# Development of Practical Design Approaches for Water Distribution Systems
## 4 Application and Results
### Cycling Network  
The Cycling network is designed into the multi-objective optimization considering the least cost and maximum resilience with the pipe size continuity approach proposed this study. The optimization was independently performed 10 times by applying the same constraint conditions of both cost optimization only and the proposed approach in 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 Cycling network with consideration of flow.  
Figure 6 shows the Pareto optimal solution of the Cycling network, comparing the existing continuity approach and the proposed approach. The trend of Pareto fronts is the same, but the range of the solution using the existing approach is wider than the proposed approach. Moreover, even though the existing approach's solution had better diversity, 75% of the solutions in the Pareto optimal solution convergences for the proposed continuity approach were better. The results of the design cost statistic and continuity index in each algorithm applied in the Cycling network are in Table 6.  
The pipe size continuity search proposed in this study derives a design with a continuity index of 1, which means that the pipe size continuity is fully satisfied. Meanwhile, a cost optimization-only trial showed a mean continuity index of 0.732. The quantification indicators of pipe size continuity and  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Existing Pipe Size Continuity Search** & **Continuity Search Approach Proposed in** \\  & **Approach**[10] & **This Study** \\ \hline Cost (\$) & 1,230,844 & 1,230,385 \\ \hline Resilience & 0.1629 & 0.1634 \\ \hline Mean PCI & 0.732 & 1.00 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Optimization results and mean continuity index for the Cycling network. PCI: pipe continuity index.  
Figure 6: Pareto optimal solution for the Cycling network  
mean continuity index show a big difference between only cost optimization and a pipe size continuity search. The results from the Cycling network have shown that the pipe size continuity search of this study has a strong point when it compares the continuity index, but it has better convergence of design cost and resilience. When practical applicability is considered essential, the proposed pipe size continuity search is relatively competitive compared to existing WDSs optimization methods.  
The diameter distribution of the multi-objective optimal design using the pipe continuity approach is shown in Figure 7. The diameter of highest frequency is 226.2 mm in four cases, but the design of pipe size continuity proposed by this study uses larger pipes than the existing continuity approach. It means that the proposed approach considers flow at the confluence point.  
( TC \"Figure 4.3.2 Diameter histogram of HSA applied pipe size continuity\" \(\backslash\) f C \(\backslash\)1 \"1\" )The existing continuity approach considered all the possible flow paths in the distribution network, and the pipe size was gradually decreased on the basis of the flow direction of water, whereas this continuity approach considers not only the flow direction but also water flow at the confluence point. Therefore, relatively, many large pipes are needed after the confluence point, as shown in Figure 8.