arXiv:2605.19895cs.AI2026-05

用CNN识别解的结构模式,自动生成高效约束加速求解。

Streamlined Constraint Reasoning via CNN Pattern Recognition on Enumerated Solutions

论文配图:Streamlined Constraint Reasoning via CNN Pattern Recognition on Enumerated Solutions
图 1 · 摘自论文原文
  • 枚举可行解,用CNN对比学习识别结构模式
  • 在三个硬核问题上平均提速98%以上,最高达1103倍
  • 适合想自动化优化约束的推理系统研究者

约束求解实践中,从业者按风险等级分层应用技术:先使用标准强化(对称性破缺与隐含约束)保持可满足性,最后才启用不保真但能压缩搜索空间的流线化约束。现有自动化生成方法或搜索约束语法,或直接让大模型解析问题模型。本文提出新方法:枚举可行解,训练卷积神经网络(CNN)对比非解扰动样本以识别结构模式,并通过大模型将CNN的判别信号转化为候选MiniZinc流线化约束。该方法使大模型生成约束时基于实际解结构而非仅文本描述。我们在经过强化处理的基准模型上评估,发现流线化约束是性能提升的关键残差项。管道整体在强化后的船舱装载问题上实现98.8%的组合时间减少,在强化社交高尔夫问题上达98.6%,在黑洞问题上为89.4%;最优单个流线化约束分别带来932倍、356倍和1103倍的几何均值加速。发现的约束包括船舱装载的类别打包约束、社交高尔夫的超越强化归一化以及黑洞布局坐标边界。

原文摘要 · Abstract (English)

Constraint programming practitioners accelerate hard problems through a layered set of techniques applied in order of risk. Standard hardening (symmetry-breaking and implied constraints) is applied first and preserves satisfiability. Streamliner constraints, which restrict search to a structural sub-family of solutions, do not preserve satisfiability and are reserved as a final lever. Existing automated streamliner-synthesis approaches either search a constraint grammar or prompt a Large Language Model directly on the problem model. We propose a different approach: enumerate feasible solutions, train a Convolutional Neural Network contrastively against perturbed non-solutions to detect structural patterns, and translate the CNN's discriminative signal into candidate MiniZinc streamliners through LLM-driven synthesis. The CNN grounds the LLM's constraint generation in observed solution structure rather than model text alone. We evaluate on hardened benchmark models where streamliner discovery is the residual performance lever. Our pipeline achieves 98.8% portfolio time reduction on hardened Vessel Loading, 98.6% on hardened Social Golfers, and 89.4% on Black Hole, with best-single streamliners reaching geometric-mean speedups of 932x, 356x, and 1103x respectively. Discovered streamliners include class-based packing constraints on Vessel Loading, beyond-hardening canonicalisations on Social Golfers, and layout-coordinate bounds on Black Hole.

约束求解CNN自动化加速

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