发表机构
cortAIx Labs, Thales Deutschland; University of Osnabrück（泰雷兹德国cortAIx实验室; 奥斯纳布吕克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨硬信息视野下的组合优化，证明GNN在视野内可复现贪心算法，且信息视野比模型容量更关键，实验显示3层GATv2在MPR选择上优于贪心。
AI 中文摘要
神经组合优化通常假设一个读取整个实例的集中式求解器。我们研究相反的情况：在硬信息视野下的组合优化，其中每个节点仅看到其k跳邻域，就对其全局解决方案的份额做出承诺，并且这些承诺必须组合成全局可行的解决方案。我们将其形式化为局部集合覆盖，并在加权多点中继（MPR）选择上实例化，这是优化链路状态路由协议版本2（OLSRv2）路由协议（RFC 7181）的NP难的2跳覆盖问题，其视野由协议强加，而非由建模者选择。我们证明两个结果。任何视野短一跳的确定性选择器要么无法覆盖，要么与最优解相差因子Δ；而在决策节点读出的L层图神经网络（GNN）恰好是L跳选择器，因此容量不能买回半径。相反，在视野内，深度为O(Δ)的GNN重现RFC 7181覆盖贪心算法，宽度为O(c_max Δ)时重现其度量感知加权版本，在两种情况下都继承(1+lnΔ_2)近似比。实验上，一个3层GATv2，带有覆盖完成解码器，从CP-SAT最优解行为克隆，达到成本/最优=1.030±0.001，而贪心为1.138，在100%覆盖下缩小了79.1%的差距。将同一学习器限制为一跳，在相同实例、相同解码器和演示下，其性能降至1.344，远差于贪心。两项迁移检查针对真实网络。OLSRv2未修改的选择代码在200/200个单位成本实例上与我们的基数贪心匹配，在40,308个真实营级机动性实例上，冻结模型在完全覆盖下缩小了48%的差距。信息视野，而非模型容量，是最重要的变量。
英文摘要
Neural combinatorial optimization typically assumes a centralized solver that reads the whole instance. We study the opposite: combinatorial optimization under a hard information horizon, where every node commits to its share of a global solution seeing only its $k$-hop neighborhood, and those commitments must compose into a globally feasible solution. We formalize this as local set cover and instantiate it on weighted multipoint relay (MPR) selection, the NP-hard 2-hop covering problem of the Optimized Link State Routing Protocol version 2 (OLSRv2) routing protocol (RFC~7181), whose horizon is imposed by the protocol, not chosen by the modeler. We prove two results. Any deterministic selector whose horizon is one hop short must either fail coverage or land a factor $Δ$ from optimal, and an $L$-layer graph neural network (GNN) read out at the deciding node is exactly an $L$-hop selector, so capacity cannot buy back radius. Conversely, at the horizon a \ac{GNN} of depth $O(Δ)$ reproduces the RFC~7181 covering greedy, and at width $O(c_{\max}Δ)$ its metric-aware weighted analogue, inheriting the $(1+\lnΔ_2)$-approximation in both cases. Empirically, a 3-layer \ac{GATv2} with a coverage-completing decoder, behavior-cloned from the CP-SAT optimum, reaches $\text{cost}/\text{opt}=1.030\pm0.001$ against greedy's $1.138$, closing $79.1\%$ of the gap at $100\%$ coverage. Restricting the same learner to one hop, on identical instances with the same decoder and demonstrations, collapses it to $1.344$, far worse than greedy. Two transfer checks target real-world networks. OLSRv2's unmodified selection code matches our cardinality greedy on $200/200$ unit-cost instances, and on $40{,}308$ instances of real battalion mobility the frozen model closes $48\%$ of the gap at full coverage. The information horizon, not the model capacity, is the most significant variable.
