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

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.

Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

“…Later, in references [22,23], a neighboring extremal approach was developed to determine an optimal feedback control policy. A variation of this optimal control problem in which the price of shrimp is defined in terms of a piecewise-constant function of the average shrimp weight is considered in reference [7].…”

Stochastic differential game for management of non-renewable fishery resource under model ambiguity

“…A remark on economic aspects of the present mathematical model are presented based on the results obtained in this section. Firstly, the boundedness of the value function in (7) seems to be somewhat not intuitive since it means that is bounded for arbitrary and possibly unbounded T even if there exists no explicit discount factor as in the standard optimal control models [8,25,34]. This property distinguishes the present model for management of non-renewable resources from the existing ones for renewable ones.…”

“…Although this paper focuses on fishery resources management in rivers under ambiguity, the present framework of mathematical modelling can also be applied to effectively handling problems in aquaculture systems [7,32,73,78], in which the population dynamics is seen as non-renewable. Robust management of the aquacultured fishery resources can be analysed by considering ambiguities of the body growth rate and the decrease of the population.…”

Optimization model to start harvesting in stochastic aquaculture system

“…Marutani [34] analyzed economically optimal paths of harvesting deterministic population dynamics of non-renewable resources in an infinite horizon [35] and its modified counterpart in a finite horizon. Blanchard et al [36] and Yu and Leung [37] considered impulsive harvesting strategies of aquacultured organisms with density-dependent growth. Kunow et al [38] analyzed a cost-effective optimal exploitation strategy of non-renewable resources subject to a prescribed demand rate.…”

“…Blanchard et al . and Yu and Leung considered impulsive harvesting strategies of aquacultured organisms with density‐dependent growth. Kunow et al .…”