Crossover Bias in Genetic Programming

  • Maarten Keijzer
  • James Foster
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4445)


Path length, or search complexity, is an understudied property of trees in genetic programming. Unlike size and depth measures, path length directly measures the balancedness or skewedness of a tree. Here a close relative to path length, called visitation length, is studied. It is shown that a population undergoing standard crossover will introduce a crossover bias in the visitation length. This bias is due to inserting variable length subtrees at various levels of the tree. The crossover bias takes the form of a covariance between the sizes and levels in the trees that form a population. It is conjectured that the crossover bias directly determines the size distribution of trees in genetic programming. Theorems are presented for the one-generation evolution of visitation length both with and without selection. The connection between path length and visitation length is made explicit.


Path Length Genetic Program Binary Tree Internal Node Catalan Distribution 
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Maarten Keijzer
    • 1
  • James Foster
    • 2
  1. 1.No Affiliation 
  2. 2.University of Idaho 

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