Concentrator Location Problem Research Articles

Topological design of centralized computer networks

Topological design of centralized computer-communication networks is an important issue that has been investigated by a large number of researchers. Such networks typically involve a large number of terminals connected by low or medium speed lines to concentrators, which are then connected to a central computing site by high speed lines. This problem is known to be a very difficult one. In general, the design problem involves determining the following: (a) the numbers and locations of concentrators that are to be opened; (b) the topology of connecting user nodes to concentrations sites; and (c) determining the links between open concentrators and the central node. Since the overall design problem belongs to the class of problems that are NP Hard, most prior research has investigated ways in which to disaggregate the problem into several simpler problems that can be solved iteratively until a satisfactory solution is reached. The problem we solve is this research involves multipoint lines between terminals and concentrators, and dedicated lines between concentrators and the central node. This problem therefore combines features of concentrator location problems as well as local access network design problems. We utilize a Lagrangian heuristic designed to efficiently solve this problem with gaps ranging from 2.7 to 10.4% of the lower bound.

Topological Design of Centralized Computer Networks

Topological design of centralized computer‐communication networks is an important issue that has been investigated by a large number of researchers. Such networks typically involve a large number of terminals connected by low or medium speed lines to concentrators, which are then connected to a central computing site by high speed lines. This problem is known to be a very difficult one. In general, the design problem involves determining the following: (a) the numbers and locations of concentrators that are to be opened; (b) the topology of connecting user nodes to concentrations sites; and (c) determining the links between open concentrators and the central node. Since the overall design problem belongs to the class of problems that are NP Hard, most prior research has investigated ways in which to disaggregate the problem into several simpler problems that can be solved iteratively until a satisfactory solution is reached. The problem we solve is this research involves multipoint lines between terminals and concentrators, and dedicated lines between concentrators and the central node. This problem therefore combines features of concentrator location problems as well as local access network design problems. We utilize a Lagrangian heuristic designed to efficiently solve this problem with gap ranging from 2.7 to 10.4% of the lower bound.

A Location Based Heuristic for General Routing Problems

We present a general framework for modeling routing problems based on formulating them as a traditional location problem called the capacitated concentrator location problem. We apply this framework to two classical routing problems: the capacitated vehicle routing problem and the inventory routing problem. In the former case, the heuristic is proven to be asymptotically optimal for any distribution of customer demands and locations. Computational experiments show that the heuristic performs well for both problems and, in most cases, outperforms all published heuristics on a set of standard test problems.

Analytical results and algorithms for vehicle routing problems with bin-packing features: Bramel, Julien Dana, Ph.D. Columbia University, 1993. 120 pp. adviser:David Simchi-Levi

Due to the increased importance of the service sector of the economy, there is a need for a better analytical understanding of service and distribution systems. In such systems, servers based at a single warehouse provide delivery, customer pick-up or repair and maintenance services to customers geographically dispersed in a given region. Such distribution systems integrate problems involving inventory and routing issues, as well as vehicle capacity and time constraints. At the core of these distribution problems is the Capacitated Vehicle Routing Problem (CVRP). Here, a fleet of vehicles of limited capacity must be dispatched and routed so that each customer receives a certain load. A thorough analysis of the CVRP entails an understanding of a sub-problem, called the bin-packing problem. Here, a set of items of different sizes must be packed into equal size bins in such a way that the total size assigned to any one bin is at most the capacity of the bin and the number of bins used is as small as possible. We show that as the number of customers increases the capacitated vehicle routing problem can be solved using results from the bin-packing literature. We then look at some of the classical heuristics designed for the CVRP and show that a class of these are provably inefficient. That is, as the number of customers increases, the solutions produced by heuristics in this class tend to be far from the optimal solution. These results are in agreement with the empirical performance reported in the literature for heuristics of this class. We next discuss practical algorithms for the CVRP and the problem of integrating inventory issues with transportation cost. We develop a general framework to solve these problems that involves a traditional location model commonly called the Capacitated Concentrator Location Problem. In the next chapter, we consider a vehicle routing problem where each customer requests service and provides a time window in which service is desired. The objective is to serve each customer in its time window in such a way that the total distance traveled is as small as possible. We show that the problem can be solved using similar techniques to the capacitated vehicle routing problem. Finally, we study the bin-packing problem with a different cost structure. We consider the problem when the cost of a bin is a function of the number of items in the bin. We derive results that bound the relative difference between the heuristics solution and the optimal solution. As a result of this analysis, we also derive some new results for the classical bin-packing problem.

