In this paper we address the Distance-Constrained Capacitated Vehicle Routing Problem (DCVRP), where k minimum-cost routes through a central depot have to be constructed so as to cover all customers while satisfying, for each route, both a capacity and a total-distance-travelled limit. Our starting point is the following refinement procedure proposed in 1981 by Sarvanov and Doroshko for the pure Travelling Salesman Problem (TSP): given a starting tour, (a) remove all the nodes in even position, thus leaving an equal number of “empty holes” in the tour; (b) optimally re-assign the removed nodes to the empty holes through the efficient solution of a min-sum assignment (weighted bipartite matching) problem. We first extend the Sarvanov-Doroshko method to DCVRP, and then generalize it. Our generalization involves a procedure to generate a large number of new sequences through the extracted nodes, as well as a more sophisticated ILP model for the reallocation of some of these sequences. An important feature of our method is that it does not rely on any specialized ILP code, as any general-purpose ILP solver can be used to solve the reallocation model. We report computational results on a large set of capacitatedVRP instances from the literature (with symmetric/ asymmetric costs and with/without distance constraints), along with an analysis of the performance of the new method and of its features. Interestingly, in 13 cases the new method was able to improve the best-know solution available from the literature.

A new ILP-based refinement heuristic for Vehicle Routing Problems

FISCHETTI, MATTEO;
2006

Abstract

In this paper we address the Distance-Constrained Capacitated Vehicle Routing Problem (DCVRP), where k minimum-cost routes through a central depot have to be constructed so as to cover all customers while satisfying, for each route, both a capacity and a total-distance-travelled limit. Our starting point is the following refinement procedure proposed in 1981 by Sarvanov and Doroshko for the pure Travelling Salesman Problem (TSP): given a starting tour, (a) remove all the nodes in even position, thus leaving an equal number of “empty holes” in the tour; (b) optimally re-assign the removed nodes to the empty holes through the efficient solution of a min-sum assignment (weighted bipartite matching) problem. We first extend the Sarvanov-Doroshko method to DCVRP, and then generalize it. Our generalization involves a procedure to generate a large number of new sequences through the extracted nodes, as well as a more sophisticated ILP model for the reallocation of some of these sequences. An important feature of our method is that it does not rely on any specialized ILP code, as any general-purpose ILP solver can be used to solve the reallocation model. We report computational results on a large set of capacitatedVRP instances from the literature (with symmetric/ asymmetric costs and with/without distance constraints), along with an analysis of the performance of the new method and of its features. Interestingly, in 13 cases the new method was able to improve the best-know solution available from the literature.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/1562232
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 86
  • ???jsp.display-item.citation.isi??? 73
social impact