Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.6.2022.2.04

Volume 6, Issue 2, 1 April 2022, Pages 35-64

 

Abstract. In this paper, we consider a nonlinear time-delay dynamic (NTDD) system with uncertain time-delay in batch culture of glycerol bioconversion to 1,3-propanediol (1,3-PD) induced by Klebsiella pneumoniae. Our goal is to design an optimization scheme for the NTDD system with the aim of balancing two competing objectives: (i) system cost (the relative error between experimental data and the output of the mathematical model); (ii) system sensitivity (the variation of the system cost with respect to uncertain time-delay). Thus, a multi-objective optimization problem (MOOP) governed by the NTDD system and subject to continuous state inequality constraints is proposed, where the two competing objective functions are to be minimized. The optimization variables in this problem are the initial concentrations of biomass and glycerol along with the free terminal time. The MOOP is first converted into a sequence of single-objective optimization problems (SOOCPs) by using convex weighted sum and modified normal boundary intersection methods. By incorporating the time scaling transformation, the constraint transcription and locally smoothing approximation, a parallel hybrid SOOCP solver is developed based on gradient-based method and genetic algorithm. Finally, numerical results are provided to verify the effectiveness of the proposed solution method.

 

How to Cite this Article:
L. Wang, J. Yuan, L. Meng, S. Zhao, J. Xie, M. Huang, K.L. Teo, Multi-objective optimization of a nonlinear batch time-delay system with minimum system sensitivity, J. Nonlinear Var. Anal. 6 (2022), 35-64.