In this work, we consider the multiobjective design of bioprocesses, i.e., those from the biotechnological, pharmaceutical, and food industries. We present and compare extensions for three solution strategies for multiobjective optimization of this class of problems, which can be a very challenging task due to the frequent nonconvex nature of the associated nonlinear programming problems (NLPs), a consequence of the highly nonlinear character of most bioprocess models. Details of these new implementations are provided, especially focusing on several modifications of the original methods which we have developed in order to improve their efficiency and robustness. In addition, bifurcation analysis will be used to provide the decision maker with additional stability criteria to further select a suitable compromise solution among the set of optimal design alternatives. As a case study, we consider the optimal design of a fermentation process with respect to two economic criteria.