Optimizing Programs with Estimation of Bayesian Network

Genetic programming (GP) is a powerful optimization algorithm and has been applied to many problems. GP is an extension of genetic algorithm (GA) which can handle programs, functions, etc. GP evolves with genetic operators such as crossover and mutation. The crossover operator in GP however selects sub-trees randomly and this selection is done regardless of the problem. This gives rise to the destruction of good building blocks. Recently, probabilistic model building techniques have been applied to GP to estimate the building blocks properly. This type of algorithm is called probabilistic model building GP (PMBGP). Because GP uses many types of nodes, prior PMBGPs have been faced with the problem of huge CPT (Conditional Probability Table) size. The large CPT not only consumes a lot of memory but also requires many samples to construct networks. We propose a new PMBGP that uses Bayesian network for generating new individuals. In our approach, a special chromosome called expanded parse tree is used to improve the problem of huge CPT size.