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Louis-Martin Rousseau

Publications and source records attributed to Louis-Martin Rousseau.

At least 19 recordsLinked to original sources
arXiv2026

Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition

Decision-focused learning has shown great promise for addressing predict-then-optimize problems, particularly in the presence of under-specified models. However, its practical deployment is often hindered by high computational costs and limited scalability, as it requires solving a constrained optimization problem for each training instance at every iteration. To address these challenges, we propose a novel framework that incorporates Lagrangian decomposition into the decision-focused learning paradigm. Specifically, we introduce a new surrogate objective along with two loss functions for evaluating and training the underlying prediction model. We further propose two variants of our approach, which offer different trade-offs between computational efficiency and solution quality. Our framework can be seamlessly integrated with standard decision-focused learning methods, including Smart Predict-then-Optimize (SPO+) and Implicit Maximum Likelihood Estimation (IMLE). Through experiments on two standard benchmarks, the multi-dimensional knapsack problem and quadratic portfolio optimization, we demonstrate that our approach achieves competitive performance while remaining amenable to parallelization. In particular, it consistently outperforms traditional decision-focused learning methods on large-scale instances, involving up to eight times more variables than those typically considered in related work. The implementation is available at https://github.com/corail-research/DFL-LD.

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arXiv2026

Imitation Learning for Combinatorial Optimisation under Uncertainty

Imitation learning (IL) provides a data-driven framework for approximating policies for large-scale combinatorial optimisation problems formulated as sequential decision problems (SDPs), where exact solution methods are computationally intractable. A central but underexplored aspect of IL in this context is the role of the \emph{expert} that generates training demonstrations. Existing studies employ a wide range of expert constructions, yet lack a unifying framework to characterise their modelling assumptions, computational properties, and impact on learning performance. This paper introduces a systematic taxonomy of experts for imitation learning in combinatorial optimisation under uncertainty. The literature is classified along three principal dimensions: (i) treatment of uncertainty; (ii) level of optimality, distinguishing task-optimal and approximate experts; and (iii) interaction mode with the learner, ranging from one-shot supervision to iterative, interactive schemes. We further identify additional categories capturing other relevant expert characteristics. Building on this taxonomy, we propose a generalised Dataset Aggregation (DAgger) framework that accommodates multiple expert queries, expert aggregation, and flexible interaction strategies. The proposed framework is evaluated on a dynamic physician-to-patient assignment problem with stochastic arrivals and capacity constraints. Computational experiments compare learning outcomes across expert types and interaction regimes. The results show that policies learned from stochastic experts consistently outperform those learned from deterministic or full-information experts, while interactive learning improves solution quality using fewer expert demonstrations. Aggregated deterministic experts provide an effective alternative when stochastic optimisation becomes computationally challenging.

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arXiv2026

Implicit Decision Diagrams

Decision Diagrams (DDs) have emerged as a powerful tool for discrete optimization, with rapidly growing adoption. DDs are directed acyclic layered graphs; restricted DDs are a generalized greedy heuristic for finding feasible solutions, and relaxed DDs compute combinatorial relaxed bounds. There is substantial theory that leverages DD-based bounding, yet the complexity of constructing the DDs themselves has received little attention. Standard restricted DD construction requires $O(w \log(w))$ per layer; standard relaxed DD construction requires $O(w^2)$, where $w$ is the width of the DD. Increasing $w$ improves bound quality at the cost of more time and memory. We introduce implicit Decision Diagrams, storing arcs implicitly rather than explicitly, and reducing per-layer complexity to $O(w)$ for restricted and relaxed DDs. We prove this is optimal: any framework treating state-update and merge operations as black boxes cannot do better. Optimal complexity shifts the challenge from algorithmic overhead to low-level engineering. We show how implicit DDs can drive a MIP solver, and release ImplicitDDs, an open-source Julia solver exploiting the implementation refinements our theory enables. Experiments demonstrate the solver outperforms Gurobi on Subset Sum. Code (https://github.com/IsaacRudich/ImplicitDDs.jl)

