Scalability of using Restricted Boltzmann Machines for combinatorial optimization

Abstract

Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Restricted Boltzmann Machines (RBMs) are generative neural networks with these desired properties. We integrate an RBM into an EDA and evaluate the performance of this system in solving combinatorial optimization problems with a single objective. We assess how the number of fitness evaluations and the CPU time scale with problem size and with problem complexity. The results are compared to the Bayesian Optimization Algorithm, a state-of-the-art EDA. Although RBM-EDA requires larger population sizes and a larger number of fitness evaluations, it outperforms BOA in terms of CPU times, in particular if the problem is large or complex. RBM-EDA requires less time for model building than BOA. These results highlight the potential of using generative neural networks for combinatorial optimization.

Denoising Autoencoders for Fast Combinatorial Black Box Optimization

“…The batch size for SGD is b = 100. We apply the simple parameter control scheme from [11] to determine when to stop DAE training.…”

Learning and Searching Pseudo-Boolean Surrogate Functions from Small Samples

“…Bayesian networks have also been used to model distributions in EDAs, for example the Bayesian Optimisation Algorithm (BOA) (Pelikan et al, 2000) and a hierarchical version (hBOA) (Pelikan, 2005) have been proposed. Both deep Boltzmann machines (Probst and Rothlauf, 2015) and restricted Boltzmann machines (Probst et al, 2014) have also been used as EDAs.…”

“…They represent dynamic systems that can be used to generate data in a Boltzmann distribution using Gibbs sampling. Both deep Boltzmann machines (Probst and Rothlauf, 2015) and restricted Boltzmann machines (Probst et al, 2014) have been used to build EDAs for combinatorial optimisation.…”

“…Both (Probst and Rothlauf, 2015) and (Probst et al, 2014) present results for searching mktrap problems of various sizes with Boltzmann EDAs, reporting the number of fitness evaluations and the CPU time taken to find a solution. They used an AMD Opteron 6272 processor with 2.1 GHz.…”

“…For comparison, the MOHN process was run on a single core Intel i7 processor Learning and Searching pseudo-Boolean Functions running at 2.5 GHz. (Probst and Rothlauf, 2015) used deep Boltzmann machines in a method called DBM-EDA and (Probst et al, 2014) used restricted Boltzmann machines in a method called RBM-EDA. Both papers compared the performance of the EDAs to that of a Bayesian Optimisation Algorithm (BOA) on a number of problems including the mk-trap.…”