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The values of objective functions for 10 different Pareto solutions are reported in Table 1. These 10 solutions are selected from the set of 78 non-dominated solutions after sorting them based on the minimum pressure violations, maximum network reliability and minimum water age (as a surrogate measure for water quality).

Table 1

The first 10 non-dominated solutions for partitioning BWSN_Network2, sorted lexicographically based on least pressure violations, average network resilience and average water age during the last 24 hours of simulation

 DMAsCSCWSSIAexpMExpALnkExpMLnkExpPVDPEDANRWA
Sol-01 28 66 494 0.879 2,423 4,844 1.55 × 105 3.25 × 105 0 3.83 × 107 330.14 0.83 31.01 
Sol-02 30 79 624 0.860 2,263 4,206 1.56 × 105 3.23 × 105 0 3.82 × 107 329.49 0.83 31.05 
Sol-03 30 78 618 0.860 2,262 4,206 1.38 × 105 3.34 × 105 0 3.88 × 107 362.53 0.83 32.08 
Sol-04 30 87 662 0.880 2,261 4,906 1.66 × 105 3.27 × 105 2.11 1.10 × 108 317.74 0.82 32.12 
Sol-05 30 87 662 0.880 2,262 4,906 1.66 × 105 3.26 × 105 2.13 1.10 × 108 317.66 0.82 32.42 
Sol-06 30 90 629 0.882 2,262 4,969 1.42 × 105 2.93 × 105 5.32 8.53 × 107 356.80 0.81 32.41 
Sol-07 30 90 639 0.882 2,263 4,969 1.42 × 105 2.93 × 105 5.44 8.44 × 107 356.56 0.81 32.45 
Sol-08 30 84 588 0.875 2,263 4,719 1.56 × 105 3.33 × 105 9.92 8.33 × 107 329.31 0.81 32.45 
Sol-09 30 82 562 0.879 2,262 4,850 1.56 × 105 3.86 × 105 11.1 8.65 × 107 330.67 0.80 32.46 
Sol-10 31 94 673 0.859 2,190 4,175 1.34 × 105 3.02 × 105 17 8.28 × 107 365.31 0.80 32.43 
 DMAsCSCWSSIAexpMExpALnkExpMLnkExpPVDPEDANRWA
Sol-01 28 66 494 0.879 2,423 4,844 1.55 × 105 3.25 × 105 0 3.83 × 107 330.14 0.83 31.01 
Sol-02 30 79 624 0.860 2,263 4,206 1.56 × 105 3.23 × 105 0 3.82 × 107 329.49 0.83 31.05 
Sol-03 30 78 618 0.860 2,262 4,206 1.38 × 105 3.34 × 105 0 3.88 × 107 362.53 0.83 32.08 
Sol-04 30 87 662 0.880 2,261 4,906 1.66 × 105 3.27 × 105 2.11 1.10 × 108 317.74 0.82 32.12 
Sol-05 30 87 662 0.880 2,262 4,906 1.66 × 105 3.26 × 105 2.13 1.10 × 108 317.66 0.82 32.42 
Sol-06 30 90 629 0.882 2,262 4,969 1.42 × 105 2.93 × 105 5.32 8.53 × 107 356.80 0.81 32.41 
Sol-07 30 90 639 0.882 2,263 4,969 1.42 × 105 2.93 × 105 5.44 8.44 × 107 356.56 0.81 32.45 
Sol-08 30 84 588 0.875 2,263 4,719 1.56 × 105 3.33 × 105 9.92 8.33 × 107 329.31 0.81 32.45 
Sol-09 30 82 562 0.879 2,262 4,850 1.56 × 105 3.86 × 105 11.1 8.65 × 107 330.67 0.80 32.46 
Sol-10 31 94 673 0.859 2,190 4,175 1.34 × 105 3.02 × 105 17 8.28 × 107 365.31 0.80 32.43 

DMAs: number of identified sectors; CS: cut size; CW: cut weight; SSI: sector size imbalance; AExp: average number of customer connections per sector; MExp: maximum number of customer connections in a sector; ALnkExp: average pipe length per sector; MLnkExp: maximum pipe length in a sector; PV: pressure violations; DP: dissipated power; ED: sum of the standard deviations of elevation differences within sectors; ANR: mean network resilience; WA: average water age during the last 24 hours of the simulation.

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