Natural Computing

, Volume 3, Issue 1, pp 21–35 | Cite as

A study of drift analysis for estimating computation time of evolutionary algorithms

  • Jun He
  • Xin Yao
Article

Abstract

This paper introduces drift analysis and its applications in estimating average computation time of evolutionary algorithms. Firstly, drift conditions for estimating upper and lower bounds of the mean first hitting times of evolutionary algorithms are presented. Then drift analysis is applied to two specific evolutionary algorithms and problems. Finally, a general classification of easy and hard problems for evolutionary algorithmsis given based on the analysis.

algorithm analysis combinatorial optimisation evolutionary computation meta-heuristics 

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References

  1. Beyer H-G (2001) The Theory of Evolutionary Strategies. Springer, BerlinGoogle Scholar
  2. Beyer H-G, Schwefel H-P and Wegener I (2002) How to analyse evolutionary algorithms. Theoretical Computer Science 287(1): 101–130Google Scholar
  3. Chow YS and Teicher H (1988) Probability Theory: Independence, Interchangeability and Martingales, 2nd edn. Springer-Verlag, New YorkGoogle Scholar
  4. Droste S, Jansen T and Wegener I (1998) A rigorous complexity analysis of the (1 + 1)-evolutionary algorithm for linear functions with Boolean inputs. Evolutionary Computation 6(2): 185–196Google Scholar
  5. Droste S, Jansen T and Wegener I (2002) On the analysis of the (1 + 1)-evolutionary algorithms. Theoretical Computer Science 276(1–2): 51–81Google Scholar
  6. Eiben AE and Rudolph G (1999) Theory of evolutionary algorithms: A bird's eye view. Theoretical Computer Science 229(1–2): 3–9Google Scholar
  7. Hajek B (1982) Hitting time and occupation time bounds implied by drift analysis with applications. Advances in Applied Probability 14(3): 502–525Google Scholar
  8. He J and Yao X (2001) Drift analysis and average time complexity of evolutionary algorithms. Artificial Intelligence 127(1): 57–85 (Erratum in (2002) Artificial Intelligence 140(1): 245–248)Google Scholar
  9. He J and Yao X (2002) From an individual to a population: An analysis of the first hitting time of population-based evolutionary algorithms. IEEE Transactions on Evolutionary Computation 6(5): 495–511Google Scholar
  10. He J and Yao X (2003) Towards an analytic framework for analysing the computation time of evolutionary algorithms. Artificial Intelligence 145(1–2): 59–97Google Scholar
  11. Meyn SP and Tweedie RL (1993) Markov Chains and Stochastic Stability. Springer-Verlag, New YorkGoogle Scholar
  12. Rudolph G (1994) Convergence of non-elitist strategies. In: Proc. of the First IEEE conference on Evolutionary Computation, Vol. 1, pp. 63–66. IEEE Press, Piscataway, NJGoogle Scholar
  13. Rudolph G (1998) Finite Markov chain results in evolutionary computation: A tour d'horizon. Fundamenta Informaticae 35(1–4): 67–89Google Scholar
  14. Sasaki GH and Hajek B (1988) The time complexity of maximum matching by simulated annealing. J ACM 35(2): 387–403Google Scholar
  15. Syski R (1992) Passage Times for Markov Chains. IOS Press, AmsterdamGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Jun He
    • 1
  • Xin Yao
    • 1
  1. 1.The Centre of Excellence for Research in Computational Intelligence and Applications (CERCIA), School of Computer Sciencethe University of BirminghamEdgbastonUK)

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