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

对于依赖于大数据集的工程问题，一个固有的问题是处理数据中的不确定性。数据的大致可能情景范围可能是可用的，但即使这些情景也可能随着时间的推移而不可预测地发生变化。本研究计划的目的是为大规模不确定数据集的工程应用开发新的优化方法，并展示这些方法在放射治疗（RT）治疗计划中的实用性。放射疗法是最常见的癌症治疗方法，它使用高能光束照射癌变目标；这种方法的一个固有挑战是尽可能地限制周围健康组织暴露于辐射。在某些癌症部位，如肺或乳房，心脏等重要器官因过度辐射而受损的风险很高。在整个治疗过程中，由于呼吸引起的运动或患者内部解剖结构的变化，目标和周围健康器官的精确位置是不确定的；这尤其具有挑战性，因为这些动作是不规则和不可预测的。通过本研究项目，我们将开发考虑所有可能的器官运动和变形情况的自适应和鲁棒优化模型，并找到考虑潜在不确定性的最佳治疗方案。我们的自适应方法将从数据观察中学习，并随着时间的推移不断改进解决方案。例如，在放射治疗中，我们将在整个治疗过程中跟踪器官的运动，并对未来可能出现的情况提供更好的预测。

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.