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Fitness-levels for non-elitist populations

Published:12 July 2011Publication History

ABSTRACT

This paper introduces an easy to use technique for deriving upper bounds on the expected runtime of non-elitist population-based evolutionary algorithms (EAs). Applications of the technique show how the efficiency of EAs is critically dependant on having a sufficiently strong selective pressure. Parameter settings that ensure sufficient selective pressure on commonly considered benchmark functions are derived for the most popular selection mechanisms. Together with a recent technique for deriving lower bounds, this paper contributes to a much-needed analytical tool-box for the analysis of evolutionary algorithms with populations.

References

  1. T. Chen, J. He, G. Sun, G. Chen, and X. Yao. A new approach for analyzing average time complexity of population-based evolutionary algorithms on unimodal problems. IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, 39(5):1092--1106, Oct. 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms. McGraw Hill, New York, NY, 2nd edition, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. S. Droste, T. Jansen, and I. Wegener. On the analysis of the (1Google ScholarGoogle Scholar
  4. 1) Evolutionary Algorithm. Theoretical Computer Science, 276:51--81, 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. D. E. Goldberg and K. Deb. A comparative analysis of selection schemes used in genetic algorithms. In Foundations of Genetic Algorithms, pages 69--93. Morgan Kaufmann, 1991.Google ScholarGoogle Scholar
  6. E. Happ, D. Johannsen, C. Klein, and F. Neumann. Rigorous analyses of fitness-proportional selection for optimizing linear functions. In Proc. of the 10th annual conference on Genetic and evolutionary computation (GECCO 2008), pages 953--960, New York, NY, USA, 2008. ACM. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. J. He and X. Yao. Drift analysis and average time complexity of evolutionary algorithms. Artificial Intelligence, 127(1):57--85, March 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. W. Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58(301):13--30, 1963.Google ScholarGoogle ScholarCross RefCross Ref
  9. T. Kötzing, F. Neumann, D. Sudholt, and M. Wagner. Simple max-min ant systems and the optimization of linear pseudo-boolean functions. To appear in Proc. of Foundations of Genetic Algorithms (FOGA 2011), 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. J. Lässig and D. Sudholt. General scheme for analyzing running times of parallel evolutionary algorithms. In Proc. of the 11th international conference on Parallel problem solving from nature: Part I, (PPSN 2010), pages 234--243, Berlin, Heidelberg, 2010. Springer-Verlag. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. P. K. Lehre. Negative drift in populations. In Proc. of the 11th international conference on Parallel problem solving from nature: Part I, (PPSN 2010), pages 244--253, Berlin, Heidelberg, 2010. Springer-Verlag. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. P. K. Lehre and X. Yao. On the impact of mutation-selection balance on the runtime of evolutionary algorithms. To appear in IEEE Trans. on Evolutionary Computation, 2011.Google ScholarGoogle Scholar
  13. F. Neumann, P. S. Oliveto, and C. Witt. Theoretical analysis of fitness-proportional selection: landscapes and efficiency. In Proc. of the 11th Annual conference on Genetic and evolutionary computation (GECCO 2009), pages 835--842, New York, NY, USA, 2009. ACM. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. P. S. Oliveto, J. He, and X. Yao. Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results. Intl. Journal of Automation and Computing, 4(1):100--106, 2007.Google ScholarGoogle Scholar
  15. D. Sudholt. General lower bounds for the running time of evolutionary algorithms. In Proc. of the 11th international conference on Parallel problem solving from nature: Part I, (PPSN 2010), pages 124--133, Berlin, Heidelberg, 2010. Springer-Verlag. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. I. Wegener and C. Witt. On the analysis of a simple evolutionary algorithm on quadratic pseudo-boolean functions. Journal of Discrete Algorithms, 3(1):61--78, 2005.Google ScholarGoogle ScholarCross RefCross Ref
  17. C. Witt. Runtime Analysis of the (μGoogle ScholarGoogle Scholar
  18. $1$) EA on Simple Pseudo-Boolean Functions. Evolutionary Computation, 14(1):65--86, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library

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      cover image ACM Conferences
      GECCO '11: Proceedings of the 13th annual conference on Genetic and evolutionary computation
      July 2011
      2140 pages
      ISBN:9781450305570
      DOI:10.1145/2001576

      Copyright © 2011 ACM

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      Publication History

      • Published: 12 July 2011

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