Step-Optimized Particle Swarm Optimization

Abstract

Particle swarm optimization (PSO) is widely used in industrial and academic research to solve optimization problems. Recent developments of PSO show a direction towards adaptive PSO (APSO). APSO changes its behaviour during the optimization process based on information gathered at each iteration. It has been shown that APSO is able to solve a wide range of difficult optimization problems efficiently and effectively. In classical PSO, all parameters are fixed for the entire swarm. In particular, all particles share the same settings of their velocity weights. We propose four APSO variants in which every particle has its own velocity weights. We use PSO to optimize the settings of the velocity weights of every particle at every iteration, thereby creating a step-optimized PSO (SOPSO). We implement four known PSO variants (global best PSO, decreasing weight PSO, time-varying acceleration coefficients PSO, and guaranteed convergence PSO) and four proposed APSO variants (SOPSO, moving bounds SOPSO, repulsive SOPSO, and moving bound repulsive SOPSO) in a PSO software package. The PSO software package is used to compare the performance of the PSO and APSO variants on 22 benchmark problems. Test results show that the proposed APSO variants outperform the known PSO variants on difficult optimization problems that require large numbers of function evaluations for their solution. This suggests that the SOPSO strategy of optimizing the settings of the velocity weights of every particle improves the robustness and performance of PSO.