Memetic Algorithm for the Generalized Asymmetric Traveling Salesman Problem

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The aim of this paper is to present a new memetic algorithm for GTSP which clearly outperforms the state-of-the-art memetic algorithm of Snyder and Daskin [21] with respect to the quality of solutions. Computational experiments conducted to compare the two heuristics also show that our improvements come at a cost of longer running times, but the running times still remain within reasonable bounds (at most a few minutes). While the Snyder-Daskin memetic algorithm is designed only for the Symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances. Unlike the Snyder-Daskin heuristic, we use a simple machine learning approach as well.