Abstract
Artificial neural networks (ANNs) have emerged as powerful surrogate models in process design and optimisation, capable of capturing complex nonlinear process behaviour while significantly reducing computational cost compared to detailed first-principles simulations. However, ANN prediction errors in safety-critical applications can lead to suboptimal or vulnerable designs, necessitating rigorous treatment of approximation uncertainties. While probabilistic approaches exist for surrogate-based decision making, risk-averse contexts that require formal robustness guarantees face a fundamental challenge: the nonconvex nature of ANN-embedded models hinders the employment of standard robust optimisation methods. To this end, in this work we explore the global robust optimisation of process design problems with embedded ANNs. A robust spatial branch-and-bound (RsBB) algorithm to achieve global optimality is proposed while enforcing constraint satisfaction across all uncertainty realisations. This approach integrates spatial branch-and-bound with adversarial cuts generation, concurrently searching for the global optimum while ensuring robust feasibility despite ANN prediction uncertainties. We test the proposed algorithm on the ANN-embedded optimisation of a cumene manufacturing process, across a range of conservatism levels. The algorithm computes solutions within the prescribed optimality tolerance while quantifying the robustness-performance trade-off.