The challenges of this case study involve balancing trade-offs between conflicting mechanical properties, such as strength (the ability to resist an applied force without being damaged) and ductility (the ability to stretch without breaking), and incorporating mixed-integer design choices. This case study is selected due to the mixed-integer nature of the problem and the availability of an adequate number of HTE experimental data to train an emulator . Similar procedures can be followed to design chemicalrelated units, e.g., chemical reactors, if data acquisition is possible via experiments or high-fidelity simulations.