  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.
