Chaotic Search for Traveling Salesman Problems by Using 2-opt and Or-opt Algorithms

  • Authors:
  • Takafumi Matsuura;Tohru Ikeguchi

  • Affiliations:
  • Graduate School of Science and Engineering, Saitama University, Saitama-city, Japan 338-8570;Graduate School of Science and Engineering, Saitama University, Saitama-city, Japan 338-8570

  • Venue:
  • ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part II
  • Year:
  • 2008

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Abstract

The traveling salesman problem (TSP) is one of the widely studied combinatorial optimization problems. Because, the TSP belongs to a class of $\mathcal{NP}$-hard, it is almost impossible to obtain an optimal solution in a reasonable time frame. To find the near optimum solutions of TSPs, a method with chaotic neurodynamics has already been proposed. In this paper, we propose a new method to solve TSP introducing chaotic neurodynamics, which uses not only the 2-opt algorithm but also the Or-opt algorithm, which is one of the powerful local searches. Namely, in the proposed method, the 2-opt and the Or-opt algorithms are adaptively driven by the chaotic neurodynamics. Thus, the local minimum problem in these algorithms is resolved by controlling executions of these local searches. As a result, the proposed method shows higher performance than the previous chaotic search methods.