Abstract.
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abbass HA (2002) The self-adaptive pareto differential evolution algorithm. In: Proceedings of the congress on evolutionary computation, pp 831–836
Bandemer H (1995) Fuzzy sets, fuzzy logic, fuzzy methods with applications. Wiley, Chichester, pp 27–28, 80–81, and 96–98
Eiben AE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms, IEEE Trans. Evolutionary Computation, vol 3, No. 2, pp 124–141
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
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
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
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
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
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
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
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
Michalewicz Z (1992) Genetic algorithms + data structures = evolution programs. Springer Berlin Heidelberg New York, pp 349–352
Pedrycz W (1993) Fuzzy control and fuzzy systems – second, extended, edition. Research Studies Press LTD. Taunton, Somerset, pp 94–110
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
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
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
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
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
Storn R, Price K (1997) Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Global Optim 11(4): 341–359
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
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
Zimmermann HJ (1986) Fuzzy set theory – and its applications. Kluwer-Nijhoff, Boston, pp 11–12 and 61
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, J., Lampinen, J. A Fuzzy Adaptive Differential Evolution Algorithm. Soft Comput 9, 448–462 (2005). https://doi.org/10.1007/s00500-004-0363-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-004-0363-x