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Adaptive differential evolution algorithm for multiobjective optimization problems. (English) Zbl 1148.65042
Summary: A new adaptive differential evolution algorithm (ADEA) is proposed for multiobjective optimization problems. In ADEA, the variable parameter $F$ based on the number of the current Pareto-front and the diversity of the current solutions is given for adjusting search size in every generation to find Pareto solutions in mutation operator, and the select operator combines the advantages of the differential evolution algorithm with the mechanisms of Pareto-based ranking and crowding distance sorting. ADEA is implemented on five classical multiobjective problems, the results illustrate that ADEA efficiently achieves two goals of multiobjective optimization problems: find the solutions converge to the true Pareto-front and uniform spread along the front.

##### MSC:
 65K05 Mathematical programming (numerical methods) 90C29 Multi-objective programming; goal programming
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##### References:
 [1] Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation 6, 182-197 (2002) [2] Xue, F.; Sanderson, A. C.; Graves, R. J.: Pareto-based multi-objective differential evolution. Proceedings of the 2003 congress on evolutionary computation (CEC’2003) 2, 862-869 (2003) [3] Knowles, J.; Corne, D.: The Pareto archived evolution strategy: a new baseline algorithm for multiobjective optimization. Proceedings of the 1999 congress on evolutionary computation, 98-105 (1999) [4] Price, K. V.; Storn, R.: Differential evolution-a simple evolution strategy for fast optimization. Dr. dobb’s journal 22, 18-24 (1997) [5] Abbass, H. A.; Sarker, R.; Newton, C.: PDE: A Pareto-frontier differential evolution approach for multi-objective optimization problems. Proceedings of the congress on evolutionary computation 2001 (CEC’2001) 2, 971-978 (2001) [6] Abbass, H. A.: The self-adaptive Pareto differential evolution algorithm. Proceedings of the congress on evolutionary computation (CEC’2002) 1, 831-836 (2002) [7] Madavan, N. K.: Multiobjective optimization using a Pareto differential evolution approach. Proceeding of the congress on evolutionary computation (CEC’2002) 2, 1145-1150 (2002) [8] Tea Rolič, Bogdan Filipic˘, in: C.A. Coello, et al. (Eds.), DEMO: Differential Evolution for Multiobjective Optimization, EMO 2005, LNCS 3410, 2005, pp. 520 -- 533. · Zbl 1109.68633 [9] J. Lampinen, A bibliography of differential evolution algorithm. <http://www2.lut.fi/ jlampine/debiblio.htm>. [10] Goldberg, D. E.: Genetic algorithms in search, optimization, and machine learning. (1989) · Zbl 0721.68056