Estimation of Bayesian Network for Program Generation

Genetic Programming (GP) is a powerful optimization algorithm, which employs crossover for a main genetic operator. Because a crossover operator in GP selects sub-trees randomly, the building blocks may be destroyed by crossover. Recently, algorithms called PMBGPs (Probabilistic Model Building GP) based on probabilistic techniques have been proposed in order to improve the problem above. We propose a new PMBGP employing Bayesian network for generating new individuals with a special chromosome called expanded parse tree, which much reduces the 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. A computational experiment on a deceptive MAX problem (DMAX problem) demonstrates that our new PMBGP is superior to other program evolution methods.