MIXED-INTEGER OPTIMIZATION FOR NANOMATERIAL DESIGN AND OPTIMIZATION UNDER UNCERTAINTY FOR NONLINEAR PROCESS MODELS

In the first part of this work, we consider small nanoparticles, a.k.a. nanoclusters, of transition metals. Transition metal nanoclusters have been studied extensively for a wide range of applications due to their highly tunable properties dependent on size, structure, and composition. For these small particles, there has been considerable effort towards theoretically predicting what is the most energetically favorable arrangement of atoms. To that end, we develop a computational framework that couples density-functional theory calculations with mathematical optimization modeling to identify highly stable, mono-metallic transition metal nanoclusters at various sizes.

Next, we devise a novel computational framework for the robust optimization of highly nonlinear, non-convex models that possess uncertain data. The proposed method is a generalization of a robust cutting-set algorithm that can handle models containing irremovable equality constraints, as is often the case with models in the process systems engineering domain. Additionally, we accommodate general forms of decision rules to facilitate recourse in second-stage degrees of freedom. Our proposed approach is demonstrated on three process flowsheet models, including a relatively complex model for amine-based CO2 capture. Finally, we propose an open-source robust optimization solver implementation of our cutting-set approach called PyROS. PyROS is a Python-based robust optimization meta-solver for solving non-convex, two-stage optimization models using adjustable robust optimization. The PyROS solver enables facile robust optimization tasks given a deterministic model and description of uncertainty.

With each of the applications presented here, we illustrate that mathematical optimization modeling and algorithms can be effectively utilized to address open problems in engineering.