## 3 Optimization Strategies and Results
The results obtained from the current solution strategy are given in Table 2.  
**Strategy III:** Problem (10) is solved using a sequentially refined surrogate model. The strategy assumes starting from a low-resolution surrogate model and employs an adaptation of a design grid \begin{table}
\begin{tabular}{c c c c} \hline \hline \begin{tabular}{c} **Wire Diameter** \\ **Enumation Index** \\ \end{tabular} & \begin{tabular}{c} **Final Value of Objective** \\ **Function 1, mW** \\ \end{tabular} & \
\begin{tabular}{c} **Surrogate Model** \\ **Creation Time, s** \\ \end{tabular} &
\begin{tabular}{c} **Nonlinear Search** \\ **Execution Time, s** \\ \end{tabular} \\ \hline
1 & 6.08 & 4798.5 & 2.6 \\
2 & 6.58 & 4798.5 & 1.6 \\
3 & 6.72 & 4798.5 & 1.7 \\
4 & 6.91 & 4798.5 & 0.9 \\
5 & 6.73 & 4798.5 & 0.8 \\
6 & 6.66 & 4798.5 & 1.6 \\ \hline \hline \end{tabular}  
* Values obtained from computer model.  
\end{table} 
Table 2: Results of optimization using Strategy II. around the extremum to provide a reduction of execution time involving the creation of the surrogate model. The adaptation is performed repeatedly by adding extra LHS samples around the extremum unless the relative variation of the extremum is lower than the assumed error tolerance. At each adaptation step the algorithm adds ten extra LHS points. The term \"around extremum\" means that these points are generated in the same design space, although with the boundary limited to 20 percent (in each direction) of the value of solution in previous step. The search itself is carried out once again using the genetic and interior point algorithms one after another. The integer variable is constrained using the \"integer\" constraint equation, as in strategy 1. The pseudocode below explains the strategy: \begin{tabular}{l} \hline Set i = 0 \\  Generate coarse LHS grid \(\mathbf{X}_{\text{i}}\) \\  Round integer variable \\  Assume \(|\Delta\mathbf{X}|_{\text{max}}=0.01\) \\  Set \(|\Delta\mathbf{X}|=1\) \\  while \(|\Delta\mathbf{X}|>|\Delta\mathbf{X}|_{\text{max}}\) \\  Create 4-D surrogate model using \(\mathbf{X}_{\text{i}}\) \\  Find \(\mathbf{X}_{\text{i+1}}\) by optimization of surrogate model \\ \(\Delta\mathbf{X}=|\mathbf{X}_{\text{i+1}}-\mathbf{X}_{\text{i}}|/\|\mathbf{X}_{ \text{i}}\|\) \\  Add 10 LHS grid points around \(\mathbf{X}_{\text{i+1}}\) within \(\pm 20\%\) of directional value \\  Round integer variable \\  i = i + 1 \\  end \\ \hline \end{tabular}   
The results for different numbers of coarse LHS grid points are summarized in Table 3.  
The synthesis of all results leads to the following conclusions:  
* The most direct strategy (1) did not provide as high a value of power \(P\) as the other strategies even for a relatively fine LHS grid. The reason resides in the flatness of the objective function around the extremum. * Strategy 2 provides nearly the same values of power \(P\) as strategy 1, though exploration of the whole design space becomes extremely expensive. * Strategy 3 demonstrates the best performance with respect to the mentioned criteria. The highest value of power \(P\) found by the strategy confirms the flatness of the objective function, which can be correctly explored using only very fine design grids. It can also be seen from Table 3 that starting from a finer LHS grid can reduce the number of adaptation sequences. The differences between the values in the second and third row are related with the assumed error tolerance equal to 0.01 (see the pseudocode of the strategy III). The maximum power is given in the second row of Table 3. The corresponding optimum solution is \(\mathbf{X}_{opt}=(N_{t}=746,D=0.4\text{ mm},L=10.5\text{ mm},R_{t}=1824\text{ }\Omega)\). Figure 4 displays the distribution of