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This article proposes a competent hierarchical optimization method called the hierarchical Bayesian optimization algorithm (hBOA). hBOA extends the Bayesian optimization algorithm (BOA) by incorporating three important features for robust and scalable optimization of hierarchical problems: proper decomposition, chunking, and preservation of alternative solutions. Additionally, the article proposes a class of difficult hierarchical problems called hierarchical traps, hBOA is shown to provide a scalable solution to the class of hierarchically decomposable problems and anything easier. Specifically, hBOA can solve hierarchical traps and other nearly decomposable problems in approximately O(n1.55 log n) to O(n2) function evaluations, where n is the number of decision variables in the problem.