On the Running Time Analysis of the (1+1) Evolutionary Algorithm for the Subset Sum Problem

  • Yuren Zhou
  • Zhi Guo
  • Jun He
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4688)


Theoretic researches of evolutionary algorithms have received much attention in the past few years. This paper presents the running time analysis of evolutionary algorithm for the subset sum problems. The analysis is carried out on (1+1) EA for different subset sum problems. It uses the binary representation to encode the solutions, the method “superiority of feasible point” that separate objectives and constraints to handle the constraints, and the absorbing Markov chain model to analyze the expected runtime. It is shown that the mean first hitting time of (1+1) EA for solving subset sum problems may be polynomial, exponential, or infinite.




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Garey, M.R., Johnson, D.S.: Computers and intractability-A guide to the theory of NP-completeness. Freeman, New York (1979)MATHGoogle Scholar
  2. 2.
    Hochbaum, D.S.: Approximation algorithms for NP-Hard problems. Wadworth publish company (1997)Google Scholar
  3. 3.
    Michalewicz, Z.: Genetic algorithms + data structures = Evolution programs. Springer, Heidelberg (1992)MATHGoogle Scholar
  4. 4.
    Wang, R.: A genetic algorithm for subset sum problem. Neurocomputing, 463–468 (2004)Google Scholar
  5. 5.
    Lin, F.T., Kao, C.Y., Hsu, C.C.: Applying the genetic approach to simulated annealing in solving some NP-hard problems. IEEE transactions on system, man, and cybernetics 23, 1752–1767 (1993)CrossRefGoogle Scholar
  6. 6.
    Witt, C.: Worst-case and average-case approximations by simple randomized search heuristics. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 44–56. Springer, Heidelberg (2005)Google Scholar
  7. 7.
    Beyer, H.-G., Schwefel, H.-P., Wegener, I.: How to analyze evolutionary algorithms. Theoretical Computer Science, 101–130 (2002)Google Scholar
  8. 8.
    Garnier, J., Kallel, L., Schoenauer, M.: Rigorous hitting times for binary mutations. Evolutionary Computation, 167–203 (1999)Google Scholar
  9. 9.
    Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1)-evolutionary algorithm. Theoretical Computer Science, 51–81 (2002)Google Scholar
  10. 10.
    Wegener, I., Witt, C.: On the analysis of a simple evolutionary algorithm on quadratic pseudo-boolean function. Journal of discrete algorithms, 61–78 (2005)Google Scholar
  11. 11.
    He, J., Yao, X.: Towards an analytic framework for analyzing the computation time of evolutionary algorithms. Artificial Intelligence, 59–97 (2003)Google Scholar
  12. 12.
    Iosifescu, M.: Finite Markov processes and their applications. John Wiley & Sons, Chichester (1980)MATHGoogle Scholar
  13. 13.
    Coello, C.A.C.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Computer methods in applied mechanics and engineering 19, 1245–1287 (2002)CrossRefGoogle Scholar
  14. 14.
    Deb, K.: An efficient constraint handling method for genetic algorithms. Computer methods in applied mechanics and engineering 186(2-4), 311–338 (2000)MATHCrossRefGoogle Scholar
  15. 15.
    Coffman, J.W.W.: Recent asymptotic results in the probabilistic analysis of schedule makespans. In: Scheduling Theory and its applications, pp. 15–31. Wiley, Chichester (1995)Google Scholar
  16. 16.
    Motwani, R., Raghavan, P.: Randomized algorithms. Cambridge University Press, Cambridge (1995)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Yuren Zhou
    • 1
  • Zhi Guo
    • 1
  • Jun He
    • 2
  1. 1.School of Computer Science and Engineering, South China University of Technology, Guangzhou 510640China
  2. 2.School of Computer Science, University of Birmingham, Birmingham, B15 2TTUK

Personalised recommendations