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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=573777
• 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关的研究线。我们的第一个研究流探讨了确定随机降低失败的系统的最佳筛选时间表的问题。筛选提供了有关系统当前劣化水平的不完美信息，该信息基于确定最佳预防措施（即替换，维修）的最佳预防措施。对于包括疾病筛查在内的各种实际应用，此问题非常重要。特别是，为此问题开发的建模框架可用于优化预防性癌症筛查，这可能会对社会产生重大影响。在这种情况下，我们探索了基于马尔可夫决策过程和控制理论的最佳筛选问题的新颖建模框架。我们将分析这些复杂模型以证明某些结构特性的存在。我们将使用此类属性来开发更快的解决方案算法来解决此问题。此外，我们开发了一种用于多目标最佳筛选问题的解决方案方法，该方法决定了占主导地位的帕累托最佳解决方案。拟议的研究还将解决人群的最佳筛查问题，以确定应如何将有限的筛查资源分配给人群中的个人。 作为次要研究流，我们将开发出最佳和近似的解决方案方法，以最大程度地减少迟到（晚）作业和加权流动时间的数量，以确定特定任务的帕托特时间计划。为此问题开发建模和解决方案框架是一个重大贡献，因为它在几个领域的实际重要性。例如，在医院中，这个问题的特征是医生的观点是，其目标是增加在预定义的时间间隔内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Branch＆Bound建模并解决此多标准调度问题。我们还基于梁搜索和遗传算法开发了近似解决方案方法。