A Divide-and-Conquer Technique to Solve the Frequency Assignment Problem

Abstract

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. Tabu search, simulated annealing, simulated neural networks and other heuristic algorithms have been applied to this problem. In this paper we describe a divide and conquer technique incorporating heuristics and present results using test data from real problems which show that with respect to both quality of solutions and speed of execution it is superior to simulated annealing and steepest descent algorithms. It is particularly successful in minimising the span and order of the set of frequencies required to solve the problem.