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/完全组合问题的神经网络方法是一个具有挑战性的研究方向，其目标在于超越经典近似算法。该领域的长期目标是通过从训练数据中学习生成更优解，从而超越针对NP难/完全问题人工设计的启发式方法。当前基于神经网络的组合优化问题解决方法往往忽视了问题固有的"算法"本质。相比之下，针对组合优化问题（如旅行商问题）设计的启发式方法，通常会充分利用既有的成熟算法，例如寻找最小生成树的算法。本文提出利用神经算法推理的最新进展来改进组合优化问题的学习效果。具体而言，我们建议在组合优化实例上训练神经网络模型之前，先针对相关算法对其进行预训练。结果表明，采用这种学习框架后，我们相比未使用算法信息的深度学习模型获得了更优的性能表现。