An Improved Particle Swarm Optimization Method for Nonlinear Optimization

Abstract

Nonlinear optimization is becoming more challenging in information sciences and various industrial applications, but nonlinear problems solved by the classical particle swarm-based methods are usually characterized by low efficiency, accuracy, and convergence speed in specific issues. To solve these problems and enhance the nonlinear optimization performance, an improved metaheuristic particle swarm optimization (PSO) model is proposed here. First, the optimization principles and model of the new method are introduced, and algorithms of the improved PSO are presented by updating the displacement and velocity of the moving particle according to Euler–Maruyama (EM) principle rather than traditional standard normal distribution. Then, the influence of the model parameters, input dimensions, and different nonlinear problems on the PSO optimization characterizations are studied by Pareto set solving and optimization performance comparison. The analysis regarding diverse nonlinear problems and optimization methods manifests that the improved method is capable of solving various nonlinear problems especially for multiobjective models, while the robustness and reliability can always keep consistent regardless of the change of model parameters. Finally, the performance evaluation is exhibited by the case study of nonlinear parameter optimization, 3 groups of CEC benchmark problems, and rank-sum test for 6 comparable optimization algorithms, which all verify its effectiveness and reliability, as well as the significance and great application promise. The results show that the new proposed PSO method has the fastest convergence speed and least iteration numbers in searching for the global best solution of 9 nonlinear problems among 8 different optimization models indicated by the p values smaller than 0.05. Additionally, the main conclusions showing the calculation efficiency, stability, robustness, and great application promise of the proposed method are summarized, and future work is discussed.