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arXiv2025

Notification Timing for On-Demand Personnel Scheduling

Modern business models have enabled service systems to leverage a large pool of casual employees with flexible hours, paid based on piece rates, to fulfill on-demand work. These systems have been successfully implemented in sectors such as ride-sharing, delivery services, and microtasks. However, because casual employees engage infrequently and may lack experience, maintaining service quality remains a key challenge. We introduce a novel scheduling system designed to provide experienced casual employees to service companies, optimizing their operations through a dynamic, data-driven approach. Similar to traditional on-call systems, it contacts casual personnel in order of seniority to inform them about available work. However, our system offers greater flexibility, allowing employees to take time to decide and freely select from available shifts. Senior employees can also replace (bump) junior employees from the schedule if no other preferred shift is available, subject to certain conditions. While permitted, these replacements create disruptions and dissatisfaction among employees. The management aims to efficiently assign all shifts while minimizing bumps. However, uncertainty arises regarding when an employee will select a shift. The key challenge is determining the optimal timing to notify employees to reduce disruptions. We first establish that this problem is $\mathcal{NP}$-complete even with perfect information. To address this, we propose a two-stage stochastic formulation for the dynamic problem and develop a heuristic algorithm that approximates the optimal policy using a threshold-based structure. These policies are fine-tuned using offline solutions with pre-known uncertainty, allowing for optimization. Testing on real-world data demonstrates that our approach outperforms the current strategy used by our industry partner.

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arXiv2025

Chance-constrained battery management strategies for the electric bus scheduling problem

The global transition to battery electric buses (EBs) presents an opportunity to reduce air and noise pollution in urban areas. However, the adoption of EBs introduces challenges related to limited driving range, extended charging times, and battery degradation. This study addresses these challenges by proposing a novel chance-constrained model for the electric vehicle scheduling problem (E-VSP) that accounts for stochastic energy consumption and battery degradation. The model ensures compliance with recommended state-of-charge (SoC) ranges while optimizing operational costs. A tailored branch-and-price heuristic with stochastic pricing problems is developed. Computational experiments on realistic instances demonstrate that the stochastic approach can provide win-win solutions compared to deterministic baselines in terms of operational costs and battery wear. By limiting the probability of operating EBs outside the recommended SoC range, the proposed framework supports fleet management practices that align with battery leasing company and manufacturer guidelines for battery health and longevity.

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arXiv2024

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

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. To our knowledge, this work presents the first generic method for learning valid dual bounds in constraint programming.

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arXiv2024

An Exact Framework for Solving the Space-Time Dependent TSP

Many real-world scenarios involve solving bi-level optimization problems in which there is an outer discrete optimization problem, and an inner problem involving expensive or black-box computation. This arises in space-time dependent variants of the Traveling Salesman Problem, such as when planning space missions that visit multiple astronomical objects. Planning these missions presents significant challenges due to the constant relative motion of the objects involved. There is an outer combinatorial problem of finding the optimal order to visit the objects and an inner optimization problem that requires finding the optimal departure time and trajectory to travel between each pair of objects. The constant motion of the objects complicates the inner problem, making it computationally expensive. This paper introduces a novel framework utilizing decision diagrams (DDs) and a DD-based branch-and-bound technique, Peel-and-Bound, to achieve exact solutions for such bi-level optimization problems, assuming sufficient inner problem optimizer quality. The framework leverages problem-specific knowledge to expedite search processes and minimize the number of expensive evaluations required. As a case study, we apply this framework to the Asteroid Routing Problem (ARP), a benchmark problem in global trajectory optimization. Experimental results demonstrate the framework's scalability and ability to generate robust heuristic solutions for ARP instances. Many of these solutions are exact, contingent on the assumed quality of the inner problem's optimizer.

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arXiv2023

Learning Lagrangian Multipliers for the Travelling Salesman Problem

Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient propagators in constraint programming (such as the weighted circuit constraint). However, the conventional process of deriving Lagrangian multipliers (e.g., using subgradient methods) is often computationally intensive, limiting its practicality for large-scale or time-sensitive problems. To address this challenge, we propose an innovative unsupervised learning approach that harnesses the capabilities of graph neural networks to exploit the problem structure, aiming to generate accurate Lagrangian multipliers efficiently. We apply this technique to the well-known Held-Karp Lagrangian relaxation for the travelling salesman problem. The core idea is to predict accurate Lagrangian multipliers and to employ them as a warm start for generating Held-Karp relaxation bounds. These bounds are subsequently utilized to enhance the filtering process carried out by branch-and-bound algorithms. In contrast to much of the existing literature, which primarily focuses on finding feasible solutions, our approach operates on the dual side, demonstrating that learning can also accelerate the proof of optimality. We conduct experiments across various distributions of the metric travelling salesman problem, considering instances with up to 200 cities. The results illustrate that our approach can improve the filtering level of the weighted circuit global constraint, reduce the optimality gap by a factor two for unsolved instances up to a timeout, and reduce the execution time for solved instances by 10%.

