An Investigation into the Performance of Particle Swarm Optimization with Various Chaotic Maps

Akugbe Martins Arasomwan,Aderemi Oluyinka Adewumi

doi:10.1155/2014/178959

Akugbe Martins Arasomwan, Aderemi Oluyinka Adewumi

Open Access

https://doi.org/10.1155/2014/178959

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Abstract

This paper experimentally investigates the effect of nine chaotic maps on the performance of two Particle Swarm Optimization (PSO) variants, namely, Random Inertia Weight PSO (RIW-PSO) and Linear Decreasing Inertia Weight PSO (LDIW-PSO) algorithms. The applications of logistic chaotic map by researchers to these variants have led to Chaotic Random Inertia Weight PSO (CRIW-PSO) and Chaotic Linear Decreasing Inertia Weight PSO (CDIW-PSO) with improved optimizing capability due to better global search mobility. However, there are many other chaotic maps in literature which could perhaps enhance the performances of RIW-PSO and LDIW-PSO more than logistic map. Some benchmark mathematical problems well-studied in literature were used to verify the performances of RIW-PSO and LDIW-PSO variants using the nine chaotic maps in comparison with logistic chaotic map. Results show that the performances of these two variants were improved more by many of the chaotic maps than by logistic map in many of the test problems. The best performance, in terms of function evaluations, was obtained by the two variants using Intermittency chaotic map. Results in this paper provide a platform for informative decision making when selecting chaotic maps to be used in the inertia weight formula of LDIW-PSO and RIW-PSO.

Highlights

Particle Swarm Optimization (PSO) algorithm is one of the many algorithms that have been proposed over the years for global optimization
This paper experimentally investigates the effect of nine chaotic maps on the performance of two Particle Swarm Optimization (PSO) variants, namely, Random Inertia Weight PSO (RIW-PSO) and Linear Decreasing Inertia Weight PSO (LDIW-PSO) algorithms
These characteristics can enhance the search ability of PSO. This seems to be the motivation behind the introduction of chaos feature into inertia weight strategy (IWS) in [10], which led to improved optimizing capabilities of CDIW-PSO and CRIWPSO due to better global search mobility compared with LDIW-PSO and RIW-PSO, respectively

Summary

Introduction

PSO algorithm is one of the many algorithms that have been proposed over the years for global optimization. Randomness comes into play at the point of initializing the particles in the solution space and in updating the velocities of particles at each iteration of the algorithm. This random feature has contributed immensely to the performance of PSO [1,2,3]. Chaos is mathematically defined as randomness generated by simple deterministic system [2] It is generally characterised by three dynamic properties, namely, ergodicity, stochastic, and sensitivity, to its initial conditions [2, 9]. In [12], twelve different chaos maps were implemented to tune the attraction parameter of accelerated PSO algorithm

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