Location tracking in mobile ad hoc networks using particle filters

Mobile ad hoc networks (MANETs) are dynamic networks formed on-the-fly as mobile nodes move in and out of each others' transmission ranges. In general, the mobile ad hoc networking model makes no assumption that nodes know their own locations. However, recent research shows that location-awareness can be beneficial to fundamental tasks such as routing and energy-conservation. On the other hand, the cost and limited energy resources associated with common, low-cost mobile nodes prohibits them from carrying relatively expensive and power-hungry location-sensing devices such as GPS. This paper proposes a mechanism that allows non-GPS-equipped nodes in the network to derive their approximated locations from a limited number of GPS-equipped nodes. In our method, all nodes periodically broadcast their estimated location, in terms of a compressed particle filter distribution. Non-GPS nodes estimate the distance to their neighbors by measuring the received signal strength of incoming messages. A particle filter is then used to estimate the approximated location, along with a measure of confidence, from the sequence of distance estimates. Simulation studies show that our solution is capable of producing good estimates equal or better than the existing localization methods such as APS-Euclidean for the more difficult scenario when the network connectivity is low.     

基于最大最小蚂蚁系统的物流配送中心选址算法的研究

提出了一种基于信息素自适应调节的最大最小蚂蚁系统的多物流配送中心选址算法,利用改进的蚁群算法的路径寻优机制结合蚂蚁聚集尸体的行为模式,根据物流配送总成本最低的原则将各配送点与候选配送中心进行聚类,合理选择配送中心。将已有物流配送模型进行拓展,加入经营管理成本。分别利用基本蚁群聚类算法和改进的蚁群聚类算法对配送中心选址进行仿真,实验结果表明在解决大规模配送中心选址问题时,改进的算法在解的质量和收敛速度方面明显优于基本蚁群聚类算法。     

Local improvement in planar facility location using vehicle routing

In physical distribution the location of depots and vehicle routes are interdependent problems, but they are usually treated independently. Location-routing is the study of solving locational problems such that routing considerations are taken into account. We present an iterative heuristic for the location-routing problem on the plane. For each depot the Weber problem is solved using the end-points of the routes found previously as input nodes to the Weiszfeld procedure. Although the improvements found are usually small they show that it pays not to ignore the routing aspects when solving continuous location problems. Possible research avenues in continuous location-routing will also be suggested.     

The hierarchical traveling salesman problem

The distribution of relief aid is a complex problem where the operations have to be managed efficiently due to limited resources. We present a routing problem for relief operations whose primary goal is to satisfy demand for relief supplies at many locations taking into account the urgency of each demand. We have a single vehicle of unlimited capacity. Each node (location) has a demand and a priority. The priority indicates the urgency of the demand. Typically, nodes with the highest priorities need to be visited before lower priority nodes. We describe a new and interesting model for humanitarian relief routing that we call the hierarchical traveling salesman problem (HTSP). We compare the HTSP and the classical TSP in terms of worst-case behavior. We obtain a simple, but elegant result that exhibits the fundamental tradeoff between efficiency (distance) and priority and we provide several related observations and theorems.     

The multiple server location problem

In this paper, we introduce the Multiple Server location problem. A given number of servers are to be located at nodes of a network. Demand for these servers is generated at each node, and a subset of nodes need to be selected for locating one or more servers in each. There is no limit on the number of servers that can be established at each node. Each customer at a node selects the closest server (with demand divided equally when the closest distance is measured to more than one node). The objective is to minimize the sum of the travel time and the average time spent at the server, for all customers. The problem is formulated and analysed. Results using heuristic solution procedures: descent, simulated annealing, tabu search and a genetic algorithm are reported. The problem turns out to be a very difficult combinatorial problem when the total demand is very close to the total capacity of the servers.     

Network hub location problems: The state of the art

Hubs are special facilities that serve as switching, transshipment and sorting points in many-to-many distribution systems. The hub location problem is concerned with locating hub facilities and allocating demand nodes to hubs in order to route the traffic between origin–destination pairs. In this paper we classify and survey network hub location models. We also include some recent trends on hub location and provide a synthesis of the literature.     

IP modeling of the survivable hop constrained connected facility location problem

We consider a generalized version of the rooted connected facility location problem which occurs in planning of telecommunication networks with both survivability and hop-length constraints. Given a set of client nodes, a set of potential facility nodes including one predetermined root facility, a set of optional Steiner nodes, and the set of the potential connections among these nodes, that task is to decide which facilities to open, how to assign the clients to the open facilities, and how to interconnect the open facilities in such a way, that the resulting network contains at least λ edge-disjoint paths, each containing at most H edges, between the root and each open facility and that the total cost for opening facilities and installing connections is minimal. We study two IP models for this problem and present a branch-and-cut algorithm based on Benders decomposition for finding its solution. Finally, we report computational results.     

