Learning and Searching Pseudo-Boolean Surrogate Functions from Small Samples

Abstract

When searching for input configurations that optimise the output of a system, it can be useful to build a statistical model of the system being optimised. This is done in approaches such as surrogate model-based optimisation, estimation of distribution algorithms, and linkage learning algorithms. This article presents a method for modelling pseudo-Boolean fitness functions using Walsh bases and an algorithm designed to discover the non-zero coefficients while attempting to minimise the number of fitness function evaluations required. The resulting models reveal linkage structure that can be used to guide a search of the model efficiently. It presents experimental results solving benchmark problems in fewer fitness function evaluations than those reported in the literature for other search methods such as EDAs and linkage learners.

Characterizing Permutation-Based Combinatorial Optimization Problems in Fourier Space

“…More generally, the FT that we are considering is the permutation version of the Walsh transform, which operates on pseudo-Boolean functions. Therefore, it could be interesting to see whether the studies that have been published for the Walsh transform, such as the use of surrogate functions based on it (Swingler, 2020;Verel et al, 2018), could be extended to permutations as well.…”

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

“…Specifically, these studies attempted to optimize the cost-expensive black-box problems. In particular, several studies have proposed the use of Walsh-based surrogate models to reduce the computational cost associated with pseudo-Boolean problems [27][28][29].…”