Table of Contents
Journal of Artificial Evolution and Applications
Volume 2008 (2008), Article ID 482032, 15 pages
Research Article

Particle Swarm Optimization for Multimodal Functions: A Clustering Approach

Dipartimento di Informatica, Università di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy

Received 13 July 2007; Revised 18 December 2007; Accepted 8 February 2008

Academic Editor: Riccardo Poli

Copyright © 2008 Alessandro Passaro and Antonina Starita. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The particle swarm optimization (PSO) algorithm is designed to find a single optimal solution and needs some modifications to be able to locate multiple optima on a multimodal function. In parallel with evolutionary computation algorithms, these modifications can be grouped in the framework of niching. In this work, we present a new approach to niching in PSO based on clustering particles to identify niches. The neighborhood structure, on which particles rely for communication, is exploited together with the niche information to locate multiple optima in parallel. Our approach was implemented in the k-means-based PSO (kPSO), which employs the standard k-means clustering algorithm, improved with a mechanism to adaptively identify the number of clusters. kPSO proved to be a competitive solution when compared with other existing algorithms, since it showed better performance on a benchmark set of multimodal functions.