Heuristic Approaches to Solve the Frequency Assignment Problem

The frequency assignment problem is a computationally hard problem with many applications including the mobile telephone industry and tactical communications. The problem may be modelled mathematically as a T-colouring problem for an undirected weighted graph; it is required to assign to each vertex a value from a given set such that for each edge the difference in absolute value between the values at the corresponding vertices is greater than or equal to the weight of the edge. This problem was solved using novel and existing metaheuristic algorithms and their relative successes were compared. Early work of this thesis used greedy, steepest descent and backtracking algorithms as a means of investigating the factors which influence the performance of an algorithm (selection of frequency, ordering of variables, provision of an incremental objective function). Later simulated annealing, tabu search and divide and conquer techniques were used and the results compared. A novel divide and conquer technique incorporating metaheuristics is described and results using test data based on real problems is presented. The divide and conquer technique (with either tabu search or simulated annealing) was found to improve significantly upon the corresponding metaheuristic when implemented alone and acting on non-trivial scenarios. The results were significant and consistent. The divide and conquer (with simulated annealing) algorithm in particular was shown to be robust and efficient in its solution of the frequency assignment problems presented. The results presented in this thesis consistently out-perform those obtained by the Defence, Evaluation and Research Agency, Malvern. In addition this method lends itself to parallelisation since the problem is broken into smaller independent parts. The divide and conquer algorithm does not exploit knowledge of the constraint network and should be applicable to a number of different problem domains. Algorithms capable of solving the frequency assignment problem most effectively will become valuable as demand for the electromagnetic spectrum continues to grow