Advancing Sustainability Research Using Mathematical Programming Techniques

The central thesis of this dissertation is that mathematical programming techniques can be successfully applied to gain novel insight into problems in the energy sector related to building assessment systems and wind farms. We focus on the novel application of mathematical programming to the Leadership in Energy and Environmental Design (LEED) rating system, and wind farm layout optimization (WFLO). In the first part of this dissertation, we use an inverse optimization technique to assess and propose improvements to the LEED rating system for buildings. Due to the large dimensionality of the inverse optimization problem, we develop an approximation to improve tractability, and provide numerical evidence to validate the approximation method. Based on the results from our inverse model, we perform a statistical analysis and determine that some of the valuation of LEED credits by building designers may be based on specific building attributes not previously considered. Second, we develop a new mathematical programming approach for wind farm layout optimization. We use Jensen's wake decay model to represent multi-turbine wake effect, develop mixed-integer linear and quadratic optimization formulations, and apply our formulations to several example layouts cases. Compared to previous approaches, our models generate layouts that are more symmetric and produce more power. We also develop a heuristic bounding policy for a special class of quadratic integer programs to speed up computational times, useful in this case, and potentially other applications. Finally, in the last part of this dissertation, we develop a comprehensive WFLO framework that simultaneously takes into account wake effect, sound regulations, turbine infrastructure, and landowner compensation. A financial analysis is performed to determine a common measure of comparison for these different factors, and we develop various mixed-integer linear formulations by combinations of specific factors. We perform six different experiments using our formulations to demonstrate the value of our framework, and from the results we determine the factors impact on the optimal positioning of turbines, infrastructure, and landowner compensation.Ph.D