arXiv subjects

Léo Baty

Publications and source records attributed to Léo Baty.

4 recordsLinked to original sources

arXiv2026

Managing delay in tail assignment: from minimum turn time to stochastic routing at Air France

On-time performance is a critical challenge in the airline industry, leading to large operational and customer dissatisfaction costs. The tail assignment problem builds the sequences of flights or routes followed by individual airplanes. While airlines cannot avoid some sources of delay, choosing routes wisely limits propagation along these. This paper addresses the stochastic tail assignment problem at Air France. We propose a column generation approach for this problem. The key ingredient is the pricing algorithm, which is a stochastic shortest path problem. We use dedicated bounds to discard paths in an enumeration algorithm, and introduce new bounds based on a lattice ordering of the set of piecewise linear convex functions to strike a balance between bounds quality and computational cost. A diving heuristic enables us to retrieve integer solutions. Numerical experiments on real-world Air France instances demonstrate that our algorithms lead to an average 0.28% optimality gap on instances with up to 600 flight legs in a few hours of computing time. The resulting solutions effectively balance operational costs and delay resilience, outperforming previous approaches based on minimum turn time.

math.OC↗

arXiv2025

Structured Reinforcement Learning for Combinatorial Decision-Making

Reinforcement learning (RL) is increasingly applied to real-world problems involving complex and structured decisions, such as routing, scheduling, and assortment planning. These settings challenge standard RL algorithms, which struggle to scale, generalize, and exploit structure in the presence of combinatorial action spaces. We propose Structured Reinforcement Learning (SRL), a novel actor-critic paradigm that embeds combinatorial optimization-layers into the actor neural network. We enable end-to-end learning of the actor via Fenchel-Young losses and provide a geometric interpretation of SRL as a primal-dual algorithm in the dual of the moment polytope. Across six environments with exogenous and endogenous uncertainty, SRL matches or surpasses the performance of unstructured RL and imitation learning on static tasks and improves over these baselines by up to 92% on dynamic problems, with improved stability and convergence speed.

cs.LG↗

arXiv2023

Combinatorial Optimization enriched Machine Learning to solve the Dynamic Vehicle Routing Problem with Time Windows

With the rise of e-commerce and increasing customer requirements, logistics service providers face a new complexity in their daily planning, mainly due to efficiently handling same day deliveries. Existing multi-stage stochastic optimization approaches that allow to solve the underlying dynamic vehicle routing problem are either computationally too expensive for an application in online settings, or -- in the case of reinforcement learning -- struggle to perform well on high-dimensional combinatorial problems. To mitigate these drawbacks, we propose a novel machine learning pipeline that incorporates a combinatorial optimization layer. We apply this general pipeline to a dynamic vehicle routing problem with dispatching waves, which was recently promoted in the EURO Meets NeurIPS Vehicle Routing Competition at NeurIPS 2022. Our methodology ranked first in this competition, outperforming all other approaches in solving the proposed dynamic vehicle routing problem. With this work, we provide a comprehensive numerical study that further highlights the efficacy and benefits of the proposed pipeline beyond the results achieved in the competition, e.g., by showcasing the robustness of the encoded policy against unseen instances and scenarios.

math.OC↗

arXiv2022

Learning with Combinatorial Optimization Layers: a Probabilistic Approach

Combinatorial optimization (CO) layers in machine learning (ML) pipelines are a powerful tool to tackle data-driven decision tasks, but they come with two main challenges. First, the solution of a CO problem often behaves as a piecewise constant function of its objective parameters. Given that ML pipelines are typically trained using stochastic gradient descent, the absence of slope information is very detrimental. Second, standard ML losses do not work well in combinatorial settings. A growing body of research addresses these challenges through diverse methods. Unfortunately, the lack of well-maintained implementations slows down the adoption of CO layers. In this paper, building upon previous works, we introduce a probabilistic perspective on CO layers, which lends itself naturally to approximate differentiation and the construction of structured losses. We recover many approaches from the literature as special cases, and we also derive new ones. Based on this unifying perspective, we present InferOpt.jl, an open-source Julia package that 1) allows turning any CO oracle with a linear objective into a differentiable layer, and 2) defines adequate losses to train pipelines containing such layers. Our library works with arbitrary optimization algorithms, and it is fully compatible with Julia's ML ecosystem. We demonstrate its abilities using a pathfinding problem on video game maps as guiding example, as well as three other applications from operations research.

stat.ML↗