Incremental approach to particle swarm assisted function optimization

Abstract

Requirements of function optimization widely exist. The investigation mainly focuses on two aspects. On one hand, incremental optimization in the input space, which optimizes the variable set incrementally for global optimization problems, is studied. On the other hand, incremental optimization in the output space, which optimizes the objective set incrementally for multi-objective problems, is researched. With regard to the incremental global optimization (IGO), the principles are stated mathematically, based on which an incremental model in the input space is proposed. By employing PSO as a vehicle for this model, a novel IPSO is obtained. Further, we investigate the parallel implementation of the IPSO. Given the parallel IPSO (PIPSO), the information gained from searching in the spaces with reduced dimensionality could be shared with higher efficiency. With regard to the incremental multi-objective optimization (IMOO), the rationale is analyzed and proved, followed by building a general incremental model in the output space. By applying this model to MOPSO, a novel IMOPSO is proposed. Further, the objective ordering issue is explored for IMOO, resulting in the present of an ordering approach.