软容量限制设施选址问题的竞争决策算法

软容量设施选址问题是NP-Hard问题之一，具有广泛的应用价值。为了求解软容量设施选址问题，提出一种基于数学性质的竞争决策算法。首先研究该问题的数学性质，运用这些数学性质不仅可以确定某些设施必定开设或关闭，还可以确定部分顾客由哪个设施提供服务，从而缩小问题的规模，加快求解速度。在此基础上设计了求解该问题的竞争决策算法，最后经过一个小规模的算例测试并与精确算法的结果比较，得出了最优解；针对大规模的问题快速地求出了可行解，得到了令人满意的结果。     

一种加权距离连续K中心选址问题求解方法

K中心选址作为一种经典问题,学者们提出了很多好的解决方法,但是对于加权距离连续K中心选址问题的研究一直没有很好的进展.本文针对连续K中心选址问题,以最小加权距离作为优化目标提出改进的粒子群优化算法(SA-PSO).本文将模拟退火机制引入PSO算法并且加入惯性权重等策略对算法进行改进,使得该算法可以更快收敛于全局最优.仿真实验结果表明,SA-PSO算法相比于GA算法和K-means算法,具有更强的稳定性,收敛速度更快,并且优化得到的加权距离更小.     

An Approximation Algorithm for a Large-Scale Facility Location Problem

We developed a new practical optimization method that gives approximate solutions for large-scale real instances of the Uncapacitated Facility Location Problem. The optimization consists of two steps: application of the Greedy—Interchange heuristic using a small subset of warehouse candidates, and application of the newly developed heuristic named Balloon Search that takes account of all warehouse candidates, and runs in ( O (3n + 2n log n ) ) expected time (n is the number of nodes of the underlying graph). Our experiments on the spare parts logistics of a Japanese manufacturing company with 6000 customers and 380,000 warehouse candidates led us to conclude that the Greedy heuristic improved the total cost by 9%-11%, that the Interchange heuristic improved the total cost by an additional 0.5%—1.5%, and that Balloon Search improved it by a further 0.5%—1.5%.     

An Approximation Algorithm for a Large-Scale Facility Location Problem

We developed a new practical optimization method that gives approximate solutions for large-scale real instances of the Uncapacitated Facility Location Problem. The optimization consists of two steps: application of the Greedy—Interchange heuristic using a small subset of warehouse candidates, and application of the newly developed heuristic named Balloon Search that takes account of all warehouse candidates, and runs in ( O (3n + 2n log n ) ) expected time (n is the number of nodes of the underlying graph). Our experiments on the spare parts logistics of a Japanese manufacturing company with 6000 customers and 380,000 warehouse candidates led us to conclude that the Greedy heuristic improved the total cost by 9%-11%, that the Interchange heuristic improved the total cost by an additional 0.5%—1.5%, and that Balloon Search improved it by a further 0.5%—1.5%.     

应急设施选址问题研究综述

合理的应急设施选址能够显著提高应急服务的质量和效率,在医疗、救灾和人道主义物流等领域具有重要的研究意义。根据时效性和应用领域对应急设施进行分类,从不同设施种类的角度阐述国内外研究的主要区别。按照基本选址问题、动态选址问题、随机选址问题、鲁棒选址问题和其他选址问题5种类型论述应急设施选址模型的研究现状,从求解方式、优化算法、测试用例3个角度对模型优化求解方法进行对比分析,指出当前研究存在的不足,并对应急设施选址问题的未来研究方向进行展望。     

带惩罚的无容量设施选址问题的降阶回溯算法

无容量设施选址问题（Uncapacitated Facility Location Problem,UFLP）是组合优化中经典的NP-Hard问题之一。针对UFLP的变形问题之一,即带惩罚的无容量设施选址问题（Uncapacitated Facility Location Problem With Penalties,UFLPWP）,研究了UFLPWP的数学性质,其中包括可以批量确定某些设施一定关闭的性质,并进行了数学证明,利用这些数学性质可以对问题进行降阶,进而缩小问题的规模。在此基础上设计了基于上、下界的回溯算法来求解UFLPWP。通过一个示例分析,进一步阐述该算法的原理。     

