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Very LargeScale Neighborhood Search for the Quadratic Assignment Problem
 DISCRETE APPLIED MATHEMATICS
, 2002
"... The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NPhard, and can be solved to optimality only for fairly small size instances ..."
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Cited by 106 (11 self)
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The Quadratic Assignment Problem (QAP) consists of assigning n facilities to n locations so as to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NPhard, and can be solved to optimality only for fairly small size instances (typically, n < 25). Neighborhood search algorithms are the most popular heuristic algorithms to solve larger size instances of the QAP. The most extensively used neighborhood structure for the QAP is the 2exchange neighborhood. This neighborhood is obtained by swapping the locations of two facilities and thus has size O(n²). Previous efforts to explore larger size neighborhoods (such as 3exchange or 4exchange neighborhoods) were not very successful, as it took too long to evaluate the larger set of neighbors. In this paper, we propose very largescale neighborhood (VLSN) search algorithms where the size of the neighborhood is very large and we propose a novel search procedure to heuristically enumerate good neighbors. Our search procedure relies on the concept of improvement graph which allows us to evaluate neighbors much faster than the existing methods. We present extensive computational results of our algorithms on standard benchmark instances. These investigations reveal that very largescale neighborhood search algorithms give consistently better solutions compared the popular 2exchange neighborhood algorithms considering both the solution time and solution accuracy.
Edward,“Guided Local Search
, 1995
"... Abstract Combinatorial explosion problem is a well known phenomenon that prevents complete algorithms from solving many reallife combinatorial optimization problems. In many situations, heuristic search methods are needed. This chapter describes the principles of Guided Local Search (GLS) and Fast ..."
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Cited by 56 (5 self)
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Abstract Combinatorial explosion problem is a well known phenomenon that prevents complete algorithms from solving many reallife combinatorial optimization problems. In many situations, heuristic search methods are needed. This chapter describes the principles of Guided Local Search (GLS) and Fast Local Search (FLS) and surveys their applications. GLS is a penaltybased metaheuristic algorithm that sits on top of other local search algorithms, with the aim to improve their efficiency and robustness. FLS is a way of reducing the size of the neighbourhood to improve the efficiency of local search. The chapter also provides guidance for implementing and using GLS and FLS. Four problems, representative of general application categories, are examined with detailed information provided on how to build a GLSbased method in each case.
Solving the Radio Link Frequency Assignment Problem using Guided Local Search
, 1998
"... this paper, we examine the application of the combinatorial optimisation technique of Guided Local Search to the Radio Link Frequency Assignment Problem (RLFAP). RLFAP stems from real world situations in military telecommunications and it is known to be an NPhard problem. Guided Local Search is a m ..."
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Cited by 13 (7 self)
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this paper, we examine the application of the combinatorial optimisation technique of Guided Local Search to the Radio Link Frequency Assignment Problem (RLFAP). RLFAP stems from real world situations in military telecommunications and it is known to be an NPhard problem. Guided Local Search is a metaheuristic that sits on top of local search procedures allowing them to escape from local minima. GLS is shown to be superior to other methods proposed in the literature for the problem, making it the best choice for solving RLFAPs. 2. INTRODUCTION
Exact solution of a class of frequency assignment problems in cellular networks and other regular grids
 in: 8th Italian Conf. Theor. Comp. Sci. (ICTCS’03), LNCS
, 2003
"... For any non negative real values h and k, an L(h, k)labeling of a graph G = (V, E) is a function L: V → IR such that L(u) − L(v)  ≥ h if (u, v) ∈ E and L(u) − L(v)  ≥ k if there exists w ∈ V such that (u, w) ∈ E and (w, v) ∈ E. The span of an L(h, k)labeling is the difference between th ..."
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Cited by 12 (5 self)
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For any non negative real values h and k, an L(h, k)labeling of a graph G = (V, E) is a function L: V → IR such that L(u) − L(v)  ≥ h if (u, v) ∈ E and L(u) − L(v)  ≥ k if there exists w ∈ V such that (u, w) ∈ E and (w, v) ∈ E. The span of an L(h, k)labeling is the difference between the largest and the smallest value of L, so it is not restrictive to assume 0 as the smallest value of L. We denote by λh,k(G) the smallest real λ such that graph G has an L(h, k)labeling of span λ. The aim of the L(h, k)problem is to satisfy the distance constraints using the minimum span. In this paper, we study L(h, k)labeling problem on regular grids of degree 3, 4, 6, and 8 solving several open problems left in the literature. Keywords: L(h,k)labeling, triangular grids, hexagonal grids, squared grids, octagonal grids. 1
Optimal L(h, k)labelling of regular grids
 Discrete Math. and Theor. Comp. Science
, 2006
"... The L(h, k)labeling is an assignment of non negative integer labels to the nodes of a graph such that ’close ’ nodes have labels which differ by at least k, and ’very close ’ nodes have labels which differ by at least h. The span of an L(h, k)labeling is the difference between the largest and the ..."
