Telecommunication Network Capacity Design for Uncertain Demand

The expansion of telecommunication services has increased the number of users sharing network resources. When a given service is highly demanded, some demands may be unmet due to the limited capacity of the network links. Moreover, for such demands, telecommunication operators should pay penalty costs. To avoid rejecting demands, we can install more capacities in the existing network. In this paper we report experiments on the network capacity design for uncertain demand in telecommunication networks with integer link capacities. We use Poisson demands with bandwidths given by normal or log-normal distribution functions. The expectation function is evaluated using a predetermined set of realizations of the random parameter. We model this problem as a two-stage mixed integer program, which is solved using a stochastic subgradient procedure, the Barahona's volume approach and the Benders decomposition.     

模糊网络最大流算法研究

将模糊数差值B~-A~视为模糊方程X~+A~=B~的解,进而探讨了模糊方程的求解问题,并基于目的规划理论,给出了模糊方程的广义解定义.运用目的规划的单纯型方法,得到了模糊方程广义解的计算公式及模糊方程广义解的若干性质.由模糊方程的广义解引申出了模糊数差值的定义.运用该定义将传统的网络最大流算法推广到模糊环境.结果表明,模糊数差值定义,克服了基于扩展原理意义下的模糊运算所产生的各种问题,解决了这些传统理论方法的拓展问题.     

A Dynamic Domain Contraction Algorithm for Nonconvex Piecewise Linear Network Flow Problems*

We consider the Nonconvex Piecewise Linear Network Flow Problem (NPLNFP) which is known to be -hard. Although exact methods such as branch and bound have been developed to solve the NPLNFP, their computational requirements increase exponentially with the size of the problem. Hence, an efficient heuristic approach is in need to solve large scale problems appearing in many practical applications including transportation, production-inventory management, supply chain, facility expansion and location decision, and logistics. In this paper, we present a new approach for solving the general NPLNFP in a continuous formulation by adapting a dynamic domain contraction. A Dynamic Domain Contraction (DDC) algorithm is presented and preliminary computational results on a wide range of test problems are reported. The results show that the proposed algorithm generates solutions within 0 to 0.94 % of optimality in all instances that the exact solutions are available from a branch and bound method.     

分配网络的一个最小费用流算法

分配网络流广泛应用于解决水源、电力的调度及工厂的产品运输、分配、合成等问题.本文提出一个分配网络流的最小费用流算法.     

有上下界网络最大流与最小截问题

为了便于建立与有上下界网络最大流与最小截问题有关的决策支持系统，本文给出一个求有上下界网络最大流与最小截的数值算法，证明了算法的理论依据，并举例说明了算法在堵塞流理论中的应用。该算法能判定问题是否有可行解，在问题有可行解的情况下能求得问题的最优解。该算法具有易于编程实现、收敛性好等优点。数值实验表明该算法有较高的计算效率，可用于求解最小饱和流问题。     

A Branch-and-Bound Algorithm for Concave Network Flow Problems

In this paper a Branch-and-Bound (BB) algorithm is developed to obtain an optimal solution to the single source uncapacitated minimum cost Network Flow Problem (NFP) with general concave costs. Concave NFPs are NP-Hard, even for the simplest version therefore, there is a scarcity of exact methods to address them in their full generality. The BB algorithm presented here can be used to solve optimally single source uncapacitated minimum cost NFPs with any kind of concave arc costs. The bounding is based on the computation of lower bounds derived from state space relaxations of a dynamic programming formulation. The relaxations, which are the subject of the paper (Fontes et al., 2005b) and also briefly discussed here, involve the use of non-injective mapping functions, which guarantee a reduction on the cardinality of the state space. Branching is performed by either fixing an arc as part of the final solution or by removing it from the final solution. Computational results are reported and compared to available alternative methods for addressing the same type of problems. It could be concluded that our BB algorithm has better performance and the results have also shown evidence that it has a sub-exponential time growth.     

