Optimizing design for continuous conversion of glycerol to 1,3-propanediol using discrete-valued optimal control

Abstract This paper focuses on modeling and optimizing design for continuous conversion of glycerol to 1,3-propanediol by Klebsiella pneumoniae, wherein dilution rate of the feed medium is constantly changed with fermentation time. A nonlinear three-phase hybrid system is first established to describe this bioconversion process. With mean productivity of 1,3-propanediol as objective function and dilution rate as design variable, we then formulated the optimization design problem as a discrete-valued optimal control problem, which is eventually approximated to a large-scale parameter optimization problem via time transformation and multiple shooting approach. A multi-strategy competition artificial bee colony algorithm is developed to solve this large-scale problem. Computer simulations show the rationality of the proposed hybrid system and the feasibility of dynamic dilution rate. Numerical results indicate that, on the one hand, mean productivity in continuous culture is improved obviously using dynamic dilution rate; on the other hand, the developed numerical algorithm is efficient and valid for this complex applied optimization problem.

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