Multi-objective optimization of a nonlinear switched time-delay system in microbial fed-batch process. Issue 17 (November 2020) - Gao, Xiaohua; Zhai, Jingang; Feng, Enmin
Highlights: Considering uncoupled, free terminal time, dha regulator, intracellular and extracellular environment, a nonlinear switched time-delay system model is established involving four time-delays and four switching modes for fed-batch fermentation of glycerol to 1, 3-PD. For determining optimal time-delays, a robustness index is given based expectation and variance. The gradient formulas of the indices and constraints with respect to time-delays, terminal time and feeding rates are given with their proofs. Considering the three-objective optimization model, we formulate an algorithm and obtain the valuable Pareto solutions by large scale calculation. 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.