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Global and local selection in differential evolution for constrained numerical optimization
Keywords:
Constrained Numerical Optimization, Differential Evolution, Selection MechanismsAbstract
The performance of two selection mechanisms used in the most popular variant of differential evolution, known as DE/rand/1/bin, are compared in the solution of constrained numerical optimization problems. Four performance measures proposed in the specialized literature are used to analyze the capabilities of each selection mechanism to reach the feasible region of the search space, to find the vicinity of the feasible global optimum and the computational cost (measured by the number of evaluations) required. Two parameters of the differential evolution algorithm are varied to determine the most convenient values. A set of problems with different features is chosen to test both selection mechanisms and some findings are extracted from the results obtained.
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References
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[22] M. F. Tasgetiren and P. N. Suganthan. A Multi-Populated Differential Evolution Algorithm for Solving Constrained Optimization Problem. In 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pages 340–354, Vancouver, BC, Canada, July 2006. IEEE.
[23] F. zhuo Huang, L. Wang, and Q. He. An effective co-evolutionary differential evolution for constrained optimization. Applied Mathematics and Computation, 186(1):340–356, March 1st 2007.
[24] K. Zielinski and R. Laur. Constrained Single-Objective Optimization Using Differential Evolution. In 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pages 927–934, Vancouver, BC, Canada, July 2006. IEEE.
[2] C. A. Coello Coello. Theoretical and Numerical Constraint Handling Techniques used with Evolutionary Algorithms: A Survey of the State of the Art. Computer Methods in Applied Mechanics and Engineering, 191(11-12):1245–1287, January 2002.
[3] K. Deb. An Efficient Constraint Handling Method for Genetic Algorithms. Computer Methods in Applied Mechanics and Engineering, 186(2/4):311–338, 2000.
[4] A. Eiben and J. E. Smith. Introduction to Evolutionary Computing. Natural Computing Series. Springer Verlag, 2003.
[5] W. Gong and Z. Cai. A Multiobjective Differential Evolution Algorithm for Constrained Optimization. In 2008 Congress on Evolutionary Computation (CEC’2008), pages 181–188, Hong Kong, June 2008. IEEE Service Center.
[6] V. L. Huang, A. K. Qin, and P. N. Suganthan. Self-adaptative Differential Evolution Algorithm for Constrained Real-Parameter Optimization. In 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pages 324–331, Vancouver, BC, Canada, July 2006. IEEE.
[7] S. Kukkonen and J. Lampinen. Constrained Real-Parameter Optimization with Generalized Differential Evolution. In 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pages 911–918, Vancouver, BC, Canada, July 2006. IEEE.
[8] G. Leguizam ́on and C. Coello-Coello. A Boundary Search based ACO Algorithm Coupled with Stochastic Ranking. In 2007 IEEE Congress on Evolutionary Computation (CEC’2007), pages 165–172, Singapore, September 2007. IEEE Press.
[9] Y.-C. Lin, K.-S. Hwang, and F.-S. Wang. Hybrid Differential Evolution with Multiplier Updating Method for Nonlinear Constrained Optimization Problems. In Proceedings of the Congress on Evolutionary Computation 2002 (CEC’2002), volume 1, pages 872–877, Piscataway, New Jersey, May 2002. IEEE Service Center.
[10] E. Mezura-Montes, editor. Constraint-Handling in Evolutionary Optimization, volume 198 of Studies in Computational Intelligence. Springer-Verlag, 2009.
[11] E. Mezura-Montes and A. G. Palomeque-Ortiz. Parameter Control in Differential Evolution for Constrained Optimization. In 2009 Congress on Evolutionary Computation (CEC’2009), Tronheim, Norway, May 2009. IEEE Service Center. (accepted).
[12] E. Mezura-Montes, J. Vel ́azquez-Reyes, and C. A. C. Coello. Modified Differential Evolution for Constrained Optimization. In 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pages 332–339, Vancouver, BC, Canada, July 2006. IEEE.
[13] Z. Michalewicz and D. B. Fogel. How to Solve It: Modern Heuristics. Springer, Germany, 2nd edition, 2004.
[14] Z. Michalewicz and M. Schoenauer. Evolutionary Algorithms for Constrained Parameter Optimization Problems. Evolutionary Computation, 4(1):1–32, 1996.
[15] K. Price, R. Storn, and J. Lampinen. Differential Evolution: A Practical Approach to Global Optimization. Natural Computing Series. Springer-Verlag, 2005.
[16] K. V. Price and J. I. R ̈onkk ̈onen. Comparing the uni-modal scaling performance of global and local selection in a mutationonly differential evolution algorithm. In 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pages 7387–7394, Vancouver, Canada, July 2006. IEEE Press.
[17] S. S. Rao. Engineering Optimization. John Wiley and Sons, third edition, 1996.
[18] G. V. Reklaitis, A. Ravindran, and K. M. Ragsdell. Engineering Optimization. Methods and Applications. John Wiley and Sons, 1983.
[19] M. Schoenauer and S. Xanthakis. Constrained GA Optimization. In S. Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms (ICGA-93), pages 573–580, San Mateo, California, July 1993. University of Illinois at Urbana-Champaign, Morgan Kauffman Publishers.
[20] A. E. Smith and D. W. Coit. Constraint Handling Techniques—Penalty Functions. In T. B ̈ack, D. B. Fogel, and Z. Michalewicz, editors, Handbook of Evolutionary Computation, chapter C 5.2. Oxford University Press and Institute of Physics Publishing, 1997.
[21] T. Takahama and T. Sakai. Solving difficult constrained optimization problems by the ǫ constrained differential evolution with gradient-based mutation. In E. Mezura-Montes, editor, Constraint-Handling in Evolutionary Optimization, volume 198, pages 51–72. Springer-Verlag, Studies in Computational Intelligence Series, ISBN:978-3-642-00618-0, 2009.
[22] M. F. Tasgetiren and P. N. Suganthan. A Multi-Populated Differential Evolution Algorithm for Solving Constrained Optimization Problem. In 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pages 340–354, Vancouver, BC, Canada, July 2006. IEEE.
[23] F. zhuo Huang, L. Wang, and Q. He. An effective co-evolutionary differential evolution for constrained optimization. Applied Mathematics and Computation, 186(1):340–356, March 1st 2007.
[24] K. Zielinski and R. Laur. Constrained Single-Objective Optimization Using Differential Evolution. In 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pages 927–934, Vancouver, BC, Canada, July 2006. IEEE.
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Published
2009-10-01
How to Cite
Mezura-Montes, E., & Monterrosa-López, C. A. (2009). Global and local selection in differential evolution for constrained numerical optimization. Journal of Computer Science and Technology, 9(02), p. 43–52. Retrieved from https://journal.info.unlp.edu.ar/JCST/article/view/716
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Invited Articles
