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/完全组合优化问题的神经网络方法是一个具有挑战性的研究领域，旨在超越经典近似算法。其长期目标是通过从训练数据中学习生成更优解，在NP难/完全问题上超越人工设计的启发式算法。当前基于神经网络的组合优化问题求解方法常忽略问题固有的"算法本质"。与此相反，针对组合优化问题（如旅行商问题）设计的启发式算法往往借助成熟算法（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网络模型，再在组合优化实例上训练。实验结果表明，采用这种学习框架后，相比未融入算法信息的深度学习模型，我们取得了更优的性能表现。