Algorithms for frequency assignment problems (original) (raw)
Related papers
Models and methods for frequency assignment with cumulative interference constraints
International Transactions in Operational Research, 2008
In this paper, a realistic modeling of interferences for frequency assignment in hertzian telecommunication networks is presented. In contrast with traditional interference models based only on binary interference constraints involving two frequencies, this new approach considers the case of cumulative disruptions that are modeled through a unique non-binary constraint. To deal with these complex constraints, we propose extensions of classical integer linear programming formulations. On a set of realistic instances, we propose hybrid constraint programming and large neighborhood search solution methods to solve minimum interference and minimum span frequency assignment problems. We compare their performances with those of existing heuristics. Finally, we show how the end-user benefits from using the cumulative model instead of the traditional one.
Lower bounds for Minimum Interference Frequency Assignment Problems
In this paper we describe a new lower bound procedure for the minimum interference frequency assignment problem MI-FAP. In the MI-FAP we h a v e to assign frequencies to transmitter-receiver pairs in such a w a y that the cumulative i n terference in the communication network is minimized. Mainly due to the fairly large numb e r o f a v ailable frequencies, exact methods fail to solve the more di cult instances. In this paper we describe a procedure that produces a non-decreasing sequence of lower bounds. In each iteration of the algorithm we h a v e to solve MI-FAPs that are substantially smaller than the original instance. These subproblems can be solved with either integer programming techniques or a dynamic programming algorithm based on a tree decomposition of the underlying graph. Computational results show that integer programming and dynamic programming supply very good results.
A Potential Reduction Approach to the Radio Link Frequency Assignment Problem
The frequency assignment problem is the problem of assigning frequencies to transmission links such that either no interference occurs and the number of used frequencies is minimized, or the amount of interference is minimized. We present an algorithm for this problem that is based on Karmarkar's interior point potential reduction approach to combinatorial optimization problems. We develop a new quadratic formulation of the problem that reduces the problem size signi cantly. Several preprocessing techniques are discussed. We report on computational experience with real-life instances, applying Karmarkar's algorithm to the quadratic model. I am grateful for getting the opportunity to attend meetings in Maastricht, Scheveningen and London. At this meetings, I learned a lot and was also stimulated to think as creatively as possible to solve the frequency assignment problem. Finally, I would like to thank all my colleague students who made life at the university pleasant. Of these students, one may not remain nameless: a big thank you goes to Henk van Benthem; without him and his problems life would have been much harder.
The frequency assignment problem (FAP) is the problem of assigning frequencies to transmission links such that no interference occurs, and such that the number of used frequencies is minimized. We present an algorithm for the FAP that employs row generation and polyhedral techniques, primal heuristics, and branch-and-bound to obtain good lower and upper bounds to a vertex packing formulation of the problem. The valid inequalities added to the linear formulation are all based on cliques that can be found in an associated graph. We develop an efficient heuristic to identify two types of cliques. Moreover, we suggest two branching strategies. We report on computational experience with real-life instances. Table of contents 1 Introduction 3 2 Problem formulation 3 3 The branch-and-cut algorithm 5 3.1 Preprocessing: Reducing the Problem Size : : : : : : : : : : : : : 5 3.1.1 Technique 1 : : : : : : : : : : : : : : : : : : : : : : : : : : 5 3.1.2 Technique 2 : : : : : : : : : : : : : : :...
Local search algorithms for the radio link frequency assignment problem
2000
The radio link frequency assignment problem occurs when a network of radio links has to be established. Each link must be assigned an operating frequency from a given domain. The assignment has to satisfy certain restrictions so as to limit the interference between links. The number of frequencies used is to be minimized. Problems of this type were investigated by a consortium consisting of research groups from Delft, Eindhoven, London, Maastricht, Norwich, and Toulouse. The participants developed optimization algorithms based on branch-and-cut and constraint satisfaction, and approximation techniques including a variety of local search methods, genetic algorithms, neural networks, and potential reduction. These algorithms were tested and compared on a set of real-life instances.
A potential reduction approach to the frequency assignment problem
Discrete Applied Mathematics, 1997
The frequency assignment problem is the problem of assigning frequencies to transmission links such that either no interference occurs, or the amount of interference is minimized. We present an algorithm for this problem that is inspired by Karmarkar's interior point potential reduction approach to combinatorial optimization problems. We develop a nonconvex quadratic model of the problem that is very compact as all interference constraints are incorporated in the objective function. Moreover, optimizing this model may result in nding multiple solutions to the problem simultaneously. Several preprocessing techniques are discussed. We report on computational experience with both real{life and randomly generated instances.
A branch-and-cut algorithm for the frequency assignment problem
The frequency assignment problem FAP is the problem of assigning frequencies to transmission links such that no interference between signals occurs. This implies distance constraints between assigned frequencies of links. The objective is to minimize the number of used frequencies. We present a n i n teger linear programming formulation that is closely related to the vertex packing problem. Although the size of this formulation is an order of magnitude larger than the underlying network of links, we use the integer linear programming formulation within a branch-and-cut algorithm. This algorithm employs problem speci c and generic techniques such as reduction methods, primal heuristics, and branching rules to obtain optimal solutions. We report on computational experience with real-life instances.
Algorithms for Radio Link Frequency Assignment: The Calma Project
Operations Research, 2002
The radio link frequency assignment problem occurs when a network of radio links has to be established. Each link must be assigned an operating frequency from a given domain. The assignment has to satisfy certain restrictions so as to limit the interference between links. The number of frequencies used is to be minimized. Problems of this type were investigated by a consortium consisting of research groups from Delft, Eindhoven, London, Maastricht, Norwich, and Toulouse. The participants developed optimization algorithms based on branch-and-cut and constraint satisfaction, and approximation techniques including a variety of local search methods, genetic algorithms, neural networks, and potential reduction. These algorithms were tested and compared on a set of real-life instances.
Tabu Search for the Radio Links Frequency Assignment Problem
. In this paper Tabu Search has been compared with random search on solving a constraint satisfaction problem, namely the Radio Links Frequency Assignment Problem (RLFAP). The effect of Arc-Consistency has been demonstrated. Search Heuristics have been optimised. Results on scaling behaviour and performance of the algorithm under perturbation of a problem are presented. A method for reducing the number of distinct frequencies used, as well as satisfying constraints, is described. Furthermore, a method of constraint variation has been shown to halve processing times and secure solutions to harder problems. 1 Introduction Tabu Search is a modern heuristic method which was introduced by Glover [1, 2] as an efficient way of finding high quality solutions to hard combinatorial optimisation problems, such as the Radio Links Frequency Assignment Problem (RLFAP). The radio links frequency assignment problem occurs in many civil and military applications [3, 4]. The main objective is to assi...