This thesis presents novel algorithms to advance robotic object rearrangement, a critical task for autonomous systems in applications like warehouse automation and household assistance. Addressing challenges of high-dimensional planning, complex object interactions, and computational demands, our work integrates deep learning for interaction prediction, tree search for action sequencing, and parallelized computation for efficiency. Key contributions include the Deep Interaction Prediction Network (DIPN) for accurate push motion forecasting (over 90% accuracy), its synergistic integration with Monte Carlo Tree Search (MCTS) for effective non-prehensile object retrieval (100% completion in specific challenging scenarios), and the Parallel MCTS with Batched Simulations (PMBS) framework, which achieves substantial planning speed-up while maintaining or improving solution quality. The research further explores combining diverse manipulation primitives, validated extensively through simulated and real-world experiments.