Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations

This dissertation examines methods that use kriging approximations to solve constrained nonlinear design optimization problems where the function evaluations are computationally expensive.; The expense of the functions creates unique challenges for global optimization. Utilizing genetic algorithms or simulated annealing is impractical due to the large number of function evaluations required to reach convergence. Design problems involving computer simulations often yield noisy and/or discontinuous responses, which causes difficulty for gradient-based algorithms. One class of algorithms, referred to as Bayesian analysis algorithms, has shown promise at overcoming these difficulties.; Bayesian analysis algorithms use global approximations of the functions to compute a statistics-based criterion for selecting the next iterate. By optimizing this inexpensive selection criterion over the entire design space, they retain global search properties without compromising local solution accuracy. The Efficient Global Optimization (EGO) algorithm of Jones, Schonlau and Welch is the Bayesian analysis algorithm that forms the basis of this work. It uses kriging models for approximations and the expected improvement function as the sampling criterion.; The dissertation advances the state-of-the-art in Bayesian analysis in four ways: improving the abilities and accuracy of the global approximations, increasing the flexibility of the search strategy by incorporating a wide variety of sampling criteria, improving the ability to solve constrained problems, and increasing the efficiency and accuracy of the search by considering the computational burden of each response function. The version of the algorithm enhanced by the proposed changes is referred to as superEGO to signify that it can solve a superset of the problems EGO was originally designed to solve.; Several examples are shown to demonstrate the benefits of these advancements. Incorporating available inexpensive information when searching for the next iterate reduced the number of iterations required to solve a simulation-based vehicle design problem by between 50% and 90%. In addition, the approximate models generated during an ergonomics experiment were shown to be three times more accurate using 25% fewer data samples when the sampling strategy was performed with superEGO using a criteria specifically designed for the study.