Dynamics of personal best oriented particle swarm optimizer

Abstract

Personal best oriented particle swam optimizer (PPSO), a variant of conventional particle swarm optimization (PSO), is a promising optimizer. It has been shown in a previous paper (Chen and Yeh, 2006) that PPSO performs better than PSO both in solution quality and convergent speed for some benchmark functions. This paper tries to figure out its behavior via the analysis of a first‐order linear difference equation with time‐varying coefficient, derived from PPSO. The analysis shows that a particle stochastically moves within a region in real space. The center of the region, similar to PSO, approximately equals the weighted mean of the best positions found by an individual and its neighbors. Comparison of the trajectories between PSO and PPSO is given to clarify the behavior of PPSO. The performances of PPSO tested on a suite of benchmark functions are also given. Furthermore, a case study on economic power dispatch problem with nonsmooth cost function verifies the feasibility of PPSO.