All Stackelberg Location Equilibria in the Hotelling's Duopoly Model on a Tree with Parametric Prices

The sequential Hotelling's duopoly model on a tree was studied by Eiselt (1992), who developed conditions for the existence of location equilibria when location decisions are nodes and prices are parametric. In this paper, this competition model is also analyzed, but considering that locations for the two firms can be any pair of points on the tree, nodes or points in the edges. First, a condition is given under which both the leader and the follower get a positive profit. In this setting, the problem of finding optimal locations for each of them is studied with different and equal prices. In both cases, the set of optimal locations for the follower is generated for any location of the leader as well as the set of optimal locations for the leader. As a consequence the entire set of Stackelberg solutions to this competition model is obtained.     

A hub covering network design problem for cargo applications in Turkey

Hub location problems involve locating hub facilities and allocating demand nodes to hubs in order to provide service between origin–destination pairs. In this study, we focus on cargo applications of the hub location problem. Through observations from the Turkish cargo sector, we propose a new mathematical model for the hub location problem that relaxes the complete hub network assumption. Our model minimizes the cost of establishing hubs and hub links, while designing a network that services each origin–destination pair within a time bound. We formulate a single-allocation hub covering model that permits visiting at most three hubs on a route. The model is then applied to the realistic instances of the Turkish network and to the Civil Aeronautics Board data set.     

Hub and spoke network design with single-assignment,capacity decisions and balancing requirements

In this paper, an extension of the capacitated single-allocation hub location problem is considered in which the capacity of the hubs is part of the decision making process and balancing requirements are imposed on the network. The decisions to be made comprise (i) the selection of the hubs, (ii) the allocation of the spoke nodes to the hubs, (iii) the flow distribution through the sub network defined by the hubs and (iv) the capacity level at which each hub should operate. In the latter case, for each potential hub, a set of available capacities is considered among which one can be chosen. The objective is to minimize the total cost, which includes the setup cost for the hubs as well as the flow routing cost. Economies of scale are assumed for the costs. Balancing requirements are imposed to the network. In particular, a value is considered for the maximum difference between the maximum and minimum number of spoke nodes that are allocated to the hubs. Two mixed-integer linear programming formulations are proposed and analyzed for this problem. The results of a set of computational experiments using an off-the-shelf commercial solver are presented. These tests aim at evaluate the possibility of solving the problem to optimality using such a solver with a particular emphasis to the impact of the balancing requirements. The tests also allow an analysis of the gap of the bounds provided by linear relaxation.     

The multiple server center location problem

In this paper, we introduce the multiple server center location problem. p servers are to be located at nodes of a network. Demand for services of these servers is located at each node, and a subset of nodes are to be chosen to locate one or more servers in each. Each customer selects the closest server. The objective is to minimize the maximum time spent by any customer, including travel time and waiting time at the server sites. The problem is formulated and analyzed. Results for heuristic solution approaches are reported. Paper was partially supported by a College of Business Administration, California State University San Marcos summer grant of the first author. Paper was partially supported by an NSERC grant of the second author.     

Isodistant points in competitive network facility location

An isodistant point is any point on a network which is located at a predetermined distance from some node. For some competitive facility location problems on a network, it is verified that optimal (or near-optimal) locations are found in the set of nodes and isodistant points (or points in the vicinity of isodistant points). While the nodes are known, the isodistant points have to be determined for each problem. Surprisingly, no algorithm has been proposed to generate the isodistant points on a network. In this paper, we present a variety of such problems and propose an algorithm to find all isodistant points for given threshold distances associated with the nodes. The number of isodistant points is upper bounded by nm, where n and m are the number of nodes and the number of edges, respectively. Computational experiments are presented which show that isodistant points can be generated in short run time and the number of such points is much smaller than nm. Thus, for networks of moderate size, it is possible to find optimal (or near-optimal) solutions through the Integer Linear Programming formulations corresponding to the discrete version of such problems, in which a finite set of points are taken as location candidates.     

Monotonicity and Asymptotic Queue-Length Distribution in Discrete-Time Networks

For closed, cyclic, discrete-time networks with one server per node and with independent, geometric service times, in equilibrium, the joint queue-length distribution can be realized as the joint distribution of independent random variables, conditionally given their sum. This tool helps establish monotonicity properties of performance measures and also helps show that the queue-length random variables are negatively associated. The queue length at a node is asymptotically analyzed through a family of networks with a fixed number of node types, where the number of nodes approaches infinity, the ratio of jobs to nodes has a positive limit, and each node type has a limiting density. The queue-length distribution at any node is shown to converge, in a strong sense, to a distribution that is conditionally geometric. As a by-product, this approach settles open issues regarding occupancy proportion and average queue length at a node type.     

