Title: GDaT: Generalizable Density-aware Transformer for Solving the Traveling Salesman Problem
Primary area: applications to robotics, autonomy, planning
Keywords: Neural Combinatorial Optimization, Traveling Salesman Problem, Generalization, Density-Aware Modeling

Abstract: Recently, Neural Combinatorial Optimization (NCO) solvers have demonstrated significant potential in solving the Traveling Salesman Problem (TSP). However, existing NCO solvers typically model only the positional features of nodes, neglecting the differences in regional density among the unvisited nodes during route construction. This would hinder their generalization capability on tasks with unseen distributions and varying scales. To address this issue, we propose the $\textbf{G}$eneralizable $\textbf{D}$ensity-$\textbf{a}$ware $\textbf{T}$ransformer ($\textbf{GDaT}$) for solving the TSP. Specifically, GDaT mainly includes two modules: the multi-scale density extraction module and the density-aware attention module. The former generates multiple nested subgraphs of each unvisited node via the k-nearest neighbors strategy and estimates its densities using Gaussian kernels under each nested subgraph. These densities are then fused by a multi-layer perceptron for capturing multi-scale density features for each unvisited node during route construction. The latter leverages the extracted multi-scale density features to guide the attention-based modeling of positional features, enabling the model to perceive variations in problem scale and node distribution, thereby facilitating more accurate next-node selection under unseen distributions and varying scales. Experimental results on synthetic and real-world TSP datasets across diverse scales and distributions demonstrate that GDaT achieves superior generalization performance.

TL;DR: GDaT