Analyzing Probabilistic Models in Hierarchical BOA

The hierarchical Bayesian optimization algorithm (hBOA) can solve nearly decomposable and hierarchical problems of bounded difficulty in a robust and scalable manner by building and sampling probabilistic models of promising solutions. This paper analyzes probabilistic models in hBOA on four important classes of test problems: concatenated traps, random additively decomposable problems, hierarchical traps and two-dimensional Ising spin glasses with periodic boundary conditions. We argue that although the probabilistic models in hBOA can encode complex probability distributions, analyzing these models is relatively straightforward and the results of such analyses may provide practitioners with useful information about their problems. The results show that the probabilistic models in hBOA closely correspond to the structure of the underlying optimization problem, the models do not change significantly in consequent iterations of BOA, and creating adequate probabilistic models by hand is not straightforward even with complete knowledge of the optimization problem.