Learning to Insert for Constructive Neural Vehicle Routing Solver

TL;DR

This paper introduces L2C-Insert, a novel insertion-based neural method for vehicle routing problems that improves solution quality by allowing flexible node insertions, outperforming traditional appending-based approaches.

Contribution

The paper proposes a new insertion-based framework for neural combinatorial optimization, including a model architecture, training scheme, and inference method, enhancing solution flexibility and quality.

Findings

L2C-Insert outperforms existing methods on TSP and CVRP instances.

The insertion paradigm improves solution quality over appending methods.

The approach is effective across various problem sizes.

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.