Using a Genetic Algorithm with a Mathematical Programming Solver to Optimize a Real Water Distribution System

Parameter

Cost (Currency Units)

Worst

295,975

Mean

281,618

Best

251,850

Mean

±

Standard deviation

281,618

±

7883

Median

279,987

Table 4.

Summary of the data for the best solution found for the FRM network

Pipes

Nodes

Tanks

Reservoirs

Valves

Standard

Demand

(LPS)

Minimum

Pressure

(mca)

Maximum

Pressure

(mca)

Pipe

Diameters

(mm)

367

350

9

1

7

0.003

10

60

22.7–101.6

The optimum location of the valves, the proper configuration of the storage tanks and the suitable

diameters for the pipes allow the FRM water distribution network to improve. Using the symbols

presented in Table

1

, Figure

8

shows the pipes where a PRV is added in order to control pressure

throughout the system. Three tanks and three pipes were also added in different sections of the

network. According to the color scale, which shows pressure, Figure

9

indicates that all nodes meet

the minimum and maximum pressure requirements.

Water 2018, 10, x FOR PEER REVIEW   

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executions and their standard deviation. This information indicates how dispersed the solutions are 

with respect to the mean. 

The best cost obtained due to tanks was 237,150, valves were 4700 and pump was 2650 of the 

FRM. The best cost of the FRM network was 251,850. In this best cost scenario, three storage tanks, 

three pipes, and seven pressure-reducing valves would have to be added. The complete data 

summary of the network solution is presented in Table 4. 

Table 3. Results of the cost of the FRM network using the genetic algorithm