A cognitive radio network can be employed in any wireless communication systems, including military communications, public safety, emergency networks, aeronautical communications, and wireless-based Internet of Things, to enhance spectral efficiency. The performance of a cognitive radio network (CRN) can be enhanced through the use of cooperative relays with buffers; however, this incurs additional delays which can be reduced by using virtual duplex relaying that requires selection of a suitable relay pair. In a virtual duplex mode, we mimic full-duplex links by using simultaneous two half-duplex links, one transmitting and the other one receiving, in such a way that the overall effect of duplex mode is achieved. The relays are generally selected based on signal-to-interference-plus-noise ratio (SINR). However, other factors such as power consumption and buffer capacity can also have a significant impact on relay selection. In this work, a multiobjective relay selection scheme is proposed that simultaneously takes into account throughput, delay performance, battery power, and buffer status (i.e., both occupied and available) at the relay nodes while maintaining the required SINR. The proposed scheme involves the formulation of four objective functions to, respectively, maximize throughput and buffer space availability while minimizing the delay and battery power consumption. The weighted sum approach is then used to combine these objective functions to form the multiobjective optimization problem and an optimal solution is obtained. The assignments of weights to objectives have been done using the rank sum (RS) method, and several quality-of-service (QoS) profiles have been considered by varying the assignment of weights. The results gathered through simulations demonstrate that the proposed scheme efficiently determines the optimal solution for each application scenario and selects the best relay for the respective QoS profile. The results are further verified by using the genetic algorithm (GA) and particle swarm optimization (PSO) techniques. Both techniques gave identical solutions, thus validating our claim.