  Model-based design of experiments (MBDoE) is a powerful framework for
selecting and calibrating science-based mathematical models from data. This
work extends popular MBDoE workflows by proposing a convex mixed integer
(non)linear programming (MINLP) problem to optimize the selection of
measurements. The solver MindtPy is modified to support calculating the
D-optimality objective and its gradient via an external package,
\texttt{SciPy}, using the grey-box module in Pyomo. The new approach is
demonstrated in two case studies: estimating highly correlated kinetics from a
batch reactor and estimating transport parameters in a large-scale rotary
packed bed for CO$_2$ capture. Both case studies show how examining the
Pareto-optimal trade-offs between information content measured by A- and
D-optimality versus measurement budget offers practical guidance for selecting
measurements for scientific experiments.
