Abstract
In optimization algorithms, the value of design variables are updated according to some criterion and it is nesessary to evaluate objective functions and constraints repeatedly if design variables are updated. In design problems, performances are often taken as the objective functions or constraints and it needs a time to evaluate the performances. A same situation is observed in the multi-objective optimization problems that can handle several objective function simultaneously and is suitable for the real design. Therefore it is desiable to decrease the number of evaluation count of the objective function and constrains. The response surface methodology is helpful for such a situation and many studies have been done. In real design problems, nonlineality of the objective function and constraints can been seen and this make the objective function or constraints the complex form about the design variables. On the other hand, in the mult-objective optimization problems, we have to calculate the pareto optimal set that could not be defined the inferiority or supriority among the solutions. The pareto optimal set forms the hyper plane in objective function space and the sensitivity of this plane make us to be able to do the trade-off analysis among the objective functions. The difficulty to obtain pareto optimal set could be seen in calculation because of the nonlinearity of the objective function and constraints. That is, it seems to be difficult to fund some part of pareto optimal set in probablistic method. In this study, we will approximate the pareto optimal set using response surface methodology and identify the region that needs evaluation. Through numerical example, we will discuss the fundamental charastaristics of the proposed method
