Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
An analysis of genetic programming
An analysis of genetic programming
Schema theory for genetic programming with one-point crossover and point mutation
Evolutionary Computation
A tree-based genetic algorithm for building rectilinear Steiner arborescences
Proceedings of the 8th annual conference on Genetic and evolutionary computation
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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.