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Journal of Applied Mathematics
Volume 2014, Article ID 895629, 12 pages
Research Article

An Improved Central Force Optimization Algorithm for Multimodal Optimization

1School of Mathematics and Statistics, Xi’dian University, Xi’an 710071, China
2College of Science, Xi’an University of Science and Technology, Xi’an 710054, China
3School of Computer, Xi’dian University, Xi’an 710071, China

Received 24 June 2014; Revised 22 September 2014; Accepted 12 October 2014; Published 7 December 2014

Academic Editor: Boris Andrievsky

Copyright © 2014 Jie Liu and Yu-ping Wang. 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.


This paper proposes the hybrid CSM-CFO algorithm based on the simplex method (SM), clustering technique, and central force optimization (CFO) for unconstrained optimization. CSM-CFO is still a deterministic swarm intelligent algorithm, such that the complex statistical analysis of the numerical results can be omitted, and the convergence intends to produce faster and more accurate by clustering technique and good points set. When tested against benchmark functions, in low and high dimensions, the CSM-CFO algorithm has competitive performance in terms of accuracy and convergence speed compared to other evolutionary algorithms: particle swarm optimization, evolutionary program, and simulated annealing. The comparison results demonstrate that the proposed algorithm is effective and efficient.