Strategy for Global Optimization and Post-Optimality Using Local Kriging Approximations

A strategy for global optimization based upon local approximate optimization has been developed in this research. The global design space is divided into local regions. Accurate Kriging approximations are constructed in the local regions to provide an inexpensive formulation of the system behavior. Each Kriging approximation is validated by using a cross-validation scheme. Gradient based local optimizers are used to identify local optima in each of the regions. A reduced trust region around the local optimum is further analyzed to provide the global optimum solutions. This approach possesses the capability of identifying global optimum solutions within reduced time frames as compared to existing methods. A second investigation focused on the formulation and development of a nonlinear post-optimality analysis. The non-linear response of the system is captured through local approximations. A cumulative approximation is constructed from the local response surface approximations via a blending function. The post-optimal solution is obtained by performing optimization over the cumulative approximation of the objective function and the constraints.