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Branch-and-bound is a systematic enumerative method for combinatorial optimization, where the performance highly relies on the variable selection strategy. State-of-the-art handcrafted heuristic strategies suffer from relatively slow inference time for each selection, while the current machine learning methods require a significant amount of labeled data. We propose a new approach for solving the data labeling and inference latency issues in combinatorial optimization based on the use of the reinforcement learning (RL) paradigm. We use imitation learning to bootstrap an RL agent and then use Proximal Policy Optimization (PPO) to further explore global optimal actions. Then, a value network is used to run Monte-Carlo tree search (MCTS) to enhance the policy network. We evaluate the performance of our method on four different categories of combinatorial optimization problems and show that our approach performs strongly compared to the state-of-the-art machine learning and heuristics based methods.