Asparagos96 and the traveling salesman problem

Abstract

The paper describes a spatially structured evolutionary algorithm being applied to the symmetric and asymmetric traveling salesman problem (TSP). This approach shows that a genetic algorithm with high degree of isolation-by-distance in combination with a simple repairing mechanism is able to find high quality solutions for the TSP. The evolutionary part of the algorithm presented differs from the original version of Asparagos in the choice of the topological pattern being now a ring structure and the support of hierarchy. The application part in contrast has been revised in more depth. A new representation which the author calls the bi-directional array representation is used for the TSP. This representation is invariant concerning the starting point of a tour and allows the realization of a k-Opt move in O(1). The crossover operator MPX is slightly modified in the sense that if there are differing edges in the parent tours, it is now guaranteed that at least one differing edge will occur in the offspring's tour. The mutation operator has been exchanged by the double-bridge 4-Opt move. The complexity of Asparagos96 for the symmetric TSP is O(N/sup 1.1/); for the asymmetric TSP it is O(N).