## 1 Introduction  
Nowadays, aerospace technology and knowledge are part of everyday life in civil and military applications, being used, for example, at weather stations, aircrafts, weapon systems and satellite networks. In many of these applications, large and long range aerospace vehicles (e.g., rockets) are used for spatial surveys, air defense or satellite transportation. These features are found in launching centers with appropriate locations and specialized infrastructure to execute scientific and commercial activities [1; 2; 3; 4; 5; 6]. The activities of these centers can be divided into two areas: launching and tracking. The first one is responsible for preparing and integrating vehicles and their payloads, besides doing the launching itself from platforms. On the other hand, the tracking area obtains in real time the location of the launched vehicles and their likely point of impact, for monitoring and safety purposes. The main element of the tracking area is the Rocket Tracking System (RTS), which consists of radar sensors and is responsible for collecting and processing trajectory data. Parabolic reflector radars (PRRs) are usually used, due to their long range and high pointing accuracy [3; 7; 8]. However, there are Phased Arrays Radars (PARs), which consist of antenna arrays that allow electronic control of the radiation pattern, eliminating electromechanical devices [9; 10]. Therewith, new functionalities are offered, since it is now possible to determine the shape of the radiation pattern and to increase the scanning speed. At the same time, reliability is increased by removing electromechanical devices, maintenance is reduced and it is possible to continue tracking even when the sensor is degraded, that is, if there is damage to some of the array elements during tracking. Arrays directly used as transmitting and/or receiving antennas are well known in the control of the radiation pattern [11]. Transmitarrays are another option in which the arrays are set as lenses that shape the radiation pattern after being traversed by antenna-radiated waves [12]. In both cases, adjustment of the radiation pattern in real time requires electronic control with an active array, whose excitation can be adjusted in each element in order to regulate their radiation characteristics. The electronic control is dynamic, less susceptible to failures and has become more common with the increasing capacity and decreasing costs of digital processors. However, due to the large number of possible combinations for the excitation signals of the array elements, the electronic control should be carefully designed, aided by optimization methods. Thus, the PARs radiation pattern control for an RTS relies on three steps: specification, modeling and implementation. The specification is determined by requirements of the application and the implementation is determined by the available technology and associated costs, so that the greatest difficulty for the designer lies in the modeling step, due to an optimization problem with various boundary conditions imposed by the other steps. Such optimization is a difficult task, which demands the designer to have experience and time. In order to ease such process, flexible optimization tools have been used, which can be applied in different situations and requirements, at the expense of small adjustments. An example occurs in PARs, when they are initially designed for a particular applicationbut, over time, end up having new functions, so that it is necessary to redo the setting of the radiation pattern of a phased array (PA) already built, in order to meet new operating requirements. The aforementioned flexibility is achieved through the probabilistic optimization method of genetic algorithms (GAs), which allows converging to a set of optimal or nearly optimal solutions through the application of [PERSON]'s Theory of Evolution and fundamentals of genetics [13, 14, 15, 16, 17, 18, 19]. They manipulate the numerous restrictions imposed on projects in several areas, with a fairly generic method.