# Development of Practical Design Approaches for Water Distribution Systems
## 4 Application and Results  
This section presents the results of the computational experiments obtained using the practical WDSs design approach for the pipe size continuity of the three WDSs introduced in the previous section. For the hydraulic analysis, the Application for Modeling Drinking Water Distribution Systems (EPANET) [24] hydraulic solver was used to calculate the hydraulics and check the necessary hydraulic constraints. This model contains a flow conservation method and various types of head loss formulations (i.e., Hazen-Williams, Darcy-Weisbach, and Chez-Manning equations). Combining this model with the proposed WDSs design approach, the hydraulic analysis results (i.e., the nodal pressure and pipe velocity) and flow direction (i.e., upstream and downstream) were checked as design constraints. The simulation was performed on a Windows 7 Home Premium K 64-bit OS, Intel i7 CPU 3.40 GHz processor and 8.00 GB RAM computer. The parameters of the optimization  
Figure 4: Layout of study networks (**a**) Hanoi network, (**b**) Fossolo network, and (**c**) Cycling network.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Problem** & **NP** & **NN** & **PD** & **PCD** & **SS** & **Iteration** \\ \hline \multirow{3}{*}{Hanoi network} & \multirow{3}{*}{34} & \multirow{3}{*}{32} & 304.8, 406.4, 508.0, & 45.72, 70.40, 98.37, & \multirow{3}{*}{\(2.87\times 10^{26}\)} \\  & & & 609.6, 762.0, 1016 & 278.28 & \\ \hline \multirow{6}{*}{Fossolo network} & \multirow{6}{*}{36} & \multirow{6}{*}{58} & 16, 20.4, 26, 32.6, & 0.38, 0.56, 0.88, & \multirow{6}{*}{\(1.35\), \(2.02\), \(3.21\), \(4.44\), \(6.45\), \(9.59\), \(1.05\), \(11.98\), \(14.93\), \(19.61\), \(24.78\), \(30.55\), \(38.71\), \(47.63\), \(59.7\), \(75.61\), \(16.24\), \(46.25\), \(160.29\), \(197.71\)} \\  & & & 113, 126.6, 144.6, & 72.2, 9.1, 11.92, & \multirow{6}{*}{\(1.16\times 10^{178}\)} \\  & & & 162.8, 180.8, 226.2, & 14.84, 18.38, 28.6, & \\ \cline{1-1}  & & & 285.0, 361.8, 452.2, & 45.39, 76.32, & \multirow{6}{*}{\(1.16\times 10^{178}\)} \\ \cline{1-1}  & & & 581.8 & 124.64, 215.85 & \\ \hline \hline \end{tabular} Note: NP = number of pipes; NN = number of nodes; PD = pipe diameter (mm); PCD = pipe cost data (m/unit cost); SS = search space size.  
\end{table}
Table 3: The specification of the applied networks.  
algorithm are applied through the sensitivity analysis. The HMCR is varied from 0.7 to 0.95, and the PAR is varied from 0.05 to 0.3 in 0.05 intervals. Therefore, a total of 36 parameter sets are used for 10 independent optimization runs. The 10 results for each test problem and optimization algorithm are compared using performance and the best parameter set is decided. For the same comparison, the parameters and penalty function are the same in the results applying the existing study and the proposed continuity approach.  
First, design problems i.e., the Hanoi network is used to compare the performance of the proposed approach and the existing study [10] on optimal design cost and computation time for each standard iteration number. The Fossolo network shows continuity at the confluence point, which is an improvement of the proposed continuity approach. This network is performed in a single-objective optimization framework condition such as the Hanoi network. The Cycling network is applied to the multi-objective optimization framework. The simulation results compare the pipe diameter distribution and network configuration for the proposed technique and existing approach. The following chapter shows the simulation results for these three applied WDSs.