Mathematical
Modeling
and
Optimization
under
Uncertainty
for
Process
Operations
and
Materials
Design
Prof. Chrysanthos
E.
Gounaris
Dept.
of
Chemical
Engineering
Carnegie
Mellon
University
Pittsburgh,
PA
USA
In this talk, we introduce and motivate a number of practically interesting problems that arise in the areas of process scheduling and distribution logistics. We then derive various mathematical models and custom-built optimization algorithms in order to obtain optimal decisions for such operations, which are combinatorially complex and usually intractable to address with commercial optimization software.
A common underlying theme of the above problems is the multi-stage nature of the decision-making they involve, whereby an operator can defer certain decisions until later time points. In these settings, it is of interest to derive solutions that maintain their feasibility across long time horizons and across a wide range of possible variability for the system parameters. It is also of interest to ensure that any solution one adopts remains competitive under many scenarios and is not subject to an unnecessarily excessive amount of risk premium. In this context, we apply and extend various principles and methodologies of Robust Optimization (RO) to manage such risk due to parameter uncertainty, and we show how novel RO frameworks can be used to improve upon solutions obtained via traditional means, including cases where traditional RO is not applicable.
Finally, we discuss recent efforts towards the design of heterogeneous catalyst systems where, due to the combinatorial nature of how atoms can arrange themselves on crystalline lattices, the best catalytic structures are often unintuitive and likely impossible to identify without a rigorous decision-making approach. To that end, we formalize a mathematical optimization approach for materials design and show how correlations linking catalytic activity to appropriate site descriptors can be used to determine the most promising designs of transition metal crystalline surfaces. Our results show that careful nanostructuring of these surfaces can dramatically enhance performance as compared to the various crystallographic planes that are more commonly used.