A Wavefront Approach to Center Location Problems with Barriers

Center location problems have many applications, for example, in the public sector, and various different algorithms have been developed for their solution. This paper suggests a novel solution strategy to the problem that is based on the propagation of circular wavefronts. The approach is discussed theoretically and implemented both as a physical experiment and as a computer simulation.     

An Equivalence Result for Single Facility Planar Location Problems with Rectilinear Distance and Barriers

This paper considers planar location problems with rectilinear distance and barriers, where the objective function is any convex, nondecreasing function of distance. Such problems have a non-convex feasible region and a non-convex objective function. A modification of the barriers is developed based on properties of the rectilinear distance. It is shown that the original problem with barriers is equivalent to the problem with modified barriers. A particular modification is given that reduces the feasible region and permits its partitioning into convex subsets on which the objective function is convex. A solution algorithm based on the partitioning is the subject of a companion paper.     

Solving Rectilinear Planar Location Problems with Barriers by a Polynomial Partitioning

This paper considers planar location problems with rectilinear distance and barriers where the objective function is any convex, nondecreasing function of distance. Such problems have a non-convex feasible region and a nonconvex objective function. Based on an equivalent problem with modified barriers, derived in a companion paper [3], the non convex feasible set is partitioned into a network and rectangular cells. The rectangular cells are further partitioned into a polynomial number of convex subcells, called convex domains, on which the distance function, and hence the objective function, is convex. Then the problem is solved over the network and convex domains for an optimal solution. Bounds are given that reduce the number of convex domains to be examined. The number of convex domains is bounded above by a polynomial in the size of the problem.     

大洪水算法在平面选址问题中的应用

大洪水算法是通过模拟洪水上涨过程来进行全局寻优的启发式算法.针对连续优化问题,基于三种不同的邻域搜索策略对其进行改进,并针对一类平面选址问题进行应用测试.仿真结果表明,大洪水算法是一类简单高效的算法,可用于连续优化问题的求解.     

平面上的min-max型点-线选址问题

本文研究两类平面选址问题：(1)求一直线到n个给定点的最大加权距离为最小；(2)求一点到n条给定直线的最大加权距离为最小．对这两个非线性优化问题，我们给出最优解的刻划及迭代次数为多项式的算法．     

Using Interval Analysis for Solving Planar Single-Facility Location Problems: New Discarding Tests

Interval analysis is a powerful tool which allows the design of branch-and-bound methods able to solve many global optimization problems. The key to the speed of those methods is the use of several tests to discard boxes or parts of boxes in which no optimal point may occur. In this paper we present three new discarding tests for two-dimensional problems which are specially suitable for planar single-facility location problems. The usefulness of the new tests is shown by a computational study.     

Solving Euclidean Distance Multifacility Location Problems Using Conjugate Subgradient and Line-Search Methods

Subgradient methods are popular for solving nondifferentiable optimization problems because of their relative ease in implementation, but are not always robust and require a careful design of strategies in order to yield an effective procedure for any given class of problems. In this paper, we present an approach for solving the Euclidean distance multifacility location problem (EMFLP) using conjugate or deflected subgradient based algorithms along with suitable line-search strategies. The subgradient deflection method considered is the Average Direction Strategy (ADS) imbedded within the Variable Target Value Method (VTVM). We also investigate the generation of two types of subgradients to be employed in conjunction with ADS. The first type is a simple valid subgradient that assigns zero values to contributions corresponding to the nondifferentiable terms in the objective function, and so, the subgradient is composed by summing the contributions corresponding to the differentiable terms alone. The second type expends more effort to derive a low-norm member of the subdifferential in order to enhance the prospect of obtaining a descent direction. Furthermore, a special Newton-based line-search that exploits the nondifferentiability of the problem is also designed to be implemented in the developed algorithm in order to study its impact on the convergence behavior. Various combinations of the above strategies are composed and evaluated on a set of test problems. The results show that a modification of the VTVM method along with the first or a certain combination of the two subgradient generation strategies, and the use of a suitable line-search technique, provides promising results. An alternative block-halving step-size strategy used within VTVM in conjunction with the proposed line-search method yields a competitive second choice performance.     

