Multi-Level Optimal Design Using Game Theory with Model Updating By Low Discrepancy Sampling

Abstract

The Design of Experiment (DOE) based response surface methodology (RSM) is a commonly used technique for solving optimization problems. The traditional DOE method has some shortcomings when used to update the RSM model. This thesis aims to develop a new DOE technique to solve the model updating problems in design optimization. Toward this end, a new DOE based RSM method is proposed to solve this problem by using low-discrepancy sequence method to generate the additional data points needed to update the model to replace the traditional factor and level based DOE method. Tested on a couple of numerical example problems, the low-discrepancy sequence method is seen to be effective not only in solving the model updating problem, but also more effective and convenient compared to the traditional DOE method. The second part of this thesis deals with using game theory for solving multi-level design optimization problems. Based on three basic game modes, the Nash game (which is also considered as non-cooperative game), cooperative game, and Stackelberg game (a game between leaders and followers), two solution approaches for Stackelberg game with multiple leaders and followers are proposed: The Decentralized mode and the Hierarchical mode. During the research on these two game systems, solution approaches for a third system namely the Decentralized-Hierarchical model is also addressed in this thesis. It is seen that the low discrepancy sampling based approaches proposed in this thesis are quite effective in solving multi-level optimization problems.