A multistart heuristic for the equality generalized traveling salesman problem

Abstract

We study the equality generalized traveling salesman problem (E-GTSP), which is a variant of the well-known traveling salesman problem. We are given an undirected graph G = (V , E ), with set of vertices V and set of edges E , each with an associated cost. The set of vertices is partitioned into clusters. E-GTSP is to find an elementary cycle visiting exactly one vertex for each cluster and minimizing the sum of the costs of the traveled edges. We propose a multistart heuristic, which iteratively starts with a randomly chosen set of vertices and applies a decomposition approach combined with improvement procedures. The decomposition approach considers a first phase to determine the visiting order of the clusters and a second phase to find the corresponding minimum cost cycle. We show the effectiveness of the proposed approach on benchmark instances from the literature. On small instances, the heuristic always identifies the optimal solution rapidly and outperforms all known heuristics; on larger instances, the heuristic always improves, in comparable computing times, the best known solution values obtained by the genetic algorithm recently proposed by Silberholz and Golden.

A Unifying Survey of Agent-Based Approaches for Equality-Generalized Traveling Salesman Problem

“…The studied techniques for solving GTSP could be also involved with success for solving other real-life problem based on large-scale graph representation, complex network or for example on improving classification techniques (Parpinelli et al, 2002;Stoean et al, 2009), on large graphs representations (Jancauskas et al, 2012). They are already used for vehicle routing problem (Pintea et al, 2011;Pop et al, 2009), the Generalized Covering Salesman Problem and compared with other existing techniques (Cacchiani et al, 2011;Karapetyan and Gutin, 2012).…”

“…Several approaches for solving the GTSP in a relatively short period of time, were considered. In Fischetti et al (2002a) a branch-and-cut algorithm for Symmetric GTSP is described and analyzed and in Cacchiani et al (2011) it is proposed a multistart heuristic with a decomposition approach combined with improvement procedures. In Renaud and Boctor (1998) it is proposed an efficient composite heuristic for the Symmetric GTSP including insertion of a node from each non-visited node-subset.…”

On the generalized directed rural postman problem

“…[8], Cacchiani et al [12]) to solve GDRPPs. To this end, the memetic algorithm presented by Gutin and Karapetyan [27] (henceforth abbreviated by 'GK') is used in this paper.…”

The Generalized Covering Salesman Problem

“…Thus the reported running times in the different papers are appropriately multiplied by the scaling factor r. We note that an identical approach was taken in Cacchiani et al (2011) to compare across these heuristics for the GTSP. Since no computer information is available for the RACS heuristic, we use a scaling factor of 1.…”