A learning tabu search for a truck allocation problem with linear and nonlinear cost components

The two‐level problem studied in this article consists of optimizing the refueling costs of a fleet of locomotives over a railway network. The goal consists of determining: (1) the number of refueling trucks contracted for each yard (truck assignment problem denoted TAP) and (2) the refueling plan of each locomotive (fuel distribution problem denoted FDP). As the FDP can be solved efficiently with existing methods, the focus is put on the TAP only. In a first version of the problem (denoted (P1)), various linear costs (e.g., fuel, fixed cost associated with each refueling, weekly operating costs of trucks) have to be minimized while satisfying a set of constraints (e.g., limited capacities of the locomotives and the trucks). In contrast with the existing literature on this problem, two types of nonlinear cost components will also be considered, based on the following ideas: (1) if several trucks from the same fuel supplier are contracted for the same yard, the supplier is likely to propose discounted prices for that yard (Problem (P2)); (2) if a train stops too often on its route, a penalty is incurred, which represents the dissatisfaction of the clients (Problem (P3)). Even if exact methods based on a mixed integer linear program formulation are available for (P1), they are not appropriate anymore to tackle (P2) and (P3). Various methods are proposed for the TAP: a descent local search, a tabu search, and a learning tabu search (LTS). The latter is a new type of local search algorithm. It involves a learning process relying on a trail system, and it can be applied to any combinatorial optimization problem. Results are reported and discussed for a large set of instances (for (P1), (P2), and (P3)), and show the good performance of LTS. © 2014 Wiley Periodicals, Inc. 62:32–45, 2015     

使用小波分层连通树结构的压缩信号重构

基于小波树模型的压缩感知可以通过较少的观测量得到鲁棒的信号重构,但采用最优树逼近时,则存在复杂度大的问题。在证明分层后的小波树仍然具备连通树性质的基础上,提出了基于小波分层连通树结构的压缩重构算法,在与原观测量一致的情况下,保证了重构精度并且提高了重构效率。实验结果表明,改进算法相对于原算法在处理大尺度数据时,效率有明显的改善。     

基于创新人才培养的高等代数教学改革探析

高等代数作为高师院校数学与应用专业学生的一门专业基础课,它对于训练学生的数学思维、培养学生的数学素养具有重要作用。文章结合当前高等代数教学中存在的一些问题,基于创新人才的培养,具体从培养学生学习兴趣、培养学生问题意识、培养学生的数学基础能力以及创新能力、加强高等代数与解析几何、近世代数课程的联系、倡导学生学习评价的多元化等多个方面进行了高等代数课程教学改革的探索。     

Approximation algorithms for capacitated stochastic inventory systems with setup costs

We develop the first approximation algorithm with worst‐case performance guarantee for capacitated stochastic periodic‐review inventory systems with setup costs. The structure of the optimal control policy for such systems is extremely complicated, and indeed, only some partial characterization is available. Thus, finding provably near‐optimal control policies has been an open challenge. In this article, we construct computationally efficient approximate optimal policies for these systems whose demands can be nonstationary and/or correlated over time, and show that these policies have a worst‐case performance guarantee of 4. We demonstrate through extensive numerical studies that the policies empirically perform well, and they are significantly better than the theoretical worst‐case guarantees. We also extend the analyses and results to the case with batch ordering constraints, where the order size has to be an integer multiple of a base load. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 304–319, 2014     

一类分段线性费用网络流问题

本文通过把一类分段线性费用网络流问题化成线性费用网络流问题,给出了求解这类分段线性费用网络流问题的算法。     

卫星在役考核相关问题研究

各类卫星在现代战争中发挥着重要和关键作用。我国传统的卫星试验和鉴定具有很强的科研试验性质,承制单位和用户重点关注的是性能检验,较少考虑作战效能和部队适用性等指标。为推动卫星装备建设和应用,装备试验鉴定部门初步组织开展了相应的在役考核工作。文章对比了美军装备作战试验与鉴定、我国作战试验与在役考核的概念;提出卫星在役考核的六大特点;分析卫星在役考核的组织方式、组织机构和组织保障的不足,提出相应发展建议;研究卫星在役考核指标体系设计、分析评估方法、问题反馈与整改等方面的不足,并提出相应措施建议。     

A balancing problem for mixed model assembly lines with a paced moving conveyor

We state a balancing problem for mixed model assembly lines with a paced moving conveyor as: Given the daily assembling sequence of the models, the tasks of each model, the precedence relations among the tasks, and the operations parameters of the assembly line, assign the tasks of the models to the workstations so as to minimize the total overload time. Several characteristics of the problem are investigated. A line‐balancing heuristic is proposed based on a lower bound of the total overload time. A practical procedure is provided for estimating the deviation of any given line‐balance solution from the theoretical optimum. Numerical examples are given to illustrate the methodology. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Warranty costs: An age‐dependent failure/repair model

An age‐dependent repair model is proposed. The notion of the “calendar age” of the product and the degree of repair are used to define the virtual age of the product. The virtual failure rate function and the virtual hazard function related to the lifetime of the product are discussed. Under a nonhomogeneous Poisson process scenario the expected warranty costs for repairable products associated with linear pro‐rata, nonrenewing free replacement and renewing free replacement warranties are evaluated. Illustration of the results is given by numerical and graphical examples. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

利用几何结构求解欧氏平面TSP的改进遗传算法

TSP是经典的组合优化问题。根据欧氏平面TSP最优环路的性质提出了子路径及相关的概念,利用点集凸壳设计了环路构造算法,并以点集Delaunay三角剖分图为启发信息设计了改进的遗传算法,通过中国144城市TSP等验证了算法的有效性。     

基于相关性模型的舰船装备测试性分析与建模

为了提高舰船装备的综合诊断能力,在舰船设计、研制阶段就必须进行装备测试性设计工作。为此,根据舰船装备测试性要求,对装备进行了故障模式影响分析,确定了装备在设计和制造过程中所有可能的故障模式,以及每一故障模式的原因和影响,据此对装备功能和结构进行了划分。然后,利用相关性模型对舰船装备进行测试性分析与建模,建立了舰船装备组成单元的相关性图示模型、数学模型,并运用考虑可靠性和费用的优选方法,建立了舰船装备诊断树,得到舰船装备的测试方案。算例分析表明:该研究可有效提高舰船装备测试的效率,提升测试的经济性。