Variants of 2-opt Approach for the Generalized Traveling Salesman Problem

Luu Van Thanh

Abstract: Generalized Traveling Salesman Problem (GTSP) is a well-known NP-hard problem. In a symmetric GTSP, the salesman must pass through a number of predefined subsets of customers, determining the order in which the subsets should be visited, and visiting exactly one customer in each subset while minimizing the sum of traveling costs of a completed undirected graph. This paper introduces a metaheuristic approach for solving this problem. The proposed algorithm is composed of two stages: (1) the constructive algorithm using the nearest neighbor heuristics (NN) ; and (2) the local improved algorithms consisting of combination of the well-known 2-opt search (2-opt classic), the adaptation of 2-opt with the NN (2-opt-NN), and the shortest path approach using Dijkstra’s algorithm (2-opt-SP). The computational results on thirty-six TSPLIB problems with up to 442 nodes are presented wherein the problems up to 300 nodes have been solved with computational time shorter than previous results cited in the literature.

Keywords: Combinatorial optimization, generalized traveling salesman problem, heuristics, local search