There is a growing technological development in intelligent teaching systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics th...There is a growing technological development in intelligent teaching systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics that helps students understand the basics of linear programming using Linear Program Solver and Service for Solving Linear Programming Problems, through which students will be able to solve economic problems. It comes down to determining the minimum or maximum value of a linear function, which is called the objective function, according to pre-set limiting conditions expressed by linear equations and inequalities. The goal function and the limiting conditions represent a mathematical model of the observed problem. Working as a professor of mathematics in high school, I felt the need for one such work and dealing with the study of linear programming as an integral part of mathematics. There are a number of papers in this regard, but exclusively related to traditional ways of working, as stated in the introductory part of the paper. The center of work as well as the final part deals with the study of linear programming using programs that deal with this topic.展开更多
针对在底层网络可能发生单点和单链路故障情况下的服务功能链(service function chain,SFC)映射问题,提出一种区分等级的可生存SFC映射方法,为提供重要服务的关键SFC预先分配备用资源,为提供普通服务的普通SFC快速重映射失效部分,从而...针对在底层网络可能发生单点和单链路故障情况下的服务功能链(service function chain,SFC)映射问题,提出一种区分等级的可生存SFC映射方法,为提供重要服务的关键SFC预先分配备用资源,为提供普通服务的普通SFC快速重映射失效部分,从而兼顾提高SFC可生存能力和降低底层网络资源开销的需求.首先,在考虑最小化SFC服务时延的条件下,分别为关键SFC和普通SFC的可生存映射问题建立混合整数线性规划模型.其次,提出2种启发式的模型求解算法,其中,面向关键SFC的主备服务路径构建算法采用贪心思想交替进行节点和链路映射,以减小SFC服务时延,并在主备服务路径之间建立桥接路径,以提高路径切换速度和降低路径切换过程的丢包率;面向普通SFC的失效服务路径重建算法引入最大流问题求解失效节点的最佳重映射位置,以提高成功恢复的失效普通SFC数目,并利用改进的Dijkstra最短路径算法选择时延低的重映射路径.最后,在不同网络条件下实验验证了启发式算法的性能,并且在模拟网络环境中所提可生存SFC映射方法能保证SFC的成功运行率在59.2%以上.展开更多
设施服务分区问题(facility service districting problem,FSDP)是指在一个地理区域内,根据服务设施位置和服务能力为其划分服务区,满足供需平衡、形状紧凑和空间连续等要求。空间连续约束使FSDP能更好地满足学区划分、医疗区划分等问...设施服务分区问题(facility service districting problem,FSDP)是指在一个地理区域内,根据服务设施位置和服务能力为其划分服务区,满足供需平衡、形状紧凑和空间连续等要求。空间连续约束使FSDP能更好地满足学区划分、医疗区划分等问题的政策需求,但同时增加了它的求解难度。构造了一个FSDP混合整型线性规划模型,并设计了一个算法框架。框架包括问题定义、初始解、搜索算子和策略等基本模块,支持精确算法、元启发算法和混合算法设计。基于算法框架,实现了数学模型、模拟退火算法、迭代局部搜索算法和数学启发混合算法,并使用4个中大规模案例进行算法测试。实验结果表明,算法框架能够很好地处理空间连续约束的FSDP,支持多种算法快速实现,且求解质量接近案例目标值下界。展开更多
文摘There is a growing technological development in intelligent teaching systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics that helps students understand the basics of linear programming using Linear Program Solver and Service for Solving Linear Programming Problems, through which students will be able to solve economic problems. It comes down to determining the minimum or maximum value of a linear function, which is called the objective function, according to pre-set limiting conditions expressed by linear equations and inequalities. The goal function and the limiting conditions represent a mathematical model of the observed problem. Working as a professor of mathematics in high school, I felt the need for one such work and dealing with the study of linear programming as an integral part of mathematics. There are a number of papers in this regard, but exclusively related to traditional ways of working, as stated in the introductory part of the paper. The center of work as well as the final part deals with the study of linear programming using programs that deal with this topic.
文摘针对在底层网络可能发生单点和单链路故障情况下的服务功能链(service function chain,SFC)映射问题,提出一种区分等级的可生存SFC映射方法,为提供重要服务的关键SFC预先分配备用资源,为提供普通服务的普通SFC快速重映射失效部分,从而兼顾提高SFC可生存能力和降低底层网络资源开销的需求.首先,在考虑最小化SFC服务时延的条件下,分别为关键SFC和普通SFC的可生存映射问题建立混合整数线性规划模型.其次,提出2种启发式的模型求解算法,其中,面向关键SFC的主备服务路径构建算法采用贪心思想交替进行节点和链路映射,以减小SFC服务时延,并在主备服务路径之间建立桥接路径,以提高路径切换速度和降低路径切换过程的丢包率;面向普通SFC的失效服务路径重建算法引入最大流问题求解失效节点的最佳重映射位置,以提高成功恢复的失效普通SFC数目,并利用改进的Dijkstra最短路径算法选择时延低的重映射路径.最后,在不同网络条件下实验验证了启发式算法的性能,并且在模拟网络环境中所提可生存SFC映射方法能保证SFC的成功运行率在59.2%以上.
文摘设施服务分区问题(facility service districting problem,FSDP)是指在一个地理区域内,根据服务设施位置和服务能力为其划分服务区,满足供需平衡、形状紧凑和空间连续等要求。空间连续约束使FSDP能更好地满足学区划分、医疗区划分等问题的政策需求,但同时增加了它的求解难度。构造了一个FSDP混合整型线性规划模型,并设计了一个算法框架。框架包括问题定义、初始解、搜索算子和策略等基本模块,支持精确算法、元启发算法和混合算法设计。基于算法框架,实现了数学模型、模拟退火算法、迭代局部搜索算法和数学启发混合算法,并使用4个中大规模案例进行算法测试。实验结果表明,算法框架能够很好地处理空间连续约束的FSDP,支持多种算法快速实现,且求解质量接近案例目标值下界。
