## 5 Comparison of the Proposed Method with the Weighted Sum Methods
### Loads Are Borne by the Entire Structure
#### 5.1.2 Problem 2  
Consider a cantilever structure with two distributed loading conditions, as shown in Figure 17. This problem differs from Problem 1 in the sense that the load type used is uniformly distributed instead of concentrated. The trend of applying the loads in the two load cases is also different; that is, LC2 is not a bending load but an axial load. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Load Combination** & **Method** & **Topology** & \(c_{1}\) & \(c_{2}\) & **Stress Level 1** & **Stress Level 2** \\ \hline  & TEWS & & 15.64 & **45.07** & 0.118 & **0.158** \\  & (Stage 1) & & & & \\  & BCM & & **42.43** & **42.43** & 0.135 & **0.152** \\  & (Stage 2) & & & & \\  & TEWS & & 40.36 & **46.96** & 0.143 & **0.164** \\  & (Stage 1) & & & & \\  & BCM & & 44.42 & **44.43** & **0.162** & 0.151 \\  & (Stage 2) & & & & \\  & TEWS & & **48.37** & **48.37** & 0.159 & **0.159** \\  & (Stage 1) & & & & \\  & BCM & & **48.37** & **48.37** & 0.159 & **0.159** \\  & (Stage 2) & & & & \\  & & & & & \\ \end{tabular}
\end{table} 
Table 4: _Cont._  
Figure 17: Loading conditions for Problem 2: **(a)** Load case 1; **(b)** Load case 2. The magnitude (\(P_{1}\)) of the loads in LC1 is defined as the sum of the distributed loads applied on the upper edge of the structure in LC1, and it can be calculated as follows:  
\[P_{1}=q_{1}\cdot l, \tag{19}\]  
Similarly, the magnitude (\(P_{2}\)) of the loads in LC2 is  
\[P_{2}=q_{2}\cdot h, \tag{20}\]  
where \(l\) and \(h\) denote the length and height of the considered structure, respectively. Like in the previous example, different load combinations were considered, in which the correlation between the two loading conditions is gradually changed in this example. When \(P_{1}=0.5\) and \(P_{2}=9.5\)  
This situation is characterized by disproportionately different force magnitudes under the two loading conditions. Such a load combination is highly uncommon in reality, and when considering this scenario in a TO context, it often results in unreasonable structures, e.g., the gray regions in the structures obtained for this particular load combination (Figure 18). Some researchers have addressed this issue using a load increment to intensify \"ill-loading\" conditions, thereby aiming to obtain a more reasonable topology [35]. Alternative approaches are available to subjectively intervene in the obtained structures to make them more realistic. These include the so-called fine-tuning process [67; 68; 69] (also known as refining, post-treatment, and post-processing), which involves modifying the structure to align it with the desired specifications. Typically, during the fine-tune process, a certain small amount of material is added to the structures to turn \"gray\" regions into \"black\" regions. At the same time, the process can also reduce stress concentration. In this article, we only consider different original load correlations and assume that in certain cases, it might be necessary to perform the \"fine-tuning\" process to the obtained structures to render them more realistic. In addition, it is straightforward to fine-tune such structures to enhance their ability to withstand the ill-loading conditions. Figure 18 illustrates the structures obtained using the TEWS and BCM methods. The two main bars in the BCM structure moved closer to each other and toward the horizontal central axis of the structure to withstand LC2 better. Thus, the BCM structure has advantages when bearing the two loading conditions compared with the structure obtained using the TEWS method, as its maximum compliance is lower (328.7 vs. 339.1) and the maximum stress level is also lower (0.16400 vs. 0.16844) (see Table 5). Both structures in Figure 18 necessitate a fine-tuning process because they both contain unreasonable regions (regions with gray elements) to bear the loads in LC1.