Algoritmo de otimização multi-objetivo assistida por metamodelagem com aplicações em problemas de aerodinâmica

Abstract

The multi-objective optimization algorithms commonly used in real engineering designs are based on evolutionary strategies. These algorithms often require a large number of evaluations of the objective function to achieve a good approximation of the Pareto front. In the case in which these algorithms are used to solve a real engineering optimization problem, which usually has computationally expensive objective functions, the time required to achieve convergence can be some time unfeasible. In this sense, the focus of this research was to develop a multi-objective optimization algorithm, based on a metamodeling strategy, to improve the optimization processes in engineering problems. The algorithm was developed, based on metamodel construction using radial based functions, to approximate the computationally expensive functions. These metamodels are optimized in an iterative sampling process to obtain new points in the decision space, with which the next expensive function evaluations must be made. In addition to being able to apply to multi-objective problems, the results showed a very satisfactory performance of the developed algorithm when applied to the select test problems chosen herein and in three real engineering problems: optimized design of wind turbine blades, aerodynamic optimization of wing geometry, and optimized design of linear cascades of axial flow machines. In most cases, the number of evaluations of expensive functions used by the developed algorithm was at least 3 times less than the expensive function evaluation employed, during the direct application of the evolutionary multi-objective optimization algorithm to achieve convergence with similar average values of coverage and diversity metrics of Pareto front.