Robust multi-objective optimal control of dynamic biological networks

For a sustainable biochemical industry, an improved design and operation of processes with respect to economic, environmental and safety aspects is vital. In practice, often more than one objective, which can be conflicting, have to be optimized (e.g., minimizing the energy consumption, while maximizing the production) and trade-offs have to be made. Uncertainty is also typically present in the process models, e.g., parametric uncertainty originating from a parameter estimation procedure based on noisy measurements. Hence, there is a need for approaches which guarantee reliable operation despite this presence of uncertainty and while making trade-offs between conflicting objectives of interest. In addition, biochemical process control can be enhanced by incorporating insights in the internal biological network. We consider the multi-objective optimization of the enzyme expression rates for a minimum enzymatic cost and minimum process time in a four step linear pathway with Michaelis-Menten kinetics in which two and five parameters are considered to be uncertain. Two approximation techniques for uncertainty propagation, i.e., sigma points approach and polynomial chaos expansion are incorporated in an optimization framework and are compared for the propagation of the parametric uncertainty towards a model output in biological networks. The resulting robustified Pareto sets containing the different trade-off solutions are analyzed.