Transfer Learning with Graph Neural Networks for Cross-Scale Complexity in Vehicle Routing

Simão Pedro Cunha Godinho Fernandes; Rui Jorge Almeida; Susana Vieira; Frank Phillipson

doi:10.1007/978-3-032-29000-7_23

Transfer Learning with Graph Neural Networks for Cross-Scale Complexity in Vehicle Routing

Simão Pedro Cunha Godinho Fernandes
, Rui Jorge Almeida^*
, Susana Vieira
, Frank Phillipson

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

The vehicle routing problem is widely studied due to its practical relevance and inherent computational complexity. In many scenarios, such as real-time delivery requests, models trained on smaller instances must generalize to larger-scale problems, where cross-scale transitions induce distributional shifts in graph topology and increased combinatorial uncertainty. This paper addresses cross-scale generalization in the capacitated vehicle routing problem using a graph convolutional network within a transfer learning framework. The proposed approach increases the scale of training instances to enhance structural representations and incorporates a Non-negative Matrix Factorization step to extract low-rank latent structural priors from graph features. These priors are integrated into an attention-based message passing framework to generate a solution probability heatmap. Systematic experiments on randomly distributed instances show that these enhancements improve the model’s generalization capability.

Original language	English
Title of host publication	Information Processing and Management of Uncertainty in Knowledge-Based Systems
Subtitle of host publication	21st International Conference, IPMU 2026, Proceedings
Editors	Barbara Vantaggi, Giulianella Coletti, Thierry Denoeux, Anne Laurent, Davide Petturiti, Enrique Miranda, Jesús Medina, Bernadette Bouchon-Meunier, Ronald R. Yager
Publisher	Springer
Pages	321-335
Number of pages	15
ISBN (Electronic)	9783032290007
ISBN (Print)	9783032289995
DOIs	https://doi.org/10.1007/978-3-032-29000-7_23
Publication status	Published - 1 Jan 2026
Event	21st International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2026 - Rome, Italy Duration: 15 Jun 2026 → 19 Jun 2026 https://www.sbai.uniroma1.it/conferenze/ipmu2026/index.php

Publication series

Series	Communications in Computer and Information Science
Volume	3021 CCIS
ISSN	1865-0929

Conference

Conference	21st International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2026
Abbreviated title	IPMU 2026
Country/Territory	Italy
City	Rome
Period	15/06/26 → 19/06/26
Internet address	https://www.sbai.uniroma1.it/conferenze/ipmu2026/index.php

Keywords

Attention Mechanisms
Graph Neural Networks
Non-Negative Matrix Factorization
Transfer Learning
Vehicle Routing Problem

Access to Document

10.1007/978-3-032-29000-7_23

Cite this

Fernandes, S. P. C. G., Almeida, R. J., Vieira, S., & Phillipson, F. (2026). Transfer Learning with Graph Neural Networks for Cross-Scale Complexity in Vehicle Routing. In B. Vantaggi, G. Coletti, T. Denoeux, A. Laurent, D. Petturiti, E. Miranda, J. Medina, B. Bouchon-Meunier, & R. R. Yager (Eds.), Information Processing and Management of Uncertainty in Knowledge-Based Systems : 21st International Conference, IPMU 2026, Proceedings (pp. 321-335). Springer. https://doi.org/10.1007/978-3-032-29000-7_23

Fernandes, Simão Pedro Cunha Godinho ; Almeida, Rui Jorge ; Vieira, Susana et al. / Transfer Learning with Graph Neural Networks for Cross-Scale Complexity in Vehicle Routing. Information Processing and Management of Uncertainty in Knowledge-Based Systems : 21st International Conference, IPMU 2026, Proceedings. editor / Barbara Vantaggi ; Giulianella Coletti ; Thierry Denoeux ; Anne Laurent ; Davide Petturiti ; Enrique Miranda ; Jesús Medina ; Bernadette Bouchon-Meunier ; Ronald R. Yager. Springer, 2026. pp. 321-335 (Communications in Computer and Information Science, Vol. 3021 CCIS).

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title = "Transfer Learning with Graph Neural Networks for Cross-Scale Complexity in Vehicle Routing",

abstract = "The vehicle routing problem is widely studied due to its practical relevance and inherent computational complexity. In many scenarios, such as real-time delivery requests, models trained on smaller instances must generalize to larger-scale problems, where cross-scale transitions induce distributional shifts in graph topology and increased combinatorial uncertainty. This paper addresses cross-scale generalization in the capacitated vehicle routing problem using a graph convolutional network within a transfer learning framework. The proposed approach increases the scale of training instances to enhance structural representations and incorporates a Non-negative Matrix Factorization step to extract low-rank latent structural priors from graph features. These priors are integrated into an attention-based message passing framework to generate a solution probability heatmap. Systematic experiments on randomly distributed instances show that these enhancements improve the model{\textquoteright}s generalization capability.",

keywords = "Attention Mechanisms, Graph Neural Networks, Non-Negative Matrix Factorization, Transfer Learning, Vehicle Routing Problem",

author = "Fernandes, \{Sim{\~a}o Pedro Cunha Godinho\} and Almeida, \{Rui Jorge\} and Susana Vieira and Frank Phillipson",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.; 21st International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2026, IPMU 2026 ; Conference date: 15-06-2026 Through 19-06-2026",

