Multi-objective optimization of a nonlinear switched time-delay system in microbial fed-batch process

Abstract

For an uncoupled microbial fed-batch fermentation process of glycerol bioconversion to 1,3-propanediol (1,3-PD), we establish a nonlinear switched system model with free terminal time and unknown time-delays, in which the reaction mechanism of extracellular and intracellular environment and the regulation of dha regulator are considered. In order to evaluate the time-delays, a robustness index is given by a weighted sum of the expectation and variance of the relative deviation between system outputs before and after time-delays are perturbed. A multi-objective optimization model is proposed for the sake of maximization of 1,3-PD and minimization of consumption of glycerol coupling with minimization of the robustness index, where the continuous state inequality constraints are involved, and the time-delays, the feeding rates of glycerol and alkali, switching instants between batch and feeding modes, and terminal time of fermentation are regarded as the decision variables. For solving this multi-objective optimization problem, we convert it into a sequence of single-objective optimization problems by using the Normal Constraint method (NC). The gradient formulas involving multiple time-delays are discussed. An algorithm of Multi-objective Programming Approximation based on SQP (MPA-SQP) is described. By large calculations, a set of Pareto solutions are obtained, which provides some references for practical fermentation experiments.