Performance improvement of heuristic algorithms for large scale combinatorial optimization problems using Lebesgue Spectrum Filter

In this paper, we analyze effectiveness of a new metaheuristic approach, which utilizes ideal spatio-temporal chaotic dynamics generated by Lebesgue Spectrum Filter (LSF). In the previous researches on the additive chaotic noise to the heuristic searches for combinatorial optimization problems, it has been shown that the chaotic sequences with negative autocorrelation improve the performance of asynchronously updated algorithms, such as mutually connected neural networks, asynchronous heuristic searches and so on. The effectiveness of chaos can be understood by the conventional theory of the chaotic CDMA, which showed that the cross-correlation between the sequences with negative autocorrelation becomes lowest. The spatio-temporal chaotic searching dynamics with such lowest cross-correlation has been shown effective to improve asynchronously updated combinatorial optimization algorithms. In this paper, as such asynchronously updated combinatorial optimization algorithms, we introduce the 2-exchange method, the k-opt method, the Lin-Kernighan method, and the Or-opt method, and improve the performance of them by applying the LSF. Our numerical simulation results show that the performances of all above heuristic methods could be improved by using negative autocorrelation.