A multistart heuristic for the equality generalized traveling salesman problem

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. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011 © 2011 Wiley Periodicals, Inc.