Kriging metamodels and global opimization in simulation
Simulation is a popular tool for analyzing complex systems. However, simulation models are often difficult to build and require significant time to run. We often need to invest much money and time to use a simulation model of a complex system. To benefit more from a simulation investment, we may use the simulation input/output data to build a metamodel (model of the simulation model). This metamodel may adequately approximate the original simulation model, but is simpler to build and run. Though there are many types of metamodels, we focus on Kriging (or Gaussian process) models. The advantage of Kriging is that it not only predicts the simulation output but also quantifies the prediction uncertainty. We may use the Kriging metamodel to guide the search for the global optimum of the simulation model. A popular method for the global optimization of deterministic simulation is so-called efficient global optimization (EGO) and its expected improvement (EI). EGO uses a Kriging metamodel to calculate EI, and balances exploitation (local search) and exploration (global search) when searching for the optimal input combination for the simulation model. In this dissertation, we investigate several methodological questions about Kriging metamodels and their use in EGO for deterministic and random simulation models. In Chapter 2, we study multivariate Kriging versus univariate Kriging for simulation models with multiple responses. In Chapter 3, we focus on two related questions: (1) How to select the next combination to be simulated when searching for the global optimum? (2) How to derive confidence intervals for outputs of input combinations not yet simulated? In Chapter 4, we study Kriging metamodels that are required to be either convex or monotonic. In Chapter 5, we introduce intrinsic Kriging as a metamodel of deterministic and random simulation models. In Chapter 6, we study the use of intrinsic Kriging as a new metamodel in global optimization of deterministic and random simulations.
