Optimized PSO algorithm based on the simplicial algorithm of fixed point theory

Abstract

Particle swarm optimization algorithm (PSO) has been optimized from various aspects since it was proposed. Optimization of PSO can be realized by optimizing its iterative process or the initial parameters and heuristic methods have been combined with the initial PSO algorithm to improve its performance. In this paper, we introduce the Simplicial Algorithm (SA) of fixed point theory into the optimization of PSO and proposed a FP-PSO (Fixed-point PSO) improved algorithm. In FP-PSO algorithm, the optimization of target function is converted into the problem of solving a fixed point equation set, and the solution set obtained by Simplicial Algorithm (SA) of fixed point theory is used as the initial population of PSO algorithm, then the remaining parameters can be obtained accordingly with classical PSO algorithm. Since the fixed point method has sound mathematical properties, the initial population obtained with FP-PSO include nearly all the approximate local extremes which maintain the diversity of population and can optimize the flight direction of particles, and shows their advantages on setting other initial parameters. We make an experimental study with five commonly used testing functions from UCI (University of California Irvine) which include two single-peak functions and three multi-peak functions. The results indicate that the convergence accuracy, stability, and robustness of FP-PSO algorithm are significantly superior to existing improve strategies which also optimize PSO algorithm by optimizing initial population, especially when dealing with complex situations. In addition, we nest the FP-PSO algorithm with four classical improved PSO algorithms that improve PSO by optimizing iterative processes, and carry out contrast experiments on three multi-peak functions under different conditions (rotating or non-rotating). The experimental results show that the performance of the improved algorithm using nested strategy are also significantly enhanced compared with these original algorithms.