The most accurate approaches to frequency assignment problems minimize a cost function based on signalto- interference ratios at points where reception is required. The merits of this approach are counterbalanced by much greater requirements for computational resources than for the traditional approach using binary frequency separation constraints. This can make run times unrealistic for the largest problems. In this paper the merits of the signal-tointerference based cost function are confirmed, but it is shown that algorithms are faster and give better quality results if this cost function is combined with the binary constraint approach. Two types of algorithm are used to illustrate the combined approach, simulated annealing and a new ant colony system algorithm. The combined approach studied is applicable to all the main classes of frequency assignment problem.