A Methodology of Extended Changing Crossover Operators to Solve the Traveling Salesman Problem

Abstract

In order efficiently to obtain an approximate solution of the traveling salesman problem (TSP), extended changing crossover operators (ECXOs) which can substitute any crossover operator of genetic algorithms (GAs) and ant colony optimization (ACO) for another crossover operator at any time is proposed. In our study ECXO uses both of EX (or ACO) and EXX (edge exchange crossover) in early generations to create local optimum sub-paths, and it uses EAX (edge assembly crossover) to create a global optimum solution after generations. With EX or ACO any individual or any ant determines the next city he visits based on lengths of edges or tours' lengths deposited on edges as pheromone, and he generates local optimum paths. With EXX the generated path converges to a provisional optimal path. With EAX a parent exchanges his edges with another parent's ones reciprocally to create sub-cyclic paths, before restructuring a cyclic path by combining the sub-cyclic paths with making distances between them minimum. In this paper validity of ECXO is verified by C experiments using medium-sized problems such as pcb442, etc. in TSPLIB. From our C experiments, we can see that the above ECXO (EX (or ACO) (rarrEXX)rarrEAX) can find the best solution earlier than EAX, where EX, ACO and EXX deliver their offspring to EAX.