Recent advances in graph neural network architectures and increased computation power have revolutionized the field of combinatorial optimization (CO). Among the proposed models for CO problems, Neural Improvement (NI) models have been particularly successful. However, existing NI approaches are limited in their applicability to problems where crucial information is encoded in the edges, as they only consider node features and node-wise positional encodings. To overcome this limitation, we introduce a novel NI model capable of handling graph-based problems where information is encoded in the nodes, edges, or both. The presented model serves as a fundamental component for hill-climbing-based algorithms that guide the selection of neighborhood operations for each iteration. Conducted experiments demonstrate that the proposed model can recommend neighborhood operations that outperform conventional versions for the Preference Ranking Problem with a performance in the 99th percentile. We also extend the proposal to two well-known problems: the Traveling Salesman Problem and the Graph Partitioning Problem, recommending operations in the 98th and 97th percentile, respectively.

翻译：近年来，图神经网络架构的进步与计算能力的提升彻底改变了组合优化领域。在针对组合优化问题的各类模型中，神经改进模型尤为成功。然而，现有神经改进方法的适用性受到限制，因其仅考虑节点特征和节点级位置编码，而无法处理关键信息编码在边上的问题。为突破这一局限，我们提出了一种新型神经改进模型，能够处理信息编码在节点、边或两者兼有的图结构问题。该模型作为基于爬山法的算法核心组件，用于指导每次迭代中邻域操作的选择。实验表明，对于偏好排序问题，所提模型推荐的邻域操作性能优于传统方法，达到第99百分位水平。我们还将该方法扩展到两个经典问题——旅行商问题和图分割问题，分别实现了第98和第97百分位的操作推荐性能。