Continuous estimation of distribution algorithms with probabilistic principal component analysis

Abstract

Many evolutionary algorithms have been studied to build and use a probability distribution model of the population for optimization problems. Most of these methods tried to represent explicitly the relationship between variables in the problem with factorization techniques or a graphical model such as Bayesian or Gaussian networks. Thus enormous computational cost is required for constructing those models when the problem size is large. We propose a new estimation of distribution algorithm by using probabilistic principal component analysis (PPCA) which can explain the high order interactions with the latent variables. Since there are no explicit search procedures for the probability density structure, it is possible to rapidly estimate the distribution and readily sample the new individuals from it. Our experimental results support that the presented estimation of distribution algorithms with PPCA can find good solutions more efficiently than other EDAs for the continuous spaces.