Analysis of chaotic maps applied to self-organizing maps for the Traveling Salesman Problem

Chaotic maps are an alternative for calculating pseudorandom numbers which have created an increased interest among researchers dealing with stochastic search and optimization algorithms in the recent past. This interest is based on promising results with respect to both the quality of the results as well as the running time of the optimization algorithms compared to the usually used standard pseudorandom number generators. In this paper we investigate the influence of nine different chaotic maps on the quality of the results obtained by a self-organizing map (SOM) which has been used to solve the Traveling Salesman Problem (TSP). The investigation is based on various sizes of both the problem instances as well as the number of iterations where all nine chaotic maps are compared against the pseudorandom number generation. As a result it is proven that chaotic maps are significantly better in several cases. Finally, possible reasons for both the superiority and inferiority of chaotic maps compared to pseudorandom number generation are analyzed and discussed.