Combinatorial optimization (CO) is the fundamental problem at the intersection of computer science, applied mathematics, etc. The inherent hardness in CO problems brings up challenge for solving CO exactly, making deep-neural-network-based solvers a research frontier. In this paper, we design a family of non-autoregressive neural networks to solve CO problems under positive linear constraints with the following merits. First, the positive linear constraint covers a wide range of CO problems, indicating that our approach breaks the generality bottleneck of existing non-autoregressive networks. Second, compared to existing autoregressive neural network solvers, our non-autoregressive networks have the advantages of higher efficiency and preserving permutation invariance. Third, our offline unsupervised learning has lower demand on high-quality labels, getting rid of the demand of optimal labels in supervised learning. Fourth, our online differentiable search method significantly improves the generalizability of our neural network solver to unseen problems. We validate the effectiveness of this framework in solving representative CO problems including facility location, max-set covering, and traveling salesman problem. Our non-autoregressive neural solvers are competitive to and can be even superior to state-of-the-art solvers such as SCIP and Gurobi, especially when both efficiency and efficacy are considered. Code is available at https://github.com/Thinklab-SJTU/NAR-CO-Solver

本研究针对组合优化（CO）问题的解决难度，提出了一种新的非自回归神经网络框架，能够处理广泛的正线性约束下的CO问题。该方法在提高效率和保持排列不变性方面优于现有的自回归神经网络，并且通过离线无监督学习减少了对高质量标签的依赖。最终验证表明，该框架在解决设施选址、最大集合覆盖和旅行商问题等典型CO问题时，表现出与最先进求解器竞争甚至优越的性能。

通过非自回归神经网络解决正线性约束下的组合优化问题