Locating a semi-obnoxious covering facility with repelling polygonal regions

A facility is to be located in the Euclidean plane to serve certain sites by covering them closely. Simultaneously, a set of polygonal areas must be protected from the negative effects from that facility. The problem is formulated as a margin maximization model. Necessary optimality conditions are studied and a finite dominating set of solutions is obtained, leading to a polynomial algorithm. The method is illustrated on some examples.     

0-1 reformulations of the multicommodity capacitated network design problem

We study 0-1 reformulations of the multicommodity capacitated network design problem, which is usually modeled with general integer variables to represent design decisions on the number of facilities to install on each arc of the network. The reformulations are based on the multiple choice model, a generic approach to represent piecewise linear costs using 0-1 variables. This model is improved by the addition of extended linking inequalities, derived from variable disaggregation techniques. We show that these extended linking inequalities for the 0-1 model are equivalent to the residual capacity inequalities, a class of valid inequalities derived for the model with general integer variables. In this paper, we compare two cutting-plane algorithms to compute the same lower bound on the optimal value of the problem: one based on the generation of residual capacity inequalities within the model with general integer variables, and the other based on the addition of extended linking inequalities to the 0-1 reformulation. To further improve the computational results of the latter approach, we develop a column-and-row generation approach; the resulting algorithm is shown to be competitive with the approach relying on residual capacity inequalities.     

有害废弃物处理站选址近似帕累托集合的有效产生

本文研究有害废弃物处理站选址问题。在Ravi等研究的MAX—MIN问题的基础上,考虑了处理站点容量的因素,建立了双目标优化问题,并给出了一个多项式时间算法,该算法能够产生一个（1,ε）一近似帕累托解集合。所得结论对实际的有害废弃物处理站选址决策具有理论意义,同时也完善了已有相关研究结果。     

A polyhedral study of triplet formulation for single row facility layout problem

The single row facility layout problem (SRFLP) is the problem of arranging n departments with given lengths on a straight line so as to minimize the total weighted distance between all department pairs. We present a polyhedral study of the triplet formulation of the SRFLP introduced by Amaral [A.R.S. Amaral, A new lower bound for the single row facility layout problem, Discrete Applied Mathematics 157 (1) (2009) 183-190]. For any number of departments n, we prove that the dimension of the triplet polytope is n(n−1)(n−2)/3 (this is also true for the projections of this polytope presented by Amaral). We then prove that several valid inequalities presented by Amaral for this polytope are facet-defining. These results provide theoretical support for the fact that the linear program solved over these valid inequalities gives the optimal solution for all instances studied by Amaral.     

连续设施选址:模型、方法与应用

给定度量空间和该空间中的若干顾客,设施选址为在该度量空间中确定新设施的位置使得某种目标达到最优。连续设施选址是设施选址中的一类重要问题,其中的设施可在度量空间的某连续区域上进行选址。本文对连续设施选址的模型、算法和应用方面的工作进行了综述。文章首先讨论了连续设施选址中几个重要元素,包括新设施个数、距离度量函数、目标函数;然后介绍了连续选址中的几种经典模型和拓展模型;接着概述了求解连续选址问题的常用优化方法和技术,包括共轭对偶、全局优化、不确定优化、变分不等式方法、维诺图;最后介绍了连续设施选址的重要应用并给出了研究展望。     

考虑应急设施中断风险与防御的可靠性选址模型研究

为提高应急设施运行的可靠性和抵御中断风险的能力, 研究中断情境下的应急设施选址-分配决策问题。扩展传统无容量限制的固定费用选址模型, 从抵御设施中断的视角和提高服务质量的视角建立选址布局网络的双目标优化模型, 以应急设施的建立成本和抵御设施中断的加固成本最小为目标, 以最大化覆盖服务质量水平为目标, 在加固预算有限及最大最小容量限制约束下, 构建中断情境下应急设施的可靠性选址决策优化模型。针对所构建模型的特性利用非支配排序多目标遗传算法(NSGA-Ⅱ)求解该模型, 得到多目标的Pareto前沿解集。以不同的算例分析和验证模型和算法的可行性。在获得Pareto前沿的同时对不同中断概率进行灵敏度分析, 给出Pareto最优解集的分布及应急设施选址布局网络的拓扑结构。     

制造单元布局问题的双目标模型与算法研究

单元制造系统的布局对于提高系统的效率起着十分重要的作用。以最小化物料周转量和设施面积为目标,建立了一个单元制造系统布局的双目标优化模型,在该模型中不同制造单元的布局、单元内部不同设施的位置与方向这几个问题可以同时进行优化。基于模拟退火邻域解的变尺度生成机制和双目标抽样准则设计了模型的求解算法。算例表明本文算法所得Pareto解集优于经典的NSGA-Ⅱ算法。     

Algorithms for a Facility Location Problem with Stochastic Customer Demand and Immobile Servers

This paper studies a facility location problem with stochastic customer demand and immobile servers. Motivated by applications to locating bank automated teller machines (ATMs) or Internet mirror sites, these models are developed for situations in which immobile service facilities are congested by stochastic demand originating from nearby customer locations. Customers are assumed to visit the closest open facility. The objective of this problem is to minimize customers' total traveling cost and waiting cost. In addition, there is a restriction on the number of facilities that may be opened and an upper bound on the allowable expected waiting time at a facility. Three heuristic algorithms are developed, including a greedy-dropping procedure, a tabu search approach and an -optimal branch-and-bound method. These methods are compared computationally on a bank location data set from Amherst, New York.     

1+1/2对转涡轮短周期试验台性能测试

本文介绍了工程热物理所暂冲式短周期实验台及其涡轮试验方案,使用该试验台对1 1／2对转涡轮进行了性能测试,并使用Numeca软件包对该涡轮进行了定常数值模拟,给出了试验和计算结果对比。试验结果表明该短周期试验台性能良好,能提供大约200 ms的测试时间,能够满足涡轮性能测试的要求。为了以后的研究工作,试验方案和技术,尤其是流量测试技术还有必要进行进一步的改进。     

磁化套筒惯性聚变初步探索研究与实验可行性分析

磁化套筒惯性聚变(MagLIF)构型可充分利用现有大型脉冲功率驱动装置,如聚龙一号等。基于磁流体力学方程组和1∶1比例氘氚(DT)混合燃料聚变模型,开发了零维MagLIF数值模拟程序并进行了初步探索研究。计算结果表明初始负载参数(如轴向磁场强度,预加热温度、时刻,负载半径等)与聚变产额之间有着密切的联系,在给定条件下,可依据计算给出的定性关系进行负载优化设计。值得注意的是,根据计算结果,即使在理想条件下,氘氚燃料要实现能量收支平衡,则驱动器的电流必须大于21.2 MA。这意味着聚龙一号装置(10 MA)无法开展集成化的MagLIF实验,进一步的校验计算验证了上述观点,并在此基础上提出铝套筒分解实验的建议和负载设计参数。所取得的计算结果有利于加深对MagLIF套筒压缩阶段物理过程的认知和理解。