Optimal control of fed-batch fermentation involving multiple feeds using Differential Evolution

Differential Evolution (DE), an exceptionally simple and robust evolutionary algorithm with Lagrangian like method, was used for solving optimal control and parameter selection problems of fed-batch fermentation involving general constraints on state variables. These infinite dimensional optimization problems were approximated into the finite dimensional optimization problems by control vector parameterization. Integration of the dynamic penalty functions was used to ensure the feasible solution of these dynamic optimization problems. State and end-point constraints were included in the formulation to reflect the operating objectives. The optimization strategy was able to accommodate these constraints in a relatively simple manner. The concept of non-uniform discretization in control vector parameterization was evaluated and shown to give superior results. Simple representative problems as well as a complex, multiple feed problem of simultaneous saccharification and fermentation (SSF) has been considered here to demonstrate the validity of the proposed methodology. The proposed methodology yielded an increase in productivity of approximately 20% in the case studies considered here.