Neural Improvement Heuristics for Graph Combinatorial Optimization Problems
This addresses a bottleneck for researchers and practitioners in combinatorial optimization by enabling more effective neural improvement heuristics for graph-based problems, though it is incremental as it builds on existing NI approaches.
The paper tackled the limitation of Neural Improvement models in handling graph combinatorial optimization problems where information is encoded in edges by introducing a novel model that works with node, edge, or both features, resulting in performance in the 99th percentile for the Preference Ranking Problem and 98th and 97th percentiles for the Traveling Salesman and Graph Partitioning Problems.
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.