Neural Improvement Heuristics for Graph Combinatorial Optimization Problems

Recent advances in graph neural network (GNN) 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, the 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 nodewise positional encodings (PEs). 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 (PRP) with a performance in the
$99$
th percentile. We also extend the proposal to two well-known problems: the traveling salesman problem and the graph partitioning problem (GPP), recommending operations in the
$98$
th and
$97$
th percentile, respectively.