# Development of a Multi-Objective Optimal Design Approach for Combined Water Systems
## 1 Introduction  
A combined water system is an operations and modeling system that analyzes and combines a water distribution system (WDS), an urban drainage system (UDS), and a water reuse system (WRS). A water distribution system aims to supply a sufficient quantity of water from water sources to consumers at an adequate water pressure and safe water quality so that water is supplied even in abnormal circumstances in the same way as that used under normal circumstances. A stormwater drainage system aims to prevent inundation damage caused by flooding and improve public health and sustainable development to allow for coexistence with the local environment. Although the frequency and intensity of floods are increasing in Republic of Korea due to an increase in precipitation due to climate change, it is expected that usable water will continue to be insufficient [1, 2]. In addition, it declares water shortage due to the increase in water consumption per capita and urban development. Accordingly, it is necessary to establish a stormwater drainage system, efficient operation of a water supply system, and a WRS. Previous studies have focused on using rainwater to minimize the impact of drought and water shortage. The hydrological operation method and optimal capacity of the rainwater storage tank in the building were determined through the analysis of thecapacity, usage rate, and reliability of the rainwater storage tank, and the effectiveness and applicability were judged [3; 4; 5; 6]. In addition, [PERSON] and [PERSON] [7] performed an optimal design by introducing a hydraulic-hydrological optimization formula using the trade-off between the capacity of a rainwater storage tank for rainwater collection and the capacity of use time. Furthermore, the feasibility of water reuse in large-scale areas, rather than existing buildings or small-scale greywater use, was evaluated from a hydraulic point of view, and a positive evaluation was made in areas with water shortages [8]. Moreover, in a study using gray water to solve water shortage, a collaborative hydraulic analysis approach was presented with EPANET, a WDS hydraulic analysis solver, for hydraulic analysis. [PERSON] and [PERSON] [9] presented a simulation methodology for small-scale WRSs, and the efficiency and feasibility analysis results of WRSs emphasized the need for WRSs in the future in terms of sustainability [10; 11]. [PERSON] et al. [12] demonstrated the economic effect of water demand reduction and water supply when using WRSs through various simulations. In addition, some studies have improved the hydraulic stability of WDSs by predicting the demand and supply of WDSs to prepare for water shortages [13; 14]. However, although the above studies improved the hydraulic stability of WDSs through rainwater reuse or water reuse, UDSs lacked preparation for future uncertainties such as water shortage prevention, urban population concentration, and water shortage. In this way, combined hydraulic simulation is needed to solve the problems of WDSs and UDSs at the same time. To solve this problem, [PERSON] and [PERSON] [15] and [PERSON] et al. [16] developed a model that integrates EPANET, a WDS hydraulic solver, and EPASWMM, an urban flood analysis program. However, although the above studies predicted demand through an integrated model, reused water in the WRS does not undergo chemical disinfection and sterilization, unlike normal tap water for WDSs; therefore, WRSs and WDSs should be designed separately. Therefore, this study proposed an optimal design technique for combining WDSs, UDSs, and WRSs to overcome water shortage and reduce excessive flooding damage due to extreme climate change. The proposed design approach combines EPANET and EPASWMM, which are the hydraulic solvers for WDS and UDS analysis. In addition, since the hydraulic analysis for WRSs has not been developed, EPANET was configured to supply water to consumers using water from rainwater storage tanks as a limited reservoir to simulate a WRS.