Add optimization flowchart and update manuscript for clarity in surrogate validation process

Code/data/width_optimization/5W/ml_FEMdata_B34_H60.csv

@@ -65,3 +65,4 @@ tw1,tw2,tw3,tw4,tw5,Exymax_tw1,Exymax_tw2,Exymax_tw3,Exymax_tw4,Exymax_tw5,Eyyma
 5.68,13.91,12.58,11.42,5.93,0.066269,0.0164049,0.0266002,0.0471815,0.0612316,0.1382278,123.0662,24.2749,43.1425,56.6075,108.8461,93.968
 5.97,7.38,8.56,6.7,5,0.0563488,0.0518778,0.0596584,0.0712373,0.058239,0.1229254,84.9512,90.6505,87.9108,81.0599,74.1754,79.1536
 5.76,7.37,8.46,6.67,5,0.0639787,0.0567935,0.0649195,0.0784367,0.0623609,0.123282,95.5551,95.9207,92.8609,85.1741,71.371,75.1903
+5.74,7.46,8.5,6.37,5,0.0608158,0.0533472,0.0592435,0.0745284,0.0584155,0.122158,91.9273,89.749,87.5211,86.6953,72.876,78.1919

Manuscript/RESILINK_surrogate_optimization_manuscript.tex

@@ -304,12 +304,13 @@ H30\_B34 & 0.0410, 0.0265, 0.0240, 0.0098, 0.0098 \\
 
 The surrogate-optimized geometry is not accepted directly. Instead, once an optimal geometry is identified by the surrogate-assisted optimizer, it is re-evaluated with FEM to verify that the surrogate remains accurate in the region of the design space where the optimum lies. This validation step checks whether the surrogate has remained reliable in the region of the design space selected by the optimizer. The candidate geometry is accepted only if: (i) the prediction error of all damage and distortion variables remains below the prescribed tolerance, equal to 5\%; (ii) the absolute error of the objective function remains within the admissible limit, set to 10; and (iii) the optimized window thicknesses remain stable between consecutive optimization iterations, with variations smaller than the 5\% of the full design range. If any of these criteria is not satisfied, the new FEM result is incorporated into the training dataset and the surrogate models are retrained.
 
-If all criteria are satisfied, the FEM-validated geometry is accepted as the optimized design. If at least one criterion is not satisfied, the new FEM result is added to the dataset, the surrogate models are retrained and the DE optimization is repeated. This loop is summarized in Figure~\ref{fig:adaptive_loop}. The process reduces the risk of accepting a geometry that is optimal only because of surrogate extrapolation error.
+If all criteria are satisfied, the FEM-validated geometry is accepted as the optimized design. If at least one criterion is not satisfied, the new FEM result is added to the dataset, the surrogate models are retrained and the DE optimization is repeated. This loop is summarized in Figure~\ref{fig:OptimizationFlowChart}. The process reduces the risk of accepting a geometry that is optimal only because of surrogate extrapolation error.
 
-\begin{figure}[t]
-\centering
-\fbox{\parbox[c][0.24\textheight][c]{0.85\textwidth}{\centering Placeholder for adaptive loop: FEM dataset $\rightarrow$ surrogate training $\rightarrow$ DE optimization $\rightarrow$ FEM validation $\rightarrow$ accept or retrain.}}
-\caption{Adaptive FEM validation and retraining loop. The optimized geometry is accepted only when prediction errors, objective error and geometry stability criteria are simultaneously satisfied.}\label{fig:adaptive_loop}
+\begin{figure}[!ht]
+  \centering
+  \includegraphics[width=1.0\textwidth]{./Figures/OptimizationFlowChart.png}
+  \caption{Surrogate-assisted optimization and FEM validation retraining loop.}
+  \label{fig:OptimizationFlowChart}
 \end{figure}
 
 \section{Planned numerical assessment}\label{sec:planned_results}