Dealing with the electromagnetic issue might bring a sort of discontinuous and nondifferentiable regions. Thus, it is of great interest to implement an appropriate optimisation approach, which can preserve the computational resources and come up with a global optimum. While not being trapped in local optima, as well as the feasibility to overcome some other matters such as nonlinear and phenomena of discontinuous with a large number of variables. Problems such as lengthy computation time, constraints put forward for antenna requirements and demand for large computer memory, are very common in the analysis due to the increased interests in tackling high-scale, more complex and higher-dimensional problems. On the other side, demands for even more accurate results always expand constantly. In the context of this statement, it is very important to find out how the recently developed optimization roles can contribute to the solution of the aforementioned problems. Thereafter, the key goals of this work are to model, study and design low profile antennas for wireless and mobile communications applications using optimization process over a computational electromagnetics numerical solution. The numerical solution method could be performed over one or hybrid methods subjective to the design antenna requirements and its environment. Firstly, the thesis presents the design and modelling concept of small uni-planer Ultra- Wideband antenna. The fitness functions and the geometrical antenna elements required for such design are considered. Two antennas are designed, implemented and measured. The computed and measured outcomes are found in reasonable agreement. Secondly, the work is also addressed on how the resonance modes of microstrip patches could be performed using the method of Moments. Results have been shown on how the modes could be adjusted using MoM. Finally, the design implications of balanced structure for mobile handsets covering LTE standards 698-748 MHz and 2500-2690 MHz are explored through using firefly algorithm method. The optimised balanced antenna exhibits reasonable matching performance including near-omnidirectional radiations over the dual desirable operating bands with reduced EMF, which leads to a great immunity improvement towards the hand-held. / General Secretariat of Education and Scientific Research Libya