Under Cognitive radio (CR), the Quality of Service (QoS) suffers from many dimensions or metrics of communication quality for improving spectrum utilization. To investigate this issue, this paper develops a methodology based on the multiobjective optimization model with genetic algorithms (GAs). The influence of evolving a radio defined by a chromosome is identified. The Multiobjective Cognitive Radio (MOCR) algorithm from genetically manipulating the chromosomes is proposed. Using adaptive component as an example, the bounds for the maximum benefit is predicted by a proposed model that considers Pareto front. To find a set of parameters that optimize the radio for userpsilas current needs, several solutions are presented. Simulation results show that MOCR is able to find a comparatively better spread of compromise solutions.