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$/kWh, the annual interest rate is 12%, and the annual increase rate in the energy is 6%, for a lifetime of 20 years. The Hazen–Williams equation is used and two distinct values for the parameter α were used: Table 1 Nodes and pipes for the Grande Setor WDN Node/PipeElevation (m)Demand (L/s)Pipe length (m) 6.0 0.00 2,540 5.5 47.78 1,230 5.5 80.32 1,430 6.0 208.60 1,300 4.5 43.44 1,490 4.0 40.29 1,210 1,460 1,190 Node/PipeElevation (m)Demand (L/s)Pipe length (m) 6.0 0.00 2,540 5.5 47.78 1,230 5.5 80.32 1,430 6.0 208.60 1,300 4.5 43.44 1,490 4.0 40.29 1,210 1,460 1,190 Table 2 Available diameters for the Grande Setor WDN Diameter (m)Cost (US$/m)Roughness coefficientDiameter (m)Cost (US$/m)Roughness coefficient 0.1084 23.55 145 0.3662 158.93 130 0.1564 31.90 145 0.4164 187.50 130 0.2042 43.81 145 0.4666 218.12 130 0.2520 59.30 145 0.5180 257.80 130 0.2998 76.12 145 0.6196 320.15 130 Diameter (m)Cost (US$/m)Roughness coefficientDiameter (m)Cost (US\$/m)Roughness coefficient