Dynamic optimization of a two-stage fractional system in microbial batch process

Xiaopeng Yi; Huey Tyng Cheong; Zhaohua Gong; Chongyang Liu; Kok Lay Teo; Xiaopeng Yi; Huey Tyng Cheong; Zhaohua Gong; Chongyang Liu; Kok Lay Teo

doi:10.3934/era.2024312

Electronic Research Archive

2024, Volume 32, Issue 12: 6680-6697. doi: 10.3934/era.2024312

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Dynamic optimization of a two-stage fractional system in microbial batch process

1.
School of Mathematical Sciences, Sunway University, Kuala Lumpur 47500, Malaysia
2.
School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China
3.
School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth 6845, Australia
4.
Yantai Key Laboratory of Big Data Modeling and Intelligent Computing, Yantai 264005, China

Received: 27 September 2024 Revised: 25 November 2024 Accepted: 04 December 2024 Published: 12 December 2024

In this paper, we proposed a dynamic optimization problem involving a two-stage fractional system subjected to both a terminal state inequality constraint and continuous state inequality constraints in a microbial batch process. The objective function was the productivity of 1,3-propanediol at the terminal time, while the decision variables were the initial concentrations of biomass and glycerol, and the terminal time of the batch process. We first equivalently transformed the problem with free terminal time into one with fixed terminal time in a new time horizon by applying a proposed time-scaling transformation. We then converted the equivalent problem into an optimization problem with only box constraints by using an exact penalty function method. A novel third-order numerical scheme was presented for solving the two-stage fractional system. On this basis, we developed an improved particle swarm optimization algorithm to solve the resulting optimization problem. Finally, numerical results showed that a significant increase in the productivity of 1,3-propanediol at the terminal time was obtained compared with the previously reported results.
- two-stage fractional system,
- dynamic optimization,
- numerical scheme,
- particle swarm optimization,
- batch process
Citation: Xiaopeng Yi, Huey Tyng Cheong, Zhaohua Gong, Chongyang Liu, Kok Lay Teo. Dynamic optimization of a two-stage fractional system in microbial batch process[J]. Electronic Research Archive, 2024, 32(12): 6680-6697. doi: 10.3934/era.2024312

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Abstract

In this paper, we proposed a dynamic optimization problem involving a two-stage fractional system subjected to both a terminal state inequality constraint and continuous state inequality constraints in a microbial batch process. The objective function was the productivity of 1,3-propanediol at the terminal time, while the decision variables were the initial concentrations of biomass and glycerol, and the terminal time of the batch process. We first equivalently transformed the problem with free terminal time into one with fixed terminal time in a new time horizon by applying a proposed time-scaling transformation. We then converted the equivalent problem into an optimization problem with only box constraints by using an exact penalty function method. A novel third-order numerical scheme was presented for solving the two-stage fractional system. On this basis, we developed an improved particle swarm optimization algorithm to solve the resulting optimization problem. Finally, numerical results showed that a significant increase in the productivity of 1,3-propanediol at the terminal time was obtained compared with the previously reported results.

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