HTS-LB: Hypergraph tree search for learning branch

Mixed integer linear programming (MILP) is a fundamental combinatorial optimization problem with wide-ranging applications in resource-constrained scenarios. Recent studies have focused on using machine learning to imitate the decision-making process in MILP solving, often representing MILPs as bipartite graphs for learning branching policies. We analyze these studies and identify three key issues that need to be addressed for solving MILPs, namely scalability, richness of information, and branching accuracy. In this study, we propose a hypergraph tree search framework for learning branch (HTS-LB) to address the above issues. In HTS-LB, MILPs are first represented by hypergraphs to make them available for large-scale scenarios. Second, a hypergraph attention network (HAN) for branching policy encoding is constructed to map the hypergraph representation to the probability distributions of branching variables. In HAN, a dual multi-head attention mechanism is used to obtain more accurate information when nodes update their representations. Finally, we design a tree search gating mechanism to capture rich dynamic information for subsequent updates of the variable representation. Extensive experiments on NP-hard MILP problems and practical scenarios demonstrate that our model is effective and outperforms popular machine learning algorithms in terms of branching accuracy, branch and bound nodes, and the dual–primal gap. Additionally, the integration of HTS-LB into the SCIP solver shows its strong generalization performance in large-scale MILPs.