Collab-Solver: Collaborative Solving Policy Learning for Mixed-Integer Linear Programming

Abstract

Mixed-integer linear programming (MILP) has been a fundamental problem in combinatorial optimization. Conventional MILP solving mainly relies on carefully designed heuristics embedded in the branch-and-bound framework. Driven by the strong capabilities of neural networks, recent research is exploring the value of machine learning alongside conventional MILP solving. Although learning-based MILP methods have shown great promise, existing works typically learn policies for individual modules in MILP solvers in isolation, without considering their interdependence, which limits both solving efficiency and solution quality. To address this limitation, we propose Collab-Solver, a novel multi-agent-based policy learning framework for MILP that enables collaborative policy optimization for multiple modules. Specifically, we formulate the collaboration between cut selection and branching in MILP solving as a Stackelberg game. Under this formulation, we develop a two-phase learning paradigm to stabilize collaborative policy learning: the first phase performs data-communicated policy pretraining, and the second phase further orchestrates the policy learning for various modules. Extensive experiments on both synthetic and large-scale real-world MILP datasets demonstrate that the jointly learned policies significantly improve solving performance. Moreover, the policies learned by Collab-Solver have also demonstrated excellent generalization abilities across different instance sets.