Schema disruption in tree-structured chromosomes

We study if and when the inequality dp(H) ≤ rel∆(H) holds for schemas H in chromosomes that are structured as trees. The disruption probability dp(H) is the probability that a random cut of a tree limb will separate two fixed nodes of H. The relative diameter rel∆(H) is the ratio (max distance between two fixed nodes in H) / (max distance between two tree nodes), and measures how close together are the fixed nodes of H. Inequality dp(H) ≤ rel∆(H) is of significance in proving Schema Theorems for non-linear chromosomes, and so bears upon the success we can expect from genetic algorithms. For linear chromosomes, dp(H) = rel∆(H). Our results include the following. There is no constant c such that dp(H) ≤ c · rel∆(H) holds for arbitrary schemas and trees. This is illustrated in trees with eccentric, stringy shapes. Matters improve for dense, ball-like trees, explained herein. Inequality dp(H) ≤ rel∆(H) always holds in such trees, except for certain atypically large sc...

• Type: Conference
• Year: 2005
• Where: GECCO
• Authors: William A. Greene
• Keywords: Disruption Probability, Fixed Nodes, GECCO 2005, Genetic Algorithms