Many engineering design problems can be formulated as constrained optimization problems. So far, penalty function methods have been the most popular methods for constrained optimization due to their simplicity and easy implementation. However, it is often not easy to set suitable penalty factors or to design adaptive mechanism. By employing the notion of co-evolution to adapt penalty factors, this paper proposes a co-evolutionary particle swarm optimization approach (CPSO) for constrained optimization problems, where PSO is applied with two kinds of swarms for evolutionary exploration and exploitation in spaces of both solutions and penalty factors. The proposed CPSO is population based and easy to implement in parallel. Especially, penalty factors also evolve using PSO in a self-tuning way. Simulation results based on well-known constrained engineering design problems demonstrate the effectiveness, efficiency and robustness on initial populations of the proposed method. Moreover, the CPSO obtains some solutions better than those previously reported in the literature.
|Number of pages
|Engineering Applications of Artificial Intelligence
|Published - Feb 2007
Bibliographical noteFunding Information:
The authors wish to thank the Editor-in-Chief Prof. R. Vingerhoeds and anonymous reviewers for their constructive and valuable comments. And this research is partially supported by National Science Foundation of China (60204008, 60374060 and 60574072) and 973 Program (2002CB312200).
- Particle swarm optimization
- Penalty function