An Improved Snake Optimization Algorithm for Sparse Conformal Array Beamforming

This paper presents an improved snake optimization (ISO) algorithm for the beamforming design of sparse conformal arrays. To reduce the array element number and achieve the best sparse array configuration, the ISO algorithm employs the Sobol sequences for population initialization, resulting in enhanced uniformity and comprehensive coverage of the solution space as compared with the conventional random initialization method. Besides, the ISO algorithm employs the Cauchy mutation operator to escape local optimization and suppress the sidelobe levels of the conformal array. To increase array sparseness and optimize the radiation patterns, the ISO algorithm is further equipped with a nonlinear time-varying factor inspired by the whale algorithm and a modified flag control function, which improve its capacity for global exploration and local development. Simulation verification of a sparse cylindrically conformal array has demonstrated the superior performance of the proposed ISO algorithm over conventional optimization algorithms. It achieves a 50% array sparsity, and lower sidelobe levels as compared with the genetic algorithm (GA), particle swarm optimizer and traditional snake optimizer (SO). Moreover, it features notably faster convergence rates, outpacing the SO by 10% and GA by 46%, respectively. In addition, the sparse conformal array exhibits good radiation characteristics over a relatively wide beam scanning range of 54° in the azimuthal plane and 90° in the elevation plane, respectively.