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.

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