A Hybrid Multi-Step Probability Selection Particle Swarm Optimization with Dynamic Chaotic Inertial Weight and Acceleration Coefficients for Numerical Function Optimization

Yuji Du,Fanfan Xu

doi:10.3390/sym12060922

Abstract

As a meta-heuristic algoriTthm, particle swarm optimization (PSO) has the advantages of having a simple principle, few required parameters, easy realization and strong adaptability. However, it is easy to fall into a local optimum in the early stage of iteration. Aiming at this shortcoming, this paper presents a hybrid multi-step probability selection particle swarm optimization with sine chaotic inertial weight and symmetric tangent chaotic acceleration coefficients (MPSPSO-ST), which can strengthen the overall performance of PSO to a large extent. Firstly, we propose a hybrid multi-step probability selection update mechanism (MPSPSO), which skillfully uses a multi-step process and roulette wheel selection to improve the performance. In order to achieve a good balance between global search capability and local search capability to further enhance the performance of the method, we also design sine chaotic inertial weight and symmetric tangent chaotic acceleration coefficients inspired by chaos mechanism and trigonometric functions, which are integrated into the MPSPSO-ST algorithm. This strategy enables the diversity of the swarm to be preserved to discourage premature convergence. To evaluate the effectiveness of the MPSPSO-ST algorithm, we conducted extensive experiments with 20 classic benchmark functions. The experimental results show that the MPSPSO-ST algorithm has faster convergence speed, higher optimization accuracy and better robustness, which is competitive in solving numerical optimization problems and outperforms a lot of classical PSO variants and well-known optimization algorithms.

Highlights

With the development of scientific research, engineering technology and social economy, optimization issues have gradually become high dimensionality, high level and great difficulty.Conventional optimization has become increasingly unsuitable for dealing with these optimization problems
We propose the Multi-Step Probability Selection Particle Swarm Optimization (MPSPSO)-ST algorithm, which can facilitate the algorithm performance of the traditional
The multimodal functions are used the sine chaotic inertial weight and symmetric tangent chaotic acceleration coefficients, which are to evaluate the ability of the algorithm to avoid the local point and reach to global solution since they integrated into the MPSPSO-ST algorithm

Summary

Introduction

With the development of scientific research, engineering technology and social economy, optimization issues have gradually become high dimensionality, high level and great difficulty. In [28] Taherkhani et al obtained different adaptive inertial weight based on the optimal position and distance in particle history, which improved the convergence accuracy and speed of the algorithm. Javidrad et al [31] used the simulated annealing algorithm (SA) as a local search mechanism, which improves the convergence behavior of PSO, forming a PSO-SA hybrid algorithm These PSO variants inherit the advantages of PSO and overcome some shortcomings of PSO, which makes them increasingly have advantages over conventional optimization, the deficiencies of being trapped in a local optimal solution and lacking swarm diversity still exist [32] which leads to the unsatisfactory in addressing complex optimization problems with different characteristics. A hybrid multi-step probability selection particle swarm optimization with sine chaotic inertial weight and symmetric tangent chaotic acceleration coefficients called MPSPSO-ST is proposed.

Related Theory about PSO

Position

Sine Chaotic Inertia Weight ω

Experimental Results and Discussion

Conclusions