Abstract
The traveling salesman problem (TSP) is one of the typical \({\cal NP}\)-hard problems. Then, it is inevitable to develop an effective approximate algorithm. We have already proposed an effective algorithm which uses chaotic neurodynamics. The algorithm drives a local search method, such as the 2-opt algorithm and the adaptive k-opt algorithm, to escape from undesirable local minima. In this paper, we propose a new chaotic search method using the Lin-Kernighan algorithm. The Lin-Kernighan algorithm is one of the most effective algorithms for solving TSP. Moreover, to diversify searching states, we introduce the double bridge algorithm. As a result, the proposed method exhibits higher performance than the conventional algorithms. We validate the applicability of the proposed method for very large scale instances, such as 105 order TSPs.
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References
Lin, S., Kernighan, B.: An effective heuristic algorithm for the traveling-salesman problem. Operations Research 21, 498–516 (1973)
Glover, F.: Tabu search–part I. ORSA J. Computing 1, 190–206 (1989)
Kirkpatrick, S., Gelatt, C.D., Vecchi, P.M.: Optimization by simulated annealing. Science 220, 671–680 (1983)
Holland, J.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. The University of Michigan Press (1975)
Hasegawa, M., Ikeguchi, T., Aihara, K.: Combination of chaotic neurodynamics with the 2-opt algorithm to solve traveling salesman problems. Physical Review Letters 79, 2344–2347 (1997)
Hasegawa, M., Ikeguchi, T., Aihara, K.: Solving large scale traveling salesman problems by chaotic neurodynamics. Neural Networks 15, 271–283 (2002)
Hasegawa, M., Ikeguchi, T., Aihara, K.: On the effects of the k-opt method with chaotic neurodynamics. IEICE Technical Report 101, 25–32 (2001)
Motohashi, S., Matsuura, T., Ikeguchi, T.: Chaotic search method using the Lin-Kernighan algorithm for traveling salesman problems. In: Proceedings of International Symposium on Nonlinear Theory and its Applications (NOLTA), pp. 144–147 (2008)
Aihara, K., Takabe, T., Toyoda, M.: Chaotic neural networks. Physics Letters A 144, 333–340 (1990)
TSPLIB, http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/
Johnson, D.S., McGeoch, L.A., Glover, F., Rego, C.: 8th DIMACS implementation challenge: The traveling salesman problem (2000), http://www.research.att.com/~dsj/chtsp/
Held, M., Karp, R.M.: The traveling-salesman problem and minimum spanning trees. Operations Research 18, 1138–1162 (1970)
Held, M., Karp, R.M.: The traveling-salesman problem and minimum spanning trees: Part II. Mathematical Programming 1, 6–25 (1971)
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Motohashi, S., Matsuura, T., Ikeguchi, T., Aihara, K. (2009). The Lin-Kernighan Algorithm Driven by Chaotic Neurodynamics for Large Scale Traveling Salesman Problems. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds) Artificial Neural Networks – ICANN 2009. ICANN 2009. Lecture Notes in Computer Science, vol 5769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04277-5_57
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DOI: https://doi.org/10.1007/978-3-642-04277-5_57
Publisher Name: Springer, Berlin, Heidelberg
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