SIMULATION METAMODELING AND OPTIMIZATION WITH GAUSSIAN PROCESS MODELS UNDER INPUT UNCERTAINTY

Abstract

This thesis proposes three pieces of work on Gaussian process (GP) metamodeling and GP-based optimization algorithms for stochastic simulations with the consideration of input uncertainty. First, we consider input-parameter uncertainty and propose an approximation model for the mean response. We refine four GP-based optimization algorithms to explicitly account for this uncertainty, and compare these algorithms to draw some general conclusions and recommendations. Next, we extend the consideration of input uncertainty in simulation optimization to include distributional uncertainty and propose a nonparametric Bayesian approach to address this. We prove the consistency of our approach, and provide the asymptotic normality results to show its robustness. We refine a GP-based algorithm to efficiently solve the problem with a theoretical guarantee. Third, we generalize a GP multi-fidelity model to incorporate both input and location uncertainties, and apply the proposed model to solve a ranking problem for emissions mitigation strategies in the maritime industry.