Multi-objective optimization of nonlinear switched time-delay systems in fed-batch process

• Published in: Applied mathematical modelling Vol. 40; no. 23-24; pp. 10533 - 10548
• Main Authors: Liu, Chongyang, Gong, Zhaohua, Teo, Kok Lay, Feng, Enmin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2016
• Subjects: Convex weighted sum; Fed-batch process; Multi-objective optimization; Normal boundary intersection; Switched time-delay system; Fed-batch process; Convex weighted sum; Multi-objective optimization; Switched time-delay system; Normal boundary intersection
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2016.07.010

•A novel multi-objective problem is proposed to optimize fed-batch process.•Multi-objective problem is converted into a sequence of single-objective problems.•A new gradient-based single-objective solver is developed. Maximization of productivity and minimization of consumption are two top priorities for biotechnological industry. In this paper, we model a fed-batch process as a nonlinear switched time-delay system. Taking the productivity of target product and the consumption rate of substrate as the objective functions, we present a multi-objective optimization problem involving the nonlinear switched time-delay system and subject to continuous state inequality constraints. To solve the multi-objective optimization problem, we first convert the problem into a sequence of single-objective optimization problems by using convex weighted sum and normal boundary intersection methods. A gradient-based single-objective solver incorporating constraint transcription technique is then developed to solve these single-objective optimization problems. Finally, a numerical example is provided to verify the effectiveness of the numerical solution approach. Numerical results show that the normal boundary intersection method in conjunction with the developed single-objective solver is more favourable than the convex weighted sum method.