Advertisement

Pure Strategy or Mixed Strategy?

An Initial Comparison of Their Asymptotic Convergence Rate and Asymptotic Hitting Time
  • Jun He
  • Feidun He
  • Hongbin Dong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7245)

Abstract

Mixed strategy evolutionary algorithms (EAs) aim at integrating several mutation operators into a single algorithm. However no analysis has been made to answer the theoretical question: whether and when is the performance of mixed strategy EAs better than that of pure strategy EAs? In this paper, asymptotic convergence rate and asymptotic hitting time are proposed to measure the performance of EAs. It is proven that the asymptotic convergence rate and asymptotic hitting time of any mixed strategy (1+1) EA consisting of several mutation operators is not worse than that of the worst pure strategy (1+1) EA using only one mutation operator. Furthermore it is proven that if these mutation operators are mutually complementary, then it is possible to design a mixed strategy (1+1) EA whose performance is better than that of any pure strategy (1+1) EA using only one mutation operator.

Keywords

Mixed Strategy Pure Strategy Asymptotic Convergence Rate Asymptotic Hitting Time Hybrid Evolutionary Algorithms 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fogel, D., Michalewicz, Z.: Handbook of Evolutionary Computation. Oxford Univ. Press (1997)Google Scholar
  2. 2.
    Grosan, C., Abraham, A., Ishibuchi, H.: Hybrid Evolutionary Algorithms. Springer (2007)Google Scholar
  3. 3.
    Dutta, P.: Strategies and Games: Theory and Practice. MIT Press (1999)Google Scholar
  4. 4.
    He, J., Yao, X.: A Game-Theoretic Approach for Designing Mixed Mutation Strategies. In: Wang, L., Chen, K., Ong, Y.S. (eds.) ICNC 2005, Part III. LNCS, vol. 3612, pp. 279–288. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Dong, H., He, J., Huang, H., Hou, W.: Evolutionary programming using a mixed mutation strategy. Information Sciences 177(1), 312–327 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Shen, L., He, J.: A mixed strategy for evolutionary programming based on local fitness landscape. In: Proceedings of 2010 IEEE Congress on Evolutionary Computation, pp. 350–357. IEEE Press, Barcelona (July 2010)Google Scholar
  7. 7.
    Varga, R.: Matrix Iterative Analysis. Springer (2009)Google Scholar
  8. 8.
    He, J., Chen, T.: Population scalability analysis of abstract population-based random search: Spectral radius. Arxiv preprint arXiv:1108.4531 (2011)Google Scholar
  9. 9.
    Michalewicz, Z.: Genetic Algorithms + Data Structure = Evolution Program. Springer, New York (1996)Google Scholar
  10. 10.
    He, J., Zhou, Y.: A Comparison of GAs Using Penalizing Infeasible Solutions and Repairing Infeasible Solutions on Average Capacity Knapsack. In: Kang, L., Liu, Y., Zeng, S. (eds.) ISICA 2007. LNCS, vol. 4683, pp. 100–109. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Rudolph, G.: Convergence analysis of canonical genetic algorithms. IEEE Transactions on Neural Networks 5(1), 96–101 (1994)CrossRefGoogle Scholar
  12. 12.
    He, J., Kang, L.: On the convergence rate of genetic algorithms. Theoretical Computer Science 229(1-2), 23–39 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    He, J., Yao, X.: Towards an analytic framework for analysing the computation time of evolutionary algorithms. Artificial Intelligence 145(1-2), 59–97 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Iosifescu, M.: Finite Markov Chain and their Applications. Wiley, Chichester (1980)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jun He
    • 1
  • Feidun He
    • 2
  • Hongbin Dong
    • 3
  1. 1.Department of Computer ScienceAberystwyth UniversityCeredigionU.K.
  2. 2.School of Information Science and TechnologySouthwest Jiaotong UniversityChengduChina
  3. 3.College of Computer Science and TechnologyHarbin Engineering UniversityHarbinChina

Personalised recommendations