Evolutionary multi-objective optimization with the heuristic solver for multiple traveling salesman problem

Abstract

In one approach to the multiple traveling salesman problem (MTSP), a group of cities to be visited has been assigned to each salesman based only on the cities’ geographic information, and the visiting routes of the salesmen are planned. However, there is no guarantee that the adopted clustering method is appropriate for route planning. In this study, we proposed a two-stage search method where the clustering is performed using an artificial neural network, its weights are designed through a multi-objective evolutionary algorithm, and each salesman’s visiting route is solved using a traveling salesman problem heuristic solver. In addition, we examined two kinds of objective function formulations for MTSP. We conducted computational experiments on test problems to compare the performance of the proposed methods using two kinds of objective function formulations with a canonical clustering method. In addition, we investigated the characteristics of the balanced solution selected from the obtained non-dominated solution set.