A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations
This paper introduces a computational approach for solving non-linear optimal control problems in which the objective function is a discontinuous function of the state. We illustrate this approach using a dynamic model of shrimp farming in which shrimp are harvested at several intermediate times dur...
| Main Authors: | , , |
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| Format: | Journal Article |
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Elsevier Inc.
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/27690 |
| _version_ | 1848752333588004864 |
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| author | Blanchard, E. Loxton, Ryan Rehbock, Volker |
| author_facet | Blanchard, E. Loxton, Ryan Rehbock, Volker |
| author_sort | Blanchard, E. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper introduces a computational approach for solving non-linear optimal control problems in which the objective function is a discontinuous function of the state. We illustrate this approach using a dynamic model of shrimp farming in which shrimp are harvested at several intermediate times during the production cycle. The problem is to choose the optimal harvesting times and corresponding optimal harvesting fractions (the percentage of shrimp stock extracted) to maximize total revenue. The main difficulty with this problem is that the selling price of shrimp is modelled as a piecewise constant function of the average shrimp weight and thus the revenue function is discontinuous. By performing a time-scaling transformation and introducing a set of auxiliary binary variables, we convert the shrimp harvesting problem into an equivalent optimization problem that has a smooth objective function. We then use an exact penalty method to solve this equivalent problem. We conclude the paper with a numerical example. |
| first_indexed | 2025-11-14T08:06:57Z |
| format | Journal Article |
| id | curtin-20.500.11937-27690 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:06:57Z |
| publishDate | 2013 |
| publisher | Elsevier Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-276902019-02-19T04:28:02Z A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations Blanchard, E. Loxton, Ryan Rehbock, Volker Shrimp farming Exact penalty function Non-smooth optimization Optimal control This paper introduces a computational approach for solving non-linear optimal control problems in which the objective function is a discontinuous function of the state. We illustrate this approach using a dynamic model of shrimp farming in which shrimp are harvested at several intermediate times during the production cycle. The problem is to choose the optimal harvesting times and corresponding optimal harvesting fractions (the percentage of shrimp stock extracted) to maximize total revenue. The main difficulty with this problem is that the selling price of shrimp is modelled as a piecewise constant function of the average shrimp weight and thus the revenue function is discontinuous. By performing a time-scaling transformation and introducing a set of auxiliary binary variables, we convert the shrimp harvesting problem into an equivalent optimization problem that has a smooth objective function. We then use an exact penalty method to solve this equivalent problem. We conclude the paper with a numerical example. 2013 Journal Article http://hdl.handle.net/20.500.11937/27690 10.1016/j.amc.2013.02.070 Elsevier Inc. fulltext |
| spellingShingle | Shrimp farming Exact penalty function Non-smooth optimization Optimal control Blanchard, E. Loxton, Ryan Rehbock, Volker A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations |
| title | A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations |
| title_full | A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations |
| title_fullStr | A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations |
| title_full_unstemmed | A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations |
| title_short | A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations |
| title_sort | computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations |
| topic | Shrimp farming Exact penalty function Non-smooth optimization Optimal control |
| url | http://hdl.handle.net/20.500.11937/27690 |