Analysis of the Effective Degrees of Freedom in Genetic Algorithms

  • Stephens C
  • Waelbroeck H
  • 1


    Mendeley users who have this article in their library.
  • N/A


    Citations of this article.


An evolution equation for a population of strings evolving under the genetic operators: selection, mutation and crossover is derived. The corresponding equation describing the evolution of schematas is found by performing an exact coarse graining of this equation. In particular exact expressions for schemata reconstruction are derived which allows for a critical appraisal of the ``building-block hypothesis'' of genetic algorithms. A further coarse-graining is made by considering the contribution of all length-l schematas to the evolution of population observables such as fitness growth. As a test function for investigating the emergence of structure in the evolution the increase per generation of the in-schemata fitness averaged over all schematas of length l, $\Delta_l$, is introduced. In finding solutions of the evolution equations we concentrate more on the effects of crossover, in particular we consider crossover in the context of Kauffman Nk models with k=0,2. For k=0, with a random initial population, in the first step of evolution the contribution from schemata reconstruction is equal to that of schemata destruction leading to a scale invariant situation where the contribution to fitness of schematas of size l is independent of l. This balance is broken in the next step of evolution leading to a situation where schematas that are either much larger or much smaller than half the string size dominate over those with $l \approx N/2$. The balance between block destruction and reconstruction is also broken in a k>0 landscape. It is conjectured that the effective degrees of freedom for such landscapes are landscape connective trees that break down into effectively fit smaller blocks, and not the blocks themselves. Numerical simulations confirm this ``connective tree hypothesis'' by showing that correlations drop off with connective distance and not with intrachromosomal distance.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

There are no full text links


  • C. R. Stephens

  • H. Waelbroeck

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free