Neural Improvement Heuristics for Graph Combinatorial Optimization Problems

TL;DR

This paper introduces a versatile neural improvement model for graph combinatorial optimization that effectively handles edge and node information, outperforming traditional methods on several benchmark problems.

Contribution

The paper presents a novel neural improvement model capable of processing edge and node information, enhancing hill-climbing algorithms for various graph optimization problems.

Findings

Outperforms conventional methods on Preference Ranking Problem (99th percentile)

Achieves high performance on Traveling Salesman Problem (98th percentile)

Effective on Graph Partitioning Problem (97th percentile)

Abstract

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.