For expensive computational simulations, such as the finite element method (FEM) or computational fluid dynamics (CFD), whose evaluation can take even tens of hours or more, the use of direct optimization is often not feasible in practice. If simplifying the model is not an acceptable option, an alternative is to train a cheaper surrogate model on a limited amount of samples. This is called the surrogate-based optimization (SBO) approach. It consists of four main steps: 1) sampling , 2) computational analyses, 3) surrogate’s training, 4) optimization. Due to the repetitiveness, the evaluation of the samples is the primary bottleneck, therefore the smart selection of the training samples is of primary importance. The design of experiments (DoE) is a systematic approach of determining the samples. Static DoEs have been used and studied extensively. However, they are designed to covert only the input space uniformly, which means that only a half of the available information is used. Therefore, adaptive DoE methods that consider also the response in the determination of new samples have been proposed as an improvement. In the last 10 years, their research has gained momentum and numerous adaptive DoE methods have been proposed. The identified scientific gap is the lack of their overview as well as numerical benchmarking. Within this master thesis project, a modular SBO framework, suitable for such benchmarking, was developed, and the proposed adaptive DoE methods reviewed in more detail. With this at hand, a follow-up work can smoothly proceed into the actual benchmarking, which is estimated a task of itself for a project of similar master thesis scale. The results presented within this master thesis include the validation of the framework on the MATLAB peaks, Binh and Tanaka benchmark problems and the proof-of-concept evaluation of adaptive DoE on the MATLAB peaks, Judge, McCormick and Michalewicz problems against static DoE. It is demonstrated that using an adaptive DoE, the amount of required training samples is lower, or the same at worst, as with the static DoE. Additionally, thanks to the cooperation with Škoda Transportation, the practical use of the framework is presented on a structural FEM optimization of a novel tram car body, the SegTram. The developed framework is suitable both for research purposes as well as practical, industrial applications, and it is openly available at github.com/apanzo/optimization.