Taylor Kriging Metamodeling for Simulation Interpolation, Sensitivity Analysis and Optimization

Abstract

The dissertation explores Kriging metamodeling for the interpolation, sensitivity analysis and optimization of simulation models with costly computational or economic expenses. The key theoretical contribution is that a novel Kriging model based on Taylor expansion is developed and named Taylor Kriging (TK) where Taylor expansion is used to identify a drift function. Taylor expansion has excellent nonlinear function approximation capabilities, thus enhancing the interpolation potentials of Kriging. Another contribution is the use of sample standard deviation as the metric for influence distance of covariance, which makes simulations with data of differing magnitudes have a consistent measurement unit.

The partial differentiation equation of Kriging is developed and used together with analysis of variance to assist in sensitivity analysis on a simulation model. A physical simulation case based on cost estimation shows that Kriging sensitivity analysis is effective. While fitting metamodels, the dissertation compares the simulation interpolation accuracy of Kriging with those of regression and artificial neural networks. A significant feature is that the comparison considers multicollinearity, heteroscedasticity and specification error.

A novel simulation optimization algorithm named SOAKEA is created. SOAKEA integrates Kriging with evolutionary algorithms to optimize simulation models with costly run-time expenses. The properties of SOAKEA are investigated, and some important empirical conclusions about parameter settings are obtained. Several typical multimodal benchmark functions are used to test and compare SOAKEA with other well-known metaheuristics. The results indicate that SOAKEA is a promising optimization tool for simulation models with expensive running costs.

The Kriging software is developed in order to satisfy application needs. The software is multi-functional and user-friendly. The software can be used not only for simulation interpolation but also for wider interpolation applications.