arXiv subjects

Christine Solnon

Publications and source records attributed to Christine Solnon.

9 recordsLinked to original sources

arXiv2026

Impact of Scaling and Rounding on Metaheuristic Performance for the Vehicle Routing Problem with Time Windows

Classical Euclidean instances for the Vehicle Routing Problem with Time Windows (VRPTW) have floating-point arc costs derived from node coordinates. This raises reproducibility and numerical consistency issues. Hence, a common practice is to scale and round data to integer values, yet the impact of these choices is poorly understood. This paper studies the effect of integer scaling by a factor P and compares three rounding schemes with distinct feasibility and optimality guarantees. We analyze how scaling and rounding influence empirical performance of two well-known VRPTW solvers: Hybrid Genetic Search (HGS) and OR-Tools. We evaluate the quality of solutions mapped back to the original floating-point instances. Our results show that scaling and rounding can significantly affect both solver performance and solution quality. Based on these findings, we provide practical recommendations for scaling and rounding in VRPTW benchmarks to improve efficiency, robustness and reproducibility.

math.OC↗

arXiv2026

Randomized Constructive Heuristics for the VRPTW: A Focus on Regret-k

The Vehicle Routing Problem with Time Windows (VRPTW) requires a fleet of capacitated vehicles to serve customers within strict time windows while minimizing total travel time. Constructive heuristics are fundamental for generating solutions and commonly serve as starting points for metaheuristics such as Iterated Local Search (ILS), Genetic Algorithms, and Ant Colony Optimization (ACO). This work studies three classical constructive heuristics - Nearest Neighbor, Best Insertion, and Regret-k - within a randomized, multi-start framework, a setting that remains largely under-explored despite their well-established deterministic use. We address how to effectively randomize these heuristics and, in particular, propose a novel randomization of Regret-k by separating the ''who'' (which customer to insert next) and ''where'' (insertion position) decisions, applying a probabilistic selection proportional to the regret value to preserve the heuristic's foresight while injecting the diversity needed for a multi-start approach. We further study the impact of combining these greedy randomized constructions with Local Search and ACO. Experiments follow the DIMACS 2021 conventions (integer, truncated Euclidean distances) on the Solomon and Gehring \& Homberger benchmarks (100--1000 customers), comparing against the Best-Known Solutions and the state-of-the-art Hybrid Genetic Search solver, with all critical components implemented in modern C++ and bound to Python via pybind11. To the best of our knowledge, the randomization of Regret-k has never been examined; our analysis highlights the trade-off between solution quality and computational cost, providing a preliminary step toward hybrid methods (ACO, ILS, Branch-and-Price) for the Time-Dependent VRPTW within the MAMUT project.

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arXiv2026

Branch \& Price \& Cut for the Time-Dependent Vehicle Routing Problem with Time Windows (TDVRPTW)

In urban contexts, travel times vary strongly with the time of day and traffic conditions. The Time-Dependent Vehicle Routing Problem with Time Windows (TDVRPTW) extends the classical VRPTW by making travel times depend on departure time, with the objective of minimizing the total travel time of at most $k$ vehicle routes serving customers within strict time windows. Exact resolution of this realistic yet understudied problem currently relies on the Branch \& Price approach of Dabia et al. (2013), in which a Column Generation scheme decomposes the problem into a set-partitioning master problem and a resource-constrained shortest-path pricing problem solved by dynamic programming. This work, conducted within the MAMUT project (Machine Learning and Matheuristics for Urban Transport), aims to advance the state of the art for the exact and explainable resolution of the TDVRPTW. We propose to reimplement and revisit the pioneering Branch \& Price algorithm by transferring recent advances made on the single-vehicle variant (TDTSPTW) to the multi-vehicle setting, notably an exact anytime extension of A* and a Large Neighborhood Search guided by dynamic programming for the pricing sub-problem. We further explore the integration of data mining and machine learning to guide column generation by exploiting knowledge from previously computed routes. The goal is a high-performance and interpretable solver that meets the requirements of real-world urban transport while preserving guarantees on solution quality.

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arXiv2026

Decompose, Optimize, and Reconstruct: Very Large Constant Multiplication at Scale

Efficient arithmetic circuit design for resourceconstrained hardware involves challenging combinatorial optimization problems, among which Multiple Constant Multiplication (MCM) is a prominent example. MCM aims at implementing multiplications by fixed integer constants using bit-shifts and additions/subtractions but optimal methods are typically limited to moderately-sized constants, e.g. 12 bits. For practical applications targeting larger precision, Very large Constant Multiplication (VLCM) is solved instead. Existing approaches typically address VLCM through a heuristic flow that decomposes large constants into patterns, applies MCM optimization techniques on moderately-sized targets, and reconstructs the final result. This paper proposes multiple improvements to this flow: new declarative optimization models for the pattern selection and for the reconstruction, as well as applying recent optimal MCM models. The cornerstones of the obtained improvements are (i) allowing the patterns to overlap, minimising the number of unique target constants for the MCM step and (ii) performing the reconstruction step optimally, instead of heuristically. In addition, we propose a globally-optimal VLCM approach and characterize its limits. We employ a mix of constraint programming and SAT to solve each step. Experimental results on synthetic and real-life signal processing and cryptographic benchmarks, with coefficient word lengths ranging from tens to thousands of bits, demonstrate that the proposed approach scales to very large precisions and consistently outperforms existing baselines.

