# Development of Practical Design Approaches for Water Distribution Systems
## 4 Application and Results
### Fossolo Network  
Optimal cost design was performed considering pipe size continuity in a Fossolo network. The results of the existing algorithm were compared to the results from the algorithm of this study. As a result of the pipe size continuity search algorithm in this study, we derived the optimal cost design satisfying pipe size continuity in which reasonable pipe sizes were placed at various joint points in the Fossolo network with consideration of flow. The average computation time for the optimal cost design was reduced by approximately 87% when compared to the existing algorithm.  
The results regarding the design costs and the average computation time in each algorithm applied in the Fossolo network are shown in Table 5. In the left panel of Figure 5, the red circle indicates the joint point showing the differences between the existing algorithm and the algorithm of this study. In the right panel of Figure 5, a magnified view of the red circle indicates the node number, pipe number, and flow direction. In other words, pipes P46 and P48 meet at node J23, then the water moves to pipe P47. The flow is increased from pipe P46 to pipe P47. However, the existing approach places the smaller size pipe in the position of pipe P47 rather than pipe P46. It is against the reasonable pipe size continuity considering the flow.  
On the other hand, the pipe size continuity search algorithm of this study reasonably places the pipe with a larger size pipe than pipe P46, because the increased flow at the pipe P47 is considered. Since we derive a design in which the larger pipe is placed in the position of pipe P47, the design cost is \(\copyright\)28,971.63, which is higher than that of the existing algorithm. However, reasonable pipe size continuity handling with consideration of flow can be made at the joint point where more than three pipes meet. The average time spent for the pipe size continuity search is reduced by 87% when compared to the existing algorithm. When the number of iterations was 500,000, the computation time was reduced by 43 h. When compared with the results of applying the algorithm in the Hanoi network, the reduction rate was changed from 83% to 87%, which was not a significant difference when compared with the existing algorithm. However, when the actual reduced time was compared with iterations = 500,000, it had changed by 30 h--from 13 h to 43. This suggests that the reduced search time appears more clearly when the number of nodes and pipes is increased, and the scale of the distribution network is increased.  
Figure 5: Complex joint point with pipe size continuity problem TC “Figure 4.2.1 Complex joint point with pipe size continuity problem” \(\backslash\)f C \(\backslash\)1 “1” \(\backslash\) (J23) using (**a**) the existing pipe size continuity search approach [10], (**b**) the continuity search approach proposed in this study.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Method**} & **Existing Pipe Size Continuity Search** & **Continuity Search Approach** \\  & **Approach**[10] & **Proposed in This Study** \\ \hline Design cost (\(\copyright\)) & 28,0/07.78 & 28,971.63 \\ \hline Mean calculation time & 49 h 51 min (Iterations = 500,000) & 6 h 34 min (Iterations = 500,000) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Optimization results and computational time for the Fossolo network.  
When the pipe size continuity search algorithm of this study is applied in the Fossolo network, the result demonstrates its pipe size continuity handling ability at the joint point. When it is compared with results of applying it in a Hanoi network, it is confirmed that the search time in a Fossolo network with a relatively larger scale is substantially reduced.