An Improved Multimodal Artificial Immune Algorithm and its Convergence Analysis

A dynamic population immune algorithm (DPIA) for multimodal function optimization is proposed based on clone selection principle and immune network theory. This algorithm can search in the global-space and local-space simultaneously with mutation to low-bit genes and selection in subpopulation. Then the transition probability of the immune operators and the conception of multimodal algorithm convergence are given. It is proved that the DPIA is completely convergent based on the use of Markov chain. The experiment results verified the steady convergence of DPIA by optimizing the typical multi-modal functions and comparing with the similar algorithms.