Markov Chain Model and Poli Based Schema Model for Bentley’s Genetic Algorithm

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In this paper, I present the theoretical results obtained for Bentley’s genetic algorithm, which is used in CAD system to generate 3D-solids designs. The Vose-like-Markov-chain model for the Bentley’s GA is proposed. The transition matrices are found and the ergodity of the Markov chain and the asymptotic correctness in the probabilistic sense are shown by using the model. The microscopic Exact Poli GP Schema Theory for Subtree-Swapping Crossovers are applied for the Bentley’s GA to calculate the effective fitness and the total transmission probability for a fixed-size-and-shape schema under hierarchical crossover.