Mixed-integer optimisation of graph neural networks for computer-aided molecular design

Tom McDonald, Calvin Tsay, Artur M. Schweidtmann, Neil Yorke-Smith*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


ReLU neural networks have been modelled as constraints in mixed integer linear programming (MILP), enabling surrogate-based optimisation in various domains and efficient solution of machine learning certification problems. However, previous works are mostly limited to MLPs. Graph neural networks (GNNs) can learn from non-euclidean data structures such as molecular structures efficiently and are thus highly relevant to computer-aided molecular design (CAMD). We propose a bilinear formulation for ReLU Graph Convolutional Neural Networks and a MILP formulation for ReLU GraphSAGE models. These formulations enable solving optimisation problems with trained GNNs embedded to global optimality. We apply our optimisation approach to an illustrative CAMD case study where the formulations of the trained GNNs are used to design molecules with optimal boiling points.

Original languageEnglish
Article number108660
Number of pages21
JournalComputers and Chemical Engineering
Publication statusPublished - 2024

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Graph neural networks
  • GraphSAGE
  • Mixed integer programming
  • Molecular design
  • Optimal boiling point


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