Table 4. Average value ± standard deviation of the hypervolume indicator for the synthetic benchmarks.
Graph | Random | DFS | Deg | RW |
---|---|---|---|---|
BA500 | 15.65 ± 4.37 | 13.03 ± 5.37 | 28.05 ± 2.62* | 20.72 ± 4.37 |
BA1000 | 36.54 ± 21.58 | 58.38 ± 24.17 | 154.27 ± 10.54* | 68.21 ± 26.51 |
BA2500 | 6138.01 ± 1701.47 | 2924.91 ± 2828.77 | 18607.82 ± 364.64* | 8643.83 ± 1993.09 |
BA5000 | 1078479.10 ± 319614.94 | 449069.24 ± 396267.77 | 3409301.92 ± 47950.42* | 1706543.15 ± 182869.56 |
ER250 | 738.68 ± 217.41 | 2387.05 ± 342.45* | 1162.31 ± 252.49 | 1204.39 ± 319.17 |
ER500 | 1607.75 ± 920.84 | 8045.09 ± 1848.71* | 2762.01 ± 1572.09 | 2644.67 ± 919.06 |
ER1000 | 1133.40 ± 949.75 | 9407.93 ± 4141.55* | 6385.57 ± 3487.82* | 5176.12 ± 1499.51 |
ER2000 | 39323.23 ± 24560.07 | 65449.57 ± 34152.98* | 56123.63 ± 12683.44* | 72259.64 ± 26198.93* |
FF250 | 38.01 ± 6.84 | 36.34 ± 12.26* | 41.88 ± 5.39* | 45.61 ± 7.52* |
FF500 | 24.51 ± 8.19 | 51.42 ± 9.68* | 37.72 ± 4.93 | 32.98 ± 6.86 |
FF1000 | 1402.85 ± 599.70 | 1718.09 ± 647.33 | 3274.96 ± 387.73* | 3194.72 ± 409.27* |
FF2000 | 30560.10 ± 20460.26 | 16206.67 ± 13027.87 | 136548.86 ± 12378.66* | 107945.88 ± 12371.82 |
WS250 | 8132.90 ± 268.63 | 9577.11 ± 1390.61 | 8495.50 ± 636.66 | 16193.42 ± 3306.69* |
WS500 | 48526.56 ± 14388.26 | 35879.19 ± 8263.24 | 110772.29 ± 31047.79 | 203301.59 ± 30420.58* |
WS1000 | 159361.50 ± 503.68 | 159202.10 ± 0.32 | 162811.19 ± 11412.20 | 337726.99 ± 90573.11* |
WS1500 | 484347.05 ± 140137.66 | 708776.63 ± 223377.92 | 1923479.18 ± 351573.85 | 5058526.43 ± 1741808.94* |
Notes.
An asterisk (*) indicates the best results which are based on a Wilcoxon sign-rank test.