Significant and continuous contributions related to 4G/5G cellular networks are still accelerating the investigation of the approaches that can boost the cell characteristics following the new aspirations of the users. The challenge of achieving sufficient coverage at the cell edge; represents a constant concern for both users and operators; in addition to ensuring a reasonable cost, are the most important search fields and in our scope of interest. As relay nodes can provide a solution, a scenario for a plan of relay nodes deployment at the cell edge is proposed, taking into account the interference due to the relay nodes. Since optimization algorithms are effective in terms of planning, an advanced hybrid particle swarm optimization and gravitational search algorithm (PSOGSA) is applied to the proposed scenario to detect the optimum solution. The optimum solution represents the optimum plan that attains the best coverage with the minimum cost. We submit cost analysis depends on three trails of construction cost, power and channel cost efficiency. To highlight that the optimal plan has been revealed, another recently developed optimization algorithm, a simplified adaptive bat algorithm based on frequency (FSABA) and a classic particle swarm optimization (PSO) algorithm are also applied to the suggested scenario. The obtained results are compared with the related findings of the PSOGSA. From the simulations, it is found that the PSOGSA achieves better performance than the other two algorithms with fruitful and promising results, and the optimal plan featuring great coverage at the cell edge and cost-saving is attained. INDEX TERMS A simplified adaptive bat algorithm based on frequency (FSABA), cell edge, particle swarm optimization and gravitational search algorithm (PSOGSA), relay nodes. RANA M. MOKHTAR received the B.Sc. degree in communication and electronics engineering from Suez Canal University, Port Said, Egypt, in 2009. She is currently pursuing the M.Sc. degree in communication engineering with the Faculty of Engineering. Her current research interests include cellular network planning, relaying network, and optimization techniques. DR. HEBA M. Abdel-Atty received the Ph.D. degree in Electronics and Communications Engineering from the Faculty of Engineering-Port Said University, Egypt 2012. She is working as an associate professor at the Electronics and Communications Engineering Department from 2018 until now. She is founder and counselor of IEEE in Port-Said University student branch. She is a member of IoT Egypt Forum She published a lot of papers in international journals and conferences and she is a reviewer at a lot of international journals. Her current