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. Previous works have designed a plethora of hard-coded heuristics to accomplish challenging MILP solving with domain knowledge. Driven by the high capability of neural networks, recent research is devoted to replacing manually designed heuristics with learned policies. Although learning-based MILP methods have shown great promise, existing worksindependentlytreatthepolicylearningineachmoduleofMILPsolvers without considering their interdependence, severely hurting the solving speed and quality. To address this issue, we propose a novel multi-agent-based policy learning framework for MILP (Collab-Solver), which can collaboratively optimize the policies for multiple modules. Specifically, we formulate the collaboration of cut selection and branching in MILP solving as a Stackelberg game. Under this formulation, we develop a two-phase learning paradigm to stabilize the collaborative policy learning, where the first phase achieves the data-communicated policy pretraining and the second phase further orchestrates the policy learning for various modules. The jointly learned policy significantly improves the solving performance on both synthetic and large-scale real-world MILP datasets. Moreover, the policies learned by Collab-Solver have also demonstrated excellent generalization abilities across different instance sets.