Optimal harvesting strategy based on rearrangements of functions
We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2018
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| Online Access: | https://eprints.nottingham.ac.uk/56208/ |
| _version_ | 1848799293390979072 |
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| author | Emamizadeh, Behrouz Farjudian, Amin Liu, Yichen |
| author_facet | Emamizadeh, Behrouz Farjudian, Amin Liu, Yichen |
| author_sort | Emamizadeh, Behrouz |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum harvesting capacity. For this generalization, we need a completely different approach. As such, we use the theory of rearrangements of functions. We prove existence of solutions, and obtain an optimality condition which indicates that the more aggressive harvesting must be pushed toward the boundary of the domain. Furthermore, we prove that radial and Steiner symmetries of the domain are preserved by the solutions. We will also devise an algorithm for numerical solution of the problem, and present the results of some numerical experiments. |
| first_indexed | 2025-11-14T20:33:22Z |
| format | Article |
| id | nottingham-56208 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:33:22Z |
| publishDate | 2018 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-562082019-11-05T04:30:12Z https://eprints.nottingham.ac.uk/56208/ Optimal harvesting strategy based on rearrangements of functions Emamizadeh, Behrouz Farjudian, Amin Liu, Yichen We study the problem of optimal harvesting of a marine species in a bounded domain, with the aim of minimizing harm to the species, under the general assumption that the fishing boats have different capacities. This is a generalization of a result of Kurata and Shi, in which the boats were assumed to have the same maximum harvesting capacity. For this generalization, we need a completely different approach. As such, we use the theory of rearrangements of functions. We prove existence of solutions, and obtain an optimality condition which indicates that the more aggressive harvesting must be pushed toward the boundary of the domain. Furthermore, we prove that radial and Steiner symmetries of the domain are preserved by the solutions. We will also devise an algorithm for numerical solution of the problem, and present the results of some numerical experiments. Elsevier 2018-03-01 Article PeerReviewed application/pdf en cc_by_nc_nd https://eprints.nottingham.ac.uk/56208/1/2018-Emamizadeh_Farjudian_Liu-Harvesting_Strategy_ROP.pdf Emamizadeh, Behrouz, Farjudian, Amin and Liu, Yichen (2018) Optimal harvesting strategy based on rearrangements of functions. Applied Mathematics and Computation, 320 . pp. 677-690. ISSN 0096-3003 Population biology; Rearrangements of functions; Reaction-diffusion; Optimization; Symmetry http://dx.doi.org/10.1016/j.amc.2017.10.006 doi:10.1016/j.amc.2017.10.006 doi:10.1016/j.amc.2017.10.006 |
| spellingShingle | Population biology; Rearrangements of functions; Reaction-diffusion; Optimization; Symmetry Emamizadeh, Behrouz Farjudian, Amin Liu, Yichen Optimal harvesting strategy based on rearrangements of functions |
| title | Optimal harvesting strategy based on rearrangements of functions |
| title_full | Optimal harvesting strategy based on rearrangements of functions |
| title_fullStr | Optimal harvesting strategy based on rearrangements of functions |
| title_full_unstemmed | Optimal harvesting strategy based on rearrangements of functions |
| title_short | Optimal harvesting strategy based on rearrangements of functions |
| title_sort | optimal harvesting strategy based on rearrangements of functions |
| topic | Population biology; Rearrangements of functions; Reaction-diffusion; Optimization; Symmetry |
| url | https://eprints.nottingham.ac.uk/56208/ https://eprints.nottingham.ac.uk/56208/ https://eprints.nottingham.ac.uk/56208/ |