CAREER: Advanced Mixed Integer Programming Formulations

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The research objective of this Faculty Early Career Development (CAREER) Program award is to improve the effectiveness of Mixed Integer Programming (MIP) by developing and using a new paradigm for constructing linear and nonlinear MIP formulations. Such formulations are used to describe the selection among a finite number of alternatives in optimization models and their attributes can significantly affect the performance of the software employed to solve these models. Unfortunately, there is often a strong trade-off between favorable formulation attributes. The research in this award will result on methods to systematically reduce these trade-offs. The approach to develop these methods will include a mathematical analysis of the proposed paradigm, the design of algorithms to construct the associated MIP formulations and extensive computational experiments to evaluate their effectiveness. The deliverables of this work include new mathematical techniques for constructing and analyzing MIP formulations, algorithms and software for using and evaluating advanced MIP formulations, and educational material for engineering students and practitioners. If successful, the results of this research will provide tools to improve the effectiveness of optimization software for a wide range of MIP applications in business, science and engineering. Recent examples of such applications include efficient energy production and dispatch, clinical trial design and analysis, and trajectory optimization of unmanned aerial vehicles. Results from this research will be disseminated through various channels to allow their integration into commercial optimization software. In addition, all developed techniques will be implemented in open-source software tools available through a variety of modeling languages. The educational material developed in this award will help students at all levels develop crucial mathematical modeling skills. Graduate and undergraduate students will further benefit from this award through lectures and research experience.