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Since Pareto optimal solutions in multi-objective optimization are not unique but makes a set, decision maker (DM) needs to select one of them as a final decision. In this event, DM tries to find a solution making a well balance among multiple objectives. Aspiration level methods support DM to do this in an interactive way, and are very simple, easy and intuitive for DMs. Their effectiveness has been observed through various fields of practical problems. One of authors proposed the satisficing trade-off method early in '80s, and applied it to several kinds of practical problems. On the other hand, in many engineering design problems, the explicit form of objective function can not be given in terms of design variables. Given the value of design variables, under this circumstance, the value of objective function is obtained by some simulation analysis or experiments. Usually, these analyses are computationary expensive. In order to make the number of analyses as few as possible, several methods for sequential approximate optimization which make optimization in parallel with model prediction has been proposed. In this paper, we form a coalition between aspiration level methods and sequential approximate optimization methods in order to get a final solution for multi-objective engineering problems in a reasonable number of analyses. In particular, we apply mu-nu-SVM which was developed by the authors on the basis of goal programming. The effectiveness of the proposed method was shown through some numerical experiments.