A high-directivity optimization technique for irregular arrays combined with maximum entropy model is presented. First, the major cause of the reduction in directivities of irregular arrays has been analyzed, namely, the so-called relative wave path difference. The larger size of subarrays and the wider scanning angle will inevitably enlarge relative wave path differences, thus resulting in the reduction of directivity. Aimed at this challenging issue, a mixed integer linear programming model is proposed to achieve high directivity and low sidelobe simultaneously for tetromino-shaped irregular arrays. An embedded structure algorithm has been applied to efficiently optimize a large-scale array with 2-D 60° maximum scanning angles. Moreover, representative numerical examples based on Vivaldi finite arrays are presented to demonstrate the effectiveness of the proposed approach. Numerical results show that the directivity of an optimized array by the proposed method outperforms those of the reported state-of-the-art methods by about 1 dB for the scan to 45°.