Neural Improvement Heuristics for Graph Combinatorial Optimization Problems

In recent years, methods based on deep neural networks, and especially Neural Improvement (NI) models, have led to a revolution in the field of combinatorial optimization. Given an instance of a graph-based problem and a candidate solution, they are able to propose a modification rule that improves its quality. However, existing NI approaches only consider node features and node-wise positional encodings to extract the instance and solution information, respectively. Thus, they are not suitable for problems where the essential information is encoded in the edges. In this paper, we present a NI model to solve graph-based problems where the information is stored either in the nodes, in the edges, or in both of them. We incorporate the NI model as a building block of hill-climbing-based algorithms to efficiently guide the election of neighborhood operations considering the solution at that iteration. Conducted experiments show that the model is able to recommend neighborhood operations that are in the $99^{th}$ percentile for the Preference Ranking Problem. Moreover, when incorporated to hill-climbing algorithms, such as Iterated or Multi-start Local Search, the NI model systematically outperforms the conventional versions. Finally, we demonstrate the flexibility of the model by extending the application to two well-known problems: the Traveling Salesman Problem and the Graph Partitioning Problem.