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Differential evolution algorithm combined with chaotic pattern search
Kybernetika, Tome 46 (2010) no. 4, pp. 684-696 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Differential evolution algorithm combined with chaotic pattern search(DE-CPS) for global optimization is introduced to improve the performance of simple DE algorithm. Pattern search algorithm using chaotic variables instead of random variables is used to accelerate the convergence of solving the objective value. Experiments on 6 benchmark problems, including morbid Rosenbrock function, show that the novel hybrid algorithm is effective for nonlinear optimization problems in high dimensional space. The comparisons with the standard particle swarm optimization (PSO), differential evolution (DE) and other hybrid algorithms verify DE-CPS algorithm has great superiority.
Differential evolution algorithm combined with chaotic pattern search(DE-CPS) for global optimization is introduced to improve the performance of simple DE algorithm. Pattern search algorithm using chaotic variables instead of random variables is used to accelerate the convergence of solving the objective value. Experiments on 6 benchmark problems, including morbid Rosenbrock function, show that the novel hybrid algorithm is effective for nonlinear optimization problems in high dimensional space. The comparisons with the standard particle swarm optimization (PSO), differential evolution (DE) and other hybrid algorithms verify DE-CPS algorithm has great superiority.
Classification : 49M37, 65K10, 90C30
Keywords: hybrid algorithm; differential evolution(DE); chaotic pattern search; global optimization 
@article{KYB_2010_46_4_a6,
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     title = {Differential evolution algorithm combined with chaotic pattern search},
     journal = {Kybernetika},
     pages = {684--696},
     year = {2010},
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     zbl = {1203.65090},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010_46_4_a6/}
}
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He, Yaoyao; Zhou, Jianzhong; Lu, Ning; Qin, Hui; Lu, Youlin. Differential evolution algorithm combined with chaotic pattern search. Kybernetika, Tome 46 (2010) no. 4, pp. 684-696. http://geodesic.mathdoc.fr/item/KYB_2010_46_4_a6/

[1] Audet, C., Dennis, J. E.: Pattern search algorithms for mixed variable programming. SIAM J. Optim. 11 (2001), 3, 573–594. | DOI | MR

[2] Cai, J. J., Ma, X. Q., Li, X.: Chaotic ant swarm optimization to economic dispatch. Electron. Power Systems Research 77 (2007), 10, 1373–1380. | DOI

[3] Fan, H. Y., Lampinen, J.: A trigonometric mutation operation to differential evolution. J. Global Optim. 27 (2003), 1, 105–129. | DOI | MR | Zbl

[4] HART, W. E.: Evolutionary pattern search algorithms for unconstrained and linearly constrained optimization. IEEE Trans. Evol. Comput. 5 (2001), 4, 388–397. | DOI

[5] He, Y. Y., Zhou, J. Z., Li, C. S.: A precise chaotic particle swarm optimization algorithm based on improved tent map. ICNC 7 (2008), 569–573.

[6] He, Y. Y., Zhou, J. Z., Xiang, X. Q.: Comparison of different chaotic maps in particle swarm optimization algorithm for long term cascaded hydroelectric system scheduling. Chaos Solitons Fractals 42 (2009), 5, 3169–3176. | DOI | Zbl

[7] He, Y. Y., Zhou, J. Z., Qin, H.: Flood disaster classification based on fuzzy clustering iterative model and modified differential evolution algorithm. FSKD 3 (2009), 85–89.

[8] Ji, M. J., Tang, H. W.: Application of chaos in simulated annealing. optimization. Chaos Solitons Fractals 21 (2004), 933–941. | DOI | Zbl

[9] Kaelo, P., Ali, M. M.: A numerical study of some modified differential evolution algorithms. European J. Oper. Res. 169 (2006), 1176–1184. | DOI | MR | Zbl

[10] Kennedy, J., Eberhan, R. J.: Particle swarm optimization. In: IEEE Internat. Conf on Neural Networks 1995, Vol. 4, pp. 1942–1948.

[11] Storn, R., Price, K.: Differential Evolution: A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces. Technical Report TR-95-012, International Computer Science Institute, Berkeley 1995.

[12] Storn, R., Price, K.: Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11 (1997), 341–359. | DOI | MR | Zbl

[13] Storn, R., Price, K.: Differential evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces. University of California, Berkeley 2006.

[14] Tavazoei, M. S., Haeri, M.: Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl. Math. Comput. 187 (2007), 1076–1085. | DOI | MR | Zbl

[15] Xiang, T., Liao, X. F., Wong, K. W.: An improved particle swarm optimization algorithm combined with piecewise linear chaotic map. Appl. Math. Comput. 190 (2007), 1637–1645. | DOI | MR | Zbl

[16] Yang, D. X., Li, G., Cheng, G. D.: On the efficiency of chaos optimization algorithms for global optimization. Chaos Solitons Fractals 34 (2007), 1366–1375. | DOI

[17] Yuan, X. H., Yuan, Y. B., Zhang, Y. C.: A hybrid chaotic genetic algorithm for short-term hydro system scheduling. Math. Comput. Simul. 59 (2002), 4, 319–327. | DOI | MR | Zbl

[18] Yuan, X. F., Wang, Y. N., Wu, L. H.: Pattern search algorithm using chaos and its application. J. of Hunan University (Natural Sciences) 34 (2007), 9, 30-33. | Zbl

[19] Zhang, L., Zhang, C. J.: Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers. Kybernetika 44 (2008), 1, 35–42. | MR | Zbl

[20] Zhu, Z. L., Li, S. P., Yu, H.: A new approach to generalized chaos synchronization based on the stability of the error System. Kybernetika 44 (2008), 4, 492–500. | MR | Zbl