Abstract
The determination of optimal feeding profile of fed-batch fermentation requires the solution of a singular optimal control problem. The complexity in obtaining the solution to this singular problem is due to the nonlinear dynamics of the system model, the presence of control variables in linear form and the existence of constraints in both the state and control variables. Traditionally, during the optimization process, uncertainties associated with design variables, control parameters and mathematical model are not considered. In this contribution, a systematic methodology to evaluate uncertainties during the resolution of a singular optimal control problem is proposed. This approach consists of the Multi-objective Optimization Differential Evolution algorithm associated with Effective Mean Concept. The proposed methodology is applied to determine the feed substrate concentration in fed-batch penicillin fermentation process. The robust multi- objective singular optimal control problem consists of maximizing the productivity and minimizing the operation total time.
Highlights
Optimization of Feed-Batch Penicillin Fermentation ProcessThe mathematical model of the feed-batch penicillin fermentation process considered in this contribution was described and studied by San and Stephanopoulos (1989)
The determination of optimal feeding profile of fedbatch fermentation requires the solution of a singular optimal control problem
The overall profit is considered as a post- example of a Singular Optimal Control Problem (SOCP) is the fermentation process, where processing criterion in the choice and implementation of a the substrate concentration can be maintained at a fairly result contained in the Pareto set
Summary
The mathematical model of the feed-batch penicillin fermentation process considered in this contribution was described and studied by San and Stephanopoulos (1989). All approach in the literature was proposed by Edge worth dominated solutions are removed from the population (1881) and later generalized by Pareto (1896) This through the operator Fast Non- Dominated Sorting. According to the criterion of dominated front Fj+1 This procedure is repeated until Pareto, multi-objective problems have a set of trade-off each vector becomes the member of a front. Algorithms can be modified such that they generate The crowding distance describes the density of several nondominated solutions in a single run To compute the features have made them popular when tackling crowding distance for a set of population members the following procedure is conducted for each objective function: the vectors are sorted according to their objective function value. This process is executed until the total number of generations is reached
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