基于设施选址问题的费用分配问题的近似算法

许多有着重要理论和应用价值的最优化问题在算法复杂性上都是NP-hard的,其解决方法之一是近似算法。论文研究了与设施选址问题密切相关的费用分配问题,并利用原始与对偶线性规划的思想和无容量设施选址问题的一个1.52-近似算法[1]给出了该问题的一个更好的近似算法。     

需求不确定的设施选址与多阶段生产鲁棒模型研究

选址决策是长期的战略性问题,在选址问题中考虑不确定性因素至关重要。假设需求取值于有界的对称区间,在设施选址与多阶段生产问题中提出一种新的鲁棒性方法,通过调节不确定预算,来权衡解的鲁棒性与系统成本之间的关系。该鲁棒性问题不仅能够转化成线性规划,而且可以计算出设施的最低服务水平。最后,通过随机生成数值算例,得出不同鲁棒性水平下拓扑结构截然不同的设施网络,并分析了服务水平与成本之间的权衡关系,同时对需求的不确定水平作了敏感性分析。     

An Approximation Algorithm for the Fault Tolerant Metric Facility Location Problem

We consider a fault tolerant version of the metric facility location problem in which every city, j, is required to be connected to r _j facilities. We give the first non-trivial approximation algorithm for this problem, having an approximation guarantee of 3 · H _k , where k is the maximum requirement and H _k is the kth harmonic number. Our algorithm is along the lines of [2] for the generalized Steiner network problem. It runs in phases, and each phase, using a generalization of the primal–dual algorithm of [5] for the metric facility location problem, reduces the maximum residual requirement by one.     

An Approximation Algorithm for the Fault Tolerant Metric Facility Location Problem

We consider a fault tolerant version of the metric facility location problem in which every city, j, is required to be connected to r _j facilities. We give the first non-trivial approximation algorithm for this problem, having an approximation guarantee of 3 · H _k , where k is the maximum requirement and H _k is the kth harmonic number. Our algorithm is along the lines of [2] for the generalized Steiner network problem. It runs in phases, and each phase, using a generalization of the primal–dual algorithm of [5] for the metric facility location problem, reduces the maximum residual requirement by one.     

A Primal-Dual Approximation Algorithm for the Facility Location Problem with Submodular Penalties

We consider the facility location problem with submodular penalties (FLPSP), introduced by Hayrapetyan et?al. (Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 933–942, 2005), who presented a 2.50-approximation algorithm that is non-combinatorial because this algorithm has to solve the LP-relaxation of an integer program with exponential number of variables. The only known polynomial algorithm for this exponential LP is via the ellipsoid algorithm as the corresponding separation problem for its dual program can be solved in polynomial time. By exploring the properties of the submodular function, we offer a primal-dual 3-approximation combinatorial algorithm for this problem.     

一般设施定位问题计算复杂度和近似算法研究

设施定位问题即UFL问题是NP-hard的组合优化问题,是聚类问题领域的热点问题之一,在数据挖掘和分类识别方面有着重要应用.多年来其近似算法研究一直是计算机科学工作者关注的焦点,然而现有研究结果大多关于Metric空间,一般距离空间中该问题结果始终未见.针对最大连接费用至多是最小连接费用ω＞1倍的一般距离空间中设施定位问题,简称一般设施定位问题,借助集合覆盖问题,利用问题归约方法证明其不存在近似性能比小于1.243 0.316ln(ω-1)的多项式时间近似算法,除非NPDTIME(nO(log log n));设计了一般设施定位问题的局部搜索算法,证明算法近似性能比是(1 ω)/α,ω＞1,1≤α≤2.仿真实验表明,一般设施定位问题局部搜索算法的求解质量极高;通过实验进一步研究了该算法并给出了改进方法.     

