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Â¿Cognitive radioÂ¿ is an emerging technique to improve the utilization of radio frequency spectrum in wireless networks. This paper discusses the problem of spectrum sharing among primary users and secondary users, and carries out the centralized spectrum allocation with the following two goals: (1) maximize system's sum bandwidth reward, and (2) maximize second users' access fairness. The spectrum allocation problem is formulated into a multi-objective optimization problem aiming at optimizing the system's overall performance and reducing to a graph coloring problem. Graph coloring problem is a well known NP-hard problem. A swarm intelligence based algorithm, particle swarm optimization (PSO), is used to solve the problem. Simulations are conducted to compare the proposed methods with the CSGC algorithms under the Collaborative-Max-Sum-Reward (CSUM) and Collaborative-Max-Proportional-Fair (CMPF) rules. Our experiment results show that the proposed method provides a good tradeoff between the system's sum bandwidth reward and the secondary users' access fairness, and has a better system overall performance. The paper gives an effective method for the spectrum allocation of cognitive radio networks.