Abstract
Metaoptimization is a way of tuning parameters of an optimization algorithm with use of a higher-level optimizer. In this paper it is applied to the problem of choosing among possible mutation range adaptation schemes in Differential Evolution (DE). We consider a new version of DE, called DE/rand/∞. In this algorithm, differential mutation is replaced by a Gaussian one, where the covariance matrix is determined from the contents of the current population. We exploit this property to separate the adaption of search directions from the adaptation of mutation range. The former is characterized by a norm of the covariance matrix while the latter can be expressed as a normed covariance matrix multiplied by the scaling factor. Such separation allows us to introduce a few schemes of direct, explicit control of the mutation range and to compare them with the basic, implicit scheme present in DE/rand/∞. To ensure fair comparisons all versions of DE/rand/∞ are first metaoptimized and then assessed on the CEC’05 benchmark.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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(6), 646–657 (2006)
Grefenstette, J.J.: Optimization of control parameters for genetic algorithms. IEEE Transactions on Systems, Man and Cybernetics 16(1), 122–128 (1986)
Hansen, N.: Compilation of results on the 2005 CEC benchmark function set (2006)
Hansen, N.: The CMA evolution strategy webpage (November 2009)
Hansen, N., Auger, A., Ros, R., Finck, S., Posik, P.: Comparing results of 31 algorithms from the black-box optimization benchmarking BBOB-2009 (2010)
Neri, F., Tirronen, V.: Recent advances in differential evolution: a survey and experimental analysis. Artificical Intelligence Reviews 33(1-2), 61–106 (2010)
Opara, K., Arabas, J.: Differential Mutation Based on Population Covariance Matrix. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 114–123. Springer, Heidelberg (2010)
Pedersen, M.: Tuning & Simplifying Heuristical Optimization. PhD thesis, University of Southampton (2010)
Price, K., Storn, R., Lampien, J.: Differential evolution. A practical approach to global optimization. Springer, Heidelberg (2005)
Qin, A., Huang, V., Suganthan, P.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Transaction on Evolutionary Computation 13(2), 398–417 (2009)
Suganthan, P., Hansen, N., Liang, J., Deb, K., Chen, Y., Auger, A., Tiwari, S.: Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Opara, K., Arabas, J. (2012). Decomposition and Metaoptimization of Mutation Operator in Differential Evolution. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Swarm and Evolutionary Computation. EC SIDE 2012 2012. Lecture Notes in Computer Science, vol 7269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29353-5_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-29353-5_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29352-8
Online ISBN: 978-3-642-29353-5
eBook Packages: Computer ScienceComputer Science (R0)