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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 two common test problems: concatenated traps and 2D Ising spin glasses with periodic boundary conditions. We argue that although Bayesian networks with local structures can encode complex probability distributions, analyzing these models in hBOA 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 problem, the models do not change significantly in subsequent iterations of BOA, and creating adequate probabilistic models by hand is not straightforward even with complete knowledge of the optimization problem.

The Bayesian optimization algorithm (BOA) uses Bayesian networks to learn linkages between the decision variables of an optimization problem. This paper studies the influence of different selection and replacement methods on the accuracy of linkage learning in BOA. Results on concatenated m-k deceptive trap functions show that the model accuracy depends on a large extent on the choice of selection method and to a lesser extent on the replacement strategy used. Specifically, it is shown that linkage learning in BOA is more accurate with truncation selection than with tournament selection. The choice of replacement strategy is important when tournament selection is used, but it is not relevant when using truncation selection. On the other hand, if performance is our main concern, tournament selection and restricted tournament replacement should be preferred. These results aim to provide practitioners with useful information about the best way to tune BOA with respect to structural model accuracy and overall performance.

Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling probabilistic models of promising candidate solutions. While the primary goal of applying EDAs is to discover the global optimum (or an accurate approximation), any EDA also provides us with a sequence of probabilistic models, which hold a great deal of information about the problem. Although using problemspecific knowledge has been shown to significantly improve performance of EDAs and other evolutionary algorithms, this readily available source of information has been largely ignored by the EDA community. This paper takes the first step towards the use of probabilistic models obtained by EDAs to speed up the solution of similar problems in the future. More specifically, we propose two approaches to biasing model building in the hierarchical Bayesian optimization algorithm (hBOA) based on knowledge automatically learned from previous runs on similar problems. We show that the methods lead to substantial speedups and argue that they should work well in other applications that require solving a large number of problems with similar structure.