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A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
219
Issue
16
Identifiers
DOI: 10.1016/j.amc.2013.02.070
Keywords
  • Optimal Control
  • Non-Smooth Optimization
  • Shrimp Farming
  • Exact Penalty Function
Disciplines
  • Computer Science

Abstract

Abstract 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.

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