# Development of Practical Design Approaches for Water Distribution Systems
## 1 Introduction  
Water distribution systems (WDSs) are one of the fundamental social factors for reliably supplying the water required for all human activities in modern society. The main purpose of WDSs is to provide sufficient amounts of water with excellent quality at sufficient pressure. To satisfy these objectives, research has been performed for optimal operation/maintenance and design. The optimal design of WDSs started with a cost-effective objective while satisfying the hydraulic and water quality constraints. Early WDSs were designed by trial and error based on the experience of designers. However, such designs could not guarantee optimal or near-optimal solutions, because they overly relied on professional experience. Subsequently, the mathematical design algorithms such as linear programming [1], dynamic programming [2], and non-linear programming [3] have been explored for achieving optimal cost design. Mathematical optimization algorithms are easy to apply in small-scalesystems in which the elements of all systems can be easily expressed in equations. However, it is not easy to apply in real-world systems [4]. This is relevant because the governing equations of WDSs (i.e., the energy and conservation of mass equations) are characterized by non-linearity for the hydraulic analysis. In the case of distribution networks characterized by the loop form, the flow direction through each pipe is variable. Taken together, an increase in the number of joint points and pipes exponentially increases the range of possible solutions. Therefore, there are limitations for optimal cost design using mathematical equations. For these reasons, a metaheuristic algorithm was developed and applied in WDSs design to overcome the drawback of previous approaches. There are examples of metaheuristic techniques being applied in the optimal cost design of water distribution networks, such as genetic algorithm (GA) [5; 6], simulated annealing (SA) [7], ant colony optimization (ACO) [8], and harmony search (HS) [9]. Since these algorithms address the non-linearity and complexity of designing WDSs by using probability-based approaches, they have advantages over mathematical design methods. However, the application of a metaheuristic algorithm for the optimal design of WDSs has limitations in the real world. The construction of real-world WDSs considers the conditions of the construction site and the efficiency of construction (i.e., pipe continuity and abnormal conditions). On the other hand, the design using the metaheuristic algorithm generally determines the optimal pipe diameter set for minimizing construction cost under satisfactory hydraulic and water quality regulations. [PERSON] et al. [10] concluded that when the optimal cost design of real-world WDSs is used by the metaheuristic algorithms, it does not satisfy the pipe size continuity of pipes, and its practical applicability declines. Moreover, they emphasized that if the optimal cost design is performed with the consideration of hydraulic constraints such as nodal water pressure and flow rate in pipes, the neighbor pipe diameter may have abnormal unevenness (e.g., a concave-convex pattern) of flow direction. They defined the pattern of the neighbor pipe diameter as a pipe continuity. If the design did not satisfy the pipe size continuity, it had low practical applicability for the WDSs construction [11]. Therefore, these studies improved the drawback of the design approach that used the metaheuristic optimization algorithm, which determines the abnormal concave-convex pipe diameter pattern based on the objective function, e.g., minimum cost. These studies controlled the pipe size to smoothly increase and decrease, thereby obviating the abnormal unevenness pattern. Due to increasing urbanization and population, the previous system's capacity was exceeded, and even a minor failure in the system caused serious damage for both water users and the system.