Novel mathematical models for optimal screening and multicriteria scheduling problems

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。

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.