The improved simulated annealing method which is based on the self-similatiry of cost function is proposed. The simulated annealing method is a stochastic computational algorithm derived from statistical mechanics, and has much success in various fields. However, this method wastes too much computational time to obtain a solution. In practical problems it can be expected that cost functions are statistically self-similar. If cost functions have self-similar property, a quasi reduction of the state space will be achieved, then, computational time can be reduced. Moreover, this procedure can be applied hierarchically by the degree of smoothness. Based on this idea, the proposed method hierarchically repeats the search for the region in which higher quality solutions seem to exist. Finally the standard simulated annealing method is also applied in the highly restricted region of the state space.
The traveling saleman problems are dealt with in this paper. After verifying the cost functions which have statistical self-similar property for the traveling salesman problem, computational experiments for the benchmark data, i. e., the 249-city problem and the 600-city problem will show that the proposed method can achieve much reduction of computational time compared with the standard simulated annealing method.