Solving the Traveling Salesman Problem through Extended Changing Crossover Operators

Abstract

In order to efficiently 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 this investigation our ECXO uses both 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 from 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 our C experiments using medium-sized problems in TSPLIB, and it is shown that ECXO can find the best solution earlier than EAX.