EUCLID CALMA Radio Link Frequency Assignment Project Technical Annex T-2.2.1 A: A Branch-and-Cut Algorithm for the Frequency Assignment Problem (original) (raw)

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.

Radio Link Frequency Assignment

Constraints - An International Journal, 1999

The problem of radio frequency assignment is to provide communication channels from limited spectral resources whilst keeping to a minimum the interference suffered by those whishing to communicate in a given radio communication network. This problem is a combinatorial (NP-hard) optimization problem. In 1993, the CELAR (the French "Centre d'Electronique de l'Armement") built a suite of simplified versions of Radio Link Frequency Assignment Problems (RLFAP) starting from data on a real network . Initially designed for assessing the performances of several Constraint Logic Programming languages, these benchmarks have been made available to the public in the framework of the European EUCLID project CALMA (Combinatorial Algorithms for Military Applications).

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.

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.

Upper and lower bounding techniques for frequency assignment problems

We consider two v ariants of the radio link frequency assignment problem. These problems arise in practice when a network of radio links has to be established. Each radio link has to be assigned a particular frequency. T h e i n terference level between the frequencies assigned to the di erent links has to be acceptable, since otherwise communication will be distorted. The frequency assignments have to comply with certain regulations and physical characteristics of the transmitters. Moreover, the number of frequencies is to be minimized, because each frequency used in the network has to be reserved at a certain cost. We d e v elop several approximation algorithms for the problems, which are based on local search, and we compare their performance on some practical instances. Lower bounding techniques based on nonlinear programming and the chromatic number of a graph are used to estimate the quality of the approximate solutions for these instances.

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.

Frequency assignment in mobile radio systems using branch-and-cut techniques

European Journal of Operational Research, 2000

We present a new exact method to plan frequency assignment for mobile radio systems in a geographical region. Frequencies are to be assigned to`cells' so that the required service is performed under the particular constraint that the overall noise±signal ratio, related to interference, should not exceed a given level for each cell±frequency pair. This NPhard problem is formulated as an Integer Linear Program and solved by an exact branch-and-cut technique, based on strong cutting planes. We start with very few constraints and use separation procedures to detect the violated constraints. The method and its implementation are tested on a library containing 85 real-world instances provided by CSELT, a major research laboratory operating with TIM (one of the Italian mobile radio system managers). We report the exact solution of instances with up to 203 cells within acceptable computing time. Ó

Optimal Solutions for Frequency Assignment Problems via Tree Decomposition

Lecture Notes in Computer Science, 1999

In this paper we describe a computational study to solve hard frequency assignment problems (FAPs) to optimality using a tree decomposition of the graph that models interference constraints. We present a dynamic programming algorithm which solves FAPs based on this tree decomposition. With the use of several dominance and bounding techniques it is possible to solve small and medium-sized real-life instances of the frequency assignment problem to optimality. Moreover, with an iterative version of the algorithm we obtain good lower bounds for large-sized instances within reasonable time and memory limits.