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Mathematical Problems in Engineering
Volume 2013, Article ID 762372, 13 pages
Research Article

Bidirectional Dynamic Diversity Evolutionary Algorithm for Constrained Optimization

1Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China
2Institute of Advanced Control Technology, Dalian University of Technology, Dalian, Liaoning 116024, China

Received 1 September 2013; Accepted 13 November 2013

Academic Editor: D. Baleanu

Copyright © 2013 Weishang Gao et al. 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.


Evolutionary algorithms (EAs) were shown to be effective for complex constrained optimization problems. However, inflexible exploration-exploitation and improper penalty in EAs with penalty function would lead to losing the global optimum nearby or on the constrained boundary. To determine an appropriate penalty coefficient is also difficult in most studies. In this paper, we propose a bidirectional dynamic diversity evolutionary algorithm (Bi-DDEA) with multiagents guiding exploration-exploitation through local extrema to the global optimum in suitable steps. In Bi-DDEA potential advantage is detected by three kinds of agents. The scale and the density of agents will change dynamically according to the emerging of potential optimal area, which play an important role of flexible exploration-exploitation. Meanwhile, a novel double optimum estimation strategy with objective fitness and penalty fitness is suggested to compute, respectively, the dominance trend of agents in feasible region and forbidden region. This bidirectional evolving with multiagents can not only effectively avoid the problem of determining penalty coefficient but also quickly converge to the global optimum nearby or on the constrained boundary. By examining the rapidity and veracity of Bi-DDEA across benchmark functions, the proposed method is shown to be effective.