To cope with drastically increasing user demands for spectrum resource, spectrum sharing is a strategy that greatly alleviates scarcity. However, without a proper spectrum sharing scheme, the use of concurrently shared channels between primary (or licensed) users and secondary (or unlicensed) users within one cell can lead to harmful interference, lowing spectral efficiency and throughput of the system. In this paper, we address the problem of spectrum assignment (SA) in an underlay spectrum sharing network. An SA algorithm is considered as the mechanism for secondary users exploit primary channels while maintaining the interference in acceptable levels, ensuring that the primary system performance is not compromised. We model this scenario as a multi-objective problem (MOP) and we propose the application of Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to face the throughput and spectral efficiency tradeoff. The simulation results demonstrate through the Pareto optimal set, that our approach maintains the quality of service (QoS) of primary and secondary networks and maximizes the throughput of the system at the cost of spectral efficiency. The experiments and results are compared with Weighted Sum Rate (WSA) and the Parallel Cell Coordinate System Adaptative Multiobjective Particle Swarm Optimization (pccsAMOPSO) for different cases for the SA problem.