Methodological and computational framework for model-based design of parallel experiment campaigns under uncertainty

The model-based determination of maximally-informative campaigns involving multiple parallel experimental runs remains a challenging task. Effort-based methodologies are well suited to the design of such experiment campaigns through discretizing the experiment control domain into a finite sample of candidate experiments. However, this approach can lead to suboptimal results if the discretization fails to cover the experiment domain sufficiently well. We present a comprehensive computational framework that combines an effort-based optimization step with a gradient-based refinement as part of an iterative procedure. The convexity of classical design criteria in the effort space allows for a globally optimal effort selection over the discretization, which is exploited to warm-start the gradient-based search for a refined discretization. Our framework also considers parametric model uncertainty by formulating risk-inclined, risk-neutral and risk-averse design criteria, and it enables the solution of exact designs in the effort-based step. Through the case study of a fed-batch fermentation, we show that the integrated effort-based optimization with gradient-based refinement procedure consistently outperforms an effort-only optimization. The results demonstrate the benefits of robust design approaches compared to their local counterparts, and establish the computational tractability of the framework in computing robust experiment campaigns with up to a dozen dimensions.