Graph-structured data is ubiquitous throughout natural and social sciences, and Graph Neural Networks (GNNs) have recently been shown to be effective at solving prediction and inference problems on graph data. In this paper, we propose and demonstrate that GNNs can be applied to solve Combinatorial Optimization (CO) problems. CO concerns optimizing a function over a discrete solution space that is often intractably large. To learn to solve CO problems, we formulate the optimization process as a sequential decision making problem, where the return is related to how close the candidate solution is to optimality. We use a GNN to learn a policy to iteratively build increasingly promising candidate solutions. We present preliminary evidence that GNNs trained through Q-Learning can solve CO problems with performance approaching state-of-the-art heuristic-based solvers, using only a fraction of the parameters and training time.

翻译：图结构化数据在自然科学和社会科学中无处不在，图神经网络（GNNs）近期已被证明在解决图数据的预测和推理问题上十分有效。本文提出并证明，GNNs可应用于求解组合优化（CO）问题。组合优化涉及在通常规模庞大到难以处理的离散解空间上优化某个函数。为学习求解组合优化问题，我们将优化过程建模为一个序列决策问题，其中回报与候选解接近最优解的程度相关。我们采用GNN来学习一种策略，以迭代方式构建出越来越有前景的候选解。初步证据表明，通过Q-Learning训练的GNNs能够以逼近最先进启发式求解器的性能求解组合优化问题，且仅需使用其参数和训练时间的一小部分。