Breeding Perturbed City Coordinates and Fooling Travelling Salesman Heuristic Algorithms
Standard heuristic algorithms for the geometric travelling salesman problem (GTSP) frequently produce poor solutions in excess of 25% above the true optimum. In this paper we present some preliminary work that demonstrates the potential of genetic algorithms (GAs) to perturb city coordinates in such a way that the heuristic is ‘fooled’ into producing much better solutions to the GTSP. Initial results for our GA show that by using the nearest neighbour tour construction heuristic on perturbed coordinate sets it is possible to consistently obtain solutions to within a fraction of a percent of the optimum for problems of several hundred cities.
KeywordsHeuristic Algorithm Minimum Span Tree Near Neighbour Uniform Crossover Optimal Tour
Unable to display preview. Download preview PDF.
- D.J. Cavicchio. Adaptive search using simulated evolution. Unpublished doctorial dissertation, University of Michigan, Ann ArborGoogle Scholar
- B. Codenotti L. Margara, G. Manzini and G Resta. Global strategies for augmenting the efficiency of TSP heuristics, volume 709. Springer-Verlag, Berlin, 1993.Google Scholar
- D.S. Johnson. Local optimization and the traveling salesman problem. In Automata Languages and Programming: 17th International Colloquium Proceedings, 1990.Google Scholar
- M. Held and R.M. Karp. The travelling salesman problem and minimum spanning trees. Oper. Res, 18:1138–1162.Google Scholar
- M. Held and R.M. Karp. The travelling salesman problem and minimum spanning trees: part ii. Maths. Programming, 1:6–25.Google Scholar
- J.H Holland. Adaptation in natural and artificial systems. The University of Michigan Press, Ann ArborGoogle Scholar
- L.A. McGeoch D.S. Johnson and E.E. Rothberg. Asymptotic experimental analysis for the Held-Karp traveling salesman bound. In Proceeding 1996 ACM-SIAM symp. on Discrete Algorithms, 1996.Google Scholar
- G. Syswerda. Uniform crossover in genetic algorithms. In Proceedings of the Third International Conference on Genetic Algorithms, Hillsdale, NJ, 1996. Lawrence Erlbaum Associates.Google Scholar
- C.L. Valenzuela and A.J. Jones. A parallel implementation of evolutionary divide and conquer for the TSP. In Proceedings of the First IEE/IEEE conference on Genetic ALgorithms in Engineering Systems: Innovations and Applications (GALESIA), pages 499–504, Sheffield, U.K., September 1995.Google Scholar
- C.L. Valenzuela and A.J. Jones. Estimating the Held-Karp lower bound for the geometric TSP. European Journal of Operational Research, to appear.Google Scholar
- C.L. Valenzuela. Evolutionary Divide and Conquer: a Novel Genetic approach to the TSP. PhD thesis, University of London, 1995.Google Scholar