# Development of a Multi-Objective Optimal Design Approach for Combined Water Systems
## 4 Conclusions  
This study developed a multi-objective optimal design approach for a combined water system comprising a WDS, a UDS, and a WRS as one system. To consider the combined water systems design, the existing WDS demand was divided into drinking water and other uses (e.g., flushing toilets, cooling of industrial units, gardening water, etc.). Water for other uses is supplied by the WRS, and the resources of the WRS were assumed by the capacity of the rainwater storage tank for covering the amount of exceeding precipitation. To design the three combined water systems (i.e., WDS, UDS, and WRS), the objective functions were applied to the minimum construction cost of these systems, the maximum  
Figure 11: Pareto-optimal solutions of urban drainage systems and the red circle is each Pareto-optimal solution considering the minimum design cost and minimum flood volume as the objective functions. Figure 12: Pareto optimal solutions for combined water systems and WDSs. system resilience of the WDS and WRS, and the minimum flooding volume exceeding the designed rainfall intensity of the UDS. For the constraints, the minimum nodal pressures for the WDS and WRS and zero flooding in the designed rainfall intensity of the UDS were applied. The diameter of pipes and conduit was used as the decision variables, and to derive the reasonable optimal solution for three highly correlated systems, single- and multi-objective optimizations were performed and compared. First, the existing and optimal designs for the stormwater drainage system and the water distribution system were compared and analyzed. Doing so confirmed that, in the case of the water distribution system, the optimal design produces better resiliency than the existing one despite its low design cost. In the case of the stormwater drainage system, all the optimal designs were superior to the existing designs despite considering the continuity of the pipe. This confirmed that the existing designs are vulnerable to flooding and inundation despite being overdesigned. Second, an optimal single-objective design was created for the combined water system. A water distribution system analysis program and an urban runoff analysis program were combined to perform the optimization. The flood volumes produced as a result of the urban inundation analysis program were used as input data in the water distribution system analysis program to derive an optimal design that is superior in terms of both hydraulic stability and design cost. Third, an optimal design was derived for the combined water systems based on the multi-objective optimal design of the stormwater drainage system. The increase in the plan resiliency factor was slight compared with the increase in cost, but the results were superior to those of the existing design and the optimal design for the water distribution system in terms of resiliency and pressure. The stormwater reuse water was modeled as multiple sources to ensure resiliency against urban population concentration and rapidly increasing water usage. The increase in the resiliency factor was slight compared with the increase in design cost, but it was possible to develop an effective pipe network design method when considering future water resource usage costs and water reuse costs. Currently, water in WDSs is used for various uses such as drinking, irrigation landscapes, flushing toilets, river restoration water, and dividing water demand for reused water is expected to reduce the water treatment costs for generating drinking water. In future studies, the multi-objective optimization of WDSs, UDSs, and WRSs can be performed by examining the tradeoffs between the water treatment costs and design cost, system resilience, and CO\({}_{2}\) emission in the combined water systems. Furthermore, studies that consider not only hydraulic stability but also water quality safety should be able to assist managers and designers in their decision-making by providing various Pareto-optimal solutions. Conceptualization, Y.H.C. and M.J.K. ; Data curation, M.J.K.