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Towards an optimal mutation probability for genetic algorithms

  • Genetic Algorithms
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Parallel Problem Solving from Nature (PPSN 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 496))

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Abstract

In this paper the optimal parameter setting of Genetic Algorithms (GAs) is investigated. Particular attention has been paid to the dependence of the mutation probability P M upon two parameters, the dimension of the configuration space l and the population size M. Assuming strict conditions on both the problem to be optimized and the GA, P M converges to 0 as the population size M or the dimension of the configuration space l converges to infinity. For direct application a heuristic comprising these results is presented. The parameter settings obtained by applying this heuristic are in accordance with those which have been obtained earlier by experiment.

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References

  1. K. De Jong. Analysis of the Behavior of a Class of Genetic Adaptive Systems. PhD. Diss., Univ. of Michigan, 1975

    Google Scholar 

  2. M. Nowack; P. Schuster. Error Thresholds of Replication in Finite Populations Mutations Frequencies and the Onset of Muller's Ratchet. J. Theor. Biol., Vol. 137, pages 375–395, 1989

    PubMed  Google Scholar 

  3. P. Schuster. Effects of Finite Population Size and Other Stochastic Phenomena in Molecular Evolution. Complex Systems — Operational Approaches in Neurobiology, Physics, and Computers, Springer, Heidelberg, 1985

    Google Scholar 

  4. T.C. Fogarty. Varying the probability of mutation in the Genetic Algorithm. J.D. Schaffer, Proc. 3rd Int'l Conf. Genetic Algorithms & Appl., Arlington, VA, pages 104–109, 1989

    Google Scholar 

  5. L. Booker. Improving Search in Genetic Algorithms. L. Davis, Genetic Algorithms and Simulated Annealing, Pitman, London, 1987

    Google Scholar 

  6. J.J. Greffenstette. Optimisation of Control Parameters for Genetic Algorithms. IEEE Transactions on Systems Man and Cybernetics, Vol. SMC-16, No. 1, pages 122–128, 1986

    Google Scholar 

  7. J.D. Schaffer; R.A. Caruna; L.J. Eshelman; R. Das. A Study of Control Parameters Affecting Online Performance of Genetic Algorithms for Function Optimization. J.D. Schaffer, Proc. 3rd Int'l Conf. Genetic Algorithms & Appl., Arlington, VA, pages 51–60, 1989

    Google Scholar 

  8. D. Goldberg. Sizing Populations for Serial and Parallel Genetic Algorithms. J.D. Schaffer, Proc. 3rd Int'l Conf. Genetic Algorithms & Appl., Arlington, VA, pages 70–79, 1989

    Google Scholar 

  9. H. Ros. Some Results on Boolean Concept Learning by Genetic Algorithms. J.D. Schaffer, Proc. 3rd Int'l Conf. Genetic Algorithms & Appl., Arlington, VA, pages 28–33, 1989

    Google Scholar 

  10. J. Holland. Adaption in Natural and Artificial Systems. Ann Arbor, The University of Michigan Press, 1975

    Google Scholar 

  11. D. Goldberg. Genetic Algorithms in Search, Optimization & Machine Learning. Addison Wesley, Reading, MA, 1989

    Google Scholar 

  12. K.L. Chung. Markov Chains With Stationary Transition Probabilities. Springer, Berlin, 1967

    Google Scholar 

  13. J.F. Crow; M. Kimura. An Introduction to Population Genetics Theory. Harper & Row, New York, NY, 1970

    Google Scholar 

  14. J. Hesser; R. Männer; O. Stucky. Optimization of Steiner Trees using Genetic Algorithms. J.D. Schaffer, Proc. 3rd Int'l Conf. Genetic Algorithms & Appl., Arlington, VA, pages 231–236, 1989

    Google Scholar 

  15. G. Syswerda. Uniform Crossover in Genetic Algorithms. J.D. Schaffer, Proc. 3rd Int'l Conf. Genetic Algorithms & Appl., Arlington, VA, pages 2–9, 1989

    Google Scholar 

  16. C.L. Bridges; D. Goldberg. An Analysis of Reproduction and Crossover in a Binary—Coded Genetic Algorithm. J.D. Schaffer, Proc. 3rd Int'l Conf. Genetic Algorithms & Appl., Arlington, VA, pages 28–33, 1989

    Google Scholar 

  17. J. Hesser; R. Männer. An Alternative Genetic Algorithm. In these proceedings

    Google Scholar 

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Hans-Paul Schwefel Reinhard Männer

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© 1991 Springer-Verlag Berlin Heidelberg

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Hesser, J., Männer, R. (1991). Towards an optimal mutation probability for genetic algorithms. In: Schwefel, HP., Männer, R. (eds) Parallel Problem Solving from Nature. PPSN 1990. Lecture Notes in Computer Science, vol 496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029727

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  • DOI: https://doi.org/10.1007/BFb0029727

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  • Print ISBN: 978-3-540-54148-6

  • Online ISBN: 978-3-540-70652-6

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