The Lin-Kernighan Algorithm Driven by Chaotic Neurodynamics for Large Scale Traveling Salesman Problems

  • Authors:

  • Shun Motohashi;Takafumi Matsuura;Tohru Ikeguchi;Kazuyuki Aihara

  • Affiliations:

  • Graduate school of Science and Engineering, Saitama University, Saitama, Japan 338---8570;Graduate school of Science and Engineering, Saitama University, Saitama, Japan 338---8570;Graduate school of Science and Engineering, Saitama University, Saitama, Japan 338---8570 and Aihara Complexity Modelling Project, ERATO, JST, Tokyo, Japan 153-8505;Graduate school of Information Science and Technology, The University of Tokyo, Tokyo, Japan 153-8505 and Aihara Complexity Modelling Project, ERATO, JST, Tokyo, Japan 153-8505

  • Venue:
  • ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
  • Year:
  • 2009

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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.