The design of distillation columns often considers a given fixed feedstock and nominal operating conditions. Here we present an optimization-based approach for the optimal design of these units considering a flexible operation under a range of potential feedstocks. Our method combines an artificial neural network with a support vector machine to model the crude oil distillation unit. The artificial neural network model predicts the performance of the distillation unit for a given crude oil feedstock whilst the support vector machine classifier filters out infeasible design alternatives from the solution space (i.e., designs that are unlikely to converge when simulated using a rigorous model). The inputs to the artificial neural network include the column structural variables and operating conditions, whilst the outputs are process variables linked to the column performance. The artificial neural network models and support vector machines constructed for different crude oil feedstocks are integrated into a two-stage optimization framework in order to optimize the column structural variables and operating conditions, where the minimum utility demand is estimated using the pinch analysis. An effective solution strategy that combines stochastic and deterministic optimization algorithms is applied to search for economically viable and flexible design alternatives that can operate over a given range of crude oil feedstocks while satisfying the product quality specifications. The capabilities of the proposed approach are illustrated using an industrially-relevant case study, where we clearly show that the proposed approach can identify design alternatives capable of handling various feedstocks effectively. (C) 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.