Real-Coded Bayesian Optimization Algorithm: Bringing the Strength of BOA into the Continuous World

Abstract

Abstract. 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 subspacebased 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.

Truncation Selection and Gaussian EDA: Bounds for Sustainable Progress in High-Dimensional Spaces

“…In EDAs working in real domain (real-valued EDAs), the Gaussian distribution is often employed as the model of promissing individuals ( [2], [3], [4], [5]). The distribution is often learned by maximum likelihood (ML) estimation.…”

Quality Analysis of Discretization Methods for Estimation of Distribution Algorithms

“…(1) No interaction: Each variable is modeled independently. These algorithms include the population-based incremental learning (PBIL) [2], the compact genetic algorithm (cGA) [14], and the univariate marginal distribution algorithm [23].…”

“…In EDAs, decision variables are often coded with discrete codes, such as binary codes. To enhance the applicability of EDAs over continuous domains, direct attempts to modify the type of decision variables have been made, including continuous population-based incremental learning with Gaussian distribution [31], real-coded variant of population-based incremental learning with interval updating [32], Bayesian evolutionary algorithms for continuous function optimization [33], real-coded extended compact genetic algorithm based on mixtures of models [18], and the real-coded Bayesian optimization algorithm [1]. Instead of modifying the infrastructure of the algorithm, such as the type of decision variables or the global program flow, as a more general, component-wise approach, discretization methods are employed to cooperate with EDAs [6], [7], [28], [35].…”

A review on probabilistic graphical models in evolutionary computation

“…rBOA (Ahn et al 2004) first learns a GBN to obtain a decomposition of the problem variables into smaller subproblems. Then, a separate mixture of GBNs is learnt for each of the subproblems by clustering the solutions in that subproblem.…”