Um método de reanálise adaptativa para otimização estrutural usando um algoritmo genético não-geracional

Abstract

Genetic Algorithms (GA’s) are tools of great computational power when employed in optimization problems for which the solution cannot be obtained by a trivial way. Despite being an effective tool, GA has a high computational cost due to the high number of structural analysis needed to obtain a feasible solution. Furthermore, in structural optimization, the evaluation of a candidate solution may lead to the solution of a system of equations. The solution of such a system in some cases demands a great computational effort. In this way, in order to reduce the high computational cost, a reanalysis technique using the combined approximations method is employed. This technique reduces the dimension of the system to a number of basis vectors previously defined. In the standard formulation, the choice of the number of basis vectors is not carried out in an automatic way. Hence, the reanalysis technique will be employed in a proposed adaptive scheme for which the number of basis vectors will be chosen and modified along with the optimization process. With the objective of obtaining the smallest number of complete analyses, the initial stiffness matrix will also be modified along with the optimization process. In order to illustrate the effectiveness of the proposed formulation, classical examples of structural optimization are analyzed. The numerical examples reveal that the proposed adaptive scheme provides accurate and, in some cases, better results, i.e. lowest weight with lowest computational cost, when compared to other schemes in the literature.