Maximising yield and minimising time are two top priorities for biotechnological industry. In this paper, we model the 1,3-PD uncoupled fed-batch fermentation process with a 10-dimensional nonlinear switched system. By taking both maximising 1,3-PD concentration and minimising the terminal time of fermentation as the objectives, we propose a multi-objective optimisation problem with the flow rates of glycerol and alkali, the switched times among four modes and the mode sequence as the decision variables. To solve the multi-objective optimisation problem, we use the convex weighted sum to transcribe the multi-objective optimisation problem into a sequence of single-objective optimisation problems. Then the time-scaling transformation, the binary relaxation approach and the exact penalty method are applied to solve these single-objective optimisation problems. The numerical results show that, by optimising the flow rates of glycerol and alkali, the switched times among four modes and the mode sequence, the optimum fed-batch time and the higher 1,3-PD concentration can be obtained. The obtained numerical results can provide reference for the actual fermentation experiment.

中文翻译：

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非耦合补料分批发酵非线性切换系统的多目标优化

最大化产量和最小化时间是生物技术行业的两个首要任务。在本文中，我们使用 10 维非线性切换系统对 1,3-PD 非耦合补料分批发酵过程进行建模。以最大化1,3-PD浓度和最小化发酵终止时间为目标，我们提出了一个以甘油和碱的流量、四种模式之间的切换时间和模式序列为多目标优化问题。决策变量。为了解决多目标优化问题，我们使用凸加权和将多目标优化问题转化为一系列单目标优化问题。然后是时间尺度变换，应用二元松弛法和精确惩罚法来解决这些单目标优化问题。数值结果表明，通过优化甘油和碱的流量、四种模式之间的切换时间和模式顺序，可以获得最佳的补料分批时间和较高的1,3-PD浓度。所得数值结果可为实际发酵实验提供参考。