Decomposition of Black-Box Optimization Problems by Community Detection in Bayesian Networks

Abstract

Estimation of Distribution Algorithms (EDAs) have proved themselves as an efficient alternative to Genetic Algorithms when solving nearly decomposable optimization problems. In general, EDAs substitute genetic operators by probabilistic sampling, enabling a better use of the information provided by the population and, consequently, a more efficient search. In this paper the authors exploit EDAs' probabilistic models from a different point-of-view, the authors argue that by looking for substructures in the probabilistic models it is possible to decompose a black-box optimization problem and solve it in a more straightforward way. Relying on the Building-Block hypothesis and the nearly-decomposability concept, their decompositional approach is implemented by a two-step method: 1) the current population is modeled by a Bayesian network, which is further decomposed into substructures (communities) using a version of the Fast Newman Algorithm. 2) Since the identified communities can be seen as sub-problems, they are solved separately and used to compose a solution for the original problem. The experiments showed strengths and limitations for the proposed method, but for some of the tested scenarios the authors’ method outperformed the Bayesian Optimization Algorithm by requiring up to 78% fewer fitness evaluations and being 30 times faster.