  Existing neural heuristics often train a deep architecture from scratch for
each specific vehicle routing problem (VRP), ignoring the transferable
knowledge across different VRP variants. This paper proposes the cross-problem
learning to assist heuristics training for different downstream VRP variants.
Particularly, we modularize neural architectures for complex VRPs into 1) the
backbone Transformer for tackling the travelling salesman problem (TSP), and 2)
the additional lightweight modules for processing problem-specific features in
complex VRPs. Accordingly, we propose to pre-train the backbone Transformer for
TSP, and then apply it in the process of fine-tuning the Transformer models for
each target VRP variant. On the one hand, we fully fine-tune the trained
backbone Transformer and problem-specific modules simultaneously. On the other
hand, we only fine-tune small adapter networks along with the modules, keeping
the backbone Transformer still. Extensive experiments on typical VRPs
substantiate that 1) the full fine-tuning achieves significantly better
performance than the one trained from scratch, and 2) the adapter-based
fine-tuning also delivers comparable performance while being notably
parameter-efficient. Furthermore, we empirically demonstrate the favorable
effect of our method in terms of cross-distribution application and
versatility.
