Abstract
Differential Evolution (DE) can be simplified in the sense that the number of existing parameter is decreased from two parameters to only one parameter. We eliminate the scaling factor, F, and replace this by a uniform random number within [0, 1]. As such, it is easy to tune the crossover rate, CR, through parameter sensitivity analysis. In this analysis, the algorithm is run for 50 trials from 0.1 to 1.0 with a step increment of 0.1 on 23 benchmark problems. Results show that using the optimal CR, there is room for improvement in some of the benchmark problems. With the advantage and simplicity of a single parameter, it is significantly easier to tune this parameter and thus take the full advantage of the algorithm. The proposed algorithm here has a significant benefit when applied to real-world problems as it saves time in obtaining the best parameter setting for optimal performance.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Eiben, A.E., Hinterding, R., Michalewicz, Z.: Parameter control in evolutionary algorithms. IEEE Trans. Evol. Comput. 3, 124–141 (1999)
Price, K., Storn, R.: Differential evolution – A simple and efficient heruistic for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)
Anyong, Q.: Electromagnetic inverse scattering of multiple two-dimensional perfectly conducting objects by the differential evolution strategy. IEEE Trans. Antennas Propag. 51, 1251–1262 (2003)
Ching-Tzong, S., Chu-Sheng, L.: Network reconfiguration of distribution systems using improved mixed-integer hybrid differential evolution. IEEE Trans. Power Delivery 18, 1022–1027 (2003)
Storn, R.: System design by constraint adaptation and differential evolution. IEEE Trans. Evol. Comput. 3, 22–34 (1999)
Das, S., Abraham, A., Konar, A.: Automatic Clustering Using an Improved Differential Evolution Algorithm. IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 38, 218–237 (2008)
Grefenstette, J.J.: Optimization of Control Parameters for Genetic Algorithms. IEEE Transactions on Systems, Man and Cybernetics 16, 122–128 (1986)
Smit, S.K., Eiben, A.E.: Comparing parameter tuning methods for evolutionary algorithms. In: IEEE Congress on Evolutionary Computation, CEC 2009, pp. 399–406 (2009)
Price, K.V.: Differential evolution: a fast and simple numerical optimizer. In: 1996 Biennial Conference of the North American Fuzzy Information Processing Society, NAFIPS, pp. 524–527 (1996)
Terkel, D.A., Semenov, M.A.: Analysis of convergence of an evolutionary algorthm with self-adaptation using a stochastic Lyapunov function. Evol. Comput. 11(4), 363–379 (2003)
Yao, X., He, J.: Toward an analytic framework for analysing the computation time of evolutionary algorithms. Artificial Intell. 145(1-2) (2003)
Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems. IEEE Transactions on Evolutionary Computation 10, 646–657 (2006)
Das, S., Abraham, A., Chakraborty, U.K., Konar, A.: Differential Evolution Using a Neighborhood-Based Mutation Operator. IEEE Transactions on Evolutionary Computation 13, 526–553 (2009)
Vesterstrom, J., Thomsen, R.: A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In: Congress on Evolutionary Computation, CEC 2004, vol. 1982, pp. 1980–1987 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kang, Y., Ting, T.O., Yang, XS., Cheng, S. (2013). One Parameter Differential Evolution (OPDE) for Numerical Benchmark Problems. In: Tan, Y., Shi, Y., Mo, H. (eds) Advances in Swarm Intelligence. ICSI 2013. Lecture Notes in Computer Science, vol 7928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38703-6_51
Download citation
DOI: https://doi.org/10.1007/978-3-642-38703-6_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38702-9
Online ISBN: 978-3-642-38703-6
eBook Packages: Computer ScienceComputer Science (R0)