Quality Control in Particle Precipitation via Robust Optimization

TL;DR

This paper introduces a robust optimization framework for particle precipitation processes, effectively handling uncertainties to produce high-quality particles, demonstrated through quantum dot synthesis experiments.

Contribution

It develops a novel adaptive bundle method combined with the moments approach to optimize particle synthesis under uncertainty, a significant advancement over existing methods.

Findings

Robust approach outperforms unprotected process in quality.

Algorithm efficiently handles uncertainties in total mass.

Unprotected process fails to meet quality targets under perturbations.

Abstract

In this work, we propose a robust optimization approach to mitigate the impact of uncertainties in particle precipitation. Our model incorporates partial differential equations, more particular nonlinear and nonlocal population balance equations to describe particle synthesis. The goal of the optimization problem is to design products with desired size distributions. Recognizing the impact of uncertainties, we extend the model to hedge against them. We emphasize the importance of robust protection to ensure the production of high-quality particles. To solve the resulting robust problem, we enhance a novel adaptive bundle framework for nonlinear robust optimization that integrates the exact method of moments approach for solving the population balance equations. Computational experiments performed with the integrated algorithm focus on uncertainties in the total mass of the system as it greatly influence the quality of the resulting product. Using realistic parameter values for quantum dot synthesis, we demonstrate the efficiency of our integrated algorithm. Furthermore, we find that the unprotected process fails to achieve the desired particle characteristics, even for small uncertainties, which highlights the necessity of the robust process. The latter consistently outperforms the unprotected process in quality of the obtained product, in particular in perturbed scenarios.