Probabilistic Model Building Genetic Programming based on Estimation of Bayesian Network

Abstract

Genetic Programming (GP) is a powerful optimization algorithm, which employs the crossover for genetic operation. Because the crossover operator in GP randomly selects sub-trees, the building blocks may be destroyed by the crossover. Recently, algorithms called PMBGPs (Probabilistic Model Building GP) based on probabilistic techniques have been proposed in order to improve the problem mentioned above. We propose a new PMBGP employing Bayesian network for generating new individuals with a special chromosome called expanded parse tree, which much reduces a number of possible symbols at each node. Although the large number of symbols gives rise to the large conditional probability table and requires a lot of samples to estimate the interactions among nodes, a use of the expanded parse tree overcomes these problems. Computational experiments on two subjects demonstrate that our new PMBGP is much superior to prior probabilistic models.