Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper, the concept of a multidimensional discrete spectral measure is introduced in the context of its application to the real-valued evolutionary algorithms. The notion of a discrete spectral measure makes it possible to uniquely define a class of multivariate heavy-tailed distributions, that have recently received substantial attention of the evolutionary optimization community. In particular, an adaptation procedure known from the distribution estimation algorithms (EDAs) is considered and the resulting estimated distribution is compared with the optimally selected referential distribution.
Rocznik
Tom
Strony
11--19
Opis fizyczny
Bibliogr. 30 poz., rys.
Twórcy
autor
autor
- Institute of Control and Computation Engineering, University of Zielona Gora, Podgorna st 50, 65-246 Zielona Gora, Poland, A.Obuchowicz@issi.uz.zgora.pl
Bibliografia
- [1] I. Karcz-Dule,ba, “Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process”, Int. J. Appl. Math. Comput. Sci., vol. 14, no. 3, pp. 79–90, 2004.
- [2] H. G. Beyer and H. P. Schwefel, “Evolutionary strategies – a comprehensive introduction”, Neural Computing, vol. 1, no. 1, pp. 3–52, 2002.
- [3] N. Hansen and A. Ostermeier, “Completely derandomized self-adaptation in evolutionary strategies”, Evol. Comput., vol. 9, no. 2, pp. 159–195, 2002.
- [4] N. Hansen, F. Gemperle, A. Auger, and P. Koumoutsakos, “Why do heavy-tail distributions help?” in Parallel Problem Solving from Nature PPSN IX, Springer, LNCS 4193, pp. 62–71, 2006.
- [5] X. Liu and W. Xu, “A new filled function applied to global optimization”, Comput. Oper. Res. vol. 31, pp. 61–80, 2004.
- [6] A. Obuchowicz, Evolutionary Algorithms in Global Optimization and Dynamic System Diagnosis. Zielona Gora: Lubuskie Scientific Society Press, 2003.
- [7] A. Obuchowicz and P. Pre,tki, “Phenotypic evolution with mutation based on symmetric a-stable distributions”, Int. J. Appl. Math. Comput. Sci., vol. 14, no. 3, pp. 289–316, 2004.
- [8] G. Rudolph, “Local convergence rates of simple evolutionary algorithms wich Cauchy mutations”, IEEE Trans. Evol. Comput. vol. 1, no. 4, pp. 249–258, 1997.
- [9] X. Yao and Y. Liu, “Fast evolution strategies”, in Evolutionary Programming IV, P. J. Angeline, R. G. Reynolds, J. R. MacDonnell, and R. Eberhart, Eds. Berlin: Springer, 1997, pp. 151–161.
- [10] X. Yao, Y. Liu, and G. Liu, “Evolutionary programming made faster”, IEEE Trans. Evol. Comput. vol. 3, no. 2, pp. 82–102, 1999.
- [11] P. Pre,tki, “Algorytmy ewolucyjne z mutacją a-stabilną w zadaniach globalnej optymalizacji parametrycznej”. Ph.D. thesis, University of Zielona Gora, Poland, 2008 (in Polish).
- [12] A. Obuchowicz and P. Pre,tki, “Isotropic symmetric a-stable mutations for evolutionary algorithms”, in Proc. IEEE Congr. Evol. Comput. CEC’05, Edinburgh, UK, 2005, pp. 404-410.
- [13] A. Obuchowicz and P. Pre,tki, “Evolutionary algorithms with stable mutations based on a discrete spectral measure”, in Proc. Int. Conf. Artif. Intel. Soft Comput. ICAISC’2010, Springer-Verlag, LNAI 6114, no. 2, pp. 181–188, 2010.
- [14] P. Pre,tki, “Learning stable mutation in (1,l )ES evolutionary strategy”, in Proc. 10th Conf. Evol. Algorithms Global Optimiz., Be,dlewo, Poland, 2007, pp. 233–240.
- [15] P. Larranaga and J. A. Lozano, Estimation of Distribution Algorithms: A New Tool for Evolutionary Optimization. Boston: Kluwer Academic Publishers, 2001.
- [16] A. Zolotariev,One-Dimensional Stable Distributions. Providence: American Mathematical Society Press, 1986.
- [17] M. Kanter, “Stable densities under change of scale and total variation inequalities”, Ann. Probab., vol. 3, no. 4, pp. 697–707, 1975.
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- [19] J. P. Nolan, A. K. Panorska, and J. H. McCulloch, “Estimation of stable spectral measures – stable non-Gaussian models in finanse and econometrics”, Math. Comput. Model. vol. 34, no. 9, pp. 1113–1122, 2001.
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- [21] T. Byczkowski, J. P. Nolan, and B. Rajput, “Approximation of multidimensional stable densities”, J. Mult. Anal., vol. 46, pp. 13–31, 1993.
- [22] T. B ack, Evolutionary Algorithms in Theory and Practice. Oxford University Press, 1995.
- [23] I. Rechenberg, Evolutionsstrategie: Optimierung technisher Systeme nach Prinzipien der biologishen Evolution. Stuttgard: Frommann-Holzburg Verlag, 1973.
- [24] H.-P. Schwefel, Evolution and Optimum Seeking. New York: Wiley, 1995.
- [25] F. Kemp, “An introduction to sequential Monte Carlo methods”, J. Royal Statist. Soc. vol. D52, pp. 694–695, 2003.
- [26] R. Durrett, Probability: Theory and Examples. Duxbury Press, 1995.
- [27] J. C. Spall, Introduction to Stochastic Search and Optimization. Hoboken, NJ: Wiley, 1993.
- [28] L. N. Chrysostomos and M. Shao, Signal Processing with Alpha-Stable Distribution and Applications. Chichester, UK: Wiley, 1981.
- [29] P. G. Georgiou, P. Tsakalides, and C. Kyriakakis, “Alpha-stable odeling of noise and robust time-delay in the presence of impulsive noise”, IEEE Trans. Multimedia, vol. 1, no. 3, pp. 291–301, 1999.
- [30] P. Kidmose, “Alpha-stable distributions in signal processing of audio signals”, in Proc. 41st Conf. Simulation and Modeling SIMS 2000, Scandinavian Simulation Society Press, pp. 87–94, 2000.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BATA-0015-0013