Rotationally symmetric sparse circular arrays are synthesized under multiple constraints. By combining the modified differential evolution algorithm based on the harmony search (in short HSDE) with the vector mapping (VM) method, a hybrid algorithm, called VM-HSDE, is proposed for synthesizing sparse circular arrays with low sidelobe levels. Due to the array's specific geometry, the number of optimization variables is reduced, and the constrained optimization problem is simplified. Moreover, infeasible solutions are avoided, and the problem is effectively solved by the VM-HSDE algorithm. Finally, three pattern optimization results verify the effectiveness and reliability of the VM-HSDE algorithm.
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