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。数据的可能场景的大致范围可能是可用的，但即使是这些场景也可能随着时间的推移而发生不可预测的变化。这项研究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，它使用高能射线照射癌症靶点；这种方法的内在挑战是尽可能限制周围健康组织暴露在辐射中。在某些癌症部位，如肺癌或乳腺癌，心脏等重要器官因过度辐射而受到损害的风险很高。靶点和周围健康器官的确切位置是不确定的，因为在整个治疗过程中，由于呼吸或患者内部解剖的变化而引起的运动；这特别具有挑战性，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稳健的优化模型，考虑到所有可能的器官运动和变形场景，并找到考虑潜在不确定性的最佳治疗方案。我们的适应性方法将从对数据的观察中学习，并随着时间的推移不断改进解决方案。例如，在RT中，我们将跟踪整个治疗过程中的器官运动，并对未来可能的情况提供更好的预测。 这个研究项目的范围远远超出了RT。对于许多工程问题，如金融工程、生产计划、环境工程、能源和医疗保健，基础数据受到不确定性的影响，不确定情景的范围可能会随着时间的推移而发生不可预测的变化。这项研究计划将推进自适应和稳健优化理论，以解决这些不确定性，并开发一个新的通用框架，使优化技术能够更好地用于各种数据驱动的工程应用。运筹界最近对大数据分析表现出了越来越大的兴趣。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现实世界的应用。我们将开发专门的解决算法，使之能够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，他们将接受这些专门的、受欢迎的技能方面的培训。拟议的研究计划将弥合不确定条件下大规模数据驱动应用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.