Large-Scale Adaptive and Robust Optimization with Application to Radiation Therapy

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For engineering problems that rely on large datasets, an inherent problem is dealing with uncertainties in the data. An approximate range of possible scenarios of the data may be available, but even these scenarios may change over time unpredictably. The aim of this research program is to develop new optimization methods for engineering applications with large-scale uncertain datasets and to demonstrate the utility of these methods for radiation therapy (RT) treatment planning. Radiation therapy, the most common cancer treatment method, uses high-energy beams to irradiate a cancerous target; an inherent challenge of this method is to limit exposure of surrounding healthy tissue to radiation as much as possible. In certain cancer sites, such as lung or breast, vital organs such as the heart are at a high risk of being damaged because of excessive radiation. The precise locations of the target and the surrounding healthy organs are uncertain because of movement caused by breathing or changes in the patient's internal anatomy throughout the treatment; this is particularly challenging because these movements are irregular and unpredictable. Through this research program, we will develop adaptive and robust optimization models that take into account all possible organ motion and deformation scenarios, and find the treatment plans that are optimal considering the underlying uncertainties. Our adaptive methodology will learn from observations of data and continuously improve the solution over time. In RT, for instance, we will track the organ movements throughout the treatment, and provide better predictions of future possible scenarios. The scope of this research program extends well beyond RT. For many engineering problems, such as financial engineering, production planning, environmental engineering, energy, and healthcare, the underlying data is subject to uncertainty and the range of uncertain scenarios may change over time unpredictably. This research program will advance the theory of adaptive and robust optimization to address these uncertainties, and develop a novel generalized framework that will enable a better use of optimization techniques in a variety of data-driven engineering applications. The operations research community has recently shown an increased interest in big data analytics. With large-scale datasets, the traditional optimization algorithms are often not computationally feasible for many real-world applications. We will develop specialized solution algorithms that will enable solving different classes of large-scale problems most efficiently. The development of these algorithms will require HQP, who will be trained in these specialized, sought after skills. The proposed research program will bridge the gap between the theory and application of optimization techniques for large-scale data-driven applications under uncertainty.