William A. Greene
ABSTRACT
We study if and when the inequality dp(H) ≤ relΔ(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 relΔ(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) ≤ relΔ(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) ≤relΔ(H). Our results include the following. There is no constant c such that dp(H) ≤ c • relΔ(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) ≤ relΔ(H) always holds in such trees, except for certain atypically large schemas. Thus, the more compact are our tree-structured chromo-somes, the better we can expect our genetic algorithms to work.
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Digital Library
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- Greene, William A. (2004) "Schema Disruption in Chromosomes that are Structured as Binary Trees", in K. Deb et al. (eds.), Proceedings of the Genetic and Evolutionary Computation Congress, June 26-30, 2004, Seattle, WA (pages 1197--1207). Springer Verlag LNCS 3102, New York, NY.Google Scholar
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Index Terms
- Schema disruption in tree-structured chromosomes
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