arXiv subjects

Romain Billot

Publications and source records attributed to Romain Billot.

8 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.

math.OC↗

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.

math.OC↗

arXiv2025

Hybrid Node-Destroyer Model with Large Neighborhood Search for Solving the Capacitated Vehicle Routing Problem

In this research, we propose an iterative learning hybrid optimization solver developed to strengthen the performance of metaheuristic algorithms in solving the Capacitated Vehicle Routing Problem (CVRP). The iterative hybrid mechanism integrates the proposed Node-Destroyer Model, a machine learning hybrid model that utilized Graph Neural Networks (GNNs) such identifies and selects customer nodes to guide the Large Neighborhood Search (LNS) operator within the metaheuristic optimization frameworks. This model leverages the structural properties of the problem and solution that can be represented as a graph, to guide strategic selections concerning node removal. The proposed approach reduces operational complexity and scales down the search space involved in the optimization process. The hybrid approach is applied specifically to the CVRP and does not require retraining across problem instances of different sizes. The proposed hybrid mechanism is able to improve the performance of baseline metaheuristic algorithms. Our approach not only enhances the solution quality for standard CVRP benchmarks but also proves scalability on very large-scale instances with up to 30,000 customer nodes. Experimental evaluations on benchmark datasets show that the proposed hybrid mechanism is capable of improving different baseline algorithms, achieving better quality of solutions under similar settings.

cs.AI↗

arXiv2025

Edge-Selector Model Applied for Local Search Neighborhood for Solving Vehicle Routing Problems

This research proposes a hybrid Machine Learning and metaheuristic mechanism that is designed to solve Vehicle Routing Problems (VRPs). The main of our method is an edge solution selector model, which classifies solution edges to identify prohibited moves during the local search, hence guiding the search process within metaheuristic baselines. Two learning-based mechanisms are used to develop the edge selector: a simple tabular binary classifier and a Graph Neural Network (GNN). The tabular classifier employs Gradient Boosting Trees and Feedforward Neural Network as the baseline algorithms. Adjustments to the decision threshold are also applied to handle the class imbalance in the problem instance. An alternative mechanism employs the GNN to utilize graph structure for direct solution edge prediction, with the objective of guiding local search by predicting prohibited moves. These hybrid mechanisms are then applied in state-fo-the-art metaheuristic baselines. Our method demonstrates both scalability and generalizability, achieving performance improvements across different baseline metaheuristics, various problem sizes and variants, including the Capacitated Vehicle Routing Problem (CVRP) and CVRP with Time Windows (CVRPTW). Experimental evaluations on benchmark datasets up to 30,000 customer nodes, supported by pair-wise statistical analysis, verify the observed improvements.

cs.LG↗

arXiv2025

Study of Robust Features in Formulating Guidance for Heuristic Algorithms for Solving the Vehicle Routing Problem

The Vehicle Routing Problem (VRP) is a complex optimization problem with numerous real-world applications, mostly solved using metaheuristic algorithms due to its $\mathcal{NP}$-Hard nature. Traditionally, these metaheuristics rely on human-crafted designs developed through empirical studies. However, recent research shows that machine learning methods can be used the structural characteristics of solutions in combinatorial optimization, thereby aiding in designing more efficient algorithms, particularly for solving VRP. Building on this advancement, this study extends the previous research by conducting a sensitivity analysis using multiple classifier models that are capable of predicting the quality of VRP solutions. Hence, by leveraging explainable AI, this research is able to extend the understanding of how these models make decisions. Finally, our findings indicate that while feature importance varies, certain features consistently emerge as strong predictors. Furthermore, we propose a unified framework able of ranking feature impact across different scenarios to illustrate this finding. These insights highlight the potential of feature importance analysis as a foundation for developing a guidance mechanism of metaheuristic algorithms for solving the VRP.

cs.AI↗

arXiv2024

Feature-Guided Metaheuristic with Diversity Management for Solving the Capacitated Vehicle Routing Problem

We propose a feature-based guidance mechanism to enhance metaheuristic algorithms for solving the Capacitated Vehicle Routing Problem (CVRP). This mechanism leverages an Explainable AI (XAI) model to identify features that correlate with high-quality solutions. These insights are used to guide the search process by promoting solution diversity and avoiding premature convergence. The guidance mechanism is first integrated into a custom metaheuristic algorithm, which combines neighborhood search with a novel hybrid of the split algorithm and path relinking. Experiments on benchmark instances with up to $30,000$ customer nodes demonstrate that the guidance significantly improves the performance of this baseline algorithm. Furthermore, we validate the generalizability of the guidance approach by integrating it into a state-of-the-art metaheuristic, where it again yields statistically significant performance gains. These results confirm that the proposed mechanism is both scalable and transferable across algorithmic frameworks.

cs.AI↗

arXiv2018

A clustering approach to infer Wikipedia contributors' profile

In online communities, recent studies have strongly improved our knowledge about the different types or profiles of contributors, from casual to very involved ones, through focused people. However they do so by using very complex methodologies (qualitative-quantitative mix, with a high workload to manually codify/characterize the edits), making their replication for the practitioners limited. These studies are on the English Wikipedia only. The objective of this paper is to highlight different profiles of contributors with clustering techniques. The originality is to show how using only the edits, and their distribution over time, allows to build these contributors profiles with a good accuracy and stability amongst languages. The methodology is validated with both Romanian and Danish wikis. The highlighted profiles are identifiable early in the history of involvement, suggesting that light monitoring of newcomers may be sufficient to adapt the interaction with them and increase the retention rate.

cs.HC↗