Chaotic search for traveling salesman problems by using 2-opt and Or-opt algorithms

The traveling salesman problem (TSP) is one of the widely studied combinatorial optimization problems. Because, the TSP belongs to a class of 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.