Towards a Better Basis Search through a Surrogate Model-Based Epistasis Minimization for Pseudo-Boolean Optimization

Epistasis, which indicates the difficulty of a problem, can be used to evaluate the basis of the space in which the problem lies. However, calculating epistasis may be challenging as it requires all solutions to be searched. In this study, a method for constructing a surrogate model, based on deep neural networks, that estimates epistasis is proposed for basis evaluation. The proposed method is applied to the Variant-OneMax problem and the NK-landscape problem. The method is able to make successful estimations on a similar level to basis evaluation based on actual epistasis, while significantly reducing the computation time. In addition, when compared to the epistasis-based basis evaluation, the proposed method is found to be more efficient.