VoxelOpt is a discrete optimization-based DIR framework that combines the advantages of learning-based and iterative-based deformational image registration (DIR) methods to improve the trade-off between accuracy and runtime. Unlike existing methods, VoxelOpt uses displacement entropy of the local cost volume to measure displacement signal intensity at each voxel. Key features include voxel-wise adaptive message passing, computational complexity reduction using multi-level image pyramids, and feature extraction using a pre-trained segmentation model. In abdominal CT registration experiments, VoxelOpt outperforms existing state-of-the-art iterative-based methods in both efficiency and accuracy, and achieves comparable performance to state-of-the-art learning-based methods trained under label supervision.