## 6 Conclusions  
Foremost, a finite element simulation-based two-dimensional shape optimization problem was introduced. The objective function was determined as the difference between the initial and the optimum characteristic and showed a valley-shaped behavior, which is itself a challenging task for a search algorithm. A simulated annealing algorithm with an adaptive search space and different cooling schedules was implemented in a MATLAB environment. Because of the time-consuming objective function call and the stochastic behavior of the SA algorithm, the parameter tuning process is infeasible with the direct call of the finite element simulation task. To solve the tuning process, a novel procedure was introduced using an SVR surrogate model to test the optimization algorithm performance case-specifically. Sampling took place by means of the maximin Latin hypercube design method to perform the SVR training, where the dataset of 40 samples proved to be suitable to surrogate the two-dimensional shape optimization task of the rubber product. The operation and robustness of the SA algorithm were tested by solving optimization test functions. The best performing parameters can be selected task-specifically using the empirically obtained discrete parameter domain from the literature. The optimum value is unknown by the algorithm, but it was able to approach it during the optimization of the mathematical test functions and the shape optimization task. This proves that the developed algorithm and its convergence criterion were correct. The tuned SA algorithm found an optimal design with negligible error from a technical aspect, thereby not increasing further the modelling errors due to nonlinear material behavior and large deformation. Each step of the metamodel-based parameter tuning of the optimization algorithm can be automated, thus eliminating the need for engineering intervention in simulation-based design processes. The developed method enables the prediction of the development lead time in simulation-driven optimization processes. In terms of precision and number of function runs required for optimum determination, the tuned SA algorithm proved to be efficient. The determination of the initial temperature on the surrogate model is accurate and saves a significant amount of time. Regardless of the complexity of the simulation task, the time required for the developed method is solely determined by the computation time of the surrogate model. The method aids market competitiveness due to the plannability and shorter design time. The newly introduced method opens up a slew of new research possibilities. One area is the large scale optimization problem for which the SVR surrogate model and SA algorithm are suitable methods. The surrogate model and optimization algorithm can be freely chosen in the developed parameter tuning process, allowing for the development of new methods as well as the assessment of their efficiency. Another extension of the developed method could be to perform a surrogate model-based parameter tuning of various global search algorithms to choose the best performer. In the future, the impact of the \(T_{0}\) initial \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Objective Function** & \(\overline{E}\Big{(}p_{opt}\Big{)}_{SA}\) & **SD of \(\overline{E}\Big{(}p_{opt}\Big{)}_{SA}\)** & \(\overline{T_{0}}\) & \(\overline{m}\) \\ \hline Cubic SVR & 0.07811 & 0.00032 & 20,430 & 561 \\ Ruber FEA & 0.08071 & 0.00145 & 20,367 & 576 \\ \(R\overline{E}[\%]\) & \(-3.221\) & - & 0.308 & \(-2.662\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Accuracy of the number of iterations and initial temperature determined by the run of the SVR model against the FEA. temperature of the SA can be investigated. The developed method is suitable for solving not only numerical simulation optimization problems but also for other computationally intensive model-driven optimizations. Conceptualization, D.H. and T.M. ; methodology, D.H. and T.M.