Journal of Computer Science and Technology

, Volume 19, Issue 4, pp 450–458 | Cite as

Time complexity analysis of an evolutionary algorithm for finding nearly maximum cardinality matching

  • Jun He
  • Xin Yao
Artificial Intelligence


Most of works on the time complexity analysis of evolutionary algorithms have always focused on some artificial binary problems The time complexity of the algorithms for combinatorial optimisation has not been well understood. This paper considers the time complexity of an evolutionary algorithm for a classical combinatorial optimisation problem, to find the maximum cardinality matching in a graph. It is shown that the evolutionary algorithm can produce, a matching with nearly maximum cardinality in average polynomial time.


evolutionary algorithm (EA) combinatorial optimisation time complexity maximum matching 


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  1. [1]
    Yao X (ed.). Evolutionary Computation: Theory and Applications. World Scientific Publishing, Singapore, 1999.Google Scholar
  2. [2]
    Liang K-Het al. A new evolutionary approach to cutting stock problems with and without contiguity.Computers and Operations Research, 2002, 29(12): 1641–1659.CrossRefMathSciNetGoogle Scholar
  3. [3]
    Zhang C, Yao X, Yang J. An evolutionary approach to materialized views selection in a data warehouse environment.IEEE Trans. Systems, Man, and Cybernetics, Part C, 2001, 31(3): 282–294.CrossRefMathSciNetGoogle Scholar
  4. [4]
    Rudolph G. Finite Markov chain results in evolutionary computation: A tour d'Horizon.Fundamenta Informaticae, 1998, 35(1–4): 67–89.MATHMathSciNetGoogle Scholar
  5. [5]
    Eiben A E, Rudolph G. Theory of evolutionary algorithms: A bird's eye view.Theoretical Computer Science, 1999, 229(1–2): 3–9.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Beyer H-G, Schwefel H-P, Wegener I. How to analyse evolutionary algorithms.Theoretical Computer Science, 2002, 287(1): 101–130.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Droste S, Jansen T, Wegener I. A rigorous complexity analysis of the (1+1) evolutionary algorithm for linear functions with Boolean inputs.Evolutionary Computation, 1998, 6(2): 185–196.CrossRefGoogle Scholar
  8. [8]
    Garnier J, Kallel L. Statistical distribution of the convergence time of evolutionary algorithms for long path problems.IEEE Trans. Evolutionary Computation, 2000, 4(1): 16–30.CrossRefGoogle Scholar
  9. [9]
    Droste S, Jansen T, Wegener I. On the analysis of the (1+1) evolutionary algorithmsTheoretical Computer Science, 2002, 276(1–2): 51–81.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    He J, Yao X. From an individual to a population: An analysis of the first hitting time of population-based evolutionary algorithms.IEEE Trans. Evolutionary Computation, 2002, 6(5): 495–511.CrossRefGoogle Scholar
  11. [11]
    Papadimitriou C H, Steiglitz K. Combinatorial Optimization: Algorithms and Complexity. Dover, Mineola, NY, 1998.MATHGoogle Scholar
  12. [12]
    Karpinski M, Rytter W. Fast Parallel Algorithms for Graph Matching Problems. Oxford University Press, Oxford, 1998.MATHGoogle Scholar
  13. [13]
    Sasaki G H, Hajek B. The time complexity of maximum matching by simulated annealing.J. ACM, 1988, 35(2): 387–403.CrossRefMathSciNetGoogle Scholar
  14. [14]
    Yao X. Maximum matching on Boltzmann machines.Neural Processing Letters, 1998, 7(1): 49–53.CrossRefGoogle Scholar
  15. [15]
    He J, Yao X. Drift analysis and average time complexity of evolutionary algorithms.Artificial Intelligence, 2001, 127(1): 57–85.MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    He J, Yao X. Erratum to: Drift analysis and average time complexity of evolutionary algorithms — [Artificial Intelligence, 2001, 127: 57–85].Artificial Intelligence, 2002, 140(1): 245–248.MATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    He J, Yao X. Towards an analytic framework for analysing the computationtime of evolutionary algorithms.Artificial Intelligence, 2003, 145(1–2): 59–97.MATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    Hajek B. Hitting time and occupation time bounds implied by drift analysis with applications.Advances in Applied Probability, 1982, 14(3): 502–525.MATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    Meyn S P, Tweedie R L. Markov Chains and Stochastic Stability. Springer-Verlag, New York, 1993.MATHGoogle Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 2004

Authors and Affiliations

  1. 1.State Key Lab of Software EngineeringWuhan UniversityWuhanP.R. China
  2. 2.School of Computer ScienceUniversity of BirminghamBirminghamEngland, U.K.

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