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Recently, Transformer has become a prevailing deep architecture for solvingvehicle routing problems (VRPs). However, it is less effective in learningimprovement models for VRP because its positional encoding (PE) method is notsuitable in representing VRP solutions. This paper presents a novel Dual-AspectCollaborative Transformer (DACT) to learn embeddings for the node andpositional features separately, instead of fusing them together as done inexisting ones, so as to avoid potential noises and incompatible correlations.Moreover, the positional features are embedded through a novel cyclicpositional encoding (CPE) method to allow Transformer to effectively capturethe circularity and symmetry of VRP solutions (i.e., cyclic sequences). Wetrain DACT using Proximal Policy Optimization and design a curriculum learningstrategy for better sample efficiency. We apply DACT to solve the travelingsalesman problem (TSP) and capacitated vehicle routing problem (CVRP). Resultsshow that our DACT outperforms existing Transformer based improvement models,and exhibits much better generalization performance across different problemsizes on synthetic and benchmark instances, respectively.

Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformer