Using support vector machines in multi-objective optimization

In many practical engineering design problems, the form of objective functions is not given explicitly in terms of design variables. Given the value of design variables, under this circumstance, the values of objective functions are obtained by real/computational experiments such as structural analysis, fluid-mechanical analysis, thermodynamic analysis, and so on. Since these experiments are considerably expensive and also time consuming, thus it is actually almost impossible to find the exact solution to those problems by using conventional optimization methods. Recently, approximation methods using computational intelligence, for example, evolutionary algorithms and neural networks have been developed remarkably. Even those algorithms need a tremendous number of experiments to obtain an approximate solution. Furthermore, most engineering design problems should be formulated as multi-objective optimization problems so as to meet the diversified demands of designer. This paper suggests applying the support vector machines (SVM) in order to make the number of experiments for finding the solution of problem with multi-objective functions as few as possible. It is shown that the proposed method can approximate Pareto frontiers in multi-objective optimization problems effectively by employing support vectors in SVM. Finally, the effectiveness of our method is illustrated through numerical examples.