Research Article
Bilevel Optimization for the Hazmat Transportation Problem with Lane Reservation
Table 7
Computational comparison of medium scale and large scale between EX-PSO-EX and EX-GA-EX with
, = 0.1,
= 0.1, and
= 0.7 (sets 16–30).
| Set | |N| | |A| | EX-PSO-EX | EX-GA-EX | | CPU time (sec) | | CPU time (sec) | Average Solution | Best Solution | Standard Deviation | Average Solution | Best Solution | Standard Deviation |
| 16 | 20 | 126 | 0.246 | 0.226 | 0.012 | 2.687 | 0.207 | 0.206 | 0.002 | 4.123 | 17 | 30 | 286 | 0.282 | 0.265 | 0.011 | 3.907 | 0.236 | 0.234 | 0.002 | 5.891 | 18 | 40 | 526 | 0.301 | 0.286 | 0.008 | 7.210 | 0.270 | 0.268 | 0.003 | 9.343 | 19 | 45 | 634 | 0.294 | 0.273 | 0.010 | 9.034 | 0.240 | 0.229 | 0.009 | 14.835 | 20 | 50 | 782 | 0.221 | 0.199 | 0.011 | 10.716 | 0.186 | 0.182 | 0.002 | 18.005 | 21 | 55 | 936 | 0.326 | 0.298 | 0.014 | 11.964 | 0.278 | 0.267 | 0.007 | 17.348 | 22 | 60 | 1114 | 0.305 | 0.283 | 0.011 | 14.080 | 0.263 | 0.257 | 0.004 | 23.276 | 23 | 65 | 1298 | 0.308 | 0.282 | 0.010 | 15.800 | 0.254 | 0.246 | 0.006 | 23.730 | 24 | 70 | 1498 | 0.273 | 0.256 | 0.008 | 18.095 | 0.240 | 0.236 | 0.003 | 26.656 | 25 | 75 | 1716 | 0.270 | 0.245 | 0.012 | 20.753 | 0.227 | 0.220 | 0.006 | 36.752 | 26 | 80 | 1954 | 0.301 | 0.279 | 0.014 | 24.910 | 0.248 | 0.232 | 0.009 | 47.277 | 27 | 85 | 2152 | 0.308 | 0.283 | 0.012 | 30.885 | 0.264 | 0.259 | 0.005 | 60.051 | 28 | 90 | 2404 | 0.287 | 0.273 | 0.010 | 34.500 | 0.244 | 0.237 | 0.004 | 68.128 | 29 | 95 | 2710 | 0.329 | 0.311 | 0.010 | 38.900 | 0.294 | 0.287 | 0.005 | 75.828 | 30 | 100 | 2948 | 0.284 | 0.271 | 0.007 | 42.484 | 0.244 | 0.236 | 0.005 | 85.214 |
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