cs.AI↗
arXiv2023

Learning a Generic Value-Selection Heuristic Inside a Constraint Programming Solver

Constraint programming is known for being an efficient approach for solving combinatorial problems. Important design choices in a solver are the branching heuristics, which are designed to lead the search to the best solutions in a minimum amount of time. However, developing these heuristics is a time-consuming process that requires problem-specific expertise. This observation has motivated many efforts to use machine learning to automatically learn efficient heuristics without expert intervention. To the best of our knowledge, it is still an open research question. Although several generic variable-selection heuristics are available in the literature, the options for a generic value-selection heuristic are more scarce. In this paper, we propose to tackle this issue by introducing a generic learning procedure that can be used to obtain a value-selection heuristic inside a constraint programming solver. This has been achieved thanks to the combination of a deep Q-learning algorithm, a tailored reward signal, and a heterogeneous graph neural network architecture. Experiments on graph coloring, maximum independent set, and maximum cut problems show that our framework is able to find better solutions close to optimality without requiring a large amounts of backtracks while being generic.

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arXiv2023

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

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.

math.OC↗
arXiv2022

A prediction-based approach for online dynamic patient scheduling: a case study in radiotherapy treatment

Patient scheduling is a difficult task involving stochastic factors such as the unknown arrival times of patients. Similarly, the scheduling of radiotherapy for cancer treatments needs to handle patients with different urgency levels when allocating resources. High priority patients may arrive at any time, and there must be resources available to accommodate them. A common solution is to reserve a flat percentage of treatment capacity for emergency patients. However, this solution can result in overdue treatments for urgent patients, a failure to fully exploit treatment capacity, and delayed treatments for low-priority patients. This problem is especially severe in large and crowded hospitals. In this paper, we propose a prediction-based approach for online dynamic radiotherapy scheduling that dynamically adapts the present scheduling decision based on each incoming patient and the current allocation of resources. Our approach is based on a regression model trained to recognize the links between patients' arrival patterns, and their ideal waiting time in optimal offline solutions where all future arrivals are known in advance. When our prediction-based approach is compared to flat-reservation policies, it does a better job of preventing overdue treatments for emergency patients, while also maintaining comparable waiting times for the other patients. We also demonstrate how our proposed approach supports explainability and interpretability in scheduling decisions using SHAP values.

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arXiv2022

Learning the Travelling Salesperson Problem Requires Rethinking Generalization

End-to-end training of neural network solvers for graph combinatorial optimization problems such as the Travelling Salesperson Problem (TSP) have seen a surge of interest recently, but remain intractable and inefficient beyond graphs with few hundreds of nodes. While state-of-the-art learning-driven approaches for TSP perform closely to classical solvers when trained on trivially small sizes, they are unable to generalize the learnt policy to larger instances at practical scales. This work presents an end-to-end neural combinatorial optimization pipeline that unifies several recent papers in order to identify the inductive biases, model architectures and learning algorithms that promote generalization to instances larger than those seen in training. Our controlled experiments provide the first principled investigation into such zero-shot generalization, revealing that extrapolating beyond training data requires rethinking the neural combinatorial optimization pipeline, from network layers and learning paradigms to evaluation protocols. Additionally, we analyze recent advances in deep learning for routing problems through the lens of our pipeline and provide new directions to stimulate future research.

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arXiv2022

Peel-and-Bound: Generating Stronger Relaxed Bounds with Multivalued Decision Diagrams

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. We present 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 test 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.

math.OC↗
arXiv2021

Supervised learning and tree search for real-time storage allocation in Robotic Mobile Fulfillment Systems

A Robotic Mobile Fulfillment System is a robotised parts-to-picker system that is particularly well-suited for e-commerce warehousing. One distinguishing feature of this type of warehouse is its high storage modularity. Numerous robots are moving shelves simultaneously, and the shelves can be returned to any open location after the picking operation is completed. This work focuses on the real-time storage allocation problem to minimise the travel time of the robots. An efficient -- but computationally costly -- Monte Carlo Tree Search method is used offline to generate high-quality experience. This experience can be learned by a neural network with a proper coordinates-based features representation. The obtained neural network is used as an action predictor in several new storage policies, either as-is or in rollout and supervised tree search strategies. Resulting performance levels depend on the computing time available at a decision step and are consistently better compared to real-time decision rules from the literature.

