Constraints Matrix Diffusion based Generative Neural Solver for Vehicle Routing Problems

2026-03-08

AI Summary

Existing attention-based neural solvers for the Vehicle Routing Problem (VRP) exhibit insufficient robustness under heterogeneous data distributions and suffer significant performance degradation when node features are highly similar or decision horizons are long. This work proposes a novel framework that, for the first time, integrates discrete noise graph diffusion into VRP solving by combining constraint-aware assignment matrix diffusion with an autoregressive neural solver. The approach dynamically generates and adaptively incorporates global structural constraints, effectively fusing local node features with global problem structure. Systematic evaluation across 378 combinatorial scenarios demonstrates its robustness, achieving state-of-the-art performance on multiple benchmark datasets—particularly outperforming existing heuristic and neural methods under complex heterogeneous distributions.

Technology Category

• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

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: Vertical and domain-specific search
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Vehicle Routing Problems
• Robustness
• Heterogeneous Distributions
• Attention-based Methods
• Long Decision Horizons

Innovation

• constraint matrix diffusion
• generative neural solver
• vehicle routing problems
• graph diffusion model
• autoregressive solver