## 5 Comparison of the Proposed Method with the Weighted Sum Methods
### Loads Are Borne by the Entire Structure
#### 5.1.2 Problem 2
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Load** & **Method** & **Topology** & \(c_{1}\) & \(c_{2}\) & \
\begin{tabular}{c} **Stress** \\ **Level 1** \\ \end{tabular} &
\begin{tabular}{c} **Stress** \\ **Level 2** \\ \end{tabular} \\ \hline \multirow{6}{*}{\(P_{1}=3.0\), \(P_{2}=7.0\)} & TEWS & \multirow{6}{*}{\(129.94\)} & TEWS & \multirow{6}{*}{\(196.70\)} & \multirow{6}{*}{\(\mathbf{196.70}\)} & \multirow{6}{*}{\(\mathbf{0.291}\)} & \multirow{6}{*}{\(0.143\)} \\  & (Stage 1) & & & & & \\  & BCM & & & & & \\  & (Stage 2) & & & & & \\ \hline \multirow{6}{*}{\(P_{1}=5.0\), \(P_{2}=5.0\)} & TEWS & \multirow{6}{*}{\(\mathbf{254.30}\)} & TEWS & \multirow{6}{*}{\(\mathbf{254.19}\)} & TEWS & \multirow{6}{*}{\(\mathbf{254.19}\)} & \multirow{6}{*}{\(\mathbf{0.299}\)} & \multirow{6}{*}{\(0.183\)} \\  & (Stage 1) & & & & & \\  & BCM & & & & & \\  & (Stage 2) & & & & & \\  & TEWS & & & & & \\  & (Stage 1) & & & & & \\  & BCM & & & & & \\  & (Stage 2) & & & & & \\  & TEWS & & & & & \\  & (Stage 1) & & & & & \\  & BCM & & & & & \\  & (Stage 2) & & & & & \\  & TEWS & & & & & \\  & (Stage 1) & & & & & \\  & BCM & & & & & \\  & (Stage 2) & & & & & \\  & (Stage 2) & & & & & \\ \hline \multirow{6}{*}{\(P_{1}=7.0\), \(P_{2}=3.0\)} & TEWS & \multirow{6}{*}{\(\mathbf{448.23}\)} & TEWS & \multirow{6}{*}{\(\mathbf{448.23}\)} & TEWS & \multirow{6}{*}{\(\mathbf{0.399}\)} & \multirow{6}{*}{\(0.180\)} \\  & (Stage 1) & & & & & \\  & BCM & & & & & \\  & (Stage 2) & & & & & \\  & TWS & & & & & \\  & (Stage 1) & & & & & \\  & BCM & & & & & \\  & (Stage 2) & & & & & \\  & TWS & & & & & \\  & (Stage 1) & & & & & \\  & BCM & & & & & \\  & (Stage 2) & & & & & \\  & BCM & & & & & \\  & (Stage 2) & & & & & \\  & (Stage 2) & & & & & \\ \hline \end{tabular}
\end{table} 
Table 7: _Cont._LC1 than in LC2 (0.291 vs. 0.143). This situation shows that controlling the compliance does not always help control the stress level arising in the structure. As previously discussed, this high stress level occurs in local regions where a fine-tuning operation can be applied to reduce the stress concentration phenomenon. To recapitulate Problem 2, in most load combinations, the proposed BCM method is more advantageous than the TEWS method; i.e., not only is the maximum compliance minimized; the stress level is also reduced after Stage 2. However, in certain cases, the stress level under the less severe loading condition becomes higher than that under the most critical loading condition, including cases marked in red in Table 7. In addition, some load combinations result in designs with gray regions, which require fine-tuning of the obtained structures. During the fine-tune process, local regions with stress concentrations can be modified. Thus, the stress level (under the less severe loading condition) can be reduced. By utilizing post-optimization fine-tuning operation, the proposed method can be used to minimize the maximum compliance first, and then the local stress concentration can be reduced after the fine-tuning process, obtaining the final design.