Population-based methods in the optimization of stand management

Abstract

In Finland, the growth and yield models for tree stands are simulation programs that consist of several sub-models. These models are often non-smooth and non-differentiable. Direct search methods such as the Hooke-Jeeves algorithm (HJ) are suitable tools for optimizing stand management with this kind of complicated models. This study tested a new class of direct search methods, namely population-based methods, in the optimization of stand management. The tested methods were differential evolution, particle swarm optimization, evolution strategy, and the Nelder-Mead method. All these methods operate with a population of solution vectors, which are recombined and mutated to obtain new candidate solutions. The management schedule of 719 stands was optimized with all population-based methods and with the HJ method. The population-based methods were competitive with the HJ method, producing 0.57% to 1.74% higher mean objective function values than HJ. On the average, differential evolution was the best method, followed by particle swarm optimization, evolution strategy, and Nelder-Mead method. However, differences between the methods were small, and each method was the best in several stands. HJ was alone the best method in 7% of stands, and a population based method in 3% (Nelder-Mead) to 29% (differential evolution) of stands. All five methods found the same solution in 18% of stands.