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A fuzzy adaptive differential evolution algorithm. (English) Zbl 1076.93513

Summary: The differential evolution algorithm is a floating-point encoded evolutionary algorithm for global optimization over continuous spaces. The algorithm has so far used empirically chosen values for its search parameters that are kept fixed through an optimization process. The objective of this paper is to introduce a new version of the Differential Evolution algorithm with adaptive control parameters – the fuzzy adaptive differential evolution algorithm, which uses fuzzy logic controllers to adapt the search parameters for the mutation operation and crossover operation. The control inputs incorporate the relative objective function values and individuals of the successive generations. The emphasis of this paper is analysis of the dynamics and behavior of the algorithm. Experimental results, provided by the proposed algorithm for a set of standard test functions, outperformed those of the standard differential evolution algorithm for optimization problems with higher dimensionality.

MSC:

93C42 Fuzzy control/observation systems
93C40 Adaptive control/observation systems
68T05 Learning and adaptive systems in artificial intelligence

Software:

Genocop
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References:

[1] Abbass HA (2002) The self-adaptive pareto differential evolution algorithm. In: Proceedings of the congress on evolutionary computation, pp 831–836
[2] Bandemer H (1995) Fuzzy sets, fuzzy logic, fuzzy methods with applications. Wiley, Chichester, pp 27–28, 80–81, and 96–98 · Zbl 0833.94028
[3] Eiben AE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms, IEEE Trans. Evolutionary Computation, vol 3, No. 2, pp 124–141
[4] Herrera F, Lozano M, Verdegay JL (1995) Tackling fuzzy genetic algorithms. In: Winter G, Periaux J, Galan M, Cuesta P (Eds) Genetic algorithms in engineering and computer science. John Wiley and Sons, pp 167–189
[5] Lampinen J, Zelinka I (2000) On stagnation of the differential evolution algorithm. In: Proceedings of the 6th international Mendel conference on soft computing, pp 76–83
[6] Lee MA, Takagi H (1993) Dynamic control of genetic algorithms using fuzzy logic techniques. In: Proceedings of the 5th international conference on genetic algorithms, pp 76–83
[7] Liu J, Lampinen J (2002) On setting the control parameter of the differential evolution algorithm. In: Proceedings of the 8th international Mendel conference on soft computing, pp 11–18
[8] Liu J, Lampinen J (2002) Adaptive parameter control of differential evolution. In: Proceedings of the 8th international Mendel conference on soft computing, pp 19–26
[9] Liu J, Lampinen J (2002) A fuzzy adaptive differential evolution algorithm. In: Proceedings of the 17th IEEE region 10 international conference on computer, communications, control and power engineering, Vol I of III, pp 606–611
[10] Lopez Cruz IL, Van Willigenburg LG, Van Straten G (2001) Parameter control strategy in differential evolution algorithm for optimal control. In: Proceedings of the international conference on artificial intelligence and soft computing, pp 211–216
[11] Matousek R, Osmera P, Roupec J (2000) GA with fuzzy inference system. In: Proceedings of the congress on evolutionary computation, vol 1, pp 646–651
[12] Michalewicz Z (1992) Genetic algorithms + data structures = evolution programs. Springer Berlin Heidelberg New York, pp 349–352 · Zbl 0763.68054
[13] Pedrycz W (1993) Fuzzy control and fuzzy systems – second, extended, edition. Research Studies Press LTD. Taunton, Somerset, pp 94–110
[14] Price KV (1999) An introduction to differential evolution. In: Corne D, Dorigo M, Glover F (Eds) New ideas in optimization. McGraw-Hill, London, pp 79–108
[15] Schwefel HP, Bäck T (1998) Artificial evolution: how and why? In: Quagliarella D, Périaux J, Poloni C, Winter G (Eds) Genetic algorithms and evolution strategies in engineering and computer science. John Wiley, New York, pp 1–18
[16] Storn R, Price K (1995) Differential evolution – a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report TR-95–012, ICSI, March · Zbl 0888.90135
[17] Storn R (1996) On the usage of differential evolution for function optimization. In: Biennial conference of the North American fuzzy information processing society, pp 519–523
[18] Storn R, Price K (1997) Differential evolution – a simple evolution strategy for fast optimization. Dr. Dobb’s journal 22(4): 18–24 and 78, April
[19] Storn R, Price K (1997) Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Global Optim 11(4): 341–359 · Zbl 0888.90135
[20] Zaharie D (2002) Critical values for the control parameters of differential evolution algorithms. In: Proceedings of the 8th international Mendel conference on soft computing, pp 62–67
[21] Zaharie D (2002) Parameter adaptation in differential evolution by controlling the population diversity. In: Proceedings. of 4th international workshop on symbolic and numeric algorithms for scientific computing, pp 385–397
[22] Zimmermann HJ (1986) Fuzzy set theory – and its applications. Kluwer-Nijhoff, Boston, pp 11–12 and 61
[23] Šmuc T (2002) Improving convergence properties of the differential evolution algorithms. In: Proceedings of the 8th international Mendel conference on soft computing, pp 80–86
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