Symmetry-preserving graph attention network to solve routing problems at multiple resolutions

Travelling Salesperson Problems (TSPs) and Vehicle Routing Problems (VRPs) have achieved reasonable improvement in accuracy and computation time with the adaptation of Machine Learning (ML) methods. However, none of the previous works completely respects the symmetries arising from TSPs and VRPs including rotation, translation, permutation, and scaling. In this work, we introduce the first-ever completely equivariant model and training to solve combinatorial problems. Furthermore, it is essential to capture the multiscale structure (i.e. from local to global information) of the input graph, especially for the cases of large and long-range graphs, while previous methods are limited to extracting only local information that can lead to a local or sub-optimal solution. To tackle the above limitation, we propose a Multiresolution scheme in combination with Equivariant Graph Attention network (mEGAT) architecture, which can learn the optimal route based on low-level and high-level graph resolutions in an efficient way. In particular, our approach constructs a hierarchy of coarse-graining graphs from the input graph, in which we try to solve the routing problems on simple low-level graphs first, then utilize that knowledge for the more complex high-level graphs. Experimentally, we have shown that our model outperforms existing baselines and proved that symmetry preservation and multiresolution are important recipes for solving combinatorial problems in a data-driven manner. Our source code is publicly available at https://github.com/HySonLab/Multires-NP-hard