Nonlinear Optimization under Uncertainty for Sustainable Energy Informatics Problems

Despite the undeniable importance of energy in the modern world, the majority of today's energy sources are unsustainable which has environmental drawbacks such as global climate warming. Increasing sustainable energy efficiency through optimization of resources has become one of the major goals of the century due to the potential economical and environmental benefits. The analysis, design, implementation, and use of computer science models for developing energy efficient management plans are referred to as sustainable energy informatics. In this dissertation, three optimization and data mining approaches for sustainable energy applications are proposed. These problems deal with analyzing data under uncertainty to make a robust and reliable decision.

The first approach presents the multiple instance classification problem with application in wind farm site locating. Hard margin loss formulations that minimize the number of misclassified instances are proposed to model more robust representations of outliers. Although the problem is NP-hard, medium sized problems can be solved to optimality in reasonable time using integer programming and constraint programming formulations. For larger problems a three phase heuristic algorithm is proposed which is shown to have superior generalization performance compared to other approaches.

Second, a layout optimization framework for offshore wind farms is proposed under widely accepted assumptions. Although wind has less environmental impact than conventional sources, onshore wind farms currently supply only 3% of the nation's electricity while reducing carbon emissions by 2.5%. Due to higher wind speeds off the coast, offshore wind farms' potential for electricity production is typically higher than onshore counterparts yet relatively more expensive to construct, operate, and maintain. We present a rigorous mathematical model that would minimize the cost of wind energy by examining the trade-off between the advantages of packing the turbines closer together and the loss generated by wake effects.

The purpose of the last approach is to analyze historical information on the variables that potentially have a high impact on a response variable. The goal of this study is to filter out the noise using the common ground information. Considering monthly natural gas prices, we highlight the strength of a forecasting scheme through the simultaneous selection of instances and features.