Scalability of using Restricted Boltzmann Machines for Combinatorial Optimization

TL;DR

This paper explores the use of Restricted Boltzmann Machines within Estimation of Distribution Algorithms to solve combinatorial optimization problems, demonstrating advantages in CPU time despite larger populations.

Contribution

It introduces an RBM-based EDA, showing its scalability and efficiency advantages over Bayesian Optimization Algorithm for complex and large problems.

Findings

RBM-EDA outperforms BOA in CPU time for large problems

RBM-EDA requires less time for model building than BOA

Larger populations and more evaluations are needed for RBM-EDA

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.