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arXiv2021

SeaPearl: A Constraint Programming Solver guided by Reinforcement Learning

The design of efficient and generic algorithms for solving combinatorial optimization problems has been an active field of research for many years. Standard exact solving approaches are based on a clever and complete enumeration of the solution set. A critical and non-trivial design choice with such methods is the branching strategy, directing how the search is performed. The last decade has shown an increasing interest in the design of machine learning-based heuristics to solve combinatorial optimization problems. The goal is to leverage knowledge from historical data to solve similar new instances of a problem. Used alone, such heuristics are only able to provide approximate solutions efficiently, but cannot prove optimality nor bounds on their solution. Recent works have shown that reinforcement learning can be successfully used for driving the search phase of constraint programming (CP) solvers. However, it has also been shown that this hybridization is challenging to build, as standard CP frameworks do not natively include machine learning mechanisms, leading to some sources of inefficiencies. This paper presents the proof of concept for SeaPearl, a new CP solver implemented in Julia, that supports machine learning routines in order to learn branching decisions using reinforcement learning. Support for modeling the learning component is also provided. We illustrate the modeling and solution performance of this new solver on two problems. Although not yet competitive with industrial solvers, SeaPearl aims to provide a flexible and open-source framework in order to facilitate future research in the hybridization of constraint programming and machine learning.

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arXiv2021

Predicting the probability distribution of bus travel time to move towards reliable planning of public transport services

An important aspect of the quality of a public transport service is its reliability, which is defined as the invariability of the service attributes. Preventive measures taken during planning can reduce risks of unreliability throughout operations. In order to tackle reliability during the service planning phase, a key piece of information is the long-term prediction of the density of the travel time, which conveys the uncertainty of travel times. We introduce a reliable approach to one of the problems of service planning in public transport, namely the Multiple Depot Vehicle Scheduling Problem (MDVSP), which takes as input a set of trips and the probability density function (p.d.f.) of the travel time of each trip in order to output delay-tolerant vehicle schedules. This work empirically compares probabilistic models for the prediction of the conditional p.d.f. of the travel time, as a first step towards reliable MDVSP solutions. Two types of probabilistic models, namely similarity-based density estimation models and a smoothed Logistic Regression for probabilistic classification model, are compared on a dataset of more than 41,000 trips and 50 bus routes of the city of Montréal. The result of a vast majority of probabilistic models outperforms that of a Random Forests model, which is not inherently probabilistic, thus highlighting the added value of modeling the conditional p.d.f. of the travel time with probabilistic models. A similarity-based density estimation model using a $k$ Nearest Neighbors method and a Kernel Density Estimation predicted the best estimate of the true conditional p.d.f. on this dataset.

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arXiv2021

E-commerce warehousing: learning a storage policy

E-commerce with major online retailers is changing the way people consume. The goal of increasing delivery speed while remaining cost-effective poses significant new challenges for supply chains as they race to satisfy the growing and fast-changing demand. In this paper, we consider a warehouse with a Robotic Mobile Fulfillment System (RMFS), in which a fleet of robots stores and retrieves shelves of items and brings them to human pickers. To adapt to changing demand, uncertainty, and differentiated service (e.g., prime vs. regular), one can dynamically modify the storage allocation of a shelf. The objective is to define a dynamic storage policy to minimise the average cycle time used by the robots to fulfil requests. We propose formulating this system as a Partially Observable Markov Decision Process, and using a Deep Q-learning agent from Reinforcement Learning, to learn an efficient real-time storage policy that leverages repeated experiences and insightful forecasts using simulations. Additionally, we develop a rollout strategy to enhance our method by leveraging more information available at a given time step. Using simulations to compare our method to traditional storage rules used in the industry showed preliminary results up to 14\% better in terms of travelling times.

math.OC↗
arXiv2020

Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization

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 two shortcomings: (1) they mainly focus on the standard travelling salesman problem and they cannot be easily extended to other problems, and (2) 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 two challenging problems: the traveling salesman problem with time windows, and the 4-moments portfolio optimization problem. Results obtained show that the framework introduced outperforms the stand-alone RL and CP solutions, while being competitive with industrial solvers.

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