一个关于求解k-种产品选址问题的近似算法

对于k-种产品工厂选址问题,有如下描述：存在一组客户和一组可以建立工厂的厂址。现在有k种不同的产品,要求每一个客户必须由k个不同的工厂来提供k种不同的产品,其中每个工厂都只能为客户提供唯一的一种产品。在该问题中,假定建厂费用以及任意两个结点之间的运输费用都为非负,并且任意两个结点之间的运输费用都满足对称和三角不等式关系的性质。问题的要求是要从若干厂址中选择一组厂址来建立工厂,给每个工厂指定一种需要生产的产品,并且给每一个客户提供一组指派使每个客户都能有k个工厂来为其供应这k种不同的产品。对于此类问题,优化目标是最小化建厂费用以及运输费用。论文在假设建厂费用为零的前提下,提出了求解该类问题的一种最坏性能比为3k/2-1的近似算法。     

一类多产品选址算法的若干进展

在对k-种产品选址问题的前期探讨中,提出了一种用于求解k-PUFLPN（即：设建厂费用为零时,k-种产品工厂选址问题）的近似算法ME,并证明了该算法的最坏性能比不大于3k/2-1,从而把性能比从2k-1提高到3k/2-1。基于前期对算法已有的分析和结论之上,进一步对该算法求解2-种产品选址模型的紧界进行了讨论。通过构造2-种产品模型的实例,给出了2是算法ME求解2-种产品选址问题的紧界这一结论。对2-种产品选址问题的整性间隙也进行了分析和讨论。     

改进的k-nn快速分类算法

针对传统的k-近邻（k-nn）方法的缺点,将聚类中的K均值和分类中的k近邻算法有机结合,提出了一种改进的k-nn快速分类算法。实验表明该算法在影响分类效果不大的情况下能达到快速分类的目的。     

de Bruijn序列查寻表标签的k位修正构造法

de Bruijn序列的结构是一个查寻表,其核心是它的表标签。因此构造出查寻表标签对于生成de Bruijn序列十分重要。给出两种k位修正构造法。方法1为k位提升构造法,即对大部分节点将其第k（k=1,2,…,n-1）位提升一个定值c（1≤c≤m）,来作为该节点的标签。方法2为k位收缩构造法,即对大部分节点将其第k（k=1,2,…,n-1）位向定值r（0≤r≤m）收缩,来作为该节点的标签。这些方法构造的查寻表标签数随着m,n增长而成指数式增长。与定值构造法一样,在局部看是有效的,但与查寻表标签本身数目的惊人增长比较起来就很渺小。方法2与定值标签构造法比较其速度提高了关于m,n的指数式倍。     

一种挖掘多维序列模式的有效方法

提出了一种新的多维序列模式挖掘算法,首先在序列信息中挖掘序列模式,然后针对每个序列模式,在包含此模式的所有元组中的多维信息中挖掘频繁1-项集,由得到的频繁1-项集开始,循环的由频繁（k-1）-项集（k>1）连接生成频繁k项集,从而得到所有的多维模式。该算法通过扫描不断缩小的频繁（k-1）-项集来生成频繁k项集,减少了扫描投影数据库的次数,因而减少了时间开销,实验表明该算法有较高的挖掘效率。     

一种结合服务费用特点的多产品选址问题的启发算法

工厂选址问题是现代运筹学、计算机理论研究等领域中一个经典而重要的问题.主要研究一种带有服务费用特点的多产品选址问题,给出了求解该问题的启发算法,并以定理的形式给出了该算法的最坏性能比为2-(1)/(k).     

一类具有低相关特性和较大线性复杂度的序列集

对于p=3和偶数n=2k,构造了一类周期为3ⁿ-1大容量序列集S^(r),这里r与3^k-1互素。这类序列集的相关函数取-1±3^k,-1,-1+2•3^k四值,并完全确定了相关值的分布。通过选取适当的参数r,证明了这类序列集具有较大的线性复杂度下界。     

一种二值图像的阈值可视密码方案

目前提出的许多关于二值可视密码方案的论文都致力于研究在可视秘密共享方案里如何使像素扩展比较小或恢复图像的对比度比较高的问题。基于Shamir的秘密共享方案的思想,提出一种新的二值图像（k,n）-VCS可视密码方案。该方案利用二元域上线性方程组解的特征及多层（k,k）-VCS构造基础矩阵S⁰,S¹,给出一个强的访问结构,从而获得（k,n）-VCS可视密码方案更小的像素扩展。     

