arXiv subjects

Lina Fahed

Publications and source records attributed to Lina Fahed.

3 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↗