CAREER: Methodology for Optimization via Simulation: Bayesian Methods, Frequentist Guarantees, and Applications to Cardiovascular Medicine

这个学院早期职业发展（Career）计划奖的目标是通过模拟开发改进的优化方法，并将其应用于心血管医学的决策问题。每当我们希望在几个选项中找到最佳时，就需要通过模拟进行优化，并且评估一个选项的质量需要运行随机模拟。将开发两种改进的方法。首先，排序和选择的方法将利用贝叶斯平均情况和频率最坏情况之间的联系来开发。这些方法有望比现有方法更快地生成解决方案，对解决方案质量有更严格的频率统计保证，其形式对工程应用来说更自然。其次，基于多启动梯度的方法将利用贝叶斯信息分析值来有效地分配模拟工作，使那些更有可能具有高质量局部最优的启动首先收敛。这些方法有望比现有的跨启动分配模拟工作的方法更快地产生高质量的解决方案。新方法将通过应用于心血管医学中的两个问题来证明：设计血管内动脉瘤修复患者的术后监测策略；以及搭桥手术患者移植物的设计和放置。如果成功，这项研究将成为运筹学中的一项使能技术，并将在心血管医学中具有特定的益处。更好的术后监测可以更快地发现术后出现的问题，从而降低动脉瘤破裂的风险。更好的移植物设计将提高手术修复的可靠性和寿命，改善患者的健康状况。更广泛地说，作为一种使能技术，该奖项开发的改进的仿真优化方法将使从业者和研究人员能够以更快的速度和准确性通过仿真问题解决更广泛的优化问题。

The objective of this Faculty Early Career Development (CAREER) Program award is to develop improved methods for optimization via simulation, and to apply them to decision-making problems in cardiovascular medicine. Optimization via simulation is required whenever we wish to find the best among several options, and evaluating the quality of an option requires running a stochastic simulation. Two types of improved methods will be developed. First, methods for ranking and selection will be developed using a link between Bayesian average-case and frequentist worst-case performance. These methods promise to produce solutions more quickly than do existing methods, with frequentist statistical guarantees on solution quality that are tighter and whose form is more natural for engineering applications. Second, multistart gradient-based methods will be developed using Bayesian value of information analysis to efficiently allocate simulation effort across starts, allowing those starts more likely to have high-quality local optima to converge first. These methods promise to produce high-quality solutions more quickly than do existing approaches for allocating simulation effort across starts. The new methods will be demonstrated via application to two problems in cardiovascular medicine: the design of post-operative surveillance strategies for patients undergoing endovascular aneurysm repair; and the design and placement of grafts in patients undergoing bypass surgery.If successful, this research will both serve as an enabling technology within operations research, and will have specific benefits within cardiovascular medicine. Better post-operative surveillance will allow problems occurring after surgery to be detected more quickly, reducing the risk of aneurysm rupture. Better graft design will improve the reliability and longevity of surgical repairs, improving patient health. More broadly, as an enabling technology, the improved simulation optimization methods developed with this award will allow practitioners and researchers to solve a wider variety of optimization via simulation problems with greater speed and accuracy.