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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 103591, 10 pages
http://dx.doi.org/10.1155/2013/103591
Research Article

An Improved Hybrid Genetic Algorithm with a New Local Search Procedure

1Department of Biostatistics, Virginia Commonwealth University, Richmond, VA 23298-0032, USA
2Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0439, USA

Received 9 January 2013; Accepted 26 August 2013

Academic Editor: Bin Wang

Copyright © 2013 Wen Wan and Jeffrey B. Birch. 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.

Abstract

One important challenge of a hybrid genetic algorithm (HGA) (also called memetic algorithm) is the tradeoff between global and local searching (LS) as it is the case that the cost of an LS can be rather high. This paper proposes a novel, simplified, and efficient HGA with a new individual learning procedure that performs a LS only when the best offspring (solution) in the offspring population is also the best in the current parent population. Additionally, a new LS method is developed based on a three-directional search (TD), which is derivative-free and self-adaptive. The new HGA with two different LS methods (the TD and Neld-Mead simplex) is compared with a traditional HGA. Four benchmark functions are employed to illustrate the improvement of the proposed method with the new learning procedure. The results show that the new HGA greatly reduces the number of function evaluations and converges much faster to the global optimum than a traditional HGA. The TD local search method is a good choice in helping to locate a global “mountain” (or “valley”) but may not perform the Nelder-Mead method in the final fine tuning toward the optimal solution.