求解度约束最小生成树问题的新算法

针对网络设计和组合优化中的度约束最小生成树问题,基于第k最小生成树的求解算法,提出了一种求解网络G关于指定节点的最小k度生成树的新算法。该算法通过对网络G的最小生成树作最优可行变换,逐步构造出指定节点的度数越来越接近度约束k的最小i度生成树,最终得到了网络G关于指定节点的最小k度生成树。给出了算法实施的具体步骤,并证明了算法的正确性。最后通过仿真结果和一个运输实例,表明了该算法在解决度约束最小生成树问题中的有效性。     

基于Ward’s方法的k-平均优化算法及其应用

通过对k-平均算法存在不足的分析,提出了一种基于Ward’s方法的k-平均优化算法。算法首先在用Ward’s方法对样本数据初步聚类的基础上,确定合适的簇数目、初始聚类中心等k-平均算法的初始参数,并进行孤立点检测、删除;基于上述处理再采用传统k-平均算法进行聚类。将优化的k-平均算法应用到罪犯人格类型分析中,实验结果表明,该算法的效率、聚类效果均明显优于传统k-平均算法。     

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.     

Solving large immobile location–allocation by affinity propagation and simulated annealing. Application to select which sporting event to watch

Immobile Location-Allocation (ILA) is a combinatorial problem which consists in, given a set of facilities and a set of demand points, determining the optimal service each facility has to offer and allocating the demand to such facilities. The applicability of optimization methods is tied up to the dimensionality of the problem, but since the distance between data points is a key factor, clustering techniques to partition the data space can be applied, converting the large initial problem into several simpler ILA problems that can be solved separately. This paper presents a novel method that combines clustering and heuristic methods to solve an ILA problem, which reduces the elapsed time keeping the quality of the solution found compared with other heuristics methods.     

Tabu based heuristics for the generalized hierarchical covering location problem

The classical Hierarchical Covering Location Problem (HCLP) is the problem to find locations maximizing the number of covered customers, where the customers are assumed to be covered if they are located within a specific distance from the facility, and not covered otherwise. In the generalized HCLP (G-HCLP), customers asking a certain level of services can be served by the facility whose level is equal or the higher. The service coverage is also generalized in a way that the partial coverage is allowed if the distance from the facility is larger than the specified range although it is located in the covered distance. The locations and the levels of the facilities are to be determined, and their set of customers to serve is to be decided as well. Mixed integer programming formulation and the solution procedure using meta-heuristics is developed, and it is shown that suggested heuristic yields high quality solution in a reasonable computation time.     

The min-dist location selection and facility replacement queries

We propose and study a new type of location optimization problem, the min-dist location selection problem: given a set of clients and a set of existing facilities, we select a location from a given set of potential locations for establishing a new facility, so that the average distance between a client and her nearest facility is minimized. The problem has a wide range of applications in urban development simulation, massively multiplayer online games, and decision support systems. We also investigate a variant of the problem, where we consider replacing (instead of adding) a facility while achieving the same optimization goal. We call this variant the min-dist facility replacement problem. We explore two common approaches to location optimization problems and present methods based on those approaches for solving the min-dist location selection problem. However, those methods either need to maintain an extra index or fall short in efficiency. To address their drawbacks, we propose a novel method (named MND), which has very close performance to the fastest method but does not need an extra index. We then utilize the key idea behind MND to approach the min-dist facility replacement problem, which results in two algorithms names MSND and RID. We provide a detailed comparative cost analysis and conduct extensive experiments on the various algorithms. The results show that MND and RID outperform their competitors by orders of magnitude.     

The gravity multiple server location problem

Models for locating facilities and service providers to serve a set of demand points are proposed. The number of facilities is unknown, however, there is a given number of servers to be distributed among the facilities. Each facility acts as an M/M/k queuing system. The objective function is the minimization of the combined travel time and the waiting time at the facility for all customers. The distribution of demand among the facilities is governed by the gravity rule. Two models are proposed: a stationary one and an interactive one. In the stationary model it is assumed that customers do not consider the waiting time at the facility in their facility selection decision. In the interactive model we assume that customers know the expected waiting time at the facility and consider it in their facility selection decision. The interactive model is more complicated because the allocation of the demand among the facilities depends on the demand itself. The models are analyzed and three heuristic solution algorithms are proposed. The algorithms were tested on a set of problems with up to 1000 demand points and 20 servers.     

