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Effect of Mutation to Distribution of Optimum Solution in Genetic Algorithm

  • Yu-an Zhang
  • QingLian Ma
  • Makoto Sakamoto
  • Hiroshi Furutani
Part of the Proceedings in Information and Communications Technology book series (PICT, volume 2)

Abstract

Mutation plays an important role in the computing of Genetic Algorithms (GAs). In this paper, we use the success probability as a measure of the performance of GAs, and apply a method for calculating the success probability by means of Markov chain theory. We define the success probability as there is at least one optimum solution in a population. In this analysis, we assume that the population is in linkage equilibrium, and obtain the distribution of the first order schema. We calculate the number of copies of the optimum solution in the population by using the distribution of the first order schema. As an application of the method, we study the GA on the multiplicative landscape, and demonstrate the process to calculate the success probability for this example. Many researchers may consider that the success probability decreases exponentially as a function of the string length L. However, if mutation is included in the GA, it is shown that the success probability decreases almost linearly as L increases.

Keywords

Genetic Algorithm Markov Chain Failure Probability Markov Chain Model Extinction State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Tokyo 2010

Authors and Affiliations

  • Yu-an Zhang
    • 1
  • QingLian Ma
    • 2
  • Makoto Sakamoto
    • 2
  • Hiroshi Furutani
    • 2
  1. 1.Interdisciplinary Graduate School of Agriculture and EngineeringUniversity of MiyazakiMiyazaki CityJapan
  2. 2.Faculty of EngineeringUniversity of MiyazakiMiyazaki CityJapan

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