Constraints Matrix Diffusion based Generative Neural Solver for Vehicle Routing Problems

TL;DR

This work proposes a novel fusion neural network framework that employs a discrete noise graph diffusion model to learn the underlying constraints of vehicle routing problems and generate a constraint assignment matrix, which is subsequently integrated adaptively into the feature representation learning and decision process of the autoregressive solver.

Abstract

Over the past decade, neural network solvers powered by generative artificial intelligence have garnered significant attention in the domain of vehicle routing problems (VRPs), owing to their exceptional computational efficiency and superior reasoning capabilities. In particular, autoregressive solvers integrated with reinforcement learning have emerged as a prominent trend. However, much of the existing work emphasizes large-scale generalization of neural approaches while neglecting the limited robustness of attention-based methods across heterogeneous distributions of problem parameters. Their improvements over heuristic search remain largely restricted to hand-curated, fixed-distribution benchmarks. Furthermore, these architectures tend to degrade significantly when node representations are highly similar or when tasks involve long decision horizons. To address the aforementioned limitations, we propose a novel fusion neural network framework that employs a discrete noise graph diffusion model to learn the underlying constraints of vehicle routing problems and generate a constraint assignment matrix. This matrix is subsequently integrated adaptively into the feature representation learning and decision process of the autoregressive solver, serving as a graph structure mask that facilitates the formation of solutions characterized by both global vision and local feature integration. To the best of our knowledge, this work represents the first comprehensive experimental investigation of neural network model solvers across a 378-combinatorial space spanning four distinct dimensions within the CVRPlib public dataset. Extensive experimental evaluations demonstrate that our proposed fusion model effectively captures and leverages problem constraints, achieving state-of-the-art performance across multiple benchmark datasets.

Figures (9)

• Figure 1: Demonstrating the effects of data augmentation, the numerical value within the rectangle above each scatter point indicates the origin node index, while the value in parentheses represents the node demand. The black dashed lines in the first row of the four symmetric transformation subgraphs correspond to the symmetry axes.
• Figure 2: Constraint matrix mapping from augmented optimal solution instances
• Figure 3: Constraint-Matrix Generation and Forward Corruption/Reverse Denoising under a Discrete-Noise Diffusion
• Figure 4: Overall architecture. (a) Graph‑diffusion prior with two submodules: (1) data augmentation and (2) constraint‑matrix generation. (b) Mask‑guided encoder: a pretrained multi‑layer GAT extracts global representations, and a trainable masked GAT extracts local representations; their fusion yields node embeddings. (c) Dual‑pointer decoder: two attention pointers fuse global and local decisions, conditioned on the global graph embedding and the current system state.
• Figure 5: Performance gaps over 10,000 XML100 instances. A 0.5% gap defines significance: red denotes our model outperforming LEHD, and blue denotes POMO outperforming ours.