# Qualification of Hydraulic Analysis Models for Optimal Design of Water Distribution Systems
## 3 Application and Results
### Optimal Design Water Distribution Systems  
In the above hydraulic results, which applied abnormal system conditions (i.e., fire flow and pipe breakage), the relationship of pressure and acquired actual demand was analyzed under DDA and PDA. According to the results of the above analysis, this chapter performs the optimal design of WDSs by considering each hydraulic analysis approach and compares the results. Each optimal design of WDSs is performed using metaheuristic optimization algorithm by considering the least-cost as an objective function and the threshold for nodal pressure as constraints. In the optimal design using the PDA method, a different percentage of pressure-driven analysis is implemented to derive the characteristics (e.g., the construction cost of the design and supply flow rate) according to the degree of PDA. Moreover, to compare the construction costs of applying PDA and DDA, GA was applied to minimize the pipe construction cost for the three benchmark networks. The parameters of GA are used according to the sensitivity analysis. In the sensitivity analysis, the number of populations considers 10 to 50 interval 10. In addition, the crossover rate (0.7-0.99, interval 0.05) and the mutation rate (0.05-0.3, interval 0.05) are considered for generating parameter combinations. Among these parameter combinations, the best set of parameters is used for the comparison results. A minimum threshold that represents the minimum pressure in every node was assumed for both approaches. The two-loop network considered 20, 30, and 40 m as minimum thresholds; the Hanoi network applied 30 and 40 m; and the Balerma network assumed 20 and 30 m. Various percentages of pressure-driven analysis (PDA) were implemented (0%; DDA, 20%, 40%, 60%, and 100%) to visualize the change in the cost of designing the network. The design cost of the benchmark networks and the results of this analysis are presented in Figure 12 and Table 4.  
According to the optimal design using different hydraulic analyses (DDA and PDA), the results presented a trend of the construction cost with various PDA% under the minimum threshold. In the case of the two-loop network, by increasing the percentage of the PDA in the hydraulic design of the network with interval 20% from 0% (DDA hydraulic analysis) to 100% (full PDA hydraulic analysis), the construction cost diminishes by about 6%-17% because of the quantity of the demand change with the actual demand based on the pressure-driven model. However, the two-loop design cost is a bit higher than 60% of PDA% in 100% PDA, which would be reflected by the network characteristics for the size and network configuration (consisting of a looping system and no branch). The main cause of this trend is the decrease in pipe diameter to satisfy the minimum threshold of each node, and the PDA percentage increases and the fixed demand decreases, resulting in the reduction of the construction cost. This is because an increase in the minimum threshold caused a decrease in the construction cost. Especially, in the case of the Hanoi network,  
Figure 11: Hydraulic pressure in each node for DDA and PDA in the Balerma network (Scenario 2).  
since the network size is larger than the two-loop network, the increment of the minimum threshold and PDA percentage makes the rate of reduction in the construction cost enlarged. For the same reason, the design cost variance of the Balerma network is larger than that of the Hanoi network by up to 9%. Furthermore, when selecting a minimum threshold of 40 m and an analysis entirely using PDA, the minimum cost can be reached.  
Figure 12: Cost comparison for two minimum thresholds for the benchmark networks: (**a**) Two-loop network, (**b**) Hanoi network, (**c**) Balerma network.