Distributed array radar (DAR) achieves large-aperture performance by combining small subarrays at different locations, which reducing system burden and manufacturing complexity while meeting low-cost and highresolution requirements in modern sensing. This paper proposes a 2-dimensional (2D) subarray optimization method for regular DARs with identical subarrays, aiming to minimize beamwidth (BW) and maximum sidelobe level (MSLL) under physical layout constraints. A directional expanded beam pattern (DiEBP) is introduced to reformulate non-analytic optimization objectives into a differentiable form, which enables gradient-descent updates within an alternating direction method of multipliers (ADMM) framework for this non-convex problem, with exponential smoothing and Monte Carlo tree search (MCTS) used for stabilization and initialization. Numerical experiments show that, compared with existing algorithms, the proposed method achieves about 10-15% narrower BW and 2 dB lower MSLL on average, along with a reduced Cramer-Rao Bound (CRB). Its effectiveness is further validated through DOA estimation and near-field imaging experiments.