A TRUST-REGION ALGORITHM FOR HETEROGENEOUS MULTIOBJECTIVE OPTIMIZATION

This paper presents a trust-region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, given, for example, by a time-consuming simulation. For this function, derivative information cannot be used, and the computation of function values involves high computational effort. The other objective functions are given analytically, and derivatives can easily be computed. The method uses the basic trust-region approach by restricting the computations in every iteration to a local area and replacing the objective functions by suitable models. The search direction is generated in the image space by using local ideal points. The algorithm generates a sequence of iterates. It is proved that any limit point is Pareto critical. Numerical results are presented and compared to two other algorithms.