Avoiding local optima in thep-hub location problem using tabu search and GRASP

In the discretep-hub location problem, various nodes interact with each other by sending and receiving given levels of traffic (such as telecommunications traffic, data transmissions, airline passengers, packages, etc.). It is necessary to choosep of the given nodes to act as hubs, which are fully interconnected; it is also necessary to connect each other node to one of these hubs so that traffic can be sent between any pair of nodes by using the hubs as switching points. The objective is to minimize the sum of the costs for sending traffic along the links connecting the various nodes. Like many combinatorial problems, thep-hub location problem has many local optima. Heuristics, such as exchange methods, can terminate once such a local optimum is encountered. In this paper, we describe new heuristics for thep-hub location problem, based on tabu search and on a greedy randomized adaptive search procedure (GRASP). These recently developed approaches to combinatorial optimization are capable of examining several local optima, so that, overall, superior solutions are found. Computational experience is reported in which both tabu search and GRASP found optimal hub locations (subject to the assumption that nodes must be assigned to the nearest hub) in over 90% of test problems. For problems for which such optima are not known, tabu search and GRASP generated new best-known solutions.     

Production and location on a network under demand uncertainty

The Hakimi theorem is fundamental in location theory. It says that the set of nodes and market-places necessarily contains a profit-maximizing location when the transportation costs are concave in distance. The purpose of this letter is to discuss the validity of this theorem in the context of a two-stage stochastic model of the location of a firm on a network. In the first stage, the firm chooses its location and production level before knowing the exact demands. In the second stage, it observes the realization of the random variables representing the demands and decides upon the distribution of its production. It is shown that the Hakimi theorem still holds in this model when the firm is risk-neutral. On the other hand, in the case of a risk-averse firm, it ceases to be true in that all the points of the network must be considered to obtain an optimal location.     

Using clustering analysis in a capacitated location-routing problem

The location routing problem (LRP) appears as a combination of two difficult problems: the facility location problem (FLP) and the vehicle routing problem (VRP). In this work, we consider a discrete LRP with two levels: a set of potential capacitated distribution centres (DC) and a set of ordered customers. In our problem we intend to determine the set of installed DCs as well as the distribution routes (starting and ending at the DC). The problem is also constrained with capacities on the vehicles. Moreover, there is a homogeneous fleet of vehicles, carrying a single product and each customer is visited just once. As an objective we intend to minimize the routing and location costs.     

A distributed algorithm for equitable bandwidth allocation for content distribution in a tree network

We present a distributed algorithm for bandwidth allocation for content distribution in tree networks, where the intensive computations are executed independently at the nodes while some information is exchanged among the nodes. The root node has a server that stores and broadcasts multiple programs requested at the nodes through links with limited capacity. The bandwidth allocated for a specific program can be decreased from one link to the next in a path from the root node to an end-node, but it cannot be increased. The objective is to determine equitable bandwidth allocations among all programs across all links, which leads to a formulation of a lexicographic maximin optimization model. The performance function at each of the nodes for a specific program represents customers’ satisfaction as a function of the incoming bandwidth into the node. The distributed algorithm that determines the equitable bandwidth allocations extends the algorithm described in Luss (2010).     

A probabilistic one-centre location problem on a network

In this paper we consider the one-centre problem on a network when the speeds on links are stochastic rather than deterministic. Given a desirable time to reach customers residing at the nodes, the objective is to find the location for a facility such that the probability that all nodes are reached within this time threshold is maximized. The problem is formulated, analyzed and solved by using multivariate normal probabilities. The procedure is demonstrated on an example problem.     

p-Median theorems for competitive locations

In competitive location theory, one wishes to optimally choose the locations ofr facilities to compete againstp existing facilities for providing service (or goods) to the customers who are at given discrete points (or nodes). One normally assumes that: (a) the level of demand of each customer is fixed (i.e. this demand is not a function of how far a customer is from a facility), and (b) the customer always uses the closest available facility. In this paper we study competitive locations when one or both of the above assumptions have been relaxed. In particular, we show that for each case and under certain assumptions, there exists a set of optimal locations which consists entirely of nodes.This work was supported by a National Science Foundation Grant ECS-8121741.     

A repeated matching heuristic for the single-source capacitated facility location problem

Facility location models form an important class of integer programming problems, with application in many areas such as the distribution and transportation industries. An important class of solution methods for these problems are so-called Lagrangean heuristics which have been shown to produce high quality solutions and which are at the same time robust. The general facility location problem can be divided into a number of special problems depending on the properties assumed. In the capacitated location problem each facility has a specific capacity on the service it provides. We describe a new solution approach for the capacitated facility location problem when each customer is served by a single facility. The approach is based on a repeated matching algorithm which essentially solves a series of matching problems until certain convergence criteria are satisfied. The method generates feasible solutions in each iteration in contrast to Lagrangean heuristics where problem dependent heuristics must be used to construct a feasible solution. Numerical results show that the approach produces solutions which are of similar and often better than those produced using the best Lagrangean heuristics.