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

Abstract

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.

Reduced-order modelling of biochemical networks: application to the GTPase-cycle signalling module

“…Global against local optima-The issue whether local or global optima are found is relevant to all stochastic-search-based optimisation methods, including GA, Monte Carlo sampling [50], or related approaches such as differential evolution [51] and particle-swarm optimisation [52]. In these methods, there is no guarantee of finding the global optima.…”

“…In these methods, there is no guarantee of finding the global optima. However, the best or some of the near-best solutions found by these methods were found to be close to global optima with respect to the position in space and the value of the objective function in many practical applications such as modelling [47,49], protein folding [53], scheduling [54], circuit design [52] and control applications [51].…”

“…No additional perturbations and simulations are needed because, due to GA-based search during optimisation, the good candidate parameter sets adequately sample the various local optima that are close to the global optima of the objective function. It can be noted that besides GA, any other stochastic-search-based optimisation such as differential evolution [51] or particle-swarm optimisation [52] can be used for MPVA.…”

The use of differential evolution algorithm for solving chemical engineering problems

“…Reactors and fermentation Chiou and Wang (2001) Estimation of Monod model parameters of a bioreactor Wang et al (2001) Estimation of kinetic parameters of the ethanol fermentation process Chiou and Wang (1999) Feed batch fermentation Wang and Cheng (1999) Feed batch fermentation Kapadi and Gudi (2004) Feed batch fermentation Thermal engineering Babu et al (2004) Optimal design of an ammonia synthesis reactor Babu et al (2005) Optimization of adiabatic styrene reactor Babu and Sastry (1999) Estimation of heat transfer parameters in a trickle bed reactor Babu and Munawar (2001) Optimal design of shell and tube heat exchanger Babu and Angira (2006) Heat exchanger network design Fuel engineering Chen et al (2002) True boiling point curve of crude oil; effect of pressure on entropy Babu and Chaurasia (2003) Estimation of optimal time of pyrolysis and heating rate Angira and Babu (2006) Alkylation process optimization Babu and Angira (2006) Alkylation process optimization Unauthenticated Download Date | 5/12/18 2:14 PM are manipulated with arithmetic operators have several advantages: efficient memory utilization, ease of use, lower computational effort, and complexity (Price et al 2005). Along with efficiency, other advantages are flexibility (the algorithm adapts to modifications) and fundamentality (the principle of differentiation synthesizing in itself the fundamentals concepts of the solution search) ( Feoktistov 2006).…”

“…process optimization Kapadi and Gudi (2004) extended the optimal feed policy of a fed-batch fermentation process proposed in Chiou and Wang (1999) by including (i) systems with multiple feeds, (ii) nonuniform parameterization (the time duration of each interval is not the same), and (iii) path and endpoint constraints. In order to demonstrate the effectiveness of the methodology, the same case study as the one from Chiou and Wang (1999) was employed.…”