In this paper, a novel hybrid algorithm on beam pattern synthesis of sparse arrays is proposed, which aims at minimizing the peak sidelobe level (PSLL). Sparse arrays can provide higher spatial resolution and relatively lower sidelobe than general arrays, but it is necessary to solve the multi-constraint problem of nonconvex nonlinear. Thus, we propose a Convex Improved Genetic Algorithm (CIGA) that can adjust the positions and the excitation coefficients of arrays to achieve the minimum PSLL. The CIGA is an effective two-step approach to the synthesis of sparse array. Firstly, Improved Genetic Algorithm is proposed, which is suitable for beam pattern synthesis of sparse arrays. The Improved Genetic Algorithm is adopted to adjust the positions of arrays to achieve the local optimum PSLL, and then convex optimization method is used to calculate the excitation coefficients in expectation of reaching the minimum PSLL. Simulation results show that the PSLL obtained by CIGA is about 5dB better than the published methods in sparse linear arrays and prove that the CIGA is superior to the published methods.
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