×

Differential evolution algorithms using hybrid mutation. (English) Zbl 1145.90076

Summary: Differential evolution (DE) has gained a lot of attention from the global optimization research community. It has proved to be a very robust algorithm for solving non-differentiable and non-convex global optimization problems. In this paper, we propose some modifications to the original algorithm. Specifically, we use the attraction-repulsion concept of electromagnetism-like (EM) algorithm to boost the mutation operation of the original differential evolution. We carried out a numerical study using a set of 50 test problems, many of which are inspired by practical applications. Results presented show the potential of this new approach.

MSC:

90C30 Nonlinear programming
90C56 Derivative-free methods and methods using generalized derivatives
90C59 Approximation methods and heuristics in mathematical programming

Software:

Genocop
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Storn, R.; Price, K., Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces, J. Glob. Optim., 11, 341-359 (1997) · Zbl 0888.90135 · doi:10.1023/A:1008202821328
[2] Price, K.; Corne, D.; Dorigo, M.; Glover, F., An introduction to differential evolution, New Ideas in Optimization, 79-108 (1999), London: McGraw-Hill, London
[3] Birbil, S. I.; Fang, S. C., An electromagnetism-like mechanism for global optimization, J. Glob. Optim., 25, 3, 263-282 (2003) · Zbl 1047.90045 · doi:10.1023/A:1022452626305
[4] Birbil, S. I.; Fang, S. C.; Sheu, R. L., On the convergence of a population-based global optimization, J. Glob. Optim., 30, 301-318 (2004) · Zbl 1066.90086 · doi:10.1007/s10898-004-8270-3
[5] Michalewicz, Z., Genetic Algorithms + Data Structures = Evolution Programs (1996), Berlin: Springer, Berlin · Zbl 0841.68047
[6] Ali, M. M.; Törn, A., Population set based global optimization algorithms: some modifications and numerical studies, Comput. Oper. Res., 31, 10, 1703-1725 (2004) · Zbl 1073.90576 · doi:10.1016/S0305-0548(03)00116-3
[7] Price, W. L., Global optimization by controlled random search, J. Optim. Theory Appl., 40, 333-348 (1983) · Zbl 0494.90063 · doi:10.1007/BF00933504
[8] Kaelo, P.; Ali, M. M., Probabilistic adaptations of point generation schemes in some global optimization algorithms, Optim. Methods Softw., 21, 3, 343-57 (2006) · Zbl 1136.90440 · doi:10.1080/10556780500094671
[9] Lampinen, J.; Zelinka, I.; Corne, D.; Dorigo, M.; Glover, F., Mechanical engineering design optimization by differential evolution, New Ideas in Optimization, 127-146 (1999), London: McGraw-Hill, London
[10] Storn, R., System design by constraint adaptation and differential evolution, IEEE Trans. Evol. Comput., 3, 1, 22-34 (1999) · doi:10.1109/4235.752918
[11] Babu, B. V.; Sastry, K. K.N., Estimation of heat transfer parameters in a trickle-bed reactor using differential evolution and orthogonal collocation, Comput. Chem. Eng., 23, 3, 327-339 (1999) · doi:10.1016/S0098-1354(98)00277-4
[12] Chiou, J. P.; Wang, F. S., Hybrid method of evolutionary algorithms for static and dynamic optimization problems with applications to a fed-batch fermentation process, Comput. Chem. Eng., 23, 9, 1277-1291 (1999) · doi:10.1016/S0098-1354(99)00290-2
[13] Debels, D.; De Reyck, B.; Leus, R.; Vanhoucke, M., A hybrid scatter search/electromagnetism meta-heuristic for project scheduling, Eur. J. Oper. Res., 169, 2, 638-653 (2005) · Zbl 1079.90051 · doi:10.1016/j.ejor.2004.08.020
[14] http://www.icsi.berkey.edu/ storn/code.html
[15] Zaharie, D.: Critical values for the control parameters of differential evolution algorithms. In: Matousek, R., Osmera, P. (eds.) Proceedings of MENDEL 2002, 8th International Mendel Conference on Soft Computing, Bruno University of Technology, Faculty of Mechanical Engineering, pp. 62-67, Bruno (2002)
[16] Lee, M. H.; Han, C.; Chang, K. S., Dynamic optimization of a continuous polymer reactor using a modified differential evolution algorithm, Ind. Eng. Chem. Res., 38, 12, 4825-4831 (1999) · doi:10.1021/ie980373x
[17] Kaelo, P.: Some population set based methods for unconstrained global optimization. Ph.D. thesis, University of Witwatersrand (2005)
[18] Törn, A.; Ali, M. M.; Viitanen, S., Stochastic global optimization: problem classes and solution techniques, J. Glob. Optim., 14, 437-447 (1999) · Zbl 0952.90030 · doi:10.1023/A:1008395408187
[19] Ali, M. M.; Khompatraporn, C.; Zabinsky, Z. B., A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems, J. Glob. Optim., 31, 4, 635-672 (2005) · Zbl 1093.90028 · doi:10.1007/s10898-004-9972-2
[20] Chelouah, R.; Siarry, P., Genetic and Nelder-Mead algorithms for a more accurate global optimization of continuous multiminima functions, Eur. J. Oper. Res., 16, 2, 335-348 (2003) · Zbl 1035.90062 · doi:10.1016/S0377-2217(02)00401-0
[21] Dixon, L. C.W.; Szegö, G. P., The global optimization problem: an introduction, Towards Global Optimization, vol. 2, 1-15 (1978), Amsterdam: North-Holland, Amsterdam
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.