Managing approximation models in multiobjective optimization

In engineering problems, computationally intensive high-fidelity models or expensive computer simulations hinder the use of standard optimization techniques because they should be invoked repeatedly during optimization, despite the tremendous growth of computer capability. Therefore, these expensive analyses are often replaced with approximation models that can be evaluated at considerably less effort. However, due to their limited accuracy, it is practically impossible to exactly find an actual optimum (or a set of actual noninferior solutions) of the original single (or multi) objective optimization problem. Significant efforts have been made to overcome this limitation. The model management framework is one of such endeavours. The approximation models are sequentially updated during the iterative optimization process in such a way that their capability to accurately model the original functions especially in the region of our interests can be improved. The models are modified and improved by using one or several sample points generated by making a good use of the predictive ability of the approximation models. However, these approaches have been restricted to a single objective optimization problem. It seems that there is no reported management framework that can handle a multi-objective optimization problem. This paper will suggest strategies that can successfully treat not only a single objective but also multiple objectives by extending the concept of sequentially managing approximation models and combining this extended concept with a genetic algorithm which can treat multiple objectives (MOGA). Consequently, the number of exact analyses required to converge to an actual optimum or to generate a sufficiently accurate Pareto set can be reduced considerably. Especially, the approach for multiple objectives will lead to a surprising reduction in number. We will confirm these effects through several illustrative examples.