Evolutionary Synthesis of Bayesian Networks for Optimization

We shortly review our theoretical analysis of genetic algorithms and provide some new results. The theory has lead to the design of three different algorithms, all based on probability distributions instead of recombination of strings. In order to be numerically tractable, the probability distribution has to be factored into a small number of factors. Each factor should depend on a small number of variables only. For certain applications the factorization can be explicitly determined. In general it has to be determined from the search points used for the optimization. Computing the factorization from the data leads to learning Bayesian networks. The problem of finding a minimal structure which explains the data is discussed in detail. It is shown that the Bayesian Information Criterion is a good score for this problem. The algorithms are extended to probabilistic prototype trees used for synthesizing programs.