Intrinsic System Model of the Genetic Algorithm with α-Selection

  • André Neubauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)


Genetic algorithms are random heuristic search (RHS) algorithms which can be theoretically described with the help of a dynamical system model. This model characterises the stochastic trajectory of a population using a deterministic heuristic function and its fixed points. For practical problem sizes the determination of the fixed points is unfeasible even for the simple genetic algorithm (SGA). In this paper the novel intrinsic system model is introduced for the genetic algorithm with α-selection and the corresponding unique fixed point is determined. It is shown that this model is compatible with the equivalence relation imposed by schemata. In addition to the theoretical analysis experimental results are presented which confirm the theoretical predictions.


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  1. 1.
    Holland, J.H.: Adaptation in Natural and Artificial Systems, 1st edn. MIT Press, Cambridge (1992)Google Scholar
  2. 2.
    Neubauer, A.: Theory of the Simple Genetic Algorithm with α-Selection. In: Genetic and Evolutionary Computation Conference GECCO (to appear, 2008)Google Scholar
  3. 3.
    Reeves, C.R., Rowe, J.E.: Genetic Algorithms – Principles and Perspectives, A Guide to GA Theory. Kluwer Academic Publishers, Boston (2003)Google Scholar
  4. 4.
    Rowe, J.E., Vose, M.D., Wright, A.H.: Coarse Graining Selection and Mutation. In: Foundations of Genetic Algorithms. LNCS, pp. 176–191. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Vose, M.D., Wright, A.H.: The Simple Genetic Algorithm and the Walsh Transform – Part I Theory, Part II The Inverse. Evolutionary Computation 6(3), 253–273, 275–289 (1998)CrossRefGoogle Scholar
  6. 6.
    Vose, M.D.: The Simple Genetic Algorithm – Foundations and Theory. MIT Press, Cambridge (1999)zbMATHGoogle Scholar
  7. 7.
    Vose, M.D.: Random Heuristic Search. Theoretical Computer Science 229(1-2), 103–142 (1999)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • André Neubauer
    • 1
  1. 1.Information Processing Systems LabMünster University of Applied SciencesSteinfurtGermany

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