A Trigonometric Mutation Operation to Differential Evolution
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Previous studies have shown that differential evolution is an efficient, effective and robust evolutionary optimization method. However, the convergence rate of differential evolution in optimizing a computationally expensive objective function still does not meet all our requirements, and attempting to speed up DE is considered necessary. In this paper, a new local search operation, trigonometric mutation, is proposed and embedded into the differential evolution algorithm. This modification enables the algorithm to get a better trade-off between the convergence rate and the robustness. Thus it can be possible to increase the convergence velocity of the differential evolution algorithm and thereby obtain an acceptable solution with a lower number of objective function evaluations. Such an improvement can be advantageous in many real-world problems where the evaluation of a candidate solution is a computationally expensive operation and consequently finding the global optimum or a good sub-optimal solution with the original differential evolution algorithm is too time-consuming, or even impossible within the time available. In this article, the mechanism of the trigonometric mutation operation is presented and analyzed. The modified differential evolution algorithm is demonstrated in cases of two well-known test functions, and is further examined with two practical training problems of neural networks. The obtained numerical simulation results are providing empirical evidences on the efficiency and effectiveness of the proposed modified differential evolution algorithm.
- Bäck, T. (1996), Evolutionary Algorithms in Theory and Practice, Oxford University Press, Inc., Oxford, 1996.
- De Jong, K. (1975), An Analysis of the Behavior of a Class of Genetic Adaptive Systems, Ph.D. Thesis, Department of Computer and Communication Sciences, University of Michigan, Ann Arbor, MI.
- Lampinen, J. (2000), A bibliography of differential evolution algorithm, Technical Report, Lappeenranta University of Technology, Department of Information Technology, Laboratory of Information Processing. Available via the Internet: http://www.lut.fi/ jlampine/debiblio.htm
- Lampinen, J., and Zelinka, I. (1999), Mechanical engineering design optimization by differential evolution, In: Corne, D., Dorigo, M. and Glover, F. (eds), New Ideas in Optimization, McGraw-Hill, London (UK), pp. 127-146.
- Lampinen, J. and Zelinka, I. (2000). On stagnation of the differential evolution algorithm, In: Ošmera, P. (ed.), Proceedings of MENDEL 2000, 6th International Mendel Conference on Soft Computing, Brno, Czech Republic, pp. 76-83. Available via the Internet: http://www.lut.fi/ jlampine/MEND2000.ps.
- Hassoun, M. H. (1995), Fundamentals of Artificial Neural Networks, MIT Press, Cambridge, MA.
- Muhlenbein, H., Schomisch, M. and Born, J. (1991), The parallel genetic algorithm as function optimizer, Parallel Computing 17, 619-632.
- Price, K. (1996), DE: a fast and simple numerical optimizer, 1996 Biennial Conference of the North American Fuzzy Information Processing Society, NAFIPS, Smith, M., Lee, M., Keller, J. And Yen, J. (eds.), IEEE Press, New York, pp. 524-527.
- Price, K. (1999), An introduction to DE, In: Corne, D., Marco, D. and Glover, F. (eds.), New Ideas in Optimization, McGraw-Hill, London (UK), pp. 78-108.
- Rogalsky, T., Derksen, R.W. and Kocabiyik, S. (1999), An aerodynamic design technique for optimizing fan blade spacing, Proceedings of the 7th Annual Conference of the Computational Fluid Dynamics Society of Canada, pp 2-29 - 2-34.
- Rogalsky, T. and Derksen, R. W. (2000), Hybridization of differential evolution for aerodynamic design, Proceedings of the 8th Annual Conference of the Computational Fluid Dynamics Society of Canada, pp. 729-736.
- Stumberger, G., Dolinar, D., Pahner, U. and Hameyer, K. (2000), Optimization of radial active magnetic bearings using the finite element technique and the differential evolution algorithm, IEEE Transactions on Magnetics 36(4), 1009-1013.
- Storn, R. (1996), On the usage of differential evolution for function optimization, 1996 Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS 1996), Berkeley, IEEE, New York, pp. 519-523.
- Storn, R. and Price, K. (1995), DE-a simple and efficient adaptive scheme for global optimization over continuous space, Technical Report TR-95-012, ICSI, March 1995. Available via the Internet: ftp.icsi.berkeley.edu/pub/techreports/ 1995/tr-95-012.ps.Z.
- Storn, R. and Price, K. (1996), Minimizing the real function of the ICEC'96 contest by DE, IEEE International Conference on Evolutionary Computation, Nagoya, pp. 842-844.
- Storn, R. and Price, K. (1997), DE-a simple evolution strategy for fast optimization, Dr. Dobb's Journal April 97, 18-24 and 78.
- Storn, R. and Price, K. (1997), DE-a simple and efficient heuristic for global optimization over continuous space, Journal of Global Optimization, 11(4), 341-359.
- Zaharie, D. (2002), Critical values for control parameters of differential evolution algorithms, In: Matoušek, R. and Ošmera, P. (eds.), Proceedings of MENDEL 2002, 8th International Conference on Soft Computing, Brno, Czech Republic, pp. 62–67. ISBN 80-214-2135-5.
- A Trigonometric Mutation Operation to Differential Evolution
Journal of Global Optimization
Volume 27, Issue 1 , pp 105-129
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- Kluwer Academic Publishers
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- differential evolution
- evolutionary algorithm
- mutation operation
- nonlinear optimization
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