**3. Study Network**

The proposed optimization approach is applied for optimal design of a well-known benchmark WDS, the Anytown network. The network, which was firstly published by Walski *et al.* [56], was modified by Jung *et al.* [11] for pipe only and pipe/pump designs that minimize total cost and maximize system robustness. The original benchmark network was modified by removing the two tanks and the connected riser pipes to be solely supplied by a single reservoir with a fixed source head. The fixed source head is elevated from 3 m (10 ft) to 73.2 m (240 ft). A peaking factor of 1.8 is applied to given average-based demand (2005 average daily use) to create the daily peak condition.

Other modifications of the study network were made for application purposes. First, this study suggests new pipe layouts and sizes assuming there are no existing pipes in the system. Pump and tank design are not considered. Second, in addition to 10 commercial pipe sizes (152, 203, 254, 305, 356, 406, 457, 508, 610, and 762 mm), zero diameter can be selected suggesting no pipe installation for the potential path. The unit costs of the commercial pipes are adopted from Walski *et al.* [56].

To generate random epicenters, a 2 ˆ 2 grid was created and laid on the study network as seen in Figure 3. The rectangular boundary of the grid is defined by the four end nodes: north, south, east, and west. Total 900 earthquakes are generated and consistent number of earthquakes are assigned at each corner of the grid (marked as "x" in Figure 3). The earthquake intensity reached at the pipe is a function of the earthquake magnitude and the Euclidean distance from the epicenter. Note the earthquake magnitude of M4 was generated from each corner of the grid. The minimum pressure requirement of 28.12 m (40 psi) should be satisfied under based demand condition and is also considered in Equation (7).

**Figure 3.** Study network layout (epicenter is marked as "x").

HSA was used to find an optimal solution for the pipe sizing problem. HSA was inspired by musical performance process and widely used for WDS optimizations. While the applications encompass from pipe network design to pump scheduling, HSA was proven to be generally outperform other algorithms such as genetic algorithm [57–59].

Several assumptions and simplifications were made in this study: (1) the seismic damages of the pump, tank, reservoir, and valve are not considered; (2) the earthquake's focal depth (tectonics) is assumed to be 10 km; (3) the coordinate of the center of the pipe is used as a reference point for calculating the distance from the epicenter; (4) Pipes are cast iron pipes; and (5) the Anytown network is laid on the alluvial plain with no liquefaction. Based on the assumption (4) and (5), all correction factors except C1 in the Equation (4) (C2-4) are equal to one.
