Real-coded Bayesian optimization algorithm: Bringing the strength of BOA into the continuous world

This paper describes a continuous estimation of distribution algorithm (EDA) to solve decomposable, real-valued optimization problems quickly, accurately, and reliably. This is the real-coded Bayesian optimization algorithm (rBOA). The objective is to bring the strength of (discrete) BOA to bear upon the area of real-valued optimization. That is, the rBOA must properly decompose a problem, efficiently fit each subproblem, and effectively exploit the results so that correct linkage learning even on nonlinearity and probabilistic building-block crossover (PBBC) are performed for real-valued multivariate variables. The idea is to perform a Bayesian factorization of a mixture of probability distributions, find maximal connected subgraphs (i.e. substructures) of the Bayesian factorization graph (i.e., the structure of a probabilistic model), independently fit each substructure by a mixture distribution estimated from clustering results in the corresponding partial-string space (i.e., subspace, subproblem), and draw the offspring by an independent subspace-based sampling. Experimental results show that the rBOA finds, with a sublinear scale-up behavior for decomposable problems, a solution that is superior in quality to that found by a mixed iterative density-estimation evolutionary algorithm (mIDEA) as the problem size grows. Moreover, the rBOA generally outperforms the mIDEA on well-known benchmarks for real-valued optimization.