Gaussian Markov Random Fields for Discrete Optimization via Simulation: Framework and Algorithms

Abstract

This paper lays the foundation for employing Gaussian Markov random fields (GMRFs) for discrete decision–variable optimization via simulation; that is, optimizing the performance of a simulated system. Gaussian processes have gained popularity for inferential optimization, which iteratively updates a model of the simulated solutions and selects the next solution to simulate by relying on statistical inference from that model. We show that, for a discrete problem, GMRFs, a type of Gaussian process defined on a graph, provides better inference on the remaining optimality gap than the typical choice of continuous Gaussian process and thereby enables the algorithm to search efficiently and stop correctly when the remaining optimality gap is below a predefined threshold. We also introduce the concept of multiresolution GMRFs for large-scale problems, with which GMRFs of different resolutions interact to efficiently focus the search on promising regions of solutions.