A hybrid algorithm based on the invasive weed optimization (IWO) and the convex optimization (CVX) is proposed for minimizing the peak sidelobe level (PSLL) of linear array with focused and/or shaped beam pattern. In this approach, IWO is adopted to produce the array (described by element positions), and CVX is used to determine the excitations for each produced array. Then the corresponding PSLL acts as the fitness function of IWO to find the optimal positions which lead to the minimum PSLL. Numerical experiments are conducted to validate the effectiveness and robustness of the proposed hybrid approach. Compared with other techniques, a lower PSLL can be achieved with a fixed main beam width or with a shaped main beam using this hybrid algorithm. Moreover, this method can easily cope with some constraints on the aperture, such as the minimum element spacing and the total number of elements.
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