Most optimal design criteria in the literature are model-based criteria that rely on having an assumed model to select an optimal design for the experiment. A specified model might not be feasible in reality. The total entropy-based criterion to address the dual problem of model discrimination and parameter estimation has been in the literature for decades. This criterion has yet to be discussed due to the computation time requested. In this research, we develop the generalized entropy-based criterion for multi-stratum design and suggest some methods to reduce computation time. Examples are provided for selecting the optimal design in single-stratum completely randomized experiments and multi-stratum experiments such as split-plot designs using the new criterion.