Two-dimensional digital predistortion (2-D DPD) is one of the most commonly used approaches to linearize the concurrent dual-band radio frequency (RF) power amplifiers (PA). This paper explores the use of a hill-climbing optimization heuristic to determine the optimal structure for 2-D DPD. To improve convergence and reduce computation time, we propose a new parameterization for the 2-D DPD model. The proposed search criterion is based on the generalized information criterion, which represents the trade-off between the DPD linearization accuracy in both bands and the model complexity. A comparison against a compressed-sensing-based method is also made. The effectiveness of the proposed method is validated with two 20~MHz long-term-evolution (LTE) signals on two carriers with 100~MHz frequency separation.