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The problem was solved using the global optimizer solver BARON, in GAMS. Table 3 presents the velocities in the pipes, the pressure in the demand nodes, and flow directions. As can be seen, these values are the same when using or However, costs are different, being US$ 2,272,538.85, when , and US$ 2,272,387.49, when . These values correspond to the global optima in the considered situations. In both cases, operation costs correspond to approximately ¼ of the total WDN costs. Table 4 presents a comparison with the literature results. Different approaches were used in the works of Gomes et al. (2009), who used an iterative approach and , , and , and Surco et al. (2021), who used PSO to solve the problem with the aid of hydraulic simulators and , and the same values for and .

Table 3

Hydraulic variables calculated for the Grande Setor WDN

Pipe/NodeVelocity (m/s)Flow directionPressure (m)
1.39 R-1 30.84 
1.13 1-2 27.10 
0.64 2-3 25.00 
0.69 4-3 26.30 
1.33 1-4 26.62 
1.20 1-5 25.40 
0.50 5-6  
0.73 4-6  
Pipe/NodeVelocity (m/s)Flow directionPressure (m)
1.39 R-1 30.84 
1.13 1-2 27.10 
0.64 2-3 25.00 
0.69 4-3 26.30 
1.33 1-4 26.62 
1.20 1-5 25.40 
0.50 5-6  
0.73 4-6  
Table 4

Diameter, manometric head, and costs for the Grande Setor WDN

PipeGomes et al. (2009) Present paper DiametersSurco et al. (2021) Present paper
0.6196 0.6196 0.6196 0.6196 
0.2998 0.2998 0.2998 0.2998 
0.2998 0.2520 0.2520 0.2520 
0.2042 0.2998 0.2998 0.2998 
0.5180 0.5180 0.5180 0.5180 
0.2520 0.2520 0.2520 0.2520 
0.2042 0.2042 0.2042 0.2042 
0.1564 0.2042 0.2042 0.2042 
(m) 15.79 13.658 13.655 13.655 
(US$) 1,630,405.75 1,662,535.10 1,662,535.10 1,662,535.10 
(US$) 705,244.20 610,003.75 609,796.65 609,852.39 
(US$) 2,335,649.95 2,272,538.85 2,272,331.75 2,272,387.49 
PipeGomes et al. (2009) Present paper DiametersSurco et al. (2021) Present paper
0.6196 0.6196 0.6196 0.6196 
0.2998 0.2998 0.2998 0.2998 
0.2998 0.2520 0.2520 0.2520 
0.2042 0.2998 0.2998 0.2998 
0.5180 0.5180 0.5180 0.5180 
0.2520 0.2520 0.2520 0.2520 
0.2042 0.2042 0.2042 0.2042 
0.1564 0.2042 0.2042 0.2042 
(m) 15.79 13.658 13.655 13.655 
(US$) 1,630,405.75 1,662,535.10 1,662,535.10 1,662,535.10 
(US$) 705,244.20 610,003.75 609,796.65 609,852.39 
(US$) 2,335,649.95 2,272,538.85 2,272,331.75 2,272,387.49 

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