Step-optimized Particle Swarm Optimization

Recent developments of Particle Swarm Optimization (PSO) have successfully trended towards Adaptive PSO (APSO). APSO changes its behavior 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 remain constant for the entire swarm during the iterations. In particular, all particles share the same settings for their velocity weights. We propose a Step-Optimized PSO (SOPSO) algorithm in which every particle has its own velocity weights and an inner PSO iteration is used to take a step towards optimizing the settings of the velocity weights of every particle at every iteration. We compare SOPSO to four known PSO variants (global best PSO, decreasing weight PSO, time-varying acceleration coefficients PSO, and guaranteed convergence PSO). Experiments are conducted to compare the performance of SOPSO to the known PSO variants on 22 benchmark problems. The results show that SOPSO outperforms 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 the algorithm.