Particle Swarm Optimization Algorithm with Multiple Phases for Solving Continuous Optimization Problems

Jing Li,Yifei Sun,Sicheng Hou,Lianbo Ma

doi:10.1155/2021/8378579

Abstract

An algorithm with different parameter settings often performs differently on the same problem. The parameter settings are difficult to determine before the optimization process. The variants of particle swarm optimization (PSO) algorithms are studied as exemplars of swarm intelligence algorithms. Based on the concept of building block thesis, a PSO algorithm with multiple phases was proposed to analyze the relation between search strategies and the solved problems. Two variants of the PSO algorithm, which were termed as the PSO with fixed phase (PSOFP) algorithm and PSO with dynamic phase (PSODP) algorithm, were compared with six variants of the standard PSO algorithm in the experimental study. The benchmark functions for single-objective numerical optimization, which includes 12 functions in 50 and 100 dimensions, are used in the experimental study, respectively. The experimental results have verified the generalization ability of the proposed PSO variants.

Highlights

Particle swarm optimization (PSO) algorithm is a population-based stochastic algorithm modeled on the social behaviors observed in flocking birds [1, 2]
As a well-known swarm intelligence algorithm, each particle, which represents a solution in the group, flies through the search space with a velocity that is dynamically adjusted according to its own and its companion’s historical behaviors. e particles tend to fly toward better search areas throughout the search process [3]
As the same with the PSO with fixed phase (PSOFP) algorithm, the PSO with dynamic phase (PSODP) algorithm started with the canonical PSO (CPSO) with the star structure and ended with the standard PSO algorithm by Bratton and Kennedy (SPSO-BK) with the ring structure

Summary

Introduction

Particle swarm optimization (PSO) algorithm is a population-based stochastic algorithm modeled on the social behaviors observed in flocking birds [1, 2]. A potential solution, which is termed as a particle in PSO algorithm, is a search point in the solution space with D-dimensions For each particle, it is connected with two vectors, i.e., the vector of velocity and the vector of position. Ere are two equations, the update of velocity and position for each particle, in the basic process of PSO algorithm. Learning from a different neighbor means that a particle follows a different neighborhood (or local) best; in other words, the topology structure determines the connections among particles and the strategy used in the propagation process of searching information over iteration. If current position has a better function value than pbest, update pbest as current position; (5) Select a particle that has the best fitness value from the current particle’s neighborhood, this particle is termed as the neighborhood best (nbest); (6) for each particle do (7) Update particle’s velocity according equation (1); (8) Update particle’s position according equation (2); ALGORITHM 1: Basic process of PSO algorithm

Update pbest and nbest

Other structures

Experimental Study

Multiple dynamic phases strategy gbest not changed a er k iteration

SPSOBKS SPSOBKR SPSOCS SPSOCR