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Global convergence of genetic algorithms: A markov chain analysis

  • A. E. Eiben
  • E. H. L. Aarts
  • K. M. Van Hee
Genetic Algorithms Genetic Algorithm Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 496)

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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Literature

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • A. E. Eiben
    • 1
  • E. H. L. Aarts
    • 1
    • 2
  • K. M. Van Hee
    • 1
  1. 1.Department of Mathematics and Computing ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Philips Research LaboratoriesEindhovenThe Netherlands

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