In modern engineering finding an optimal design is formulated as an optimization problem which involves evaluating a computationally expensive black-box function. To alleviate these difficulties, such problems are often solved by using a metamodel, which approximates the computer simulation and provides predicted values at a much lower computational cost. While metamodels can significantly improve the efficiency of the design process, they also introduce several challenges, such as a high evaluation cost, the need to effectively search the metamodel landscape and to locate good solutions, and the selection of which metamodel is most suitable to the problem being solved. To address these challenges, this chapter proposes an algorithm that uses a hybrid simulated annealing and SQP search to effectively search the metamodel. It also uses ensembles that combine prediction of several metamodels to improve the overall prediction accuracy. To further improve the ensemble accuracy, it adapts the ensemble topology during the search. Finally, to ensure convergence to a valid optimum in the presence of metamodel inaccuracies, the proposed algorithm operates within a trust-region framework. An extensive performance analysis based on both mathematical test functions and an engineering application shows the effectiveness of the proposed algorithm
