On the weak ergodicity of the Markov Chain associated with a chaotic simulated annealing algorithm

Chaotic simulated annealing (CSA) is a relatively new heuristic optimization technique and has been widely applied to optimization problems because of its simplicity and capability of finding fairly good solutions rapidly. However, currently only experimental results are used for verifying its superiority. In this paper, a new of chaotic simulated annealing method (CSA) is introduced and then a mathematic proof is given. It shows that the Markov Chain associated with the algorithm is weakly ergodic, which guarantees that the asymptotic behavior of the algorithm is independent of initial states. Furthermore, the theoretical analysis of the proposed CSA is very important to understand the essential features which make the algorithm work well.