Random keys genetic algorithm with adaptive penalty function for optimization of constrained facility layout problems

Probabilistic Incremental Learning PBIL has been proposed as a model for binary coded evolutionary algorithms where the population is represented by its mean vector which is updated in an autoregressive manner In this paper we prove that under the PBIL update rule each component of the population vector converges with probability one to whenever a in the associated bit consistently yields better tness values than the oppo site setting As a corollary we obtain global convergence of PBIL for linear pseudoboolean functions including the commonly investigated Counting Ones problem