Throughput efficiency holds great importance in the present scenario of the cognitive radio system. In this paper, optimization of throughput in multi-user single relay cognitive radio system has been performed. In a multi-user cognitive radio network, collisions occur between data packets of multiple secondary users, which cause a reduction in the throughput of the network to a great extent. In this paper, a new analytical model for throughput of the multi-user cognitive radio network in terms of the probability of collision has been presented. The model is convenient for the formulation of the optimization problem in such a way that an optimal value of throughput can be achieved by keeping the probability of collision below the allowable limit. This leads to an enhancement in throughput as well as maintains system reliability in the cognitive radio network. Optimal power allocation scheme is used to allocate power among secondary users which makes the system energy efficient. The optimization of the throughput of the system is done using swarm intelligence-based optimization techniques like Particle Swarm Optimization (PSO), Human behavior based Particle Swarm Optimization (HPSO), Particle Swarm Optimization with Aging Leader and Challengers (ALCPSO) and Whale Optimization Algorithm (WOA). Simulation results illustrate that the system optimized with WOA have better throughput than that of the aforementioned optimization algorithms. Moreover, a comparative analysis of the achievable throughput in the multi-user cognitive radio system with the proposed scheme and that with the equal power allocation scheme is presented. The analysis reveals that the proposed scheme makes the system more efficient in terms of throughput than equal power allocation scheme.