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Global convergence of genetic algorithms: A markov chain analysis

  • Genetic Algorithms
  • Conference paper
  • First Online:
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 we are trying to make a step towards a concise theory of genetic algorithms (GAs) and simulated annealing (SA). First, we set up an abstract stochastic algorithm for treating combinatorial optimization problems. This algorithm generalizes and unifies genetic algorithms and simulated annealing, such that any GA or SA algorithm at hand is an instance of our abstract algorithm. Secondly, we define the evolution belonging to the abstract algorithm as a Markov chain and find conditions implying that the evolution finds an optimum with probability 1. The results obtained can be applied when designing the components of a genetic algorithm.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    A. E. Eiben, E. H. L. Aarts & K. M. Van Hee

  2. Philips Research Laboratories, P.O. Box 80000, 5600 JA, Eindhoven, The Netherlands

    E. H. L. Aarts

Authors
  1. A. E. Eiben
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  2. E. H. L. Aarts
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  3. K. M. Van Hee
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Editor information

Hans-Paul Schwefel Reinhard Männer

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© 1991 Springer-Verlag Berlin Heidelberg

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Eiben, A.E., Aarts, E.H.L., Van Hee, K.M. (1991). Global convergence of genetic algorithms: A markov chain analysis. 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/BFb0029725

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  • DOI: https://doi.org/10.1007/BFb0029725

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54148-6

  • Online ISBN: 978-3-540-70652-6

  • eBook Packages: Springer Book Archive

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