The fixed spectrum frequency assignment problem

The frequency assignment problem involves the assignment of discrete channels (frequencies) to the transmitters of a radio network. A separation between the frequencies assigned to transmitters close to each other is required to avoid interference. Unnecessary separation causes an excess requirement for spectrum, which is a valuable resource. Consequently good assignments minimise both interference and the spectrum required. The fixed spectrum frequency assignment problem, where the spectrum available is given and the target is to minimise the total interference of the system, is considered. Interference is modelled through binary constraints, and the problem is represented by an undirected weighted graph. Some integer programming formulations are discussed, together with the adaptation of two metaheuristics. Novel lower bounding techniques, which work by combining lower bounds calculated for some subproblems, are presented. The most effective method is based on a linear program which is reinforced with inequalities derived from the lower bounds calculated on clique-like subproblems. Detailed computational results, obtained on a wide range of benchmarks, are finally reported.