Técnicas de otimização evolutiva aplicadas à solução de grandes sistemas lineares

• Ano de defesa: 2010
• Autor(a) principal: Purcina, Lúcio Aurélio
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; BR; Programa de Pós-graduação em Engenharia Mecânica; Engenharias; UFU
• Palavras-chave em Português: Sistemas lineares; Métodos de otimização evolutiva; Identificação de forças; Dinâmica; Equações lineares; Otimização; Identificação de sistemas; Linear systems; Evolutionary optimization methods; Identification of forces; CNPQ::ENGENHARIAS::ENGENHARIA MECANICA
• Link de acesso: https://repositorio.ufu.br/handle/123456789/14850

Many fields of engineering and other applied sciences demand the use of the solution of algebraic linear systems. Depending on the mathematical model used to represent the phenomenon, the linear systems will have high dimensions. Traditionally, large linear systems are resolved by using iterative methods. The convergence of these methods depends on the eigenvalues of the coefficients matrix. Thus, when the coefficients matrix loses one of the following characteristics as being symmetric or positive definite, the iterative methods (stationary and nonstationary) lose efficiency. Many methods exist for solving the linear systems. The aim is to find the most effective method for a particular problem. However, a method that works well for one type of problem might not work so well for others. Indeed, it may not even work. Thus, several researches are still being developed and improved in this area of knowledge. The aim of this works is to propose the application of some techniques in solving large linear systems. On this purpose, classic no stationary iterative methods are tested (Conjugate Gradients, Minimal Residual, Bi-Conjugate Gradients, Generalized Minimal Residual) and compared with two evolutionary optimization methods, Differential Evolution and Genetic Algorithms. In this research, problems like bi-dimensional Laplace equation and identification indirect of dynamical forces are solved. The analytical solution is compared with the numerical solutions calculated by using the mentioned methods. Results are presented, analyzing the most important parameters and their influence on the convergence and efficiency of the tested methods.