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arXiv2025

Integrating ethical, societal and environmental issues into algorithm design courses

This document, intended for computer science teachers, describes a case study that puts into practice a questioning of ethical, societal and environmental issues when designing or implementing a decision support system. This study is based on a very popular application, namely road navigation software that informs users of real-time traffic conditions and suggests routes between a starting point and a destination, taking these conditions into account (such as Waze). The approach proposes to intertwine technical considerations (optimal path algorithms, data needed for location, etc.) with a broader view of the ethical, environmental and societal issues raised by the tools studied. Based on the authors' experience conducting sessions with students over several years, this document discusses the context of such a study, suggests teaching resources for implementing it, describes ways to structure discussions, and shares scenarios in different teaching contexts.

math.OC↗

arXiv2019

Progressive Focus Search for the Static and Stochastic VRPTW with both Random Customers and Reveal Times

Static stochastic VRPs aim at modeling real-life VRPs by considering uncertainty on data. In particular, the SS-VRPTW-CR considers stochastic customers with time windows and does not make any assumption on their reveal times, which are stochastic as well. Based on customer request probabilities, we look for an a priori solution composed preventive vehicle routes, minimizing the expected number of unsatisfied customer requests at the end of the day. A route describes a sequence of strategic vehicle relocations, from which nearby requests can be rapidly reached. Instead of reoptimizing online, a so-called recourse strategy defines the way the requests are handled, whenever they appear. In this paper, we describe a new recourse strategy for the SS-VRPTW-CR, improving vehicle routes by skipping useless parts. We show how to compute the expected cost of a priori solutions, in pseudo-polynomial time, for this recourse strategy. We introduce a new meta-heuristic, called Progressive Focus Search (PFS), which may be combined with any local-search based algorithm for solving static stochastic optimization problems. PFS accelerates the search by using approximation factors: from an initial rough simplified problem, the search progressively focuses to the actual problem description. We evaluate our contributions on a new, real-world based, public benchmark.

cs.AI↗

arXiv2017

The Static and Stochastic VRPTW with both random Customers and Reveal Times: algorithms and recourse strategies

Unlike its deterministic counterpart, static and stochastic vehicle routing problems (SS-VRP) aim at modeling and solving real-life operational problems by considering uncertainty on data. We consider the SS-VRPTW-CR introduced in Saint-Guillain et al. (2017). Like the SS-VRP introduced by Bertsimas (1992), we search for optimal first stage routes for a fleet of vehicles to handle a set of stochastic customer demands, i.e., demands are uncertain and we only know their probabilities. In addition to capacity constraints, customer demands are also constrained by time windows. Unlike all SS-VRP variants, the SS-VRPTW-CR does not make any assumption on the time at which a stochastic demand is revealed, i.e., the reveal time is stochastic as well. To handle this new problem, we introduce waiting locations: Each vehicle is assigned a sequence of waiting locations from which it may serve some associated demands, and the objective is to minimize the expected number of demands that cannot be satisfied in time. In this paper, we propose two new recourse strategies for the SS-VRPTW-CR, together with their closed-form expressions for efficiently computing their expectations: The first one allows us to take vehicle capacities into account; The second one allows us to optimize routes by avoiding some useless trips. We propose two algorithms for searching for routes with optimal expected costs: The first one is an extended branch-and-cut algorithm, based on a stochastic integer formulation, and the second one is a local search based heuristic method. We also introduce a new public benchmark for the SS-VRPTW-CR, based on real-world data coming from the city of Lyon. We evaluate our two algorithms on this benchmark and empirically demonstrate the expected superiority of the SS-VRPTW-CR anticipative actions over a basic "wait-and-serve" policy.

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arXiv2015

A Multistage Stochastic Programming Approach to the Dynamic and Stochastic VRPTW - Extended version

We consider a dynamic vehicle routing problem with time windows and stochastic customers (DS-VRPTW), such that customers may request for services as vehicles have already started their tours. To solve this problem, the goal is to provide a decision rule for choosing, at each time step, the next action to perform in light of known requests and probabilistic knowledge on requests likelihood. We introduce a new decision rule, called Global Stochastic Assessment (GSA) rule for the DS-VRPTW, and we compare it with existing decision rules, such as MSA. In particular, we show that GSA fully integrates nonanticipativity constraints so that it leads to better decisions in our stochastic context. We describe a new heuristic approach for efficiently approximating our GSA rule. We introduce a new waiting strategy. Experiments on dynamic and stochastic benchmarks, which include instances of different degrees of dynamism, show that not only our approach is competitive with state-of-the-art methods, but also enables to compute meaningful offline solutions to fully dynamic problems where absolutely no a priori customer request is provided.

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arXiv2009

Proceedings 6th International Workshop on Local Search Techniques in Constraint Satisfaction

LSCS is a satellite workshop of the international conference on principles and practice of Constraint Programming (CP), since 2004. It is devoted to local search techniques in constraint satisfaction, and focuses on all aspects of local search techniques, including: design and implementation of new algorithms, hybrid stochastic-systematic search, reactive search optimization, adaptive search, modeling for local-search, global constraints, flexibility and robustness, learning methods, and specific applications.

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