将大规模邻域搜索的破坏步骤重塑为密集分割
Recasting the Destroy Step of Large Neighborhood Search as Dense Segmentation
- Supply Chain Tech Team Y, JD.com（京东供应链技术团队Y）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
FOVEA将大规模邻域搜索的变量选择视为密集分割，用小型U-Net在固定画布上预测分数，在更大规模上超越图编码器并降低原始积分。
AI中文摘要：
大规模邻域搜索通过在时间限制内释放选定的变量并修复由此产生的子问题来改进当前解。FOVEA将变量选择视为在固定的$128\ imes128$画布上的密集语义分割。一个小型U-Net读取十二个语义通道并预测单元分数，这些分数被解码为受固定变量预算约束的变量集。特定于家族的布局将搜索状态连接到画布，而一组网络权重服务于四个问题家族。FP32网络输入在不同实例规模下占用$786$\,kB。我们的分析限定了空间相干区域的约束耦合，为零可能改进的轮次提供了秩证书，并限定了在扩展器家族上可达到的耦合优势。在测试的家族和硬件上，FOVEA在$10^{4}$个变量时落后于最强的图编码器，并在约$1.5\ imes10^{4}$个变量时超越它；成本模型提供了近似的交叉估计。在更大规模下，图编码器基线超出设备内存，FOVEA相对于最佳可运行基线将原始积分降低了$12$到$16\%$。在扩展器家族上，FOVEA的表现与随机选择相当，耦合优势接近一。
英文摘要：
Large neighborhood search improves an incumbent by releasing selected variables and repairing the resulting subproblem under a time limit. FOVEA casts variable selection as dense semantic segmentation on a fixed $128\times128$ canvas. A small U-Net reads twelve semantic channels and predicts cell scores, which are decoded into a variable set subject to a fixed variable budget. Family-specific layouts connect the search state to the canvas, while one set of network weights serves four problem families. The FP32 network input occupies $786$\,kB across instance sizes. Our analysis bounds constraint coupling for spatially coherent regions, gives a rank certificate for rounds with zero possible improvement, and bounds the coupling advantage attainable on an expander family. On the tested families and hardware, FOVEA trails the strongest graph encoder at $10^{4}$ variables and overtakes it near $1.5\times10^{4}$; the cost model provides an approximate crossover estimate. At larger sizes, where the graph-encoder baselines exceed device memory, FOVEA reduces the primal integral by $12$ to $16\%$ relative to the best runnable baselines. On the expander family, FOVEA performs comparably to random selection, with a coupling advantage close to one.
