to improve it or to prove optimality. In another context, constraint programming (CP) is a generic tool to solve combinatorial optimization problems. Based on a complete search procedure, it will always find the optimal solution if we allow an execution time large enough. A critical design choice, that makes CP non-trivial to use in practice, is the branching decision, directing how the search space is explored. In this work, we propose a general and hybrid approach, based on DRL and CP, for solving combinatorial optimization problems. The core of our approach is based on a dynamic programming formulation, that acts as a bridge between both techniques. We experimentally show that our solver is efficient to solve three challenging problems: the traveling salesman problem with time windows, the 4-moments portfolio optimization problem, and the 0-1 knapsack problem. Results obtained show that the framework introduced outperforms the stand-alone RL and CP solutions, while being competitive with industrial solvers.

PDF Details

AAAI Conference 2019 Conference Paper

Improving Optimization Bounds Using Machine Learning: Decision Diagrams Meet Deep Reinforcement Learning

Quentin Cappart
Emmanuel Goutierre
David Bergman
Louis-Martin Rousseau

Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower bounds that can be significantly better than classical bounding mechanisms, such as linear relaxations. It is well known that the quality of the bounds achieved through this flexible bounding method is highly reliant on the ordering of variables chosen for building the diagram, and finding an ordering that optimizes standard metrics is an NP-hard problem. In this paper, we propose an innovative and generic approach based on deep reinforcement learning for obtaining an ordering for tightening the bounds obtained with relaxed and restricted DDs. We apply the approach to both the Maximum Independent Set Problem and the Maximum Cut Problem. Experimental results on synthetic instances show that the deep reinforcement learning approach, by achieving tighter objective function bounds, generally outperforms ordering methods commonly used in the literature when the distribution of instances is known. To the best knowledge of the authors, this is the first paper to apply machine learning to directly improve relaxation bounds obtained by general-purpose bounding mechanisms for combinatorial optimization problems.

PDF Details