In this paper, we develop a novel method to design the elements of an antenna array and their feed weights simultaneously. The method is based on formulating the design problem as a non-linear multi-objective optimization model that estimates the realized gain at certain angles as a function of the element-level port signals and impedances, and the array-level weights for the elements. This enables utilization of genetic algorithms to find optimal signals, impedances, and weights for given steering range requirements. As an example, an array consisting of multi-port antenna elements is simulated and modeled with its impedance and radiation matrices. These matrices are used in the calculation of realized gain with the model. The model is then applied as part of the method to find as wide scanning range for the array as possible. The antenna elements are designed such that the multi-port system can be reduced to a single feed with physically realizable matching components and a matching network. The array designed with the proposed method is also compared to a reference antenna array of the same size. Both the simulations and measurements verify that the method can provide substantial improvements in the scanning range as compared to the reference.