A Hybrid Heuristic Approach for Solving the Generalized Traveling Salesman Problem

The generalized traveling salesman problem (GTSP) is an NP-hard problem that extends the classical traveling salesman problem by partitioning the nodes into clusters and looking for a minimum Hamiltonian tour visiting exactly one node from each cluster. In this paper, we combine the consultant-guided search technique with a local-global approach in order to solve efficiently the generalized traveling salesman problem. We use candidate lists in order to reduce the search space and we introduce efficient variants of 2-opt and 3-opt local search in order to improve the solutions. The resulting algorithm is applied to Euclidean GTSP instances derived from the TSPLIB library. The experimental results show that our algorithm is able to compete with the best existing algorithms in terms of solution quality and running time.