This case study is a real problem which consists of designing a part of the water distribution system of the city of João Pessoa, in Brazil, known as Grande Setor WDN, and was first used by Gomes et al. (2009). Figure 1 presents the network topology. There are one reservoir, eight pipes linking six demand nodes, two loops, and a hydraulic pump with a water catchment level of 30 m, responsible for pumping water to the reservoir. Table 1 presents the nodes and pipe elevation, demand, and pipe lengths. Table 2 presents 10 commercial available diameters, costs, and the Hazen–Williams roughness coefficients. The costs were provided by Gomes et al. (2009) in R$ and converted to USD (USD 1 = R$ 2). For comparison effects, we used the same cost values as used in the paper. Lower and upper bounds for the water velocity are 0.2 and 3 m/s and the minimum required pressure in the nodes demand is 25 m. The pump efficiency is considered 75% in the pump stations and the number of operation hours is 7,300 h/year. The energy cost is 0.1 US$/kWh, the annual interest rate is 12%, and the annual increase rate in the energy is 6%, for a lifetime of 20 years. The Hazen–Williams equation is used and two distinct values for the parameter α were used: