Concentrator Location Problem Research Articles

Matheuristics with performance guarantee for the unsplit and split delivery capacitated vehicle routing problem

AbstractFor the classical unsplit and split delivery capacitated vehicle routing problems, we carry out a worst‐case analysis for classes of matheuristics and compare their performance on average, on a large set of benchmark instances. The matheuristics are based on the optimal solution of the bin packing problem, the capacitated concentrator location problem, and the unsplit capacitated vehicle routing problem (CVRP). These matheuristics are compared with the classical algorithms having known finite worst‐case performance bound. For the unsplit CVRP, we provide a matheuristic having worst‐case performance bound equal to the one of the classical algorithms, but with an average percent cost increase with respect to the optimal cost equal to 1.13%. For the split delivery case, we provide a matheuristic having worst‐case performance bound 2 and an average percent cost increase with respect to the best‐known cost equal to 0.64%. Moreover, this matheuristic is able to find 22 best‐known solutions, 20 of which are new.

A new extended formulation with valid inequalities for the Capacitated Concentrator Location Problem

We present a new disaggregated formulation of the Capacitated Concentrator Location Problem (CCLP) using the notion of cardinality of terminals assigned to a concentrator. This formulation consists of O(mnn) variables and constraints, where m denotes the number of concentrators and n the number of terminals, respectively. We prove that this extended formulation is stronger than the traditional one. We also present two classes of inequalities exploiting the cardinality effect of the extended formulation. The first class is a generalization of the well-known Cover and (1, k)-Configuration inequalities, which collectively are stronger than the original Cover and (1, k)-Configuration inequalities. The second class, called the 2-Facility Cardinality Matching Inequality, holds for the uncapacitated version of the Concentrator Location Problem and can be lifted to become a strong inequality for CCLP. We solve the LP relaxation of the extended formulation and use separation heuristics to identify and sequentially add the previous valid inequalities to improve the lower bound. This approach is embedded in a branch-and-bound and results in a branch-and-cut approach. We test our solution approach on a large set of benchmark problems. The experimentation shows that we can identify the optimal solution at the root node in most of the problem instances with up to 50 concentrators and 50 terminals. For larger sized test problems with up to 100 concentrators and 1000 terminals, the branch-and-cut procedure using the disaggregated formulation outperforms the branch-and-cut procedure applied to the traditional formulation both in terms of CPU and the required number of branch-and-bound nodes.

A Hybrid Multicast Routing for Large Scale Sensor Networks with Holes

In this article, we present RE $^2$ MR, the first hybrid multicast routing protocol that builds on the strengths of existing topology-based, hierarchical and geographic multicast solutions, while addressing their limitations. In RE $^2$ MR, the multicast path search problem is formulated as the capacitated concentrator location problem (CCLP) which yields the network topology that minimizes the sum of path lengths from the multicast root to multicast members. Furthermore, its trajectory-based lightweight hole detection (THLD) discovers deployment area irregularities (i.e., network holes) that affect its solution and autonomously take them into account to generate updated routing paths, and its Energy-efficient Packet Forwarding (EPF) and Multi-level Facility Computation (MFC) reduce computational and communication overheads. We implement RE $^2$ MR in TinyOS and evaluate it extensively using TOSSIM for relatively large-scale simulations (400 nodes); we also implement RE $^2$ MR on real-hardware and perform experiments on a testbed consisting of 42 TelosB motes. Through the simulations and experiments on real-hardware, we demonstrate that RE $^2$ MR reduces the energy consumption by up to 57 percent and the end-to-end delay by up to 8 percent, when compared with the state-of-the-art multicast routing protocols.

Towards optimizing the deployment of optical access networks

In this paper we study the cost-optimal deployment of optical access networks considering variants of the problem such as fiber to the home (FTTH), fiber to the building (FTTB), fiber to the curb (FTTC), or fiber to the neighborhood (FTTN). We identify the combinatorial structures of the most important sub-problems arising in this area and model these, e.g., as capacitated facility location, concentrator location, or Steiner tree problems. We discuss modeling alternatives as well. We finally construct a unified integer programming model that combines all sub-models and provides a global view of all these FTTx problems. We also summarize computational studies of various special cases.

Near‐optimal heuristics and managerial insights for the storage constrained, inbound inventory routing problem

PurposeThe purpose of this paper is to develop efficient heuristics for determining the route design and inventory management of inbound parts which are delivered for manufacturing, assembly, or distribution operations and for which there is limited storage space. The shipment frequencies and quantities are coordinated with the available storage space and the vehicle capacities.Design/methodology/approachTwo heuristics that generate near optimal solutions are proposed. The first heuristic has an iterative routing phase that maximizes the savings realized by grouping suppliers together into routes without considering the storage constraint and then calculates the pickup frequencies in the second phase to accommodate the storage constraint. The second heuristic iteratively executes a routing and a pickup frequency phase that both account for the storage constraint. A lower bound is also developed as a benchmark for the heuristic solutions.FindingsNear optimal solutions can be obtained in a reasonable amount of time by utilizing information about the amount of storage space in the route design process.Practical implicationsThe traditional emphasis on high vehicle utilization in transportation management can lead to inefficient logistics operations by carrying excess inventory or by using longer, less efficient routes. Route formation and pickup quantities at the suppliers are simultaneously considered, as both are important from a logistics standpoint and are interrelated decisions.Originality/valueThe two proposed heuristics dynamically define seed sets such that the solutions to the capacitated concentrator location problem (CCLP) are accurately estimated. This increased accuracy helps in generating near‐optimal solutions in a practical amount of computing time.

An approximation algorithm for the [formula omitted]-Level Concentrator Location Problem

The k -Level Concentrator Location Problem is a variant of the k -Level Facility Location Problem, where in contrast to the classical model, service costs are charged only once and not proportional to the demand. We present a new approximation algorithm with a performance guarantee of 3 2 ( 3 k − 1 ) , improving over the 1.52 ⋅ 9 k − 1 -approximation algorithm proposed by Kantor and Peleg. Moreover, the analysis is considerably shortened by using complementary slackness conditions.

Solving the variable size bin packing problem with discretized formulations

In this paper we study the use of a discretized formulation for solving the variable size bin packing problem (VSBPP). The VSBPP is a generalization of the bin packing problem where bins of different capacities (and different costs) are available for packing a set of items. The objective is to pack all the items minimizing the total cost associated with the bins. We start by presenting a straightforward integer programming formulation to the problem and later on, propose a less straightforward formulation obtained by using a so-called discretized model reformulation technique proposed for other problems (see [Gouveia L. A 2n constraint formulation for the capacitated minimal spanning tree problem. Operations Research 1995; 43:130–141; Gouveia L, Saldanha-da-Gama F. On the capacitated concentrator location problem: a reformulation by discretization. Computers and Operations Research 2006; 33:1242–1258]). New valid inequalities suggested by the variables of the discretized model are also proposed to strengthen the original linear relaxation bounds. Computational results (see Section 4) with up to 1000 items show that these valid inequalities not only enhance the linear programming relaxation bound but may also be extremely helpful when using a commercial package for solving optimally VSBPP.

Polyhedral Analysis for Concentrator Location Problems

The concentrator location problem is to choose a subset of a given terminal set to install concentrators and to assign each remaining terminal node to a concentrator to minimize the cost of installation and assignment. The concentrators may have capacity constraints. We study the polyhedral properties of concentrator location problems with different capacity structures. We develop a branch and cut algorithm and present computational results.

On the capacitated concentrator location problem: a reformulation by discretization

In this paper, we present and discuss a discretized model for the two versions of the capacitated concentrator location problem: a simple version (SCCLP) and a version with modular capacities (MCCLP). We show that the linear programming relaxation of the discretized model is at least as good as the linear programming relaxation of conventional models for the two variations of the problem under study. A technique for deriving valid inequalities from the equations of the discretized model is also given. We will show that this technique provides inequalities that significantly enhance the linear programming bound of the discretized model. Our computational results show the advantage of the new models for obtaining the optimal integer solution for the two versions of the problem.

Concentrator location in telecommunications

We survey the main results in the author’s PhD Thesis presented in December 2002 at the Universite Libre de Bruxelles and supervised by Prof. Martine Labbe. The dissertation is written in English and is available at smg.ulb.ac.be. Several versions of concentrator location problems in telecommunication networks are studied. The thesis presents a list of polyhedral results for these problems and a branch and cut algorithm for the most general problem introduced.

A GRASP HEURISTIC FOR SOLVING AN EXTENDED CAPACITATED CONCENTRATOR LOCATION PROBLEM

Local Access Networks (LACNs) are often considered the "last mile" over the Internet provided that they are connected to some existing Wide Area Network backbone. In this paper, a revised LACN-WAN interconnection model is presented as an extension to the conventional Capacitated Concentrator Location Problem (CCLP). An efficient heuristic is also developed to seek near-optimal deployment of telecommunication devices (e.g. links, concentrators, etc.) while minimizing the total connection costs for the network interconnection. Our solution algorithm could serve as a decision-making tool in solving problems with a real world size (i.e. 120 nodes and 30 concentrators).

An Efficient Heuristic for Solving an Extended Capacitated Concentrator Location Problem

In this paper, a mathematical model and a solution algorithm are developed for solving an extended capacitated concentrator location problem. Our model extends the conventional formulation by simultaneously addressing the two capacity constraints, total connection ports and maximum data processing rate, on each concentrator to be selected for satisfying the communication demands of the given end-user nodes. Since the problem is NP-complete, an efficient and effective Lagrangian heuristic is developed and tested by solving 100 randomly generated test problems with sizes ranging from 30(nodes)×30(concentrators) to150×30. Altogether 58% of the tested problems are solved optimally with an average solution gap 0.36% from the optimality and average solution times are from a few seconds to one half of a minute.

A large hierarchical network star—star topology design algorithm

AbstractThe hierarchical communication network design includes solving problems like the concentrator quantity problem, the concentrator location problem and the assignment problem. Many algorithms have been proposed to solve these particular problems. The two latter problems are NP—hard and no optimal solution of these problems has been found for large networks. In this paper we present a high complexity algorithm for star—star network topology design which solves all three problems for several hierarchy levels simultaneously and finds a superior solution in a reasonable time even for large networks with a few thousand terminals due to a new and quick assignment algorithm. The computational results showed that our assignment algorithm is superior to “Simulated annealing” and “Tabu search”.

INTEGER PROGRAMMING MODEL AND EXACT SOLUTION FOR CONCENTRATOR LOCATION PROBLEM

Topological design of centralized computer networks is an important problem that has been investigated by many researchers. Such networks typically involve a large number of terminals connected to concentrators, that are then connected to a central computing site. This paper focuses on the concentrator location problem among general topological network design problems. The concentrator location problem is defined as determining the following: (i) the number and locations of concentrators that are to be open, and (ii) the allocation of terminals to concentrator sites without violating the capacities of concentrators. An exact algorithm (fractional cutting plane algorithmlbranch-and-bound) is proposed for solving this problem. In this approach an integer programming problem is formulated. Then a class of valid inequalities is derived and a greedy algorithm for a separation problem is shown. A good lower bound is obtained by a lifting procedures. We show how to implement the algorithm using a commercial software for LP and branch-and-bound. Finally, the computational efficiency of our algorithm is demonstrated.

L-SHAPED DECOMPOSITION METHOD FOR MULTI-STAGE STOCHASTIC CONCENTRATOR LOCATION PROBLEM

A stochastic version of a concentrator location problem is dealt with in which traffic demand at each terminal location is uncertain. The concentrator location problem is defined as to determine the following: (i) the numbers and locations of concentators that are to be open, and (ii) the allocation of terminals to concentrator sites. The problem is formulated as a stochastic multi-stage integer linear program, with first stage binary variables concerning network design and continuous recourse variables concerning expansion of capacity. Given a first stage decision, the series of realization of traffic demand may possibly imply a violation of the capacity constraint of the concentrator. Therefore from the second stage to the last stage, recourse action is taken to correct the violation. The objective function minimizes the cost of connecting terminals and the cost of opening concentrators and the expected recourse cost of capacity expansion. We propose a new algorithm which combines an L-shaped method and a branch-and-bound method. Under some assumptions it decomposes the problem into a set of problems as many as the number of stages in parallel. Finally we demonstrate the computational efficiency of our algorithm for the multi-stage model.

Using Simulated Annealing To Minimize The Cost Of Centralized Telecommunications Networks

The network design problems studied in this paper are typically known in the Telecommunications literature as the Concentrator Location, Terminal Assignment and Terminal Layout Problems. These are versions of well-known Operations Research models such as Capacitated Location, Capacitated Assignment, Capacitated Minimum Spanning Tree, and Vehicle Routing. We describe two Simulated Annealing algorithms for solving them and analyze the results obtained through computational testing.

A tabu search heuristic for the concentrator location problem

The concentrator location problem (CLP) is a classical problem in the network design literature. Given a set of candidate locations and the concentrator capacities, the problem is to answer the following related questions. How many concentrators should be used? Where should they be located? Which users are to be assigned to each concentrator? A Lagrangian relaxation is used to obtain lower bounds for this problem. The Lagrangian relaxation is complemented by a tabu search (TS) metaheuristic. Computational results are given for a set of randomly generated problems and for test problems available in the literature. The tabu search heuristic (TSH) is shown to be competitive with other solution procedures available for the problem.

Optimizing access to service based networks

We consider the problem of determining the optimal access topology to service based networks. The problem is formulated as a concentrator location problem with a discontinuous piece wise linear objective function that depends on the traffic of the nodes that are homed to the concentrator. Five heuristics are developed to solve the problem and are compared on an extensive set of examples. Based on this comparison a combination heuristic utilizing a Lagrangian relaxation and swap drop add approach was found to give the best solution in the minimal time.

A multiplier adjustment technique for the capacitated concentrator location problem

We describe a new dual descent method for a pure 0— location problem known as the capacitated concentrator location problem. The multiplier adjustment technique presented is aimed to find an upper bound in a Lagrangean relaxation context permitting both to decrease and to increase multipliers in the course of the search in contrast with methods where that ones are monotonically updated.

Using generalized capacitated trees for designing the topology of local access networks

The design of the topology of a local access network is a complex process which builds on many different combinatorial optimization problems such as the concentrator quantity problem, the concentrator location problem, the terminal clustering problem and the terminal layout problem. Usually, these four subproblems are solved separably and sequentially and the solution of one subproblem is used as data for the next subproblem. There are two main drawbacks associated to this four?phase approach: i) without knowing the optimal solution to the global problem it is difficult to set the parameters for some of the subproblems which appear in the earlier phases and ii) in many cases, wrong decisions taken at one of the earlier phases are "passed" to the subsequent phases. Our aim in this paper is to formulate the two last subproblems, clustering and layout, as one single generalized capacitated tree problem. We formulate the clustering/layout problem as a capacitated single?commodity network flow problem with adequate capacities on the arcs. We adapt a reformulation presented in (Gouveia, 1995) of a single?commodity flow model presented in (Gavish, 1983). We present several inequalities which can be used to tighten the LP relaxation of the original formulation. We present two heuristics for obtaining feasible solutions for the clustering/layout problem. Computational results taken from tests with 50, 100 and 200 nodes indicate that in most of the cases the best heuristic produces topologies with lower cost than the ones obtained by solving separately and sequentially the two individual subproblems.