Maximum Entropy Analysis of Genetic Algorithm Operators

A maximum entropy approach is used to derive a set of equations describing the evolution of a genetic algorithm involving crossover, mutation and selection. The problem is formulated in terms of cumulants of the fitness distribution. Applying this method to very simple problems, the dynamics of the genetic algorithm can be reduced to a set of nonlinear coupled difference equations which give good results when truncated to four variables. These equations correctly predict the best fitness after convergence as a function of the genetic search parameters. Suggestions concerning annealing rates for time-dependent search parameters are also discussed.