Research Article
A High-Performance Genetic Algorithm: Using Traveling Salesman Problem as a Case
Table 2
Simulation results of using different crossover operators.
| | Data set | PREGA(PMX) | PREGA(OX) | PREGA(HX) | PREGA(ERX) | | | | | | | | | | | | |
| | ch130 | 0.92 | (1.49%) | −80.00 | 0.85 | (1.25%) | −81.82 | 1.56 | (1.51%) | −87.50 | 1.95 | (1.50%) | −85.71 | | ch150 | 1.67 | (0.62%) | −84.62 | 1.53 | (0.69%) | −85.71 | 1.43 | (0.59%) | −90.00 | 1.31 | (0.51%) | −88.24 | | d198 | 0.80 | (1.05%) | −86.36 | 0.44 | (1.46%) | −86.96 | 0.42 | (0.90%) | −90.91 | 0.60 | (0.81%) | −89.29 | | a280 | 0.39 | (1.73%) | −86.36 | 0.09 | (1.63%) | −91.11 | −0.71 | (1.68%) | −91.80 | 0.50 | (1.37%) | −90.38 | | pcb442 | 1.18 | (0.66%) | −90.18 | 0.55 | (0.72%) | −92.98 | −2.59 | (0.69%) | −93.75 | 1.96 | (0.99%) | −91.2 | | d493 | 2.74 | (4.39%) | −81.76 | −1.15 | (1.04%) | −92.62 | −2.67 | (2.00%) | −92.55 | 1.16 | (1.10%) | −90.18 | | u574 | −1.05 | (0.80%) | −91.17 | −2.23 | (0.59%) | −95.10 | −5.51 | (0.84%) | −94.66 | 0.95 | (0.69%) | −93.38 | | u724 | −0.78 | (0.75%) | −87.41 | −2.26 | (0.64%) | −95.02 | −5.11 | (2.39%) | −94.58 | 1.22 | (0.70%) | −93.16 | | pr1002 | −1.48 | (0.58%) | −91.94 | −2.38 | (0.65%) | −95.77 | −5.08 | (2.79%) | −94.84 | 0.81 | (0.79%) | −94.79 | | u1060 | −1.14 | (0.99%) | −89.69 | −2.87 | (0.63%) | −95.52 | −3.69 | (4.31%) | −94.55 | 1.18 | (0.98%) | −94.10 | | d1291 | 0.17 | (0.74%) | −93.80 | −0.10 | (0.95%) | −96.43 | −3.38 | (0.86%) | −95.91 | 0.18 | (1.04%) | −95.93 | | u1432 | 3.53 | (4.36%) | −80.50 | −3.68 | (0.50%) | −95.19 | −2.76 | (4.20%) | −93.74 | 1.07 | (1.00%) | −93.36 | | d1655 | −0.85 | (1.75%) | −91.79 | −2.06 | (1.10%) | −96.32 | −3.39 | (2.57%) | −95.47 | 0.98 | (0.92%) | −95.36 | | u2152 | −0.77 | (2.67%) | −89.53 | −2.05 | (0.52%) | −96.38 | −3.00 | (2.41%) | −95.71 | 0.78 | (0.52%) | −95.69 |
| | Average | 0.38 | | −87.51 | −1.09 | | −92.64 | −2.46 | | −93.28 | 1.05 | | −92.2 |
| | Data set | PREGA(SBOX) | PREGA(SJOX) | PREGA(SB2OX) | PREGA(SJ2OX) | | | | | | | | | | | | |
| | ch130 | 1.03 | (1.51%) | −92.65 | 0.93 | (1.54%) | −91.24 | 1.02 | (1.45%) | −91.11 | 1.37 | (1.71%) | −90.33 | | ch150 | 1.35 | (0.58%) | −92.60 | 1.58 | (0.56%) | −92.33 | 1.57 | (0.55%) | −92.66 | 1.41 | (0.56%) | −92.48 | | d198 | 0.55 | (1.00%) | −92.36 | 0.85 | (0.92%) | −91.81 | 0.67 | (0.85%) | −90.78 | 0.86 | (0.82%) | −90.17 | | a280 | 0.84 | (1.25%) | −92.10 | 1.55 | (1.58%) | −93.13 | −0.11 | (1.67%) | −91.58 | 0.68 | (1.50%) | −91.98 | | pcb442 | 1.81 | (0.94%) | −93.48 | 1.50 | (0.80%) | −93.02 | 0.95 | (0.89%) | −93.02 | 0.80 | (1.03%) | −93.21 | | d493 | 1.07 | (0.97%) | −92.63 | 0.85 | (1.07%) | −92.98 | 0.16 | (0.75%) | −91.61 | 0.63 | (0.82%) | −90.77 | | u574 | −0.13 | (0.85%) | −92.52 | 0.06 | (0.90%) | −93.07 | −1.17 | (0.64%) | −92.28 | −1.31 | (0.80%) | −92.45 | | u724 | 0.75 | (0.79%) | −93.78 | 0.11 | (0.57%) | −93.42 | −0.85 | (0.71%) | −93.70 | −1.00 | (0.73%) | −93.39 | | pr1002 | −0.17 | (0.50%) | −94.06 | −0.26 | (0.64%) | −93.64 | −1.65 | (0.69%) | −94.17 | −1.76 | (0.74%) | −93.85 | | u1060 | −0.09 | (0.63%) | −93.35 | 0.09 | (0.72%) | −94.13 | −1.39 | (0.51%) | −93.11 | −2.05 | (0.93%) | −92.00 | | d1291 | 0.55 | (1.08%) | −93.49 | 0.48 | (0.92%) | −92.68 | −0.22 | (0.79%) | −92.78 | −0.19 | (0.82%) | −92.69 | | u1432 | −0.20 | (0.74%) | −93.41 | −0.11 | (0.73%) | −93.13 | −2.08 | (0.48%) | −93.48 | −2.18 | (0.77%) | −93.49 | | d1655 | −0.22 | (0.62%) | −94.08 | −0.55 | (0.65%) | −94.13 | −1.60 | (0.86%) | −94.29 | −1.02 | (0.91%) | −94.2 | | u2152 | −0.18 | (0.55%) | −94.78 | −0.26 | (0.57%) | −94.57 | −0.38 | (0.48%) | −94.67 | −0.66 | (0.52%) | −94.54 |
| | Average | 0.50 | | −93.23 | 0.49 | | −93.09 | −0.36 | | −92.80 | −0.32 | | −92.54 |
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: time in seconds; : coefficient of variation, which is defined to be , where is either or .
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