Domain Decomposition of Optimal Control Problems for Dynamic Networks of Elastic Strings

We consider optimal control problems related to exact- and approximate controllability of dynamic networks of elastic strings. In this note we concentrate on problems with linear dynamics, no state and no control constraints. The emphasis is on approximating target states and velocities in part of the network using a dynamic domain decomposition method (d³m) for the optimality system on the network. The decomposition is established via a Uzawa-type saddle-point iteration associated with an augmented Lagrangian relaxation of the transmission conditions at multiple joints. We consider various cost functions and prove convergence of the infinite dimensional scheme for an exemplaric choice of the cost. We also give numerical evidence in the case of simple exemplaric networks.     

Stochastic Survivable Network Design Problems

In this paper we introduce survivable network design problems under a two-stage stochastic model with fixed recourse and finitely many scenarios. We propose a new cut-based formulation based on orientation properties which is stronger than the undirected cut-based model. We use a two-stage branch&cut algorithm for solving the decomposed model to provable optimality. In order to accelerate the computations, we suggest a new cut strengthening technique for the decomposed L-shaped optimality cuts that is computationally fast and easy to implement.     

混沌神经网络优化算法用于求解无等待流水调度问题的最小最大完工时间

利用李小平等提出的相邻工件加工结束时间差矩阵,将求解无等待流水调度问题的最小最大完工时间(Makespan)问题映射为TSP问题,构造对应的能量函数,进而得到随机混沌神经网络(SCSA)算法.实验结果证明该混沌神经网络优化算法优于RAJ算法和GANRAJ算法.     

基于不确定需求的灾后应急救灾网络规划模型与算法

突发事件发生后,快速应急响应的第一步是启动应急救灾网络,合理配置应急救灾资源,以保证救灾过程顺利进行,提高救援效率。本文以台风灾害为背景,建立二阶段应急救灾网络的混合整数规划模型,解决台风灾害的灾后应急救灾网络的规划与设计问题。在求解模型时,考虑需求信息的分布难以确定,并且在一定范围内变动的特点,利用鲁棒优化的方法处理不确定性需求,从而得到合理的临时救灾中心选址以及应急资源配置信息。数值试验表明,建立的模型是实际可行的,而且算法也是有效的。     

动态供应链网络均衡模型构建与分析

基于单一商品流,考虑了时间变量和库存问题,建立了三层动态供应链网络结构模型.对制造商、零售商和需求市场的多期独立决策行为及其相互作用进行了分析,应用变分不等式构建了各层均衡模型和整个供应链网络均衡模型.最后与相关文献的模型进行了比较.     

联盟剖分型单向流动态网络生成对策

通过定义联盟同质费用研究考察具有固定联盟剖分的单向流动态网络生成对策.局中人通过采取局部行动生成网络,行动的原则是最大化其所在联盟的整益.选择B&G函数作为局中人的基本支付函数,诱导产生联盟-局中人的B&G函数.在新的规则之下,分别给出了局部纳什网的存在性、结构特性及其动态生成进程的定理.     

考虑边流量有限的网络路径博弈问题研究

考虑每条边有流量约束的网络路径博弈问题, 根据收益函数单调递增的特点分析其内在零和性质, 并建模为存在公共边的路径博弈模型。在寻找均衡解的过程中, 首先考虑非合作的情形, 在局中人风险中性的假设下, 给出了求Nash均衡流量分配的标号法并证明该均衡分配的唯一性。接着进一步考虑局中人合作的可能性, 给出模型求得所有局中人的整体最大收益, 并基于纳什谈判模型给出目标函数为凸函数的数学模型确定唯一收益分配方案。事实上, 该方案是对剩余价值的平均分配。最后给出一个算例, 验证本文理论和方法的可行性。关键词:流量约束; 均衡流量; 网络路径博弈; 收益分配     

基于线性规划的网络流量流向控制策略

互联网的快速发展给运营商带来了网络流量流向控制的需求.控制网络流量流向不但要保证服务质量,而且要尽可能降低运营费用,更要保证各网络链路具备裕量能应对突发变化.在网络流量流向控制中结合成熟的线性规划方法从能全局角度实现网络流量流向的多目标控制,保障网络的健康运行.     

