Less Is More -- On the Importance of Sparsification for Transformers and Graph Neural Networks for TSP

Abstract

Most of the recent studies tackling routing problems like the Traveling Salesman Problem (TSP) with machine learning use a transformer or Graph Neural Network (GNN) based encoder architecture. However, many of them apply these encoders naively by allowing them to aggregate information over the whole TSP instances. We, on the other hand, propose a data preprocessing method that allows the encoders to focus on the most relevant parts of the TSP instances only. In particular, we propose graph sparsification for TSP graph representations passed to GNNs and attention masking for TSP instances passed to transformers where the masks correspond to the adjacency matrices of the sparse TSP graph representations. Furthermore, we propose ensembles of different sparsification levels allowing models to focus on the most promising parts while also allowing information flow between all nodes of a TSP instance. In the experimental studies, we show that for GNNs appropriate sparsification and ensembles of different sparsification levels lead to substantial performance increases of the overall architecture. We also design a new, state-of-the-art transformer encoder with ensembles of attention masking. These transformers increase model performance from a gap of $0.16\%$ to $0.10\%$ for TSP instances of size 100 and from $0.02\%$ to $0.00\%$ for TSP instances of size 50.