Bilevel-search particle swarm optimization for computationally expensive optimization problems

Population-based global optimization algorithms often need few computational costs to find good regions which contain potential optima, while much more are needed to refine them for higher accuracies in the computationally expensive optimization problems. Such phenomenon is termed “asymptotic inefficiency” phenomenon in this paper. Inspired by the great success of bilevel or multilevel algorithms in eliminating similar phenomenon, we present the bilevel-search framework to alleviate the “asymptotic inefficiency” and apply it to SPSO2011. The main features of the proposed framework adopted to SPSO2011 are: (1) the order-2 stable in the theory and (2) the simple but efficient bilevel-search framework. The extensive numerical experiments show that the proposal framework successfully alleviates the “asymptotic inefficiency” of SPSO2011, and the proposal is a promising global optimization algorithm compared with two popular particle swarm optimization algorithms.