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The simple genetic algorithm and the Walsh transform: Part II, The inverse.

M D Vose1, A H Wright

  • 1Computer Science Dept., University of Tennessee, Knoxville 37996-1301, USA. vose@cs.utk.edu

Evolutionary Computation
|February 18, 1999
PubMed
Summary

This study reveals how genetic algorithms

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Area of Science:

  • Computational intelligence
  • Evolutionary computation
  • Signal processing

Background:

  • The relationship between genetic algorithms and Walsh transforms was explored in Part I.
  • Understanding the mixing scheme (crossover and mutation) is crucial for genetic algorithm analysis.

Purpose of the Study:

  • To extend the analysis of the genetic algorithm-Walsh transform relationship.
  • To formulate the inverse of the expected next generation operator.
  • To determine the fixed points of the genetic algorithm's mixing scheme.

Main Methods:

  • Expressing the genetic algorithm's mixing scheme in the Walsh basis.
  • Deriving the inverse of the expected next generation operator.
  • Analyzing the fixed points of the mixing scheme using mathematical formulations.

Main Results:

  • The mixing scheme is "triangularized" in the Walsh basis.
  • A formulation for the inverse of the expected next generation operator is derived.
  • A general formula for the fixed point of any starting population is obtained.

Conclusions:

  • The study provides a deeper mathematical understanding of genetic algorithm dynamics.
  • Geiringer's theorem is shown to be a special case of these findings (zero mutation).
  • These results contribute to the theoretical foundations of evolutionary computation.

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