Demand Point Aggregation for Planar Covering Location Models

The covering location problem seeks the minimum number of facilities such that each demand point is within some given radius of its nearest facility. Such a model finds application mostly in locating emergency types of facilities. Since the problem is NP-hard in the plane, a common practice is to aggregate the demand points in order to reduce the computational burden. Aggregation makes the size of the problem more manageable but also introduces error. Identifying and controlling the magnitude of the error is the subject of this study. We suggest several aggregation methods with a priori error bounds, and conduct experiments to compare their performance. We find that the manner by which infeasibility is measured greatly affects the best choice of an aggregation method.     

Bi-Objective Median Subtree Location Problems

A number of network design problems can be built on the following premise: given an undirected tree network, T, with node set, V, identify a single subtree, t, containing nodes, v, so that the subtree is located optimally with respect to the remaining, subset of unconnected nodes {V–v}. Distances between unconnected nodes and nodes in the subtree t can be defined on paths that are restricted to lie in the larger tree T (the restricted case), or can be defined on paths in an auxiliary complete graph G (the unrestricted case). The unrestricted case represents a class of problems that is not explicitly recognized in the literature, which is of intermediate complexity relative to the widely studied restricted case, and the general problem in which the underlying graph is general. This paper presents the Median Subtree Location Problem (MSLP), formulated as a bicriterion problem that trades off the cost of a subtree, t, against the population-weighted travel distance from the unconnected nodes to nodes on the subtree where both objectives are to be minimized. Integer programs were formulated for the travel restricted and travel unrestricted cases and were tested using linear programming and branch and bound to resolve fractions. Tradeoff curves between cost and travel burden were developed for sample networks.     

Geodesic Distance in Planar Graphs: An Integrable Approach

We discuss the enumeration of planar graphs using bijections with suitably decorated trees, which allow for keeping track of the geodesic distances between faces of the graph. The corresponding generating functions obey non-linear recursion relations on the geodesic distance. These are solved by use of stationary multi-soliton tau-functions of suitable reductions of the KP hierarchy. We obtain a unified formulation of the (multi-) critical continuum limit describing large graphs with marked points at large geodesic distances, and obtain integrable differential equations for the corresponding scaling functions. This provides a continuum formulation of two-dimensional quantum gravity, in terms of the geodesic distance. 2000 Mathematics Subject Classification: Primary—05C30; Secondary—05A15, 05C05, 05C12, 68R05     

Solving Nonconvex Planar Location Problems by Finite Dominating Sets

It is well-known that some of the classical location problems with polyhedral gauges can be solved in polynomial time by finding a finite dominating set, i.e. a finite set of candidates guaranteed to contain at least one optimal location.In this paper it is first established that this result holds for a much larger class of problems than currently considered in the literature. The model for which this result can be proven includes, for instance, location problems with attraction and repulsion, and location-allocation problems.Next, it is shown that the approximation of general gauges by polyhedral ones in the objective function of our general model can be analyzed with regard to the subsequent error in the optimal objective value. For the approximation problem two different approaches are described, the sandwich procedure and the greedy algorithm. Both of these approaches lead - for fixed - to polynomial approximation algorithms with accuracy for solving the general model considered in this paper.     

Filtering Policies in Loss Queuing Network Location Problems

In this paper we deal with two stationary loss queuing network location models. We analyze the influence of filtering policies on the locational aspect of the problems. We assume that requests for service are placed at nodes of a transportation network and they arrive in time as independent homogeneous Poisson processes with different input rates. The considered policies only cover a given proportion of requests even if there are idle service units. This proportion is stationary and fixed in advance and only depends on the node where the request is originated. The objective is to find the location of the facilities together with the filtering policy to be applied that minimize the expected total cost per unit time with respect to a given cost structure. Properties and computational results are presented enabling the resolution of these problems efficiently and showing the good performance of filtering policies in terms of both the overall operating costs, and the demand that is served.     

