发表机构
University of Alberta（阿尔伯塔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
EDISCO是首个具有精确E(2)不变生成分布的离散扩散模型，通过等变边得分网络和连续时间马尔可夫链，在TSP和CVRP上以更少数据超越现有方法，并具鲁棒性。
AI 中文摘要
欧几里得组合优化问题（ECOPs），如旅行商问题（TSP）和带容量约束的车辆路径问题（CVRP），在二维欧几里得群E(2)下具有内在对称性，包括旋转、反射和平移。现有的基于学习的方法，包括最近的基于扩散的方法，依赖数据增强或正则化来近似E(2)-等变性。本文提出了EDISCO，这是首个针对ECOPs的离散扩散模型，其生成分布在节点索引解上具有精确的E(2)-不变性。EDISCO引入了一个E(2)-等变边得分网络，结合了离散边变量上的分类连续时间马尔可夫链，精确的后验采样提供了高效的多步推理。这种设计赋予EDISCO局部几何归纳偏置：具有相同相对几何和组合上下文的边邻域，无论绝对位置或方向如何，都被一致地表示，使得学习比非等变方法更高效，推理更鲁棒。EDISCO在从100到10000个节点的合成TSP和从50到2000个客户的CVRP上，超越了之前基于学习的最先进求解器，同时仅使用33-50%的训练实例。仅在均匀合成数据上训练，EDISCO在空间分布偏移和CVRP约束紧密度偏移下也优于竞争性的基于学习的基线。代码可在以下网址获取：此https URL。
英文摘要
Euclidean combinatorial optimization problems (ECOPs), such as the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP), possess inherent symmetries under the two-dimensional Euclidean group E(2), including rotations, reflections, and translations. Existing learning-based methods, including recent diffusion-based methods, rely on data augmentation or regularization to approximate E(2)-equivariance. This paper presents EDISCO, the first discrete diffusion model for ECOPs with exact E(2)-invariant generative distributions over node-index solutions. EDISCO introduces an E(2)-equivariant edge-score network coupled with a categorical continuous-time Markov chain over discrete edge variables, and exact posterior sampling provides efficient multi-step inference. This design gives EDISCO a local geometric inductive bias: edge neighborhoods with the same relative geometry and combinatorial context are represented consistently regardless of absolute position or orientation, making learning more efficient and inference more robust than non-equivariant methods. EDISCO outperforms previous learning-based state-of-the-art solvers on synthetic TSP from 100 to 10000 nodes and CVRP from 50 to 2000 customers, while using only 33-50% of the training instances. Trained only on uniform synthetic data, EDISCO also outperforms competing learning-based baselines under spatial distribution shift and CVRP constraint-tightness shift. Code is available at https://github.com/ValleyC/EDISCO.
Comments45 pages, 8 figures, 18 tables, accepted to NeurIPS 2026
