# Optimization Design for Sparse Planar Array in Satellite Communications
## 4 Sparse Planar Array Optimization Design Method
### Intelligent Optimization Methods
#### 4.2.4 Sparse Array Optimization Design Based on Hybrid Algorithm  
In the field of sparse planar array design, there are often certain drawbacks and limitations due to the use of a single method. Therefore, in order to improve the efficiency of the algorithm and overcome the shortcomings of a single method in solving the optimization design problem of sparse arrays, a major research trend focuses on the design of sparse planar arrays using comprehensive hybrid methods. Commonly used hybrid methods can be divided into three categories, namely, the mixing of intelligent optimization methods and local optimization methods, the mixing of intelligent optimization methods and analysis methods, and the mixing of local optimization methods and analysis methods. In order to solve the problem that only the intelligent optimization method is used to search for a large sparse area matrix synthesis and easily falls into the local solution, combining the global optimization method and the analysis method can combine the advantages of the two, which not only ensures a fast calculation speed, but also prevents the algorithm from easily falling into local optimization. In order to prevent the IFT method from falling into the local minimum [93], an algorithm (IWO-IFT) was proposed to mix the invasive weed algorithm with the iterative Fourier transform method, which uses the IFT method to generate weeds, and performs IWO disturbance on the weeds by changing the order of the excitation amplitude of the array elements to obtain better weeds and lower peak sidelobe levels. The authors investigated the synthesized outcomes of circular arrays in [93], where each array possessed different array apertures with varying diameters \(25\lambda\), \(50\lambda\), and \(100\lambda\). The results of their inquiry proved to be nothing short of intriguing. Specifically, when the filling factor of the array was set at an alluring 40%, the _PSLL_ obtained through the IWO-IFT methodology exhibited remarkable discrepancies compared to the _PSLL_ accomplished using the IFT approach. To be exact, the _PSLL_ manifested through the IWO-IFT method was 0.73 dB lower for the \(25\lambda\) diameter aperture, 0.66 dB lower for the \(50\lambda\) diameter aperture, and 2.60 dB lower for the \(100\lambda\) diameter aperture in comparison to the _PSLL_ acquired from the IFT methodology. Nevertheless, despite these substantial variations, the directivity of the synthesized consequences via both the IWO-IFT strategy and the IFT approach was not found to possess any significant differences. The authors of [94] used the IFT method to form a sparse plane array first; then, the DE algorithm was used to optimize the position, and a two-step IFT-DE method was proposed by combining the iterative Fourier transform method and the differential evolution method to reduce the number of elements and the peak sidelobe level and accelerate the convergence speed of the algorithm. The authors explored the synthesized outcomes of rectangular arrays in [94]. Each array possessed diverse aperture dimensions with 36, 64, and 100 array elements, and the fill factor of the array was set at 50%. Upon rigorous analysis, the _PSLL_ manifested through the IFT-DE technique was lower than the _PSLL_ acquired from the IFT approach, exhibiting noteworthy differences. To be exact, the _PSLL_ portrayed via the IFT-DE method was 2.87 dB lower for the 36 elements, 2.91 dB lower for the 64 elements, and 2.28 dB lower for the 100 elements in comparison to the _PSLL_ achieved through the IFT methodology. Aiming at the optimization problem of rotationally symmetric sparse circular arrays [95], a VM-HSDE method combining the differential evolution method (HSDE) and vector mapping (VM) method based on the harmonic search was proposed to reduce the peak sidelobe level and the number of elements, as well as obtain a faster convergence speed.