THESIS DEFENSE: Statistical Modeling of the Value Function in High-Dimensional, Continuous-State SDP
A decision-making framework (DMF) for a multi-level wastewater treatment system (WTS) is developed to evaluate current and emerging technologies. Stochastic dynamic programming (SDP) is employed to model the WTS, where each level of the WTS is represented as a period in the SDP. In order to achieve a computationally tractable numerical solution for this continuous-state SDP, a statistical modeling process, which involves construction of an experimental design over the SDP state space followed by approximation of the SDP future value function with a statistical model, is applied. In this research, the statistical modeling method is Multivariate Adaptive Regression Splines (MARS), and the experimental designs are based on orthogonal array (OAs) and OA-based Latin hypercube designs (OA-LHDs).
A parallelized version of MARS is developed to improve computational efficiency in solving this twenty-dimensional SDP problem. Moreover, three alternate MARS algorithms (Mmax relaxation, MARS using Automatic Stopping Rules, Robust MARS) are presented to facilitate flexibility and robustness as well as efficiency and model accuracy.
Model discrimination techniques are used to evaluate the quality of fit for a statistical model. Four evaluation measures for the DMF are defined and exercised to quantify performance of the technologies in each period. Overall, the results on this DMF demonstrate the potential of this forum for identifying promising technology units for wastewater treatment.