Towards Efficient Constraint Handling in Neural Solvers for Routing Problems

2026-02-19 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, extended

Summary

The paper introduces Construct-and-Refine (CaR), a novel neural framework designed for efficient constraint handling in complex Vehicle Routing Problems (VRPs). Traditional neural solvers often struggle with hard constraints due to inefficient feasibility masking or implicit feasibility awareness. CaR addresses this by integrating a neural construction module with a lightweight neural improvement module through an end-to-end joint training framework. This approach guides the construction module to generate diverse, high-quality solutions suitable for rapid refinement, requiring only about 10 steps compared to 5,000 steps in prior work. CaR also features a construction-improvement-shared representation, enabling knowledge sharing across paradigms, particularly in complex constrained scenarios like Traveling Salesman Problem with Time Windows (TSPTW) and Capacitated VRP with Backhaul, Duration, and Time-Window constraints (CVRPBLTW). Experimental results demonstrate that CaR achieves superior feasibility, solution quality, and efficiency against both classical and state-of-the-art neural solvers, including LKH-3 and OR-Tools.

Key takeaway

For research scientists developing neural solvers for complex Vehicle Routing Problems, CaR offers a robust framework to overcome limitations of traditional constraint handling. You should consider implementing CaR's joint training of construction and lightweight refinement, coupled with shared representations, to achieve superior feasibility, solution quality, and efficiency, especially for hard-constrained problems like TSPTW and CVRPBLTW. This approach can significantly reduce inference time while improving solution validity and optimality.

Key insights

CaR efficiently handles complex VRP constraints by jointly training construction and lightweight refinement modules with shared representations.

Principles

• Explicit feasibility refinement is crucial for hard VRP constraints.
• Joint training of construction and refinement enhances efficiency.
• Shared representations improve generalization in complex scenarios.

Method

CaR employs an end-to-end joint training framework, optimizing construction and refinement simultaneously. It uses a shared 6-layer Transformer encoder and tailored decoders, with a Lagrangian relaxation for constraint penalization.

In practice

• Use CaR for VRPs where feasibility masking is intractable.
• Apply CaR to multi-constraint VRPs for improved performance.
• Leverage shared encoders for better generalization in complex problems.

Topics

• Neural Combinatorial Optimization
• Vehicle Routing Problems
• Constraint Handling
• Feasibility Refinement
• Shared Representation Learning

Code references

• jieyibi/CaR-constraint

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.