Abstract

This research presents an optimization problem, which aims to understand the inherent design rules of the shape of a tree. It makes use of a classical optimization problem, the Nowacki beam, which consists of a cantilever beam with a point load at the end which seeks to obtain the lowest cross-sectional area and bending stress under a set of constraints [1]. Forrester et al. developed an algorithm to address this problem [2] by means of machine learning techniques. They began defining the beam properties and building a distributed random sampling plan and then computed the objective function and constraint functions. The process starts from an initially computed dataset that is used to train Kriging models, which are later used as a filling strategy, and genetic algorithms, as an optimization strategy. The result of each iteration is added to the dataset, and the process is repeated until convergence is found. In this way, the Pareto front with the optimal solutions is obtained.