Description:

Title: Discrete Optimization via Simulation using Gaussian Markov Random Fields

Barry L Nelson
Department of Industrial Engineering & Management Sciences
Northwestern University

Abstract:

The problem is maximizing or minimizing the expected value of a stochastic performance measure that can be observed by running a dynamic, discrete-event simulation when the feasible solutions are defined by integer decision variables. Inventory sizing, call center staffing and manufacturing system design are common applications. Standard approaches are ranking and selection, which takes no advantage of the relationship among solutions, and adaptive random search, which exploits it but in a heuristic way (“good solutions tend to be clustered”). Instead, we construct an optimization procedure built on modeling the relationship as a discrete Gaussian Markov random field (GMRF). This enables computation of the expected improvement (EI) that could be obtained by running the simulation for any feasible solution, whether actually simulated or not. The computation of EI can be numerically challenging, in general, but the GMRF representation greatly reduces the burden by facilitating the use of sparse matrix methods. By employing a multiresolution GMRF, problems with millions of feasible solutions can be solved.