A Bilevel Programming Approach to Optimize C-phycocyanin Bio-production under Uncertainty

High variability and unreliable expectations on product yields substantially hinder the industrialization of microorganism derived biochemicals as they present a risk to the profitability and safety of the underlying systems. Therefore, in this work, we propose an optimization approach to determine the lower and upper product yield expectations for the sustainable production of C-phycocyanin. Kinetic modeling is adopted in this study as it is an outstanding tool for fast prototyping, prediction and optimization of chemical and biochemical processes. On the upside, parameters in bioprocess kinetic models are used as a simplification of complex metabolic networks to enable the simulation, design and control of the process. On the downside, this conglomeration of parameters may result in significant model uncertainty. To address this shortcoming, we formulate a bilevel max-min optimization problem to obtain the worst-case scenario of our system given the uncertainty on the model parameters. By constructing parameter confidence ellipsoids, we determined the feasible region along which the parameters can minimize the system’s performance, while nutrient and light controls are used to maximize the biorenewable production. The inner minimization problem is embedded by means of the optimality conditions into the upper maximization problem and hence both are solved simultaneously. Through this approach, we determined pessimistic and optimistic scenarios for the bioproduction of C-phycocyanin and hence compute reliable expectations on the yield and profit of the process.