Algoritmos evolucionários intervalares para otimização robusta multiobjetivo

• Ano de defesa: 2013
• Autor(a) principal: Marcus Henrique Soares Mendes
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Engenharia Elétrica; Algoritmos; Engenharia elétrica
• Link de acesso: http://hdl.handle.net/1843/BUBD-9P8GFZ

The real-world multi-objective optimization problems may be subjected to uncertainties which are often impossible to be avoided in practice. Hence, there is the possibility that a small uncertainty becomes a numerical optimal solution obtained for a real problem completely meaningless in practice. Thereby, the scope of the multi-objective optimization process expands and requires methodologies capable of obtaining robust solutions, namely that operate perfectly in uncertain environments. In this thesis, interval evolutionary algorithms are proposed to find robust solutions to multi-objective optimization problems. The considered notion of robustness is the worst-case scenario of uncertainties related to the decision variables, the environmental parameters, and the noise in the objective functions. The treatment of uncertainties is performed by interval analysis. Two mathematical formulations of robust multi-objective optimization problem related to the robust notion of worst-case scenario are considered: minimax and minimax regret. To deal with such formulations, the methods IRMOEA-M and IRMOEA-MR are proposed, respectively. Both methods are described in detail and have their performance evaluated against a set of test and real problems. Besides these original contributions, we cope with the major complicating factors that arise through the use of interval analysis to deal with uncertainties: (I) Difficulties in obtaining inclusion functions, and (II) Possibility of image of robust solutions does not belong to feasible image. To deal with the complicating factor I, the methods SNIF-GPA and SNIF-MOGPA, based on genetic programming are proposed. Regarding the complicating factor II, the ideal frontier of maximization is defined. Computational experiments involving test functions and real problems in the fields of electromagnetic and control engineering were performed to evaluate the performance of the proposed methods. The results indicated that methods based on genetic programming were able to obtain good inclusion functions even when compared to other methodologies. Additionally, the ideal frontier of maximizing was promising and competitive when utilized in a strictly interval robust method and in an interval evolutionary robust method.