Adaptive Variance Scaling in Clayton Copula EDA

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 113)

Abstract

Estimation of Distribution Algorithms based on copula (cEDA) divide the estimated probabilistic model about the promising population into two parts, the marginal distribution of each variable and a copula function. The copula function combines the marginal distribution of each variable together as the joint distribution. The selection of marginal distribution can affect the optimization results. In the research on Clayton cEDA, empirical distribution and normal distribution are used as the marginal distribution respectively, the results are compared with each other, then the lack of using normal distribution is simply analyzed, an adaptive variance scaling strategy introduced to the algorithms to improve the optimization efficiency, and the experiments are used to illustrate the results.

Keywords

Estimation of Distribution Algorithms (EDAs) Copula theory Clayton copula function Marginal distribution Empirical distribution Normal distribution 

Notes

Acknowledgements

This work is supported by the Youth Research Fund of ShanXi Province (No. 2010021017-2), the Science Fund of Shanxi Institution of Higher Learning (No. 2010015) and the Nature Science Fund of ShanXi Province (No. 2009011017-3).

References

  1. 1.
    Wang L, Zeng J (2010) Estimation of distribution algorithms based on copula theory. In: Chen YP (ed) Exploitation of linkage learning in evolutionary algorithms, pp 137–160 Springer, Heidelberg. ISBN: 3642128335, 265 pGoogle Scholar
  2. 2.
    Wang L, Zeng J, Hong Y (2009) Estimation of distribution algorithms based on archimedean copula. In GEC 2009: proceedings of the first ACM/SIGEVO summit on genetic and evolutionary computation. ACM, New York, pp 993–996CrossRefGoogle Scholar
  3. 3.
    Salinas-Gutierrez R, Hernandez-Aguirre A, Villa-Diharce ER (2009) Using copulas in estimation of distribution algorithms. In: Hernandez Aguirre A et al (ed.) LNAI 5845, MICAI 2009, pp 658–668Google Scholar
  4. 4.
    Wang L, Wang Y, Zeng J, Hong Y (2010) An estimation of distribution algorithm based on clayton copula and empirical margin. In: 2010 international conference on life system modeling and simulation & 2010 international conference on intelligent computing for sustainable energy and environment (LSMS & ICSEE 2010), Wuxi, China, pp 17–20Google Scholar
  5. 5.
    Larranaga P, Etxeberria R, Lozano JA, Pena JM (2000) Optimization in continuous domains by learning and simulation of Gaussian networks. In: Pelikan M et al (eds) Proceedings of the optimization by building and using probabilistic models OBUPM workshop at the genetic and evolutionary computation conference GECCO-2000. Morgan Kaufmann, San Francisco, pp 201–204Google Scholar
  6. 6.
    Larranaga P, Lozano JA, Bengoetxea E (2001) Estimation of distribution algorithms based on multivariate normal and gaussian networks. Technical report KZZA-IK-1-01. Department of Computer Science and Artificial Intelligence University of the Basque Country, MadridGoogle Scholar
  7. 7.
    Ahn CW, Ramakrishna RS, Goldberg DE (2004) Real-coded bayesian optimization algorithm: bringing the strength of BOA into the continuous world. In: Deb K (ed) Proceedings of the genetic and evolutionary computation conference GECCO 2004, Springer, Berlin, pp 840–851Google Scholar
  8. 8.
    Bosman PAN, Thierens D (2000) Expanding from discrete to continuous estimation of distribution algorithms: the IDEA. In: Proceedings of the 6th international conference on parallel problem solving from nature-PPSN VI, Springer, pp 767–776Google Scholar
  9. 9.
    Duque TS, Goldberg DE, Sastry K (2008) Enhancing the efficiency of the ECGA. In: Rudolph G et al(eds) PPSN 2008.LNCS, Springer, Heidelberg, 5199:165–174Google Scholar
  10. 10.
    Grahl J, Bosman PAN, Rothlauf F (2004) The correlation-triggered adaptive variance scaling IDEA(CT-AVS-IDEA). In: Yao X (ed) Proceedings of the 8th annual conference on genetic and evolutionary computation conference. Gecco 2006, ACM Press, New York, USA, 2006, pp 397–404 PPSNVIII, Springer, Berlin, pp 352–361Google Scholar
  11. 11.
    Bosman PAN, Grahl J, Rothlauf F(2007) SDR: a better trigger for adaptive variance scaling in normal EDAs. In: GECCO’07: Proceedings of the 9th annual conference on genetic and evolutionary computation, ACM Press, New York, USA, pp 492–499Google Scholar
  12. 12.
    Peter Bosman AN, Grahl J (2008) Matching inductive search bias and problemstructure in continuous Estimation-of-Distribution Algorithms. Eur J Oper Res 185:1246–1264CrossRefMATHGoogle Scholar
  13. 13.
    Ocenasek J, Kern S, Hanse N, Koumoutsakos P (2004) A mixed bayesian optimization algorithm with variance adaptation. In: Yao X (ed) Parallel Problem Solving from Nature-PPSNVIII. Springer, Berlin, pp 352–361CrossRefGoogle Scholar
  14. 14.
    Yuan B, Gallagher M (2005) On the importance of diversity maintenance in estimation of distribution algorithms, In: Beyer HG, O’ Reilly UM (eds) Proceedings of the genetic and evolutionary computation conference GECCO-2005, vol 1. ACM Press, New York,USA, pp.719–726Google Scholar
  15. 15.
    Grahl J, Minner S, Rothlauf F (2005) Behaviour of UMDAc with truncation selection on monotonous functions. In: The 2005 IEEE congress on evolutionary computation IEEE CEC 2005Google Scholar
  16. 16.
    Marshall AW, Olkin I (1988) Families of multivariate distributions. J Am Stat Assoc 83:834–841CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Dong’en Z (1998) Estimation of parameter for truncated normal distribution via the EM algorithm. J Beijing Inst Light Ind 16(2):123–129Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Complex System and Computational Intelligence LaboratoryTaiyuan University of Science and TechnologyTaiyuanChina
  2. 2.Colloge of Electrical and Information EngineeringLanzhou University of TechnologyLanzhouChina

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