Relevant combinatorial optimization problems (COPs) are often NP-hard. While they have been tackled mainly via handcrafted heuristics in the past, advances in neural networks have motivated the development of general methods to learn heuristics from data. Many approaches utilize a neural network to directly construct a solution, but are limited in further improving based on already constructed solutions at inference time. Our approach, Moco, learns a graph neural network that updates the solution construction procedure based on features extracted from the current search state. This meta training procedure targets the overall best solution found during the search procedure given information such as the search budget. This allows Moco to adapt to varying circumstances such as different computational budgets. Moco is a fully learnable meta optimizer that does not utilize any problem specific local search or decomposition. We test Moco on the Traveling Salesman Problem (TSP) and Maximum Independent Set (MIS) and show that it outperforms other approaches on MIS and is overall competitive on the TSP, especially outperforming related approaches, partially even if they use additional local search.

翻译：相关的组合优化问题（COPs）通常是NP难的。尽管过去主要依靠手工设计的启发式方法来解决这些问题，但神经网络的进展推动了从数据中学习启发式方法的通用方法的发展。许多方法利用神经网络直接构建解，但在推理时基于已构建的解进一步改进的能力有限。我们的方法Moco学习一个图神经网络，该网络根据从当前搜索状态提取的特征更新解的构建过程。这种元训练过程旨在利用搜索预算等信息，在搜索过程中找到整体最优解。这使得Moco能够适应不同的情况，例如不同的计算预算。Moco是一个完全可学习的元优化器，不利用任何特定问题的局部搜索或分解。我们在旅行商问题（TSP）和最大独立集（MIS）上测试了Moco，结果表明它在MIS上优于其他方法，在TSP上整体具有竞争力，尤其是优于相关方法，部分情况下甚至优于使用了额外局部搜索的方法。