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Estimation of Distribution Algorithms (EDAs) require flexible probabilitymodels that can be efficiently learned and sampled. Deep Boltzmann Machines(DBMs) are generative neural networks with these desired properties. Weintegrate a DBM into an EDA and evaluate the performance of this system insolving combinatorial optimization problems with a single objective. We comparethe results to the Bayesian Optimization Algorithm. The performance of DBM-EDAwas superior to BOA for difficult additively decomposable functions, i.e.,concatenated deceptive traps of higher order. For most other benchmarkproblems, DBM-EDA cannot clearly outperform BOA, or other neural network-basedEDAs. In particular, it often yields optimal solutions for a subset of the runs(with fewer evaluations than BOA), but is unable to provide reliableconvergence to the global optimum competitively. At the same time, the modelbuilding process is computationally more expensive than that of other EDAsusing probabilistic models from the neural network family, such as DAE-EDA.

Deep Boltzmann Machines in Estimation of Distribution Algorithms for Combinatorial Optimization