An efficient characterization of some cost allocation solutions associated with capacitated network design problems

We analyze some game-theoretic solution concepts associated with a cost allocation problem arising from the Capacitated Network Design (CND) problem. The problem is formulated as a cost cooperative game in characteristic function form to be referred to as the CND game. We provide an efficient representation of several game-theoretic solution concepts associated with the CND game. In particular, we efficiently characterize the core, and in some cases the nucleolus, the least weighted?-core and a certain "central" point in the least weighted?-core. Our model properly generalizes several previously studied cooperative games. We also employ our model to analyze cost allocation problems associated with several classes of network design problems, which were not previously studied in the literature. Specifically, we efficiently characterize the above cost allocation solutions for cost allocation problems associated with the Capacitated Concentrator Location problem, the Capacitated Minimum Spanning Tree problem, the Capacitated Fixed Cost Spanning Forest problem, and the Capacitated Steiner Tree problem.

An Algorithm for the Design of Multitype Concentrator Networks

In recent years we have witnessed remarkable progress in the development of the topological design of computer communication networks. One of the important aspects of the topological design of computer communication networks is the concentrator location problem. This problem is a complex combinatorial problem that belongs to the difficult class of NP-complete problems where the computation of an optimal solution is still a challenging task. This paper extends the standard capacitated concentrator location problem to a generalization of multitype capacitated concentrator location problems and presents an efficient algorithm based on cross decomposition. This algorithm incorporates the Benders decomposition and Lagrangean relaxation methods into a single framework and exploits the resulting primal and dual structure simultaneously. Computational results are quite satisfactory and encouraging and show this algorithm to be both efficient and effective. The use of cross decomposition as a heuristic algorithm is also discussed.

A Lagrangian heuristic for the capacitated plant location problem with single source constraints

In this paper we look at the Lagrangian relaxations of the Capacitated Plant Location Problem with Single Source constraints in terms of the bounds and solution techniques. We propose a heuristic based on a lagrangian relaxation of the problem. We also show how this heuristic can be used to solve other combinatorial problems that are related to this problem, such as the concentrator location problem and the bin packing problem.

Hierarchical concentrator location problem

This paper addresses the problem of locating concentrators in a computer communications network where a concentrator could be connected to another concentrator in a hierarchy. A mathematical programming model is developed. The objective is to minimize the costs of setting up and operating the communications network subject to capacity constraints. A Lagrangian relaxation approach is used to develop a heuristic solution procedure which is both efficient and effective. Extensive computational experiments were conducted to test the performance of the solution procedure. Problems with up to 200 terminal and 10 potential concentrator locations were studied. The gap between the feasible solution value and the best lower bound was used to judge the quality of the procedure. The mean gaps were in the range of 3–12% across a wide range of problem structures.

The K-coverage concentrator location problem

This paper studies the problem of assigning multiple concentrators to each terminal site in a centralized teleprocessing network. This problem requires that each terminal in the network be covered by more than one concentrator to provide increased reliability. We formulate the problem as an extension of the single-source capacitated warehouse location model and solve it using a subgradient algorithm. The subgradient optimization algorithm uses the Lagrangian relaxation technique to generate lower bounds on the optimal objective value. Upper bounds are generated by using a heuristic procedure that modifies the Lagrangian solution to attain feasibility. The algorithm has been tested on several hundred problems with variable dimensions of up to 1000 terminals, 100 concentrators, and five coverages. Computational experience indicates that our approach is extremely effective for obtaining near-optimal solutions. Most problems converged within 0.05 percent; of the optimum and required very little computational effort on an IBM 3090.

