Uma contribuição ao estudo dos métodos de otimização multi-objetivo

Abstract

In optimization problems, there are many situations in which the users goal is to minimize and or maximize several functions simultaneously, instead of dealing with a single objective function. These functions form a mathematical description of performance criteria, which are usually in conflict with each other. This situation is formulated as a multicriterion optimization problem (also called multi-performance, multiple objective or vector optimization). Multicriterion optimization problems arise various applications in sciences and engineering. There are several criteria that can be used to solve complex optimization problems. This dissertation presents a contribution to the study and comparison multiobjective optimization problems. The classic methods, based on function scalarization in which a vector function is transformed into a scalar function, are represented in the present work by the weighting objectives method and the global criterion method. A different approach is given by the hierarchical, trade-off and goal programming methods, which treats the objective functions as additional constraints. A method based of the min-max approach is also studied. Some multicriterion optimization problems are used to illustrate the methodology developed.