## 6 Comparisons between the Obtained Costs and Mases of Different Objective Functions
### Comparison of the Obtained Masses between the Mass Optimization and Other Performed Optimizations  
In order to investigate how different objective functions of the composite structure affect the amount of masses of the structures, the obtained optimal masses of the mass optimization (MASS) are compared with the masses and are calculated in the direct cost optimization and in the energy life-cycle cost optimization. The diagrams in Figure 13 show the calculated masses (kg/m\({}^{2}\)) of the CFSWIS structures. The diagrams are developed for different objective functions, i.e., the mass optimization of the structures (MASS), the direct cost optimization (DC), the energy life-cycle cost optimization for the energy efficient case (ELCC EEC), the energy life-cycle cost optimization for the energy inefficient case (ELCC EIC), and the energy life-cycle cost optimization for the high energy consumption case (ELCC HEC). Similarly, the diagrams in Figure 14 show the achieved masses (kg/m\({}^{2}\)) of the CFSIPE structures, while Figure 15 shows the obtained masses of the CFSHEA structures. CFSWIS structures: Figure 13 shows that when the direct cost optimization (DC) of the CFS structures is carried out, the structures exhibit 80% higher masses on average than when the optimal masses are calculated in the mass optimization (MASS). When the energy life-cycle cost optimization is performed, the composite structures exhibit 50% higher masses on average in the case of the energy efficient case (ELCC EEC), 35% higher masses on average in the case of the energy inefficient case (ELCC EEC), and 25% higher masses on average for the high energy consumption case (ELCC HEC); all of these values were compared to the optimal masses of the composite structures that were calculated in the mass optimization (MASS). CFSIPE structures: Figure 14 demonstrates that when the direct cost optimization (DC) of the CFS structures is carried out, the structures exhibit 60% higher masses on average than the optimal masses obtained in the mass optimization (MASS). When the large-cycle cost optimization is conducted, the composite structures exhibit 45% higher masses on average in the energy efficient case (ELCC EEC), 25% higher masses in the energy inefficient case (ELCC EEC), and 15% higher costs in the high energy consumption case (ELCC HEC). CFSHEA structures: Figure 15 shows that when the direct cost optimization (DC) of the CFS structures is carried out, the structures exhibit 85% higher masses on average compared to the optimal masses calculated in the mass optimization (MASS). When the energy life-cycle cost optimization is taken into account, the composite structures exhibit 60% higher masses on average in the energy efficient case (ELCC EEC), 35% higher masses on average in the energy inefficient case (ELCC EEC), and 20% higher masses on average in the high energy consumption case (ELCC HEC). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Objective** \\ **Function—Criterion** \\ \end{tabular} & \begin{tabular}{c} **Energy** \\ **Consumption** \\ **Case** \\ \end{tabular} & \begin{tabular}{c} **Welded** \\ **1 Sections** \\ **5 m \(\leq\) L \(\leq\) 50 m** \\ \end{tabular} & \begin{tabular}{c} **IPE Sections** \\ **5 m \(\leq\) L \(\leq\) 20 m** \\ \end{tabular} & \
\begin{tabular}{c} **HEA Sections** \\ **5 m \(\leq\) L \(\leq\) 25 m** \\ \end{tabular} &
\begin{tabular}{c} **Average Cost** \\ **Increment** \\ \end{tabular} \\ \hline DC & 0 kWh/m\({}^{2}\) & 1.00 & 1.00 & 1.00 & 1.00 \\ MASS & 0 kWh/m\({}^{2}\) & 1.20 & 1.15 & 1.20 & 1.20 \\ ELCC EEC & 50 kWh/m\({}^{2}\) & 1.65 & 1.45 & 1.40 & 1.50 \\ ELCC EIC & 100 kWh/m\({}^{2}\) & 2.30 & 1.85 & 1.75 & 1.95 \\ ELCC HEC & 200 kWh/m\({}^{2}\) & 3.50 & 2.60 & 2.40 & 2.85 \\ \hline \hline \end{tabular} Legend: DC, direct costs; ELCC, energy life-cycle costs; EEC, energy efficient case; EIC, energy inefficient case; HEC, high energy consumption case.  
\end{table}