A New Successive Partition Algorithm for Concave Minimization Based on Cone Decomposition and Decomposition Cuts

In this paper we propose a new partition algorithm for concave minimization. The basic structure of the algorithm resembles that of conical algorithms. However, we make extensive use of the cone decomposition concept and derive decomposition cuts instead of concavity cuts to perform the bounding operation. Decomposition cuts were introduced in the context of pure cutting plane algorithms for concave minimization and has been shown to be superior to concavity cuts in numerical experiments. Thus by using decomposition cuts instead of concavity cuts to perform the bounding operation, unpromising parts of the feasible region can be excluded from further explorations at an earlier stage. The proposed successive partition algorithm finds an -global optimal solution in a finite number of iterations.     

Stochastic Output Feedback of Uncertain Time-Delay Systems with Saturating Actuators

This paper deals with the class of uncertain continuous-time linear systems with Markovian jumps, time delay, and saturating actuators. Under norm-bounded uncertainties and based on the Lyapunov method, sufficient conditions on stochastic stability and stochastic stabilizability are developed. A design algorithm for a stabilizing observer-based robust output feedback controller is proposed in terms of the solutions of linear matrix inequalities.     

A Decomposition Methodology Applied to the Multi-Area Optimal Power Flow Problem

This paper describes a decomposition methodology applied to the multi-area optimal power flow problem in the context of an electric energy system. The proposed procedure is simple and efficient, and presents some advantages with respect to other common decomposition techniques such as Lagrangian relaxation and augmented Lagrangian decomposition. The application to the multi-area optimal power flow problem allows the computation of an optimal coordinated but decentralized solution. The proposed method is appropriate for an Independent System Operator in charge of the electric energy system technical operation. Convergence properties of the proposed decomposition algorithm are described and related to the physical coupling between the areas. Theoretical and numerical results show that the proposed decentralized methodology has a lower computational cost than other decomposition techniques, and in large large-scale cases even lower than a centralized approach.     

不确定运行时间环境下的车辆调度问题及启发式算法

考虑到物流公司或者配送中心车辆实际运行过程中时间的不确定性,提出了配送服务线路包含时间窗口、车辆容量约束的随机规划模型,以最小化车辆运行成本同时尽可能降低所服务顾客的不满意度.同时,又稍作改进给出了平均-风险模型,由于VRP问题是NP难的,给出了一种基于禁忌搜索的启发式算法,并以北京市13个点的为例,给出求解结果.     

残缺数据下动态随机算法及应用

针对指标数据残缺的动态评价问题,提出了一种基于残缺数据的动态随机算法。首先依据时间维度上的分布情况将残缺值分为两类:离散型与连续型,并提出了对应的补足方法;然后在数据补足完整的基础上,利用随机模拟技术,计算优胜度矩阵,并推导出被评价对象之间的可能性排序。该算法避免了评价对象之间排序的绝对性,在对实际问题的解释方面具有较大弹性。最后,通过一个算例对该算法进行详细说明。     

An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results

We introduce a distribution center (DC) location model that incorporates working inventory and safety stock inventory costs at the distribution centers. In addition, the model incorporates transport costs from the suppliers to the DCs that explicitly reflect economies of scale through the use of a fixed cost term. The model is formulated as a non-linear integer-programming problem. Model properties are outlined. A Lagrangian relaxation solution algorithm is proposed. By exploiting the structure of the problem we can find a low-order polynomial algorithm for the non-linear integer programming problem that must be solved in solving the Lagrangian relaxation subproblems. A number of heuristics are outlined for finding good feasible solutions. In addition, we describe two variable forcing rules that prove to be very effective at forcing candidate sites into and out of the solution. The algorithms are tested on problems with 88 and 150 retailers. Computation times are consistently below one minute and compare favorably with those of an earlier proposed set partitioning approach for this model (Shen, 2000; Shen, Coullard and Daskin, 2000). Finally, we discuss the sensitivity of the results to changes in key parameters including the fixed cost of placing orders. Significant reductions in these costs might be expected from e-commerce technologies. The model suggests that as these costs decrease it is optimal to locate additional facilities.