Cross-Problem Learning for Solving Vehicle Routing Problems

TL;DR

The paper addresses the inefficiency of training separate neural heuristics for each VRP variant by introducing cross-problem learning: a backbone Transformer pretrained on $TSP$ is modularized with problem-specific components to solve downstream VRPs. It analyzes two fine-tuning regimes—full fine-tuning and adapter-based fine-tuning (inside side and LoRA)—and demonstrates that full fine-tuning substantially outperforms training from scratch, while adapters offer comparable performance with far fewer trainable parameters. The approach yields strong cross-distribution transfer and versatility across VRP variants (e.g., OP, PCTSP, CVRP) and backbones (AM, POMO), suggesting practical gains in training efficiency and adaptability for neural heuristics in combinatorial optimization. The results highlight a scalable pathway to leverage shared structure across COPs while preserving task-specific capabilities, with potential extensions via neural architecture search and application to other COPs.

Abstract

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.

Figures (5)

• Figure 1: Modularization of Transformer for OP. Based on Transformer for TSP, we define modules for OP as three linear layers (in orange), which process problem-specific features (in dark green), i.e., depot coordinates, node prizes, total prize gathered at $t$-th step, respectively.
• Figure 2: Three types of adapter-based fine-tuning.
• Figure 3: Ablation study on fine-tuning methods and activation functions on PCTSP ($n=20, 50, 100$), respectively.
• Figure 4: Training curves with POMO on CVRP $(n=20, 50, 100)$, respectively.
• Figure 5: Cross-distribution application.