A multi-objective optimization strategy based on combined meta-models: Application to a wind turbine

Many types of optimization problems involving expensive functions have been handled successfully by meta-model-based optimization (MBO) methods. However, some particular difficult problems, such as multimodal functions, which require an accurate approximation even around local optima, still prove challenging for MBO. Generally, this type of problems is solved by combining or assembling meta-models. This paper proposes a new strategy of combining a global meta-model with many mid-range ones. The latter are constructed on sub-regions where the global meta-model is inaccurate. These mid-range meta-models are constructed in two phases. The first phase aims to explore accurately all the design space; whereas the second phase aims to provide more accurate solutions than those of the global meta-model on regions of interest (exploitation). The set of sub-regions can be updated adaptively until reaching the meta-model target accuracy. This two phases' adaptive process prevents the over sampling of non-interesting regions, which allows gaining significantly in the cost. The proposed strategy is tested using the following techniques: Radial basis function (RBF) and Non-dominated Sorting Genetic Algorithm (NSGA-II). This strategy is tested both on difficult mathematical benchmarks and on an engineering application giving satisfactory results. The considered engineering application aims to optimize the operation of a vertical axe wind turbine.