Multiobjective Optimization Techniques Applied to Engineering Problems

Optimization problems often involve situations in which the user's goal is to minimize and/or maximize not a single objective function, but several, usually conflicting, functions simultaneously. Such situations are formulated as multiobjective optimization problems, also known as multicriteria, multiperformance or vector optimizations. Because multiobjective optimization problems arise in different scientific applications, many researches have focused on developing methods for their solution. Thus, there are several criteria that can be considered to solve such complex optimizations. This paper contributes to the study of optimization problems, by comparing some of these methods. The classical method, based on function scalarization, in which a vector function is transformed into a scalar function, is represented here by the weighted objectives and global criterion methods. A different approach involves hierarchical, trade-off and goal programming, which treats the objective functions as additional constraints. Some multicriteria optimization problems are given to illustrate each methodology studied here. The techniques are initially applied to an environmentally friendly and economically feasible electric power distribution problem. The second application involves a dynamics optimization problem aimed at optimizing the first three natural frequencies.