Multi-beam antennas can be used for the sectorization of 360° azimuthal coverage. One of the suitable realizations, where four monopole antennas are placed at the corners of a square, is known as the “Monopole Four-Square Array Antenna”. This thesis presents the optimization problem for this array antenna. First, it is considered that this array is mounted on an infinite ground plane. With view to practical applications, optimization criteria are defined and a genetic algorithm is used to find the optimized values for the array variables. Next, the “Monopole Four-Square Array Antenna” is considered to be mounted on a finite ground plane (chassis). It is seen that all performance parameters of this array are changed and deteriorated due to the excitation of chassis modes, which couple to and between the monopole antennas and which radiate and produce diffraction at the edges of the ground plane. It is found, that the performance is strongly affected by the size of each antenna, the position of each antenna on the chassis as well as the size and shape of the chassis. A new optimization problem considering both the parameters of array and chassis dimensions is defined and the optimal values are found using the method of genetic algorithm. To model the chassis effects, in this step, the Theory of Characteristic Modes for the chassis is introduced and the effect of chassis modes on the radiation patterns and S-parameters are discussed. In order to allow the efficient use of the calculation-extensive chassis modes in our optimization, an Artificial Neural Network (ANN) is set-up to represent the effects of the chassis modes and the ANN is trained using results from an EM-field simulator. In a further step, the remaining mutual coupling between the elements of the monopole array is tackled. Using another ANN, a Decoupling and Matching Network (DMN) is designed for the “Monopole Four-Square Array Antenna” which considerably improves the radiation pattern. The final “full-degree” optimization problem considers all parameters of the monopole array on a small chassis as well as the variables in the DMN. It is shown that by changing the values of the weighting coefficients in the optimization problem, the resulting antenna design can be matched to priorities set by practical applications.