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

这项教师早期职业发展(CALEAR)计划奖的目标是开发通过模拟进行优化的改进方法，并将它们应用于心血管医学的决策问题。当我们希望在几个选项中找到最好的选项时，就需要通过模拟进行优化，而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，将利用贝叶斯平均情况和频繁的最差情况性能之间的联系来开发排名和选择方法。这些方法承诺比现有方法更快地产生解决方案，对解决方案质量的经常统计保证更紧密，其形式更适合工程应用。其次，将开发基于多起点梯度的方法，使用信息分析的贝叶斯价值来有效地在起点之间分配模拟工作量，允许那些更有可能具有高质量局部最优的起点首先收敛。这些方法承诺比现有的跨Start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展示：对接受血管内动脉瘤修复的患者设计术后监测策略；以及在接受搭桥手术的患者中设计和放置移植物。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产生特殊的好处。更好的术后监测将使手术后出现的问题更快地被发现，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。更广泛地说，作为一项使能技术，与该奖项一起开发的改进的模拟优化方法将允许从业者和研究人员以更快的速度和更准确的速度通过模拟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.