Otimização multi-objetivo para o projeto de sistemas de engenharia

Abstract

Due to the increasing market needs of simultaneously achieving a growing number of objectives when designing modern engineering systems, thus focusing more realistic problems from the industrial point of view, the so-called multi-criteria optimization problems, multi-objective or vectorial optimization, have deserved, recently, emphasis in the development of algorithms and specific software for the solution of these problems. Most of these objectives, in turn, are conflicting, that is, an improvement in any one of these objectives doesn't result, necessarily, in the improvement of the others. The optimal solution for these problems, unlike the optimization with an single objective, is the attainment of non-dominated solutions that form the Pareto Curve, also know as Pareto Optimal. There are two approaches for obtaining Pareto's Curve: the Deterministic one, that makes use of the Variational Calculus and the Non-Deterministic one, which is based in the natural selection processes, in population genetics or in purely structural methodologies. The use of the Non-Deterministic Approach is drawing attention in recent decades, mainly due to the fact that they do not make use of derivates, and are easy implemented and have simple conception. Evidently, the rapid development of the digital computation is also a decisive factor for the success of these techniques, since the processing time, which is greater than that of classic methods, has been decreasing significantly with the better performance of the processors. Among these, the Diferential Evolution Algorithm, an structural approach developed initially for problems without restrictions with an single objective, has been shown as a viable alternative for this purpose. Therefore, this work consists in the extension of Diferential Evolution Algorithm for problems with multiple objectives, through the incorporation of two operators into the original algorithm: the rank ordering and neighborhood exploration of potential candidates. The developed algorithm was tested on a series of classic mathematical and engineering problems of different areas, thus constituting a wide range of case studies. The obtained results were promising, as it is able to reduce the generation number, without loss of quality of Pareto's Curve, when compared with those obtained through classic evolutionary algorithms.