New EAX Crossover for Large TSP Instances
We propose an evolutionary algorithm (EA) that applies to the traveling salesman problem (TSP). The EA uses edge assembly crossover (EAX), which is known to be efficient and effective for solving TSPs. Recently, a fast implementation of EAX and an effective technique for preserving population diversity were proposed. This makes it possible to compare the EA with EAX comparable to state-of-the-art TSP heuristics based on Lin-Karnighan heuristics. We further improved the performance of EAs with EAX, especially for large instances of more than 10,000 cities. Our method can find optimal solutions for instances of up to 24978 cities within a day using a single Itanium 2 1.3-GHz processor. Moreover, our EA found three new best tours for unsolved national TSP instances in a reasonable computation time.
KeywordsTravel Salesman Problem Travel Salesman Problem Large Instance Gain Modus Intermediate Solution
Unable to display preview. Download preview PDF.
- 1.Johnson, D.S.: Local Optimization and the Traveling Salesman Problem, Automata, Languages and Programming. LNCS, vol. 442, pp. 446–461. Springer, HeidelbergGoogle Scholar
- 2.8-th DIMACS Implementation Challenge: The Traveling Salesman Problem, http://www.research.att.com/dsj/chtsp
- 4.Applegate, D., Bixby, R., Chvatal, V., Cook, W.: Finding tours in the TSP. Technical Report 99885, Forschungsinstitut fur Diskrete Mathematik, Universitat Bonn (1999)Google Scholar
- 6.Nagata, Y., Kobayashi, S.: Edge Assembly Crossover: A High-power Genetic Algorithm for the Traveling Salesman Problem. In: Proc. of the 7th Int. Conference on Genetic Algorithms, pp. 450–457 (1997)Google Scholar
- 7.Tsai, H.K., Yang, J.M., Tsai, Y.F., Kao, C.Y.: An Evolutionary Algorithm for Large Traveling Salesman Problem. IEEE Transaction on SMC-part B 34(4), 1718–1729 (2004)Google Scholar
- 8.Maekawa, K., Mori, N., Kita, H., Nishikawa, H.: A Genetic Solution for the Traveling Salesman Problem by Means of a Thermodynamical Selection Rule. In: Proc. 1996 IEEE Int. Conference on Evolutionary Computation, pp. 529–534 (1996)Google Scholar
- 10.Nagata, Y.: The EAX algorithm considering diversity loss. In: Proc. of the 8th Int. Conference on Parallel Problem Solving from Nature, pp. 332–341 (2004)Google Scholar
- 13.National Traveling Salesman Problems, http://www.tsp.gatech.edu/world/countries.html