A new adaptive Boltzmann selection schedule SDS

The Factorized Distribution Algorithm (FDA) is an evolutionary algorithm that combines mutation and recombination by using a distribution. The distribution is estimated from a set of selected points. It is then used to generate new points for the next generation. In general a distribution defined for n binary variables has 2ⁿ parameters. Therefore it is too expensive to compute. For additively decomposed discrete functions (ADFs) there exists an algorithm that factors the distribution into conditional and marginal distributions, each of which can be computed in polynomial time. We have shown a convergence theorem for the FDA, but it is only valid using Boltzmann selection. Boltzmann selection was not used in practice because a good annealing schedule was lacking. Using a Taylor expansion of the average fitness of the Boltzmann distribution, we have developed an adaptive annealing schedule called SDS (Standard Deviation Schedule) that is introduced in this work. The inverse temperature p is changed inversely proportional to the standard deviation