A memetic algorithm for the vehicle routing problem with time windows

Abstract

This article deals with the vehicle routing problem with time windows (VRPTW). This problem consists in determining a leastcost set of trips to serve customers during specific time windows. The proposed solution method is a memetic algorithm (MA), a genetic algorithm hybridised with a local search. Contrary to most papers on the VRPTW, which minimize first the number of vehicles, our method is also able to minimize the total distance travelled. The results on 56 classical instances are compared to those of the best metaheuristics. The efficiency of the MA is similar for the classical criterion, but it becomes the best algorithm available for the total distance, being much faster and improving 20 best-known solutions. Résumé. Cet article concerne le problème de tournées de véhicules avec fenêtres horaires (Vehicle Routing Problem with Time Windows ou VRPTW). Ce problème consisteà déterminer un ensemble de tournées de coût total minimal pour servir des clients dans des fenêtres horaires spécifiques. Nous proposons un algorithme mémétique (MA, algorithme génétique hybridé avec une recherche locale) pour le résoudre. Contrairementà la plupart des articles sur le VRPTW, qui minimisent en priorité le nombre de véhicules, notre méthode peut aussi minimiser la distance totale parcourue. Les résultats sur 56 problèmes-tests classiques sont comparésà ceux des meilleures métaheuristiques. Pour le critère classique, le MA offre des performances similaires, mais il devient le meilleur algorithme disponible pour la distance totale, enétant bien plus rapide et en améliorant 20 des meilleures solutions connues.

A matheuristic approach for the Pollution-Routing Problem

“…Table 5 reports the results obtained when using "double" precision distances. In both cases, ILS-SP solutions are compared with those of the current state-of-the-art approaches that use the same rounding conventions Labadi et al, 2008;Demir et al, 2012;Muter et al, 2010), and the best solutions are highlighted in boldface. The last lines of the tables report the average CPU time per run and per instance (the total time for methods that report the best solutions must thus be multiplied by the number of runs), and the type of processor used during the tests.…”

“…Comparison with the tabu search ofAlvarenga et al (2007), the MA ofLabadi et al (2008), and MetaOpt ofMuter et al (2010).…”

Memetic Algorithm for two-dimensional loading capacitated vehicle routing problem with time windows

“…An optimal splitting procedure (Split) is used to compute the best solution of the problem with respect to the sequence given by S, the capacity of vehicles, time windows and loading constraint. The Split procedure initially developed by Prins [19] for the VRP and extended to the VRPTW by Labadi et al [12] is used in our algorithm by including the loading constraint. The Split procedure computes a shortest path in an auxiliary graph using a version of Bellman's algorithm.…”

“…As in Labadi et al [12], two parents are chosen using the binary tournament. We select randomly two chromosomes from the population and keep the best one as the first parent.…”

“…In transportation it is often necessary to handle rectangular-shaped items that cannot be stacked one on the top of the other because of their fragility, weight or large dimensions. The objective of 2L-CVRPTW is to determine a set of minimum cost trips that satisfies the following constraints : [12] proposed a memetic algorithm for the VRPTW taking into account both objectives : minimization of the number of vehicle and the total travelled distance. This paper is organized as follow : Section 2 describes this new problem and introduces the notations.…”