Model-based optimization typically obtains the optimum based on a nominal identified model. However, in the presence of uncertainty, the nominal optimum leads to suboptimal operating conditions that furthermore can be highly sensitive to uncertainties. Hence, uncertainty should be considered in the optimization and, furthermore, experiments should be designed to reduce the uncertainty most important for optimization. Herein, we propose a general framework that combines model-based robust optimization with optimal experiment design. The proposed framework can take advantage of prior knowledge in the form of a mechanistic model structure, and the importance of this is demonstrated by comparing to more standard black-box models typically employed in learning. Through optimal experiment design, we repeatedly reduce uncertainties in the region where the likelihood of improvement on the worst-case performance is maximized This makes the proposed method an efficient model-based robust optimization framework, especially with limited experiment resources. The effectiveness of the method is illustrated by a cell culture development example in continuous biopharmaceutical production.