# Development of a Multi-Objective Optimal Design Approach for Combined Water Systems
## 3 Application and Results
### Combined Water System Single-Objective Optimization  
The stormwater drainage system was designed for a 30-year frequency design precipitation intensity to accommodate increased precipitation volume, and the capacity of the WRS rainwater storage tanks was calculated based on the flood volume of the stormwater drainage system at a 50-years frequency design precipitation intensity. In addition, flow control valves and dummy nodes were used to differentiate demand volumes. In the model, EPANET control rules were applied so that the water in the rainwater storage tanks could be used first, and potable water was used when the water level in the rainwater storage tanks fell to 0 m or below. In addition, the installation locations for the rainwater storage tanks were set so that they could be used primarily after chemical treatment, considering the surrounding local environment. Furthermore, the maximum height of the rainwater storage tanks was fixed at 3 m, and the diameter of the rainwater storage tanks was set according to the flood volume resulting from a 50-year frequency design precipitation intensity.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Solution** & **Cost (K KRW)** & **Resilience** \\ \hline Existing design & 12,667,965.6 & 0.537 \\ \hline Optimal design & 11,922,710.0 & 0.543 \\ \hline Difference & 745,255.6 & 0.006 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison results between optimal design and existing design for the WDS.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Solutions** & **Cost (K KRW)** & **Volume of Flood Water (10\({}^{6}\) ltr)** \\ \hline Existing design & 2,514,715 & 28.056 \\ \hline Optimal design & 2,167,664 & 0 \\ \hline Difference & 347,051 & 28.056 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison results between the optimal design and existing design for UDSs.  
Figure 9: Pareto-optimal solutions for the optimal design of urban drainage systems.  
Single-objective optimization was performed on the combined water system, which combines a water distribution system, a stormwater drainage system, and a WRS. A constraint condition was set so that flood volumes did not exist at a 30-year frequency design precipitation intensity, and the continuity of the stormwater drainage system pipe was considered. The water distribution nodes and water reuse nodes were set up so that they met the Korean water distribution system standard for the minimum pressure required by a pipe network, which is 15 m. Figure 10 shows the convergence of the single-objective optimization as it minimizes the total design cost of the combined water systems.  
Figure 10 shows the convergence of the design cost starting when the penalty function was not in effect because of the constraints, and the total construction cost was calculated as 11,880,705.78 (K KRW). This design cost is 787,259.82 (K KRW) higher than that of the existing water distribution system. A relatively high design cost was calculated because the design costs of the stormwater drainage network and water reuse network were added to it. However, it was possible to derive a design that satisfied the requirements of the stormwater drainage system regarding pipe diameter continuity and flood volume at a 30-year frequency design precipitation intensity while satisfying the hydraulic constraints for the water distribution system and the stormwater drainage system. Thus, it was possible to devise a design approach that combines a stormwater drainage system and a water distribution system.