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This paper proposes a modified real genetic algorithm (MGA) for the synthesis of sparse linear arrays and presents the basic steps of the MGA in detail. The designing requirements of the shaped-beam patterns are satisfied by using the MGA to optimize the position and excitation of the elements under the given precondition of the number of elements, aperture and minimum element spacing. The finally obtained low peak side-lobe level (PSLL) and shaped-beam radiation pattern show that the efficiency and the robustness of the proposed algorithm are improved. Additionally, this paper presents the optimized element coordinates and excitations of a sparse linear antenna array with 24 elements in the table.