Solving NP-hard/complete combinatorial problems with neural networks is a challenging research area that aims to surpass classical approximate algorithms. The long-term objective is to outperform hand-designed heuristics for NP-hard/complete problems by learning to generate superior solutions solely from training data. Current neural-based methods for solving CO problems often overlook the inherent "algorithmic" nature of the problems. In contrast, heuristics designed for CO problems, e.g. TSP, frequently leverage well-established algorithms, such as those for finding the minimum spanning tree. In this paper, we propose leveraging recent advancements in neural algorithmic reasoning to improve the learning of CO problems. Specifically, we suggest pre-training our neural model on relevant algorithms before training it on CO instances. Our results demonstrate that by using this learning setup, we achieve superior performance compared to non-algorithmically informed deep learning models.

翻译：解决NP难/完备组合问题，通过神经网络突破传统近似算法的局限，是当前极具挑战性的研究方向。其长期目标在于通过学习从训练数据中自主生成更优解，从而超越人工设计的NP难/完备问题启发式算法。现有基于神经网络的组合优化方法往往忽视问题固有的"算法化"本质。而针对组合优化问题（如旅行商问题）设计的启发式算法，则常依托成熟算法（如最小生成树算法）进行优化。本文提出利用神经算法推理领域的最新进展来改进组合优化问题的学习过程。具体而言，我们建议先在相关算法上预训练神经模型，再将其应用于组合优化实例的训练。实验结果表明，采用该学习框架后，我们的模型性能显著优于未融合算法信息的深度学习模型。