Novel mathematical models for optimal screening and multicriteria scheduling problems

用于优化筛选和多标准调度问题的新颖数学模型

• 批准号: 418663-2012
• 负责人: Erenay, Fatih
• 金额: $ 1.68万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=636694
• 关键词: Novel; mathematical; models; optimal; screening

The proposed research consists of two related lines of research. Our first research stream explores the problem of determining the optimal screening schedule of a system that stochastically deteriorates towards failure. Screenings provide imperfect information about the current deterioration level of the system, based on which optimal preventative actions (i.e., replacement, repair) are determined. This problem is of great importance for various practical applications including disease screening. In particular, the modeling framework developed for this problem can be used in optimizing preventative cancer screening, which may have a significant impact on the society. In this context, we explore novel modeling frameworks for the optimal screening problem based on Markov decision processes and control theory. We will analyze these complex models to prove the existence of certain structural properties. We will use such properties to develop faster solution algorithms to solve this problem. In addition, we develop a solution method for multi-objective optimal screening problems which determine the Pareto-optimal solutions dominating the other feasible solutions. The proposed research will also address the optimal screening problem for a population, in order to determine how limited screening resources should be allocated to the individuals within the population. As a secondary stream of research, we will develop optimal and approximate solution methods for the multicriteria scheduling problem of minimizing the number of tardy (late) jobs and weighted flow-time in order to determine Pareto-optimal schedules of particular tasks. Developing a modeling and solution framework for this problem is a significant contribution because of its practical importance in several fields. For example, in a hospital, this problem characterizes the perspective of a doctor whose objective is to increase the number of patients served within predefined time intervals and decrease the time that the patients spent in the hospital. We model and solve this multicriteria scheduling problem using MIP and Branch & Bound. We also develop approximate solution methods based on beam-search and genetic algorithms.

拟议的研究包括两个相互关联的研究方向。我们的第一个研究流探索了确定随机恶化到故障的系统的最优筛选时间表的问题。筛查提供了关于系统当前恶化程度的不完善信息，以此为基础确定最佳预防措施(即更换、修复)。这一问题对于包括疾病筛查在内的各种实际应用具有重要意义。特别是，针对这一问题开发的建模框架可以用于优化预防性癌症筛查，这可能会对社会产生重大影响。在此背景下，我们探索了基于马尔可夫决策过程和控制理论的最优筛选问题的新的建模框架。我们将分析这些复杂的模型，以证明某些结构性质的存在。我们将利用这些性质来开发更快的求解算法来解决这个问题。此外，我们还发展了一种多目标最优筛选问题的求解方法，该方法确定了支配其他可行解的Pareto最优解。拟议的研究还将解决群体的最佳筛查问题，以确定应该如何将有限的筛查资源分配给群体中的个人。作为第二个研究方向，我们将开发最小化延误(延迟)作业数和加权流时间的多目标调度问题的最优和近似解方法，以确定特定任务的Pareto最优调度。为这个问题开发一个建模和解决方案框架是一项重大贡献，因为它在几个领域具有实际重要性。例如，在医院中，这一问题的特点是医生的目标是在预定的时间间隔内增加服务的患者数量，并减少患者在医院花费的时间。我们使用MIP和分支定界法对该多目标调度问题进行建模和求解。提出了基于波束搜索和遗传算法的近似求解方法。