Comparative Analysis of Five Local Search Operators on Visiting Constrained Multiple Traveling Salesmen Problem

Abstract

Visiting constrained multiple traveling salesmen problem (VCMTSP) is an extension of the multiple traveling salesmen problem (MTSP). In this problem, each city is restricted to be only accessible to certain salesmen. Since the genetic algorithm (GA) has been widely utilized to solve the traveling salesman problem (TSP), this paper first adapts GA to solve VCMTSP. When solving TSP, local search (LS) methods are usually embedded into GA to refine the found solutions. Therefore, in this paper, we then embed five common LS operators, namely the single insertion method, the swap method, the two-optimization method (2-opt), the three-optimization method (3-opt), and the three-node permutation method (3-permute), into GA to investigate their influence on GA in solving VCMTSP. Extensive experiments on various VCMTSP instances show that LS operators can effectively help GA find more promising solutions. In particular, 2-opt brings the most benefit to GA to achieve promising performance in solving VCMTSP among the five LS operators. Except for 2-opt, the swap and 3-permute LS operators also bring considerable benefit to GA. With these investigations, it is expected that this paper could afford a basic guideline for new learners attempting to study VCMTSP.