本文针对居家健康护理路径规划与调度问题(home health care routing and scheduling problem,HHCRSP)中患者服务时间与护理人员路程时间的高度随机性,以及患者群体存在差异化优先级的挑战展开系统研究。传统确定性优化方法难以同时兼...本文针对居家健康护理路径规划与调度问题(home health care routing and scheduling problem,HHCRSP)中患者服务时间与护理人员路程时间的高度随机性,以及患者群体存在差异化优先级的挑战展开系统研究。传统确定性优化方法难以同时兼顾调度方案的鲁棒性与运营效率。为应对这一复杂性,本文从模型构建与算法设计两个层面提出创新性解决方案。在模型层面,引入分布鲁棒优化(distributionally robust optimization,DRO)框架,构建了基于一阶矩和绝对偏差矩的模糊集,以刻画随机变量的分布不确定性,从而在不依赖精确概率分布的前提下,建立以最大化总优先级收益的同时控制时间成本风险的DRO模型。在算法层面,针对模型复杂约束带来的求解困难,设计了一种精确算法,通过有效生成切割平面和收敛策略提升求解效率与稳定性。通过系统数值实验,将所提DRO模型与经典随机规划模型和确定性模型进行对比。结果表明,在不确定性环境下DRO模型表现出更优的鲁棒性能,能够通过调整置信水平平衡服务效率与风险控制,从而支持根据实际风险偏好在服务质量和运营成本之间实现有效权衡。所提精确算法与商业求解器的对比结果表明,其在复杂参数组合的算例中展现出尤为显著的效率优势。因此,所提出的DRO模型与算法框架能够为HHCRSP问题提供高效且可靠的决策支持,帮助决策者根据实际风险偏好在服务质量与运营成本之间实现权衡。展开更多
This paper studies a distributed robust resource allocation problem with nonsmooth objective functions under polyhedral uncertain allocation parameters. In the considered distributed robust resource allocation problem...This paper studies a distributed robust resource allocation problem with nonsmooth objective functions under polyhedral uncertain allocation parameters. In the considered distributed robust resource allocation problem, the（nonsmooth） objective function is a sum of local convex objective functions assigned to agents in a multi-agent network. Each agent has a private feasible set and decides a local variable, and all the local variables are coupled with a global affine inequality constraint,which is subject to polyhedral uncertain parameters. With the duality theory of convex optimization,the authors derive a robust counterpart of the robust resource allocation problem. Based on the robust counterpart, the authors propose a novel distributed continuous-time algorithm, in which each agent only knows its local objective function, local uncertainty parameter, local constraint set, and its neighbors＇ information. Using the stability theory of differential inclusions, the authors show that the algorithm is able to find the optimal solution under some mild conditions. Finally, the authors give an example to illustrate the efficacy of the proposed algorithm.展开更多
文摘本文针对居家健康护理路径规划与调度问题(home health care routing and scheduling problem,HHCRSP)中患者服务时间与护理人员路程时间的高度随机性,以及患者群体存在差异化优先级的挑战展开系统研究。传统确定性优化方法难以同时兼顾调度方案的鲁棒性与运营效率。为应对这一复杂性,本文从模型构建与算法设计两个层面提出创新性解决方案。在模型层面,引入分布鲁棒优化(distributionally robust optimization,DRO)框架,构建了基于一阶矩和绝对偏差矩的模糊集,以刻画随机变量的分布不确定性,从而在不依赖精确概率分布的前提下,建立以最大化总优先级收益的同时控制时间成本风险的DRO模型。在算法层面,针对模型复杂约束带来的求解困难,设计了一种精确算法,通过有效生成切割平面和收敛策略提升求解效率与稳定性。通过系统数值实验,将所提DRO模型与经典随机规划模型和确定性模型进行对比。结果表明,在不确定性环境下DRO模型表现出更优的鲁棒性能,能够通过调整置信水平平衡服务效率与风险控制,从而支持根据实际风险偏好在服务质量和运营成本之间实现有效权衡。所提精确算法与商业求解器的对比结果表明,其在复杂参数组合的算例中展现出尤为显著的效率优势。因此,所提出的DRO模型与算法框架能够为HHCRSP问题提供高效且可靠的决策支持,帮助决策者根据实际风险偏好在服务质量与运营成本之间实现权衡。
基金supported by the National Key Research and Development Program of China under Grant No.2016YFB0901902the National Natural Science Foundation of China under Grant Nos.61573344,61603378,61621063,and 61781340258+1 种基金Beijing Natural Science Foundation under Grant No.4152057Projects of Major International(Regional)Joint Research Program NSFC under Grant No.61720106011
文摘This paper studies a distributed robust resource allocation problem with nonsmooth objective functions under polyhedral uncertain allocation parameters. In the considered distributed robust resource allocation problem, the（nonsmooth） objective function is a sum of local convex objective functions assigned to agents in a multi-agent network. Each agent has a private feasible set and decides a local variable, and all the local variables are coupled with a global affine inequality constraint,which is subject to polyhedral uncertain parameters. With the duality theory of convex optimization,the authors derive a robust counterpart of the robust resource allocation problem. Based on the robust counterpart, the authors propose a novel distributed continuous-time algorithm, in which each agent only knows its local objective function, local uncertainty parameter, local constraint set, and its neighbors＇ information. Using the stability theory of differential inclusions, the authors show that the algorithm is able to find the optimal solution under some mild conditions. Finally, the authors give an example to illustrate the efficacy of the proposed algorithm.
