The FOS network, as well as the NYT network, is a gravitational WDN. Pipe diameters are unknown and have to be optimized to meet the given conditions. The network includes nn = 36 nodes with nr = 1 source node or reservoir, interconnected with np = 58 pipes forming nl = 22 loops. The minimum pressure head of all the demand nodes is 40 m, while the maximum pressure head of each node is given in Table 1. Besides pressure head condition, flow velocity condition needs to be satisfied, where in each pipe it has to be less than 1 m/s. For the network pipes, 22 different diameters are available in catalogue. This means that the search space has the size of 7.25 × 1077. The fitness function is made of three parts: investment in the distribution network I, penalty Ip for unfulfilled pressure head conditions and Iv penalty for failing to meet maximum velocity condition.
formula
7
Table 1

The maximum pressure heads of each demand node of FOS

NiPmax (m)NiPmax (m)NiPmax (m)NiPmax (m)NiPmax (m)NiPmax (m)
1 55.85 7 53.10 13 59.10 19 58.10 25 56.6 31 56.60 
2 56.60 8 54.50 14 58.40 20 58.17 26 57.6 32 56.80 
3 57.65 9 55.00 15 57.50 21 58.20 27 57.1 33 56.40 
4 58.50 10 56.83 16 56.70 22 57.10 28 55.35 34 56.30 
5 59.76 11 57.30 17 55.50 23 56.80 29 56.5 35 55.57 
6 55.60 12 58.36 18 56.90 24 53.50 30 56.9 36 55.10 
NiPmax (m)NiPmax (m)NiPmax (m)NiPmax (m)NiPmax (m)NiPmax (m)
1 55.85 7 53.10 13 59.10 19 58.10 25 56.6 31 56.60 
2 56.60 8 54.50 14 58.40 20 58.17 26 57.6 32 56.80 
3 57.65 9 55.00 15 57.50 21 58.20 27 57.1 33 56.40 
4 58.50 10 56.83 16 56.70 22 57.10 28 55.35 34 56.30 
5 59.76 11 57.30 17 55.50 23 56.80 29 56.5 35 55.57 
6 55.60 12 58.36 18 56.90 24 53.50 30 56.9 36 55.10 
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