Multi-stage cascade processes are fairly common, especially in manufacturing industry. Precursors or raw materials are transformed at each stage before being used as the input to the next stage. Setting the right control parameters at each stage is important to achieve high quality products at low cost. Finding the right parameters via trial and error approach can be time consuming. Bayesian optimization is an efficient way to optimize costly black-box function. We extend the standard Bayesian optimization approach to the cascade process through formulating a series of optimization problems that are solved sequentially from the final stage to the first stage. Epistemic uncertainties are effectively utilized in the formulation. Further, cost of the parameters are also included to find cost-efficient solutions. Experiments performed on a simulated testbed of Al-Sc heat treatment through a three-stage process showed considerable efficiency gain over a naive optimization approach.
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