# Mixed-Integer Optimisation of Graph Neural Networks for Computer-Aided Molecular Design

arXiv: https://arxiv.org/abs/2312.01228 · HTML: https://mlsanity.com/paper/2312.01228/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2023.

## Built on by (most cited first, 9 of 9)

- [Optimization Over Trained Neural Networks: Taking a Relaxing Walk](https://mlsanity.com/paper/2401.03451/) (2024)
- [Verifying message-passing neural networks via topology-based bounds tightening](https://mlsanity.com/paper/2402.13937/) (2024)
- [Molecular Machine Learning in Chemical Process Design](https://mlsanity.com/paper/2508.20527/) (2025)
- [Global optimization of graph acquisition functions for neural architecture search](https://mlsanity.com/paper/2505.23640/) (2025)
- [Relaxation-Informed Training of Neural Network Surrogate Models](https://mlsanity.com/paper/2604.22746/) (2026)
- [Combining Graph Neural Networks and Mixed Integer Linear Programming for Molecular Inference under the Two-Layered Model](https://mlsanity.com/paper/2507.03920/) (2025)
- [A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention](https://mlsanity.com/paper/2601.04509/) (2026)
- [Optimization over Trained (and Sparse) Neural Networks: A Surrogate within a Surrogate](https://mlsanity.com/paper/2505.01985/) (2025)
- [Chemically-Informed Machine Learning Approach for Prediction of Reactivity Ratios in Radical Copolymerization](https://mlsanity.com/paper/2512.19715/) (2025)

## Abstract (arXiv)

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 optimization approach to an illustrative CAMD case study where the formulations of the trained GNNs are used to design molecules with optimal boiling points.