## 1 Introduction
Nevertheless, part of the research is devoted not necessarily to the metamodels themselves, but to techniques that minimize the number of costly training samples needed to fit an efficient surrogate, or even to guide the sampling procedure based on areas of metamodel high uncertainty [16]--this technique is known as the infill process. Nonetheless, numerous papers utilize surrogates to replace costly computer simulations, e.g., as the authors of [17] minimized the mass of the jet engine components using ANN, which was carried out 40% faster than the optimization carried out on the numerical-analytical model. Moreover, the authors incorporated the infill process during the optimization. In [18], the Kriging method was used to solve the vibroacoustic problem when the objective function evaluation using the simulation was quite costly to perform the standard optimization. In [19], the authors incorporated the RSM to optimize the titanium alloy sheet forming process for medical applications, similar to the study in [20], where the energy system optimization was conducted using the RSM. The paper discusses and presents methods typical for problems where the calculation of the objective function is very time-consuming. Typically, the biggest problem is the determination of the parameters of the optimization algorithms. This is in most cases carried out by running the optimization algorithm multiple times with different parameters. Unfortunately, it is inefficient and the total calculation time is sometimes unacceptable. Using the methodology presented in the article, it is possible to select the parameters of optimization algorithms at a significantly lower cost, which allows for an effective, time- and price-acceptable approach to solving the optimization problem, utilizing the metamodeling technique. Metamodeling itself is usually used to replace the computer simulation during the optimization process, but for extremely nonlinear and multimodal problems, a sufficiently precise metamodel may not exist. That is why the authors use the surrogates to mimic the behavior of these complex systems and to perform the tuning of the optimization algorithm parameters, which will then be used to perform constrained mass minimization on FEM models. The description of the optimization problem is given in Section 2, highlighting the design variables, optimization objectives, and limitations of the FEM-based process. Section 2 considers the methods used to resolve the optimization problem, including the metamodeling part. The sampling plan for the surrogate training and validation process, metamodel types, and quality metrics are also described. The last part of Section 2 concerns optimization algorithms and their parameters, which will be subjected to the tuning process. The first part of Section 3 shows the results of the metamodeling approach, including a comparative study of the quality metrics. Then, the efficiency of optimization algorithms is shown depending on the algorithm parameters, which are then tuned to provide the most efficient optimization scenario. Section 3 is concluded with an example of the FEM-based optimization utilizing the best and worst algorithm parameter combinations for comparison and benchmark purposes. All conclusions and results are summarized in Section 4.