The concentrator location problem with variable coverage

This paper deals with the problem of locating concentrators in a computer communications network where the terminals have varying concentrator coverage. A mathematical programming model is developed. The objective is to minimize communication costs as well as set up and operating costs for the concentrators subject to capacity constraints. A solution procedure which makes use of a relaxation of the problem is presented. Computational results indicate that this solution procedure is very effective.

Combined capacity planning and concentrator location in computer communications networks

After an introduction we describe in Section 2 the joint capacity assignment concentrator location problem in terms of a mixed-integer-programming problem. Section 3 proposes a heuristic algorithm to solve the problem. Section 4 illustrates the algorithm in a hypothetical example and shows some results using it in a simulation context.

A two-phase algorithm and performance bounds for the star-star concentrator location problem

The introduction of concentrators in a centralized telecommunication network provides a cost-effective way to connect the network. The star-star (SS) network model is considered, and the star-star concentrator location problem (SSCLP) is then examined. The SSCLP is NP-complete and can be formulated as a 0-1 integer programming problem. A two-phase algorithm is developed to solve the SSCLP. In the first phase, dualizing the side constraints produces a Lagrangian problem that is easy to solve and has an optimal value that is a lower bound (for minimization problems) on the optimal value of the original SSCLP. Heuristics then are applied to produce an upper bound (feasible solution) to the SSCLP. In the second phase, a branch-and-bound method is used to refine the solution space to obtain a tighter lower bound. First, an enumeration heuristic is applied to improve the best feasible solution obtained from the first phase. Then, a procedure for deriving bounding problems is presented and various branching strategies are discussed. Computational examples with up to 100 terminals and 30 potential concentrators are considered. All the network designs obtained are shown to be within 2% of optimal. >

Efficient algorithms for the capacitated concentrator location problem

Topological design of computer communication networks is a very difficult problem. This problem is generally disaggregated into a number of “simpler” problems. One of these “simpler” problems is the capacitated concentrator location problem. The paper makes use of the Lagrangian relaxation approach to develop optimal and heuristic solution procedures for this problem. Computational experiments show these procedures to be both efficient and effective. The heuristic solution procedure is compared to previously developed algorithms and found to generate significantly better results.

Lagrangian relaxation for the star‐star concentrator location problem: Approximation algorithm and bounds

AbstractThe star‐star concentrator location problem (SSCLP), which is a network layout problem, is considered. SSCLP is formulated as an integer linear programming problem. The Lagrangian relaxation (LR) method is used to obtain suboptimal solutions (upper bounds) and lower bounds. Three different LRs are used for SSCLP. The resulting Lagrangian dual problems are shown to be equivalent to some linear programming problems. An approximation algorithm is suggested for SSCLP that produces both a feasible solution (upper bound) and a lower bound. It is shown that if z and z̄are the lower and upper bounds found, then z̄/z ≤ k, where k is the concentrator capacity. Some computational examples with up to 50 terminals and 20 potential concentrator sites are considered. All the network designs obtained are shown to be within 2.8% of optimal.

Large-Scale Network Topological Optimization

A cost-effective structure for a large network is a multilevel hierarchy consisting of a backbone network and a family of local access networks. The backbone network is generally a distributed network, while the local access networks are typically centralized systems. In special cases, the network may consist primarily of either centralized or distributed portions. This paper discusses topological design problems for such systems, including the concentrator location problem, the terminal assignment problem, the terminal layout problem (the constrained minimum spanning tree problem), the distributed network topological layout problem, and the backbone node location problem. Recent algorithm research, including exact and heuristic problem solutions, are described and computational experience is given. Finally, open problems in large-scale topological design are reported.