A differentiable optimization model for the management of single-species, even-aged stands

Abstract

This paper presents a model for optimizing the management of single-species, even-aged stands. The model comprises a number of state variables, given by functions initially differentiable with respect to time, which cease to be due to the discontinuities that cause instant silvicultural treatments. Nevertheless, the proposed model maintains its differentiability with respect to the decision variables (timing, type, and intensity of each thinning, and rotation age). This allows for formulation of the problem of optimal management of this type of stands as a linearly constrained smooth optimization problem, which can be efficiently solved by any derivative-based optimization method. The effectiveness of this formulation is shown by using a sequential quadratic programming (SQP) algorithm to design the optimal management of Pinus pinaster Ait. in Asturias (northwestern Spain) from an economic perspective. These results are compared with those obtained using two methods that do not require derivatives. The SQP, as representative of gradient-type methods, proved robust and much more efficient than the derivative-free methods.