## 1 Introduction
Latin hypercube design was used as a design of the experiment technique. The results showed that in all problems the introduced SVR method performed more efficiently than the other methods [23]. A two-variable aerodynamic problem was introduced in [24] where the quasi-Monte Carlo algorithm was used to determine eight sample points. Poor space-filling properties of the quasi-Monte Carlo sampling left a noticeable gap in the data. In this area, inaccuracies were found in the prediction of the kriging and RBF model, and only the SVR method mitigated this problem. In [25; 26], vehicle crashworthiness designs were presented, where SVR was utilized to construct crashworthiness responses. It was demonstrated that SVR models with Gaussian RBF and exponential RBF have good generalization performance compared to other types of kernels. SVR outperforms polynomial response surface, radial basis neural network, and kriging with good accuracy in approximating the crashworthiness responses. A multiobjective crashworthiness design of a tailor-rolled blank thin-walled structure was constructed based on the \(\varepsilon\)-support vector regression (\(\varepsilon\)-SVR) technique and nondominated sorting genetic algorithm-II. The SVR parameters were further optimized with a genetic algorithm to improve the predictive accuracy of \(\varepsilon\)-SVR [27; 28]. Shape optimization of rubber bumpers, where obtaining data with finite element simulation is independent on the optimization algorithm, was investigated [29; 30; 31; 32]. Optimal shape was determined by minimizing the objective function by calculating differences in work energy. Design options obtained from design space, such as learning points, were applied. The SVR model was applied to determine the given values of the objective functions of further constructions. Through this metamodel, the optimal shape was determined. The SVR method was investigated by [PERSON] and [PERSON] [33] to predict the optimum shape of a rubber jounce. From the results, the cubic kernel function showed the best match, therefore it was chosen for the prediction of each combination of design variables. From the predicted values, the optimum shape was selected, which was sufficiently accurate if the number of the learning points was at least 22. This observation is used in the current rubber product optimization process. Based on the professional papers, the local stochastic search method is suitable for finding the global optimum of engineering optimization tasks. However, it is vital to find the right size of the search space to achieve good results. Due to the stochastic procedure, it is to be noted that one cannot conclude whether the adjustment is correct by simply running one instance. From the literature review, it can be seen that none of the research deals with setting the parameters of the applied optimization algorithms. The parameters highly influence the required finite element run and the accuracy of the determined optimum. All the case studies indicated that if enough set of training vectors are supported, the SVRis a promising metamodel technique for highly nonlinear engineering applications. The selection of the appropriate type of kernel function and hyperparameter choice is of vital importance for the right assessment. This article first introduces what considerations are necessary for the finite element analysis of axisymmetric rubber products, especially when exposed to pressure with special attention to the selected material model type and its parameters. The rubber bumper investigated in the paper is a case study based on an industrial design problem. Secondly, the task of two-variable shape optimization of a rubber bumper is described where the objective function values of 22 uniformly distributed samples from the design area were determined from the results of finite element analysis. The SVR surrogate model with cubic kernel function was trained utilizing the sampled experiments, whereby the relationship between the design variables and objective function values was described.