# Augmenting optimization-based molecular design with graph neural networks

arXiv: https://arxiv.org/abs/2312.03613 · HTML: https://mlsanity.com/paper/2312.03613/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2023.

## Built on by (most cited first, 6 of 6)

- [Verifying message-passing neural networks via topology-based bounds tightening](https://mlsanity.com/paper/2402.13937/) (2024)
- [PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs](https://mlsanity.com/paper/2312.08074/) (2023)
- [Global optimization of graph acquisition functions for neural architecture search](https://mlsanity.com/paper/2505.23640/) (2025)
- [Combining Graph Neural Networks and Mixed Integer Linear Programming for Molecular Inference under the Two-Layered Model](https://mlsanity.com/paper/2507.03920/) (2025)
- [Designing Active Tether-Net Systems for Space Debris Capture with Graph-Learning-Aided Mixed-Combinatorial Optimization](https://mlsanity.com/paper/2605.29021/) (2026)
- [Graph4BiLO: Graph Neural Network Approximation for Bilevel Mixed-Integer Linear Optimization](https://mlsanity.com/paper/2608.30103/) (2026)

## Abstract (arXiv)

Computer-aided molecular design (CAMD) studies quantitative structure-property relationships and discovers desired molecules using optimization algorithms. With the emergence of machine learning models, CAMD score functions may be replaced by various surrogates to automatically learn the structure-property relationships. Due to their outstanding performance on graph domains, graph neural networks (GNNs) have recently appeared frequently in CAMD. But using GNNs introduces new optimization challenges. This paper formulates GNNs using mixed-integer programming and then integrates this GNN formulation into the optimization and machine learning toolkit OMLT. To characterize and formulate molecules, we inherit the well-established mixed-integer optimization formulation for CAMD and propose symmetry-breaking constraints to remove symmetric solutions caused by graph isomorphism. In two case studies, we investigate fragment-based odorant molecular design with more practical requirements to test the compatibility and performance of our approaches.