We propose a robust optimization approach to mitigate the impact of uncertainties in particle precipitation. Our model of particle synthesis incorporates, as partial differential equations, nonlinear and nonlocal population balance equations. The optimization goal is to design products with desired size distributions. Recognizing the impact of uncertainties, we extend the model to robustly hedge against them to ensure tailored particle sizes. For the robust problem, we enhance an adaptive bundle framework for nonlinear robust optimization integrating the exact method of moments approach for the population balance equations. Computational experiments focus on uncertainties in the chemical potential of the precursor solution, which greatly influence the resulting product’s quality. Using realistic parameter values for quantum dot synthesis, we demonstrate the algorithm’s efficiency and find that unprotected processes fail to achieve desired particle sizes, highlighting the need for robust processes. The latter outperforms the unprotected process concerning the product’s quality in perturbed scenarios.

中文翻译：

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通过稳健优化控制颗粒沉淀的质量

我们提出了一种稳健的优化方法来减轻颗粒降水不确定性的影响。我们的粒子合成模型包含偏微分方程、非线性和非局部总体平衡方程。优化目标是设计具有所需尺寸分布的产品。认识到不确定性的影响，我们扩展了模型以稳健地对冲不确定性，以确保定制的颗粒尺寸。对于鲁棒问题，我们增强了用于非线性鲁棒优化的自适应束框架，集成了群体平衡方程的精确矩方法。计算实验的重点是前体溶液化学势的不确定性，这极大地影响了所得产品的质量。使用量子点合成的实际参数值，我们证明了算法的效率，并发现未受保护的过程无法实现所需的颗粒尺寸，这凸显了对稳健过程的需求。在扰动情况下，就产品质量而言，后者的性能优于未受保护的过程。