Combining Multivariate Stochastic Process Models with Filter Methods for Constrained Optimization
Expensive black box systems arise in many engineering applications but can be difficult to optimize because their output functions may be complex, multi-modal, and difficult to understand. The task becomes even more challenging when the optimization is subject to constraints and no derivative information is available. In this dissertation, we combine response surface modeling, sequential Monte Carlo, and filter methods in order to solve problems of this nature. Furthermore, we propose a new model for correlated outputs of mixed type. Our modeling framework extends Gaussian process methodology for modeling of continuous multivariate spatial outputs by adding a latent process structure that allows for joint modeling of a variety of types of correlated outputs. In addition, we implement fully Bayesian inference using particle learning, which allows us to conduct fast sequential inference. By employing a filter algorithm for solving constrained optimization problems, we also establish two novel probabilistic metrics for guiding the filter. We extend these ideas to a multidimensional filter that outperforms the traditional filter method. Overall, this hybridization of statistical modeling and nonlinear programming efficiently utilizes both global and local search in order to converge to a global solution to the constrained optimization problem. To demonstrate the effectiveness of the proposed methods, we perform numerical tests on both synthetic examples and real-world hydrology computer experiment optimization problems.