A multi-objective optimization methodology based on multi-mid-range meta-models for multimodal deterministic/robust problems

Abstract

The success of meta-model-based optimization primarily relies on how accurately the black-box functions are being represented. However, sometimes a global meta-model fails to achieve sufficient accuracy. This can be the case in multi-objective deterministic problems involving multimodal functions with competitive local optima or robust problems which require an accurate local description. This paper proposes a new methodology that deals with this type of situations and that provides the required accuracy both locally and globally. We use a set of mid-range meta-models which, in contrast to other works, are not used to construct a global meta-model but are managed both to compete and collaborate to solve the problem. They are defined across overlapping regions of interest generated by a process which resizes and moves adaptively these regions until tracking the Pareto front. The accuracy of these mid-range meta-models is also improved by a new design-of-experiment (DoE) adaptive technique allowing the suppression of some inefficient DoE points. The proposed method is implemented using standard techniques, such as non-dominated sorting genetic algorithm-II (NSGA-II), whereas the optimal shape factor of radial basis functions (RBF) is calculated by combining NSGA-II and particle swarm optimization (PSO). We also use Hager’s method to detect ill-conditioned systems and avoid propagating their outcome, which significantly improves the performance. This method is tested against difficult deterministic and robust multi-objective multimodal benchmarks and is applied to the robust optimization of an aerodynamic design case.