This paper presents a new trust region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, for example given 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. It is proved that the presented algorithm converges to a Pareto critical point. Numerical results are presented and compared to another algorithm.
Citation
Technische Universität Ilmenau, Weimarer Str. 25, 98693 Ilmenau, Germany, 03/2018