Chaotic particle swarm optimization algorithm is improved by incorporating antibody concentration, adaptive propagation, optimization mechanism of the multi-population evolution strategy, elite particles chaotic traversal mechanism and constraint processing mechanism. In this paper, an improved adaptive propagation chaotic particle swarm optimization algorithm based on immune selection (IS-APCPSO algorithm for short) is proposed. The performance of several algorithms has been compared by multimodal function, functions with high dimensional and complex constraints, bi-level programming function...