## 1 Introduction  
In both military and civilian applications, such as wireless communication systems, wireless power transmission systems, and radar systems, phased antenna arrays have various benefits including flexible beam scanning, high tracking accuracy, and widespread use [1]. Flexible beam-scanning antenna design is currently a hot topic of research because of the emergence of contemporary applications that need antenna arrays with variable scanning capabilities [2]. Automotive radars, weather observations, aviation surveillance [3], and satellite communication [4] are just a few of these numerous applications. In [5], a (\(2\times 3\)) phased antenna array is developed using a rectangular microstrip patch antenna on a FR-4 dielectric substrate. The elements are excited with constant amplitude and different phases to steer the beam within a scanning range of 49\({}^{\circ}\) (from \(-25^{\circ}\) to \(+24^{\circ}\)). In [6], four leaf-shaped bow-tie slot antennas in a linear array are used for beam scanning within a scanning range from 9\({}^{\circ}\) to 13\({}^{\circ}\). In [7], the two-element antenna array is fed through two transmission lines that are inclined at an angle from a common base line. The main beam can be directed from one antenna's normal to the other antenna's normal by adjustingthe excitations of the two antennas. The scan angle depended on changing the excitation coefficient in every scan angle or changing the tilt angle. In [8], a broadband reconfigurable antenna that can guide the main beam in three distinct directions has been introduced. Besides the main radiating patch, three parasitic tiny patches are included to control the main beam steering. Three beam-steering orientations of the radiation pattern are offered by PIN diode switching. In [9], the same concept of switched parasitic patches at 60 GHz for WLAN applications has been introduced for main beam steering. In [10], a sparse substrate integrated waveguide (SIW) slot antenna array has been introduced. The genetic algorithm was utilized to optimize the position of each element over the aperture of 4.5 \(\lambda_{o}\), where \(\lambda_{o}\) is the free space wavelength. The sparse array consists of array elements, phase shifters, and power dividers on a substrate integrated with an SIW. This sparse antenna can scan the beam in the range of \(\pm 15^{\circ}\). In [11], a millimeter-wave (MMW) multi-folded frequency-dependent progressive phase shifter based on a substrate integrated waveguide (SIW) has been introduced. By combining the antenna element and the phase shifter together, the array can achieve a wide scanning range from \(-18^{\circ}\) to \(32^{\circ}\). On the other hand, array thinning has been utilized for large array synthesis to achieve desired radiation patterns with a minimum array size and cost [12; 13; 14; 15; 16]. In [12], a numerical stochastic optimization technique that is known as multiagent genetic algorithm (MAGA) has been used for planar array thinning and synthesis for both low SLL and high directivity. In [13], discrete particle swarm optimization (DPSO) has been used for large array thinning. The peak side lobe level (PSLL) performance of the algorithm is verified through several representative examples, demonstrating its effectiveness and robustness. In [14], the binary genetic algorithm (BGA) has been used for thinned planar array design, where only the outer sub-planar array elements with small amplitude excitations are optimized for thinning. The BGA has been used to remove a number of useless antenna elements while keeping the inner sub-planar elements with high amplitude excitations unchanged. In [15], a GA in combination with array thinning and tapering techniques has been introduced to minimize the SLL. Thinning is applied to idle some elements of the array, and tapering is used to achieve a superior SLL. In [16], a hybrid approach combining difference sets (DS) and discrete Fourier transform (DFT) techniques has been introduced for the synthesis of thinned planar antenna arrays.