一种基于序列图像的单镜头测距方法

针对于监视区域目标参数的测量问题,在考虑到被动式实时监控定位与便携性要求的前提下,提出了基于标定点的序列图像单镜头测距算法,并实现了核心测距算法.     

Location and shape of a rectangular facility in ℝn. Convexity properties. Convexity properties

In this paper we address a generalization of the Weber problem, in which we seek for the center and the shape of a rectangle (the facility) minimizing the average distance to a given set (the demand-set) which is not assumed to be finite. Some theoretical properties of the average distance are studied, and an expression for its gradient, involving solely expected distances to rectangles, is obtained. This enables the resolution of the problem by standard optimization techniques. The research of the authors is partially supported by Spanish DGICYT grant PB93-0927.     

Block Preconditioners for Saddle Point Problems

A general purpose block LU preconditioner for saddle point problems is presented. A major difference between the approach presented here and that of other studies is that an explicit, accurate approximation of the Schur complement matrix is efficiently computed. This is used to obtain a preconditioner to the Schur complement matrix which in turn defines a preconditioner for the global system. A number of variants are developed and results are reported for a few linear systems arising from CFD applications.     

Minmax p-Traveling Salesmen Location Problems on a Tree

Suppose that p traveling salesmen must visit together all points of a tree, and the objective is to minimize the maximum of the lengths of their tours. The location–allocation version of the problem (where both optimal home locations of the salesmen and their optimal tours must be found) is known to be NP-hard for any p2. We present exact polynomial algorithms with a linear order of complexity for location versions of the problem (where only optimal home locations must be found, without the corresponding tours) for the cases p=2 and p=3.     

会议选址问题的优化模型

国内某公司在各省会城市都设有分支机构,公司每年都有频繁的会议和培训工作需要各地分支机构派人参加,如何在大陆地区31个省会城市里选择一个城市作为会议地址,使得举办会议的成本最低且中转次数最少.建立了该会议选址问题的双目标优化模型,收集处理了有关实际数据,利用网络最短路算法和约束法等得到了该会议选址问题的解.在不考虑中转费用的情况下,得出成本最低且中转次数最少的会议地址是西安;在考虑中转费用的情况下,根据中转费用的不同给出了可供实际决策的最优会议选址方案.     

带时效性约束的配送中心多源选址问题研究

应用启发式算法求解带时效性约束的多源选址问题.分析物流配送的时效性问题,建立带时效性约束的配送中心多源选址模型.构造两步启发式算法:1)借助传统迭代算法,求解物流服务分配矩阵,把多源选址问题转化为单源选址问题;2)基于M ATLAB函数,设计优化程序,计算带时效性约束的单源选址模型.并给出算例,验证模型和算法的可行性.研究表明两步启发式算法是求解带时效性约束的物流配送中心多源连续选址问题的有效算法.     

Multicriteria Semi-Obnoxious Network Location Problems (MSNLP) with Sum and Center Objectives

Locating a facility is often modeled as either the maxisum or the minisum problem, reflecting whether the facility is undesirable (obnoxious) or desirable. But many facilities are both desirable and undesirable at the same time, e.g., an airport. This can be modeled as a multicriteria network location problem, where some of the sum-objectives are maximized (push effect) and some of the sum-objectives are minimized (pull effect).We present a polynomial time algorithm for this model along with some basic theoretical results, and generalize the results also to incorporate maximin and minimax objectives. In fact, the method works for any piecewise linear objective functions. Finally, we present some computational results.     

基于加权绝对值距离Steiner最优树的选址问题

提出基于加权绝对值距离Steiner最优树思想的选址模型,给出了该模型的蚂蚁算法实现策略.在此基础上,分析了电子商务环境下企业配送中心选址问题,并用算例验证了该选址方案的可行性.