Multi-objective Optimization Using Variable-Fidelity Models and Response Correction

Abstract

Vast majority of practical optimization problems are of multi-objective nature. In many cases, especially if the designer’s priorities are known beforehand, the problem can be turned into a single-objective one by selecting the primary goals and handling the remaining objectives through appropriately defined constraints. Also, it is possible to aggregate the objectives into a scalar cost function using a weighted sum approach or penalty functions. In some situations, however, it is important to obtain more comprehensive information about the system at hand, in particular, to identify the best possible trade-offs between conflicting criteria. In such cases, defaulting to genuine multi-objective optimization is a necessity, which further increases the complexity of the optimization task. Perhaps the most popular multi-objective optimization approaches are population-based metaheuristics (Deb 2001). These techniques are capable of yielding the entire representation of the so-called Pareto front (Fonseca 1995) in one algorithm run; however, the computational cost of evolutionary optimization may be very high: thousands or even tens of thousands of objective function evaluations. Consequently, direct multi-objective optimization of expensive simulation models is normally prohibitive. In this chapter, we discuss multi-objective optimization of expensive models using surrogate-based optimization, particularly response correction techniques. Our considerations are illustrated using examples from the areas of microwave and antenna design as well as aerospace engineering.