Inverse Optimization for Imputing Constraints in Mathematical Programs

数学程序中输入约束的逆优化

• 批准号: 2153155
• 负责人: Archis Ghate
• 金额: $ 38.48万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-15 至 2023-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2153155&HistoricalAwards=false
• 关键词: Inverse; Optimization; Imputing; Constraints; Mathematical

While forward optimization methods seek to calculate the optimal values of decision variables for given values of model parameters, the goal of inverse optimization is to infer parameters that render given values of decision variables optimal, i.e., prescribing needed actions or inputs to achieve an optimal result. This grant will contribute to the advancement of national health, prosperity, and welfare by developing a computational framework to efficiently solve a large class of inverse optimization models. The methodology will be applied to system identification problems in cancer radiotherapy to help validate current treatment protocols. The PI will mentor doctoral students on this research topic throughout the project. Results will be incorporated into a graduate-level course and two new books that the PI is drafting, as well as workshops and seminars on applications of optimization for underrepresented students in STEM. The current inverse optimization literature focuses almost entirely on imputing objective function parameters. There has been little work on imputing constraint parameters because these inverse optimization models are nonconvex, bilinear and hence difficult to solve. The project will pursue two approaches to solve these models: (1) conversion into equivalent convex problems via a variable transformation, if possible; and (2) a suite of tailored approximation algorithms that solve a sequence of convex problems, if not. The researched methods will be evaluated computationally against classic branch-and-bound algorithms using several publicly available data sets, together with an in-depth case study in cancer radiotherapy.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

虽然正向优化方法寻求针对模型参数的给定值计算决策变量的最优值，但是反向优化的目标是推断使决策变量的给定值最优的参数，即，规定所需的行动或投入，以实现最佳结果。这笔赠款将通过开发一个计算框架来有效地解决一大类逆优化模型，从而促进国家健康，繁荣和福利。该方法将被应用于系统识别问题的癌症放射治疗，以帮助验证目前的治疗方案。PI将在整个项目中指导博士生关于这一研究课题。研究结果将被纳入研究生课程和PI正在起草的两本新书，以及关于STEM中代表性不足的学生优化应用的研讨会和研讨会。目前的逆优化文献几乎完全集中在输入目标函数参数。由于这些逆优化模型是非凸的、双线性的，因此很难求解，因此在输入约束参数方面的工作很少。该项目将采用两种方法来解决这些模型：（1）如果可能的话，通过变量变换转换为等价的凸问题;（2）如果不可能，则使用一套定制的近似算法来解决一系列凸问题。研究的方法将使用几个公开可用的数据集，结合癌症放射治疗的深入案例研究，对经典分支定界算法进行计算评估。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。