Trust-region based algorithms with low-budget for multi-objective optimization

In many practical multi-objective optimization problems, evaluations of objectives and constraints are computationally time-consuming because they require expensive simulations of complicated models. In this paper, we propose a metamodel-based multi-objective evolutionary algorithm to make a balance between error uncertainty and progress. In contrast to other trust region methods, our method deals with multiple trust regions. These regions can grow or shrink in size according to the deviation between metamodel prediction and high-fidelity evaluation. We introduce a performance indicator based on hypervolume to control the size of the trust regions. We compare our results with a standard metamodel-based approach without trust region and a multi-objective evolutionary algorithm. The results suggest that our trust region based methods can effectively solve test and real-world problems using limited solution evaluations with increased accuracy.