abstract = "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 factorisation can be
explicitly determined. In general it has to be
determined from the search points used for the
optimisation. 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 synthesising programs.",