Improved Approximation Algorithm for k-level Uncapacitated Facility Location Problem (with Penalties)

We study the k-level uncapacitated facility location problem (k-level UFL) in which clients need to be connected with paths crossing open facilities of k types (levels). In this paper we first propose an approximation algorithm that for any constant k, in polynomial time, delivers solutions of cost at most α _k times OPT, where α _k is an increasing function of k, with \(\lim _{k\to \infty } \alpha _{k} = 3\). Our algorithm rounds a fractional solution to an extended LP formulation of the problem. The rounding builds upon the technique of iteratively rounding fractional solutions on trees (Garg, Konjevod, and Ravi SODA’98) originally used for the group Steiner tree problem. We improve the approximation ratio for k-level UFL for all k ≥ 3, in particular we obtain the ratio equal 2.02, 2.14, and 2.24 for k = 3,4, and 5.     

Kinetic Facility Location

We present a deterministic kinetic data structure for the facility location problem that maintains a subset of the moving points as facilities such that, at any point of time, the accumulated cost for the whole point set is at most a constant factor larger than the optimal cost. In our scenario, each point can change its status between client and facility and moves continuously along a known trajectory in a d-dimensional Euclidean space, where d is a constant.     

A Distributed O(1)-Approximation Algorithm for the Uniform Facility Location Problem

We investigate a metric facility location problem in a distributed setting. In this problem, we assume that each point is a client as well as a potential location for a facility and that the opening costs for the facilities and the demands of the clients are uniform. The goal is to open a subset of the input points as facilities such that the accumulated cost for the whole point set, consisting of the opening costs for the facilities and the connection costs for the clients, is minimized. We present a randomized distributed algorithm that computes in expectation an ${\mathcal {O}}(1)$ -approximate solution to the metric facility location problem described above. Our algorithm works in a synchronous message passing model, where each point is an autonomous computational entity that has its own local memory and that communicates with the other entities by message passing. We assume that each entity knows the distance to all the other entities, but does not know any of the other pairwise distances. Our algorithm uses three rounds of all-to-all communication with message sizes bounded to $\mathcal{O}(\log(n))$ bits, where n is the number of input points. We extend our distributed algorithm to constant powers of metric spaces. For a metric exponent ?≥1, we obtain a randomized ${\mathcal {O}}(1)$ -approximation algorithm that uses three rounds of all-to-all communication with message sizes bounded to $\mathcal{O}(\log(n))$ bits.     

A Branch and Bound Algorithm for An Uncapacitated Facility Location Problem with a Side Constraint

In this paper, a branch and bound algorithm for solving an uncapacitated facility location problem (UFLP) with an aggregate capacity constraint is presented. The problem arises as a subproblem when Lagrangean relaxation of the capacity constraints is used to solve capacitated facility location problems. The algorithm is an extension of a procedure used by Christofides and Beasley (A tree search algorithm for the p-median problem. European Journal of Operational Research , Vol. 10, 1982, pp. 196–204) to solve p -median problems and is based on Lagrangean relaxation in combination with subgradient optimization for lower bounding, simple Lagrangean heuristics to produce feasible solutions, and penalties to reduce the problem size. For node selection, a jump-backtracking rule is proposed, and alternative rules for choosing the branching variable are discussed. Computational experience is reported.     

On Constrained Facility Location Problems

Given m facilities each with an opening cost, n demands, and distance between every demand and facility, the Facility Location problem finds a solution which opens some facilities to connect every demand to an opened facility such that the total cost of the solution is minimized. The k-Facility Location problem further requires that the number of opened facilities is at most k, where k is a parameter given in the instance of the problem. We consider the Facility Location problems satisfying that for every demand the ratio of the longest distance to facilities and the shortest distance to facilities is at most ω, where ω is a predefined constant. Using the local search approach with scaling technique and error control technique, for any arbitrarily small constant > 0, we give a polynomial-time approximation algorithm for the ω-constrained Facility Location problem with approximation ratio 1 + ω + 1 + ε, which significantly improves the previous best known ratio (ω + 1)/α for some 1≤α≤2, and a polynomial-time approximation algorithm for the ω-constrained k- Facility Location problem with approximation ratio ω+1+ε. On the aspect of approximation hardness, we prove that unless NP■DTIME(nO(loglogn)), the ω-constrained Facility Location problem cannot be approximated within 1 + lnω - 1, which slightly improves the previous best known hardness result 1.243 + 0.316ln(ω - 1). The experimental results on the standard test instances of Facility Location problem show that our algorithm also has good performance in practice.