Forest management optimization according to nonlinear partial differential equation (PDE) and gradient based optimization algorithm

In the dissertation, a new optimization model to optimize forest harvests is presented. The model helps to search the economically most profitable times and intensities of forest harvests and time of clear cutting. The model can be used as help to plan forest management. In the dissertation, the model is used to optimize harvests of a pine forest stand. The same model can be fitted also for other tree species.

The forest growth model presented in the dissertation considered how diameter distribution of the trees changes as time passes. In the model, the effect of the density of the trees on the speed of the growth is taken account. In the dissertation, a model is also developed, in which not only the diameter but also the height distribution of the trees is considered. In the same way, also other distributions can be added to the model. With the model, the effect of the tree breeding on the optimal solutions can be calculated since the height distribution and the branch properties differs between improved and non-improved trees.

In the optimization, a gradient method is used. In it, at first an initial guess is made which trees are removed at every time step. Then, the direction is calculated in which the guess should be changed so that the incomes from the forest grow most. From the direction, the new guess is chosen. This process is repeated until the incomes from the forest do not get any better. In the dissertation calculated optimization results do not were significantly different as optimization results get from the models currently in use, but the results were calculated faster.