Global-local Metamodel-assisted Stochastic Programming via Simulation

Abstract

To integrate strategic, tactical, and operational decisions, stochastic programming has been widely used to guide dynamic decision-making. In this article, we consider complex systems and introduce the global-local metamodel-assisted stochastic programming via simulation that can efficiently employ the simulation resource to iteratively solve for the optimal first- and second-stage decisions. Specifically, at each visited first-stage decision, we develop a local metamodel to simultaneously solve a set of scenario-based second-stage optimization problems, which also allows us to estimate the optimality gap. Then, we construct a global metamodel accounting for the errors induced by: (1) using a finite number of scenarios to approximate the expected future cost occurring in the planning horizon, (2) second-stage optimality gap, and (3) finite visited first-stage decisions. Assisted by the global-local metamodel, we propose a new simulation optimization approach that can efficiently and iteratively search for the optimal first- and second-stage decisions. Our framework can guarantee the convergence of optimal solution for the discrete two-stage optimization with unknown objective, and the empirical study indicates that it achieves substantial efficiency and accuracy.