Many decision making problems are formulated as multi-objective optimization problems so as to satisfy diverse demands of decision maker. One of main issues in multi-objective optimization is how to find a Pareto optimal solution which meets decision maker's demands. To the end, interactive optimization methods, for example aspiration level methods, have been developed. On the other hand, several methods using genetic algorithm have been researched for generating the whole set of Pareto optimal solutions. However, those conventional methods have some problems when applying them to real practical problems considering the number of function evaluations. In many engineering design problems, generally, there are black-box objective functions whose forms are not explicitly known in terms of design variables. Under this circumstance, given design variables, the values of objective function can be obtained by sampled real/computational experiments such as structural analysis, fluid-mechanical analysis, thermodynamic analysis, and so on. These analyses are expensive and time consuming, and it is an important issue in real application problems how to make the number of necessary analyses as few as possible. In this paper, we suggest a sequential approximation method for solving multi-objective optimization problems, which is composed of two stages; i) the first stage is to predict the form of each objective function by using support vector regression on the basis of some experimental data, ii) the second stage is to find the Pareto optimal solution closest to the given aspiration level of decision maker using thepredicted objective functions, and in parallel, to generate the whole set of Pareto optimal solutions. Also, we discuss a way how to select additional experimental data for revising the form of objective function by relearning step by step. Finally, we illustrate the effectiveness of the proposed method through some numerical examples.
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