## 3 Results and Discussion
### Adjustment of Local Search Algorithm Parameters  
The optimization algorithm run in the previous section is suitable for solving shape optimization tasks. However, the question arises if there is an adjustment appropriate for increasing the precision and efficiency of the algorithm. The main goal of this section is to adjust the parameters of the local search algorithm for the investigated shape optimization task. The stochastic search algorithm can only find the acceptable environment of the global optimum with an appropriately high number of iterations, which means a computationally expensive procedure. Calculation of the finite element model is a time-consuming task, which makes it impossible to investigate the search algorithm parameters. Model SVM, which was trained before, provides a suitable approach for describing the relation between the design variables and objective function values, while running it is less time consuming. By running model SVM, there is an opportunity to test the effects of adjusting the algorithm parameters in terms of optimal search precision and efficiency. By doing so, we can observe the behavior of the original model on a well-approximating function. While training the algorithm, the \(\sigma\in[\)1; 5; 10; 30\(]\) standard deviation is selected parameter by parameter. Table 4 includes algorithms of different settings between P-I and P-IV.  
The starting point is chosen at random from the design area, while the search direction of the algorithm is stochastic too, whereby each adjustment is run ten times. The number of the better function accepted after the starting point should be marked by \(k\). Table 5 includes the last accepted \(k\) value and \(m\) iteration number belonging to it, as well as the target function value \(E\big{(}\textit{d}_{opt}\big{)}_{SVM}\) belonging to the  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **P-I** & **P-II** & **P-III** & **P-IV** \\ \hline maximum iteration number, \(m_{max}\) & 5000 & 5000 & 5000 & 5000 \\ standard deviation, \(\sigma\) (mm) & 1 & 5 & 10 & 30 \\ \hline \end{tabular}
\end{table}
Table 4: Different settings of local search algorithms.  
Figure 6: Investigated design points by the local search algorithm.  
optimum location that can be found on the surrogate model. Based on the results, it can be pointed out that the algorithms got stuck in the local optimum while being run several times. The search process adjusted by P-IV found the optimum environment expected in all ten cases of being run, but not in a sufficiently good environment. This proves the fact that it lags behind the minimum values found during the P-I adjustment. There were even cases when the algorithm did not manage to find a single better solution after iteration 370. This was mainly caused by the big search space, due to which the chance to find a better solution while approaching global optimum converges to zero. The only solution seems to tighten the search space. By applying P-IV adjustment, the algorithm moves out its local minimum environment during 1000 iterations in 8 cases out of 10, whereas it occurred in 9 cases out of 10 during 2000 iterations.