Stochastic optimal control in bio-economic simulations A comparison of solution techniques

Uncertainty has long been recognised as an important aspect of renewable resource assessment and management. Stochastic optimal control provides a framework in which to incorporate uncertainty, whether arising from fluctuations in the biological or economic environment or from lack of a precise understanding of inter-relationships within a system. However, overlaying complex and interdependent biological, physical and economic relationships with uncertainty often results in an optimal control problem which is analytically complex. In this paper, a parametric approximation to the control equation is combined with genetic search algorithms to solve the stochastic control problem. The parametric approximation to the solution of optimal control problems is compared with a collocation approach. The use of these two numerical solution techniques is explored in the context of a harvest model for a multi-species fishery. While the two techniques yielded similar solutions, they offered different advantages and disadvantages. The use of collocation methods facilitates the understanding of the problem and the nature of the solution. However, for multi-dimensional state space problems, collocation techniques require exponentially increasing computational time. Parametric approximation techniques require prior specification of an explicit relationship between the state and control variables. As a result, the approximation may impose or miss features of the solution. However, when combined with a genetic search algorithm, the technique is very robust and computation time is significantly less than for the collocation technique. The use of collocation techniques to characterise the solution to the problem followed by the application of an appropriate approximation technique may to prove to be an expedient method for dealing with larger scale problems.