%0 Journal Article
%T An Investigation into the Performance of Particle Swarm Optimization with Various Chaotic Maps
%A Akugbe Martins Arasomwan
%A Aderemi Oluyinka Adewumi
%J Mathematical Problems in Engineering
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/178959
%X 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. 1. Introduction PSO algorithm is one of the many algorithms that have been proposed over the years for global optimization. When it was proposed in 1995 [1], swarm size, particle velocity, acceleration coefficients, and random coefficients were the associated parameters that controlled its operations. A close look at the algorithm shows that randomness plays very useful role in making the algorithm effectively solve optimization problems. 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¨C3]. To further enhance the performance of PSO, inertia weight strategy (IWS) was introduced into it by [4] to facilitate the intensification and diversification characteristics of the algorithm. Intensification searches around the current best solutions and selects the best candidate, while diversification makes the algorithm explore the search space more efficiently, mostly by means of randomization. As a result, randomness has been brought into the IWS by different researchers [5¨C8]. The important role of randomization can also be played by using chaos theory. Chaos is mathematically
%U http://www.hindawi.com/journals/mpe/2014/178959/