Improving the quality of heuristic solutions for the capacitated vertex p-center problem through iterated greedy local search with variable neighborhood descent

The capacitated vertex p-center problem is a location problem that consists of placing p facilities and assigning customers to each of these facilities so as to minimize the largest distance between any customer and its assigned facility, subject to demand capacity constraints for each facility. In this work, a metaheuristic for this location problem that integrates several components such as greedy randomized construction with adaptive probabilistic sampling and iterated greedy local search with variable neighborhood descent is presented. Empirical evidence over a widely used set of benchmark data sets on location literature reveals the positive impact of each of the developed components. Furthermore, it is found empirically that the proposed heuristic outperforms the best existing heuristic for this problem in terms of solution quality, running time, and reliability on finding feasible solutions for hard instances.     

Local search heuristics for the mobile facility location problem

In the mobile facility location problem (MFLP), one seeks to relocate (or move) a set of existing facilities and assign clients to these facilities so that the sum of facility movement costs and the client travel costs (each to its assigned facility) is minimized. This paper studies formulations and develops local search heuristics for the MFLP. First, we develop an integer programming (IP) formulation for the MFLP by observing that for a given set of facility destinations the problem may be decomposed into two polynomially solvable subproblems. This IP formulation is quite compact in terms of the number of nonzero coefficients in the constraint matrix and the number of integer variables; and allows for the solution of large-scale MFLP instances. Using the decomposition observation, we propose two local search neighborhoods for the MFLP. We report on extensive computational tests of the new IP formulation and local search heuristics on a large range of instances. These tests demonstrate that the proposed formulation and local search heuristics significantly outperform the existing formulation and a previously developed local search heuristic for the problem.     

Primal–Dual Algorithms for Connected Facility Location Problems

We consider the Connected Facility Location problem. We are given a graph $G = (V,E)$ with costs $\{c_e\}$ on the edges, a set of facilities $\F \subseteq V$, and a set of clients $\D \subseteq V$. Facility $i$ has a facility opening cost $f_i$ and client $j$ has $d_j$ units of demand. We are also given a parameter $M\geq 1$. A solution opens some facilities, say $F$, assigns each client $j$ to an open facility $i(j)$, and connects the open facilities by a Steiner tree $T$. The total cost incurred is ${\sum}_{i\in F} f_i+ sum_{j\in\D} d_jc_{i(j)j}+M\sum_{e\in T}c_e$. We want a solution of minimum cost. A special case of this problem is when all opening costs are 0 and facilities may be opened anywhere, i.e., $\F=V$. If we know a facility $v$ that is open, then the problem becomes a special case of the single-sink buy-at-bulk problem with two cable types, also known as the rent-or-buy problem. We give the first primal–dual algorithms for these problems and achieve the best known approximation guarantees. We give an 8.55-approximation algorithm for the connected facility location problem and a 4.55-approximation algorithm for the rent-or-buy problem. Previously the best approximation factors for these problems were 10.66 and 9.001, respectively. Further, these results were not combinatorial—they were obtained by solving an exponential size linear rogramming relaxation. Our algorithm integrates the primal–dual approaches for the facility location problem and the Steiner tree problem. We also consider the connected $k$-median problem and give a constant-factor approximation by using our primal–dual algorithm for connected facility location. We generalize our results to an edge capacitated variant of these problems and give a constant-factor approximation for these variants.     

The network p-median problem with discrete probabilistic demand weights

We study the problem of locating p facilities to serve clients residing at the nodes of a network with discrete probabilistic demand weights. The objective is to maximize the probability that the total weighted distance from a client to the closest facility does not exceed a given threshold value. The problem is formulated as an integer program but can be solved only for very small instances because of the exponential number of decision variables and constraints. We analyze the problem and, using a normal approximation of the total weighted distance we develop branch and bound solution procedures for various cases of the problem. We also develop heuristics and meta-heuristics to solve the problem. Based on our computational experiments we make recommendations on which approach to use and when.