The bottleneck in creating dynamic models of biological networks and processes often lies in estimating unknown kinetic model parameters from experimental data. In this regard, experimental conditions have a strong influence on parameter identifiability and should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE) methods commonly rely on the Fisher Information Matrix (FIM) for defining a metric of data informativeness. When the model behavior is highly nonlinear, FIM-based criteria may lead to suboptimal designs since the FIM only accounts for the linear variation of the model outputs with respect to the parameters. In this work, we developed a multi-objective optimization (MOO) MBDOE, where model nonlinearity was taken into consideration through the use of curvature. The proposed MOO MBDOE involved maximizing data informativeness using a FIM-based metric and at the same time minimizing the model curvature. We demonstrated the advantages of the MOO MBDOE over existing FIM-based and other curvature-based MBDOEs in an application to the kinetic modeling of fed-batch fermentation of Baker's yeast.