an extension of vose's markov chain model for genetic algorithms
The paper presents an extension of Vose's Markov chain model for genetic algorithm (GA). The model contains not only standard genetic operators such as mutation and crossover but also two new operators - translation to the left/right and permutation of bits. The presented model can be used for finding the transition matrices and for the investigation of asymptotic properties by using Markov transition functions. The ergodity of the Markov chain describing the GA with new operators, translation to the left/right and permutation, is shown. The model is specialized for a case of Bentley's GA. For this GA the ergodity of the Markov chains and the asymptotic correctness in the probabilistic sense are shown. To model other aspects of the Bentley's GA (effective fitness, total transmission probability) the microscopic Exact Poli GP Schema Theory for Subtree-Swapping Crossover is used.
markov chain model genetic algorithms ergodity bentley's ga asymptotic correctness schema theory theory