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Cited by 9 (2 self)
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The L(h, k)labeling is an assignment of non negative integer labels to the nodes of a graph such that ’close ’ nodes have labels which differ by at least k, and ’very close ’ nodes have labels which differ by at least h. The span of an L(h, k)labeling is the difference between the largest and the smallest assigned label. We study L(h, k)labelings of cellular, squared and hexagonal grids, seeking those with minimum span for each value of k and h ≥ k. The L(h, k)labeling problem has been intensively studied in some special cases, i.e. when k = 0 (vertex coloring), h = k (vertex coloring the square of the graph) and h = 2k (radio or λcoloring) but no results are known in the general case for regular grids. In this paper, we completely solve the L(h, k)labeling problem on cellular grids, finding exact values of the span for each value of h and k; only in a small interval we provide different upper and lower bounds. For the sake of completeness, we study also hexagonal and squared grids. Keywords: L(h, k)labeling, cellular grids, triangular grids, hexagonal grids, squared grids. 1
Channel Assignment for Wireless Networks Modelled as ddimensional Square Grids
"... In this paper, we study the problem of channel assignment for wireless networks modelled as ddimensional grids. In particular, for ddimensional square grids, we present optimal assignments that achieve a channel separation of 2 for adjacent stations where the reuse distance is 3 or 4. We also intr ..."
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Cited by 7 (2 self)
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In this paper, we study the problem of channel assignment for wireless networks modelled as ddimensional grids. In particular, for ddimensional square grids, we present optimal assignments that achieve a channel separation of 2 for adjacent stations where the reuse distance is 3 or 4. We also introduce the notion of a colouring schema for ddimensional square grids, and present an algorithm that assigns colours to the vertices of the grid satisfying the schema constraints.
Reactive GRASP with Path Relinking for Channel Assignment In Mobile Phone Networks
, 2001
"... The Frequency Assignment Prnblem (FAP) arises in wireless networks when the number of available frequency channels is smaller than the number of users. FAP is NPhard and plays an important role in the network planning. Usually, the number of available channels is much smaller than the number of use ..."
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Cited by 6 (1 self)
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The Frequency Assignment Prnblem (FAP) arises in wireless networks when the number of available frequency channels is smaller than the number of users. FAP is NPhard and plays an important role in the network planning. Usually, the number of available channels is much smaller than the number of users accessing the wireless network. In this case, the reuse of frequency channels is mandatory. Consequently, this may cause interference. Nowadays, cellular phone operators use various techniques designed to cope with channel shortage and, as a consequence, to avoid interference. For instance, frequency division by time or code, and local frequency clustering models have been used. These techniques are bounded by the number of users, i.e. as the number of users increases, they tend to become obsolete. In this work, we propose to minimize the total interference of the system, using a netaheuristic based on GRASP (Greedy Random ized Adaptive Search Procedure). A reactive heuristic has been used in order to autonmtically balance GRASP parameters. Furthermore, Path Relinking, which consists of an intensification strategy, has been applied. We report experimental results given by our proposed approach.
Graph domination, coloring and cliques in telecommunications
 Handbook of Optimization in Telecommunications, pages 865–890. Spinger Science + Business
, 2006
"... This paper aims to provide a detailed survey of existing graph models and algorithms for important problems that arise in different areas of wireless telecommunication. In particular, applications of graph optimization problems such as minimum dominating set, minimum vertex coloring and maximum cliq ..."
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Cited by 5 (1 self)
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This paper aims to provide a detailed survey of existing graph models and algorithms for important problems that arise in different areas of wireless telecommunication. In particular, applications of graph optimization problems such as minimum dominating set, minimum vertex coloring and maximum clique in multihop wireless networks are discussed. Different forms of graph domination have been used extensively to model clustering in wireless ad hoc networks. Graph coloring problems and their variants have been used to model channel assignment and scheduling type problems in wireless networks. Cliques are used to derive bounds on chromatic number, and are used in models of traffic flow, resource allocation, interference, etc. In this paper we survey the solution methods proposed in the literature for these problems and some recent theoretical results that are relevant to this area of research in wireless networks.
Evolution of planning for wireless communication systems
 In Proc. of HICSS’03, Big Island
, 2003
"... In this paper we provide a detailed and comprehensive survey of proposed approaches for network design, charting the evolution of models and techniques for the automatic planning of cellular wireless services. These problems present themselves as a tradeoff between commitment to infrastructure and ..."
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Cited by 5 (0 self)
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In this paper we provide a detailed and comprehensive survey of proposed approaches for network design, charting the evolution of models and techniques for the automatic planning of cellular wireless services. These problems present themselves as a tradeoff between commitment to infrastructure and quality of service, and have become increasingly complex with the advent of more sophisticated protocols and wireless architectures. Consequently these problems are receiving increased attention from researchers in a variety of fields who adopt a wide range of models, assumptions and methodologies for problem solution. We seek to unify this dispersed and fragmented literature by charting the evolution of centralised planning for cellular systems. 1
Hierarchical cellular network design with channel allocation
 European Journal of Operational Research
"... The design of a cellular network is a complex process that encompasses the selection and configuration of cell sites and the supporting network infrastructure. This investigation presents a net revenue maximizing model that can assist network designers in the design and configuration of a cellular ..."
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Cited by 3 (0 self)
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The design of a cellular network is a complex process that encompasses the selection and configuration of cell sites and the supporting network infrastructure. This investigation presents a net revenue maximizing model that can assist network designers in the design and configuration of a cellular system. The integer programming model takes as given a set of candidate cell locations with corresponding costs, the amount of available bandwidth, the maximum demand for service in each geographical area, and the revenue potential in each customer area. Based on these data, the model determines the size and location of cells, and the specific channels to be allocated to each cell. To solve problem instances, a maximal clique cut procedure is developed in order to efficiently generate tight upper bounds. A lower bound is constructed by solving the discrete optimization model with some of the discrete variables fixed. Computational experiments on seventytwo problem instances demonstrate the computational viability of our new procedure. 1