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language = "English",

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pages = "321--335",

editor = "Barbara Vantaggi and Giulianella Coletti and Thierry Denoeux and Anne Laurent and Davide Petturiti and Enrique Miranda and Jes{\'u}s Medina and Bernadette Bouchon-Meunier and Yager, \{Ronald R.\}",

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Fernandes, SPCG, Almeida, RJ, Vieira, S & Phillipson, F 2026, Transfer Learning with Graph Neural Networks for Cross-Scale Complexity in Vehicle Routing. in B Vantaggi, G Coletti, T Denoeux, A Laurent, D Petturiti, E Miranda, J Medina, B Bouchon-Meunier & RR Yager (eds), Information Processing and Management of Uncertainty in Knowledge-Based Systems : 21st International Conference, IPMU 2026, Proceedings. Springer, Communications in Computer and Information Science, vol. 3021 CCIS, pp. 321-335, 21st International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2026, Rome, Italy, 15/06/26. https://doi.org/10.1007/978-3-032-29000-7_23

Transfer Learning with Graph Neural Networks for Cross-Scale Complexity in Vehicle Routing. / Fernandes, Simão Pedro Cunha Godinho; Almeida, Rui Jorge; Vieira, Susana et al.
Information Processing and Management of Uncertainty in Knowledge-Based Systems : 21st International Conference, IPMU 2026, Proceedings. ed. / Barbara Vantaggi; Giulianella Coletti; Thierry Denoeux; Anne Laurent; Davide Petturiti; Enrique Miranda; Jesús Medina; Bernadette Bouchon-Meunier; Ronald R. Yager. Springer, 2026. p. 321-335 (Communications in Computer and Information Science, Vol. 3021 CCIS).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

TY - GEN

T1 - Transfer Learning with Graph Neural Networks for Cross-Scale Complexity in Vehicle Routing

AU - Fernandes, Simão Pedro Cunha Godinho

AU - Almeida, Rui Jorge

AU - Vieira, Susana

AU - Phillipson, Frank

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

PY - 2026/1/1

Y1 - 2026/1/1

N2 - The vehicle routing problem is widely studied due to its practical relevance and inherent computational complexity. In many scenarios, such as real-time delivery requests, models trained on smaller instances must generalize to larger-scale problems, where cross-scale transitions induce distributional shifts in graph topology and increased combinatorial uncertainty. This paper addresses cross-scale generalization in the capacitated vehicle routing problem using a graph convolutional network within a transfer learning framework. The proposed approach increases the scale of training instances to enhance structural representations and incorporates a Non-negative Matrix Factorization step to extract low-rank latent structural priors from graph features. These priors are integrated into an attention-based message passing framework to generate a solution probability heatmap. Systematic experiments on randomly distributed instances show that these enhancements improve the model’s generalization capability.

AB - The vehicle routing problem is widely studied due to its practical relevance and inherent computational complexity. In many scenarios, such as real-time delivery requests, models trained on smaller instances must generalize to larger-scale problems, where cross-scale transitions induce distributional shifts in graph topology and increased combinatorial uncertainty. This paper addresses cross-scale generalization in the capacitated vehicle routing problem using a graph convolutional network within a transfer learning framework. The proposed approach increases the scale of training instances to enhance structural representations and incorporates a Non-negative Matrix Factorization step to extract low-rank latent structural priors from graph features. These priors are integrated into an attention-based message passing framework to generate a solution probability heatmap. Systematic experiments on randomly distributed instances show that these enhancements improve the model’s generalization capability.

KW - Attention Mechanisms

KW - Graph Neural Networks

KW - Non-Negative Matrix Factorization

KW - Transfer Learning

KW - Vehicle Routing Problem

U2 - 10.1007/978-3-032-29000-7_23

DO - 10.1007/978-3-032-29000-7_23

M3 - Conference article in proceeding

SN - 9783032289995

T3 - Communications in Computer and Information Science

SP - 321

EP - 335

BT - Information Processing and Management of Uncertainty in Knowledge-Based Systems

A2 - Vantaggi, Barbara

A2 - Coletti, Giulianella

A2 - Denoeux, Thierry

A2 - Laurent, Anne

A2 - Petturiti, Davide

A2 - Miranda, Enrique

A2 - Medina, Jesús

A2 - Bouchon-Meunier, Bernadette

A2 - Yager, Ronald R.

PB - Springer

T2 - 21st International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2026

Y2 - 15 June 2026 through 19 June 2026

ER -

Fernandes SPCG, Almeida RJ, Vieira S, Phillipson F. Transfer Learning with Graph Neural Networks for Cross-Scale Complexity in Vehicle Routing. In Vantaggi B, Coletti G, Denoeux T, Laurent A, Petturiti D, Miranda E, Medina J, Bouchon-Meunier B, Yager RR, editors, Information Processing and Management of Uncertainty in Knowledge-Based Systems : 21st International Conference, IPMU 2026, Proceedings. Springer. 2026. p. 321-335. (Communications in Computer and Information Science, Vol. 3021 CCIS). doi: 10.1007/978-3-032-29000-7_23

Transfer Learning with Graph Neural Networks for Cross-Scale Complexity in Vehicle Routing

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Keywords

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