Cognitive radio has been regarded as a promising technology to improve spectrum utilization significantly. In this letter, spectrum allocation model is presented firstly, and then spectrum allocation methods based on genetic algorithm (GA), quantum genetic algorithm (QGA), and particle swarm optimization (PSO), are proposed. To decrease the search space we propose a mapping process between the channel assignment matrix and the chromosome of GA, QGA, and the position of the particle of PSO, respectively, based on the characteristics of the channel availability matrix and the interference constraints. Results show that our proposed methods greatly outperform the commonly used color sensitive graph coloring algorithm.