An experimental study on local and global optima of linear antenna array synthesis by using the sequential least squares programming

Antenna array syntheses are usually nonlinear optimization problems with many local optima and constraints. A mathematical optimizer is limited to solving the synthesis problems in case that it might get trapped in a very poor local optimum. To address how poor the local optima with the synthesis problems, an experimental study is done on the local and the global optima of array syntheses by using the sequential least squares programming (SLSQP), which is a fast mathematical optimizer to search a local optimum. The experimental study show that the patterns of local optima are very close to the global optimal pattern in the case of equally spaced array, while in the case of unequally spaced array, the local and global optimal patterns are likely much different. The SLSQP algorithm is consequently recommended to quickly solve the synthesis problem in the case of equally spaced array. For the case of unequally spaced array, a DE-SLSQP hybrid algorithm is proposed to balance the global search and the quick convergence.