Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without needing expert knowledge. However, these solvers exhibit significant performance degradation when applied to large-scale CO problems. Recently, two-stage neural methods with divide-and-conquer strategies have shown superiorities in addressing large-scale CO problems. Nevertheless, the efficiency of these methods highly relies on problem-specific heuristics in either the divide or the conquer procedure, which limits their applicability to general CO problems. Moreover, these methods employ separate training schemes and ignore the interdependencies between the dividing and conquering strategies, which often leads to sub-optimal solutions. To tackle these drawbacks, this article develops a unified neural divide-and-conquer framework (i.e., UDC) for solving general large-scale CO problems. UDC offers a Divide-Conquer-Reunion (DCR) training method to eliminate the negative impact of a sub-optimal dividing policy. Employing a high-efficiency Graph Neural Network (GNN) for global dividing and a fixed-length sub-path solver for conquering sub-problems, the proposed UDC framework demonstrates extensive applicability, achieving superior performance in 10 representative large-scale CO problems.

翻译：单阶段神经组合优化求解器无需专家知识即可在各种小规模组合优化（CO）问题上取得接近最优的结果。然而，当应用于大规模CO问题时，这些求解器表现出显著的性能下降。最近，采用分治策略的两阶段神经方法在解决大规模CO问题上显示出优越性。然而，这些方法的效率高度依赖于分治过程中针对特定问题的启发式规则，这限制了它们对一般CO问题的适用性。此外，这些方法采用独立的训练方案，忽略了划分策略与求解策略之间的相互依赖关系，这通常会导致次优解。为了解决这些缺点，本文开发了一种用于求解一般大规模CO问题的统一神经分治框架（即UDC）。UDC提供了一种"划分-求解-重组"（DCR）训练方法，以消除次优划分策略的负面影响。所提出的UDC框架采用高效的图神经网络（GNN）进行全局划分，并采用固定长度子路径求解器来求解子问题，展现了广泛的适用性，在10个代表性的大规模CO问题上取得了优越的性能。