Planning in Branch-and-Bound: Model-Based Reinforcement Learning for Exact Combinatorial Optimization

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AAAI 2026

January 24, 2026

Singapore, Singapore

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Mixed-Integer Linear Programming (MILP) lies at the core of many real-world combinatorial optimization (CO) problems, traditionally solved by branch-and-bound (B\&B). A key driver influencing B\&B solvers efficiency is the variable selection heuristic that guides branching decisions. Looking to move beyond static, hand-crafted heuristics, recent work has explored adapting traditional reinforcement learning (RL) algorithms to the B\&B setting, aiming to learn branching strategies tailored to specific MILP distributions. In parallel, RL agents have achieved remarkable success in board games, a very specific type of combinatorial problems, by leveraging environment simulators to plan via Monte Carlo Tree Search (MCTS). Building on these developments, we introduce Plan-and-Branch-and-Bound (PlanB\&B), a model-based reinforcement learning (MBRL) agent that leverages a learned internal model of the B\&B dynamics to discover improved branching strategies. Computational experiments empirically validate our approach, with our MBRL branching agent outperforming previous state-of-the-art RL methods across four standard MILP benchmarks.

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