Algoritmos Evolucionários em Otimização Uni e Multi-objectivo


In this dissertation, the two best known evolutionary approaches and often applied to optimization problemas are considered: the Evolution Strategies and the Genetic Algorithms. These approaches present as main disadvantage high computational times but, on the other hand, exhibit a great °exibility in modelling engineering problems. The advantages and the drawbacks of each approach to distinct kind of optimization problems are investigated, in particular, representation issues and constraint handling. Usually, in engineering, problems are formulated with a single objective, in general, the cost. However, other objectives might exist that, when considered, transform the problem in multi-objective optimization. In the latter class of problems, usually, there are multiple con°icting objectives, giving rise to a set of compromise solutions. The evolutionary approaches, population based, seem to be useful in tackling multi-objective problems. However, in spite of its success, elitism has emerged as an e®ective way of improving the performance of the multi-objective evolutionary algorithms. In this work, a new elitist scheme, by which it is possible to control the size of the elite population, as well as, the concentration of points approximating the e±cient solutions of the multi-objective problem, is introduced. Almost all approaches to multi-objective optimization are based on Genetic Algorithms, and implementations based on Evolution Strategies are very rare. Thus, a new evolutionary approach to multi-objective optimization, based on Evolution Strategies, is proposed. Several mechanisms, like elitism, an adaptive sharing scheme and a geometric selection, have been introduced in the Multi-objective Elitist Evolution Strategy in order to improve the algorithm performance. Several applications of Evolutionary Algorithms to distinct engineering problemas were implemented. Firstly, the Evolutionary Algorithms were applied to the global optimization of mixed integer non-linear problems of the area of chemical engineering. A Genetic Algorithm was also applied to laminated plate optimization problems. These optimization plate problems are ¯rstly formulated as a constrained mixed-integer programming problem with a single objective function. The alternative multi-objective formulations of the problems were also solved. The proposed multi-objective algorithm was compared with other evolutionary multi-objective algorithms in several test problems. The new elitist scheme proves to lead to a good compromise between computational time and size of the elite population.