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

对于依赖大型数据集的工程问题，一个固有的问题是处理数据中的不确定性。数据的可能场景的大致范围可能是可用的，但即使这些场景也可能随着时间的推移而不可预测地变化。该研究计划的目的是开发新的优化方法，用于工程应用与大规模的不确定数据集，并证明这些方法的实用性，放射治疗（RT）治疗计划。放射疗法是最常见的癌症治疗方法，使用高能束照射癌症靶点;这种方法的固有挑战是尽可能限制周围健康组织暴露于辐射。在某些癌症部位，如肺或乳腺，心脏等重要器官因过度辐射而受损的风险很高。目标和周围健康器官的精确位置是不确定的，因为在整个治疗过程中呼吸或患者内部解剖结构的变化引起的运动;这是特别具有挑战性的，因为这些运动是不规则的和不可预测的。通过这项研究计划，我们将开发自适应和强大的优化模型，考虑到所有可能的器官运动和变形的情况，并找到最佳的治疗计划，考虑到潜在的不确定性。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RT中，我们将在整个治疗过程中跟踪器官运动，并对未来可能的情况提供更好的预测。** 该研究项目的范围远远超出RT。对于许多工程问题，如金融工程，生产规划，环境工程，能源和医疗保健，基础数据受到不确定性的影响，不确定场景的范围可能会随着时间的推移而不可预测地变化。该研究计划将推进自适应和鲁棒优化理论，以解决这些不确定性，并开发一种新的通用框架，使优化技术在各种数据驱动的工程应用中得到更好的利用。运筹学界最近对大数据分析表现出越来越大的兴趣。对于大规模数据集，传统的优化算法在计算上往往不适用于许多实际应用。我们将开发专门的解决方案算法，以最有效地解决不同类别的大规模问题。这些算法的开发将需要HQP，他们将接受这些专业的培训，追求技能。拟议的研究计划将弥合不确定性下大规模数据驱动应用程序的优化技术的理论和应用之间的差距。**

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.**