Multi-objective optimisation of nonlinear switched systems in uncoupled fed-batch fermentation

Abstract

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.

Keywords:

• Multi-objective optimisation
• switched system
• uncoupled fed-batch fermentation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 11771008, 11171050 and 11371164], the Provincial Natural Science Foundation of Fujian [grant numbers 2014J05001], the China Scholarship Council (CSC) [grant number 201506060121] and Natural Science Foundation of Shandong Province, China [grant number ZR2017MA005].