Assuring optimality in surrogate‐based optimization: A novel theorem and its practical implementation in pressure swing adsorption optimization

Abstract Surrogate‐based optimization has gained significant traction in several engineering fields, given its ability to handle complex systems without significant computational burdens. However, surrogate models are approximations and may have limitations, including the possibility of artificial minima. The main contribution of this work is the derivation of a robustness test that guarantees the optimality of surrogate‐based optimization. The derivation of this metric is based on the universal approximation theorem. The full framework proposed in this work is also composed by a sampling sizing methodology to randomly select samples within a feasible operating region (FOR) resulting from the optimization population, reducing the computational cost of the analysis and avoiding biases in the robustness calculation. The applicability and importance of this methodology are demonstrated through a case study of a complex chemical process—a pressure swing adsorption (PSA) unit—which presents a high computational cost to solve optimization problems. The results highlight the need and importance of evaluating the optimality of surrogate‐based optimization schemes.