Research Article
An Improved NSGA-II Algorithm for Transit Network Design and Frequency Setting Problem
Table 5
Comparison between selected nondominated solutions and the results in previous literatures.
| | Line number | Sources in literatures [3, 21, 22, 24, 32, 35, 40, 41] | Buses | User cost (min) | (%) | (%) | (%) | (%) | Maximum headway (min) | Average headway (min) | (min) | (min) |
| | 4 | Mandl (1980) | 103 | 349230.26 | 69.94 | 29.93 | 0.13 | 0.00 | 6.67 | 3.48 | 11.40 | 22.43 | | Chakroborty (2003) | 105 | 284009.56 | 89.98 | 10.02 | 0.00 | 0.00 | 9.00 | 4.06 | 13.10 | 18.24 | | Mumford (2013) | 86 | 251015.35 | 91.14 | 8.86 | 0.00 | 0.00 | 9.33 | 4.43 | 10.79 | 16.12 | | Chew and Lee (2013) | 87 | 247498.31 | 92.74 | 7.26 | 0.00 | 0.00 | 5.11 | 3.64 | 11.47 | 15.90 | | Nikolic and Teodorovic (2013) | 94 | 252596.87 | 91.91 | 8.09 | 0.00 | — | 4.32 | 3.41 | 11.71 | 16.22 | | Arbex and Cunha (2015) | 79 | 223506.75 | 98.27 | 1.73 | 0.00 | 0.00 | 8.60 | 4.60 | 11.13 | 14.35 | | Ahmed et al. (2019) | — | — | 91.84 | 8.15 | 0.00 | 0.00 | — | — | — | — | | Solution with the algorithm (Scenario with ) | 79 | 214118.67 | 98.37 | 1.63 | 0.00 | 0.00 | 9.24 | 4.98 | 12.97 | 13.75 |
| | 6 | Baaj and Mahmassani (1991) | 87 | 311983.89 | 78.61 | 21.39 | 0.00 | 0.00 | 11.33 | 4.11 | 11.14 | 20.04 | | Mumford (2013) | 98 | 234358.26 | 96.08 | 3.92 | 0.00 | 0.00 | 8.00 | 5.06 | 11.77 | 15.05 | | Chew and Lee (2013) | 110 | 231258.66 | 98.14 | 1.86 | 0.00 | 0.00 | 8.80 | 4.86 | 12.18 | 14.85 | | Nikolic and Teodorovic (2013) | 102 | 228122.02 | 97.24 | 2.76 | 0.00 | 0.00 | 10.29 | 5.25 | 11.64 | 14.65 | | Arbex and Cunha (2015) | 77 | 215781.79 | 98.20 | 1.80 | 0.00 | 0.00 | 9.56 | 6.42 | 11.55 | 13.86 | | Ahmed et al. (2019) | — | — | 97.17 | 2.82 | 0.00 | 0.00 | — | — | — | — | | Solution 1 with the algorithm (Scenario with ) | 77 | 207437.46 | 98.72 | 1.28 | 0.00 | 0.00 | 14.46 | 6.87 | 12.71 | 13.32 | | Solution 2 with the algorithm (Scenario with ) | 77 | 208802.92 | 98.55 | 1.45 | 0.00 | 0.00 | 12.94 | 6.65 | 12.72 | 13.41 | | 7 | Mumford (2013) | 102 | 243087.48 | 98.01 | 1.99 | 0.00 | — | 6.80 | 5.32 | 12.91 | 15.61 | | Chew and Lee (2013) | 94 | 214543.20 | 99.10 | 0.90 | 0.00 | — | 10.00 | 7.89 | 11.04 | 13.78 | | Nikolic and Teodorovic (2013) | 98 | 229039.11 | 98.84 | 1.16 | 0.00 | — | 17.50 | 7.00 | 11.99 | 14.71 | | Arbex and Cunha (2015) | 77 | 214989.45 | 98.52 | 1.48 | 0.00 | — | 12.80 | 7.58 | 11.91 | 13.81 | | Ahmed et al. (2019) | — | — | 98.84 | 1.15 | 0.00 | 0.00 | — | — | — | — | | Solution 1 with the algorithm (Scenario with ) | 77 | 195888.10 | 99.55 | 0.45 | 0.00 | 0.00 | 18.87 | 9.30 | 12.37 | 12.58 | | Solution 2 with the algorithm (Scenario with ) | 77 | 200534.10 | 99.14 | 0.86 | 0.00 | 0.00 | 15.53 | 9.02 | 12.46 | 12.88 | | 8 | Baaj and Mahmassani (1991) | 78 | 311059.22 | 79.96 | 20.04 | 0.00 | 0.00 | 10.67 | 4.65 | 11.00 | 19.98 | | Mumford (2013) | 101 | 224805.54 | 99.10 | 0.90 | 0.00 | 0.00 | 15.00 | 6.91 | 11.95 | 14.44 | | Chew and Lee (2013) | 88 | 213344.37 | 99.04 | 0.96 | 0.00 | — | 31.00 | 9.67 | 10.72 | 13.70 | | Nikolic and Teodorovic (2013) | 104 | 236835.24 | 98.97 | 1.03 | 0.00 | — | 29.00 | 9.66 | 12.65 | 15.21 | | Arbex and Cunha (2015) | 74 | 213682.25 | 98.65 | 1.35 | 0.00 | — | 16.00 | 7.48 | 11.24 | 13.72 | | Ahmed et al. (2019) | — | — | 99.16 | 0.83 | 0.00 | 0.00 | — | — | — | — | | Solution with the algorithm (Scenario with ) | 74 | 187988.18 | 99.81 | 0.19 | 0.00 | 0.00 | 34.67 | 14.24 | 11.98 | 12.07 |
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