Abstract
In this paper the concept of multidimensional discrete spectral measure is introduced in the context of its application to real-valued evolutionary algorithms. The notion of discrete spectral measure makes possible to uniquely define a class of multivariate heavy-tailed distributions, that have received more and more attention of evolutionary optimization commynity , recently. Simple sample illustrates advantages of such approach.
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Beyer, H.G., Schwefel, H.P.: Evolutionary strategies – a comprehensive introduction. Neural Computing 1(1), 3–52 (2002)
Byczkowski, T., Nolan, J.P., Rajput, B.: Approximation of multidimensional stable densities. J. of Mult. Anal. 46, 13–31 (1993)
Durrett, R.: Probability: Theory and Examples, 2nd edn. Duxbury Press (1995)
Gutowski, M.: Lévy flights as an underlying mechanism for a global optimization algorithm. In: Proc. 5th Conf. Evolutionary Algorithms and Global Optimization, pp. 79–86. Warsaw University of Technology Press (2001)
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolutionary strategies. Evolutionary Computation 9(2), 159–195 (2001)
Karcz-Dulȩba, I.: Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process. Int. Journ. Appl. Math. Comput. Sci. 14(1), 79–90 (2004)
Kemp, F.: An introduction to sequential Monte Carlo methods. Journal of the Royal Statistical Society D52, 694–695 (2003)
Kern, S., Uller, S., Uche, D., Hansen, N., Koumoutsakos, P.: Learning probability distributions in continuous evolutionary algorithms. In: Proc. Workshop on Fundamentals in Evolutionary Algorithms, 13th Int. Colloquium on Automata, Languages and Programming, Eindhoven (2004)
Liu, X., Xu, W.: A new filled function applied to global optimization, Comput. Oper. Res. 31, 61–80 (2004)
MacKey, D.C.J.: Introduction to Monte Carlo methods. In: Jordan, M.I. (ed.) Learning in Graphical Models. NATO Science Series, pp. 175–204. Kluwer Academmic Press, Dordrecht (1998)
Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, London (1996)
Nolan, J.P., Panorska, A.K., McCulloch, J.H.: Estimation of stable spectral measures - stable non-Gaussian models in finanse and econometrics. Math. Comput. Modelling 34(9), 1113–1122 (2001)
Obuchowicz, A.: Evolutionary Algorithms in Global Optimization and Dynamic System Diagnosis. Lubuskie Scientific Society Press, Zielona Góra (2003)
Obuchowicz, A., Prȩtki, P.: Phenotypic Evolution with Mutation Based on Symmetric α-Stable Distributions. Int. J. Applied Mathematics and Computer Science 14, 289–316 (2004)
Obuchowicz, A., Prȩtki, P.: Isotropic Symmetric α-Stable Mutations for Evolutionary Algorithms. In: Proc. IEEE Congress on Evoutionary Computation, CEC 2005, pp. 404–410 (2005)
Prȩtki, P.: α-Stable Distributions in Evolutionary Algorithms of Parametric Global Optimization. PhD Thesis, University of Zielona Góra, Poland (2008) (in Polish)
Rudolph, G.: Local convergence rates of simple evolutionary algorithms wich Cauchy mutations. IEEE Trans. Evolutionary Computation 1(4), 249–258 (1997)
Samorodnitsky, G., Taqqu, M.S.: Stable Non-Gaussian Random Processes. Chapman & Hall, New York (1994)
Spall, J.C.: Introduction to Stochastic Search and optimization. Wiley, Hoboken (1993)
Vidysagar, M.: Randomized algorithms for robust controller synthesis using statistical learning theory. Automatica 37, 1515–1528 (2001)
Yao, X., Liu, Y.: Fast evolution strategies. In: Angeline, P.J., McDonnell, J.R., Reynolds, R.G., Eberhart, R. (eds.) EP 1997. LNCS, vol. 1213, pp. 151–161. Springer, Heidelberg (1997)
Yao, X., Liu, Y., Liu, G.: Evolutionary Programming made faster. IEEE Trans. Evolutionary Computation 3(2), 82–102 (1999)
Zolotariev, A.: One-Dimensional Stable Distributions. American Mathematical Society, Providence (1986)
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Obuchowicz, A., Prȩtki, P. (2010). Evolutionary Algorithms with Stable Mutations Based on a Discrete Spectral Measure. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artifical Intelligence and Soft Computing. ICAISC 2010. Lecture Notes in Computer Science(), vol 6114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13232-2_22
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DOI: https://doi.org/10.1007/978-3-642-13232-2_22
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