Dynamic optimization of a two-stage fractional system in microbial batch process
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 t...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024312 |
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| author | Xiaopeng Yi Huey Tyng Cheong Zhaohua Gong Chongyang Liu Kok Lay Teo |
| author_facet | Xiaopeng Yi Huey Tyng Cheong Zhaohua Gong Chongyang Liu Kok Lay Teo |
| author_sort | Xiaopeng Yi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3c1afccda8c44dacb6b91b042fdde5f2 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-3c1afccda8c44dacb6b91b042fdde5f22025-01-23T07:53:06ZengAIMS PressElectronic Research Archive2688-15942024-12-0132126680669710.3934/era.2024312Dynamic optimization of a two-stage fractional system in microbial batch processXiaopeng Yi0Huey Tyng Cheong1Zhaohua Gong2Chongyang Liu3Kok Lay Teo4School of Mathematical Sciences, Sunway University, Kuala Lumpur 47500, MalaysiaSchool of Mathematical Sciences, Sunway University, Kuala Lumpur 47500, MalaysiaSchool of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, ChinaSchool of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, ChinaSchool of Mathematical Sciences, Sunway University, Kuala Lumpur 47500, MalaysiaIn 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.https://www.aimspress.com/article/doi/10.3934/era.2024312two-stage fractional systemdynamic optimizationnumerical schemeparticle swarm optimizationbatch process |
| spellingShingle | Xiaopeng Yi Huey Tyng Cheong Zhaohua Gong Chongyang Liu Kok Lay Teo Dynamic optimization of a two-stage fractional system in microbial batch process Electronic Research Archive two-stage fractional system dynamic optimization numerical scheme particle swarm optimization batch process |
| title | Dynamic optimization of a two-stage fractional system in microbial batch process |
| title_full | Dynamic optimization of a two-stage fractional system in microbial batch process |
| title_fullStr | Dynamic optimization of a two-stage fractional system in microbial batch process |
| title_full_unstemmed | Dynamic optimization of a two-stage fractional system in microbial batch process |
| title_short | Dynamic optimization of a two-stage fractional system in microbial batch process |
| title_sort | dynamic optimization of a two stage fractional system in microbial batch process |
| topic | two-stage fractional system dynamic optimization numerical scheme particle swarm optimization batch process |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024312 |
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