Heuristic methods using grasp, path relinking and variable neighborhood search for the clustered traveling salesman problem

Abstract

The Clustered Traveling Salesman Problem (CTSP) is a generalization of the Traveling Salesman Problem (TSP) in which the set of vertices is partitioned into disjoint clusters and objective is to find a minimum cost Hamiltonian cycle such that the vertices of each cluster are visited contiguously. The CTSP is NP-hard and, in this context, we are proposed heuristic methods for the CTSP using GRASP, Path Relinking and Variable Neighborhood Descent (VND). The heuristic methods were tested using Euclidean instances with up to 2000 vertices and clusters varying between 4 to 150 vertices. The computational tests were performed to compare the performance of the heuristic methods with an exact algorithm using the Parallel CPLEX software. The computational results showed that the hybrid heuristic method using VND outperforms other heuristic methods.