Learning to Insert for Constructive Neural Vehicle Routing Solver

2025-05-20

AI Summary

Existing learning-based constructive approaches for the Vehicle Routing Problem (VRP) suffer from suboptimal solution quality due to their reliance on fixed-order node insertion. To address this, we propose the first neural constructive solver based on a dynamic insertion paradigm: instead of appending unvisited nodes in a predetermined sequence, our method flexibly inserts each node into any feasible position within the current partial solution. We design a dedicated insertion-position prediction network that integrates self-attention with sequential modeling, and train it via reinforcement learning. During inference, we combine greedy decoding with post-hoc local search to further improve solution quality. Evaluated on both synthetic and real-world instances of the Traveling Salesman Problem (TSP) and Capacitated VRP (CVRP), our approach consistently outperforms state-of-the-art constructive neural combinatorial optimization (NCO) methods, achieving superior solution accuracy and significantly enhanced generalization across problem scales.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm that sequentially adds unvisited nodes to partial solutions, this rigid approach often leads to suboptimal results. To overcome this limitation, we explore the idea of insertion-based paradigm and propose Learning to Construct with Insertion-based Paradigm (L2C-Insert), a novel learning-based method for constructive NCO. Unlike traditional approaches, L2C-Insert builds solutions by strategically inserting unvisited nodes at any valid position in the current partial solution, which can significantly enhance the flexibility and solution quality. The proposed framework introduces three key components: a novel model architecture for precise insertion position prediction, an efficient training scheme for model optimization, and an advanced inference technique that fully exploits the insertion paradigm's flexibility. Extensive experiments on both synthetic and real-world instances of the Travelling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that L2C-Insert consistently achieves superior performance across various problem sizes.

Problem

• Improving flexibility in constructive NCO for VRPs
• Overcoming suboptimal results from appending-based methods
• Enhancing solution quality via strategic node insertion

Innovation

• Insertion-based paradigm enhances solution flexibility
• Novel model predicts precise insertion positions
• Advanced inference exploits insertion flexibility fully