Travelling Salesman Problem Goes Sparse With Graph Neural Networks
Keywords: Graph Neural Networks, Travelling Salesman Problem, Graph Sparsification
Abstract: Machine learning based approaches to solve the Travelling Salesman Problem (TSP) have achieved astonishing performance in the last years.
A large number of works proposing such approaches use a type of encoder in their underlying frameworks to learn vector representations of the given problem.
Since TSP can easily be interpreted as a graph theoretic problem, Graph Neural Networks (GNNs) have been a popular encoder architecture for this task.
However, most papers ignore that GNNs are not designed to operate on complete graph instances like the TSP.
We therefore propose two data preprocessing methods for GNNs to make the TSP instances sparse: a nearest neighbor based heuristic and a method based on minimum spanning tree called 1-Tree.
We show that making the underlying TSP instances sparse by deleting unpromising edges in the preprocessing step improves the performance of the overall learning framework while, at the same time, the runtime decreases.
In particular, the proposed method achieves an up to $\times 2 $ performance improvement w.r.t. the optimality gap and a decrease in runtime by 10\% during training and validation, when applied to GCNs.
For GATs, the improvements in regards of runtime and optimality gap are even bigger when sparsifying the data first: We report up to $\times 22$ improvements for the optimality gap while reducing the runtime by 50\%.
Primary Area: general machine learning (i.e., none of the above)
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Submission Number: 8240
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