## 3 Results and Discussion
### Hydraulic and Economic Analysis  
Figure 13 represents how effectively each type of pipe (Pipes 1, 2, and 3) is being utilized compared with its initial capacity. The utilization index is calculated by taking the optimized length of each pipe type and dividing it by its original length, resulting in a ratio that indicates the extent to which the pipe's capacity is being used. A higher utilization index signifies that the pipe is being used more efficiently, whereas a lower index suggests underutilization. In addition, the cost contribution reflects how much each  
Figure 12: Cost reduction through CRA optimization of water distribution networks under three demand multipliers. pipe type contributes to the overall costs of the system based on its optimized length and associated cost per unit length. This metric provides insight into which components are driving costs within the network, allowing for better decision-making regarding resource allocation and potential areas for cost savings. Pipe 3 exhibits the highest utilization index, suggesting it is being utilized most efficiently relative to its initial capacity, followed by Pipe 2, and then Pipe 1, which shows the lowest utilization. The figure also depicts the cost contribution of each pipe type to the overall system cost. Notably, while Pipe 3 has the highest utilization, it also contributes the most significantly to the total cost (82.65%), indicating that despite being efficiently used, its length and/or cost per unit length are substantial drivers of the overall system expense. Pipe 2 contributes 13.22% to the total cost, while Pipe 1 contributes only 4.13%, despite having a non-negligible utilization index. This analysis highlights the trade-off between utilization and cost, providing valuable insights for optimizing network design by identifying potential areas for cost savings, such as potentially reducing the length or using less expensive material for Pipe 3, while ensuring sufficient capacity and utilization across all pipe types. Figure 14 illustrates the impact of varying demand multipliers on both the total optimized length of pipes and the associated total costs within a water distribution network. The optimized pipe length remains relatively constant across all demand multipliers. However, the top portion of each bar, representing the total cost, increases significantly with higher demand multipliers. This indicates that while the total length of pipes used in the optimized solutions does not change drastically with increasing demand, the cost of those pipes increases substantially. This cost increase is likely due to the need for larger-diameter pipes or higher-grade materials to accommodate the increased flow demands while maintaining adequate pressure. This visualization clearly demonstrates the trade-offs between meeting higher demand and the associated cost implications, highlighting the importance of considering demand projections and cost-effectiveness in the design and  
Figure 13: Utilization and cost characteristics of pipes in an optimized network design. optimization of water distribution networks. The diagram underscores that even when pipe length remains similar, the necessary changes in pipe characteristics to handle increased demand lead to considerably higher total costs. Figure 15 presents a bar chart of the total head loss for the studied network configurations. For each network, the head loss is the sum of friction losses (from pipe length) and local losses (due to fitting). As can be seen, WDN 1 and WDN 2 have almost identical head loss values because of their nearly similar geometries and flow rate assignments. The head losses in WDN 2 and WDN 3 are also analogous, indicating that--even though WDN 3 incorporates some distinct structural features and additional cumulative hydraulic losses--its overall hydraulic performance aligns closely with that of WDN 2. Figure 14: Optimized pipe lengths and total costs under varying demand. Figure 15: Comparison of total network head losses.