Long Term Evolution (LTE) cellular networks are currently implemented in many countries at very high speed. Since manual cell planning is a time consuming process and subject to errors and inefficiency, there is a need for automated approaches to optimize coverage, capacity and quality of cellular networks in less amount of the time. This paper studies the application of branch and bound algorithms to solve the Antenna Placement Problem (APP) in Cellular networks. We are investigating the optimal placement of trans-receiver antennas in cellular systems. Our optimization framework imposes no constraints on the location of the antennas. Based on a branch and bound search technique, we adopt a formulation that is suitable for node placement optimization in various cellular network scenarios. We have shown that optimal placement of antennas within the coverage area can significantly improve the efficiency of wireless networks. We achieved the optimal placement topologies for different numbers of antennas and illustrate that the circular deployment is not optimum in all cases. Finally, we showed the optimal placement solutions through MATLAB simulations.