Research Article
A VNS Metaheuristic with Stochastic Steps for Max 3-Cut and Max 3-Section
Table 2
The numerical comparisons of 0.836-approximate algorithm with VNS metaheuristic.
| Wnp | | Obj
rsdp | 0.836-algorithm | VNS | s.v. | Obj
GM | | Obj | | | Obj | | |
| W20.1 | 990 | 121 | 117 | 22.93 | 119 | 0.28 | −1.65 | 119 | −1.65 | 0 | W20.3 | 570 | 232 | 225 | 25.58 | 228 | 0.29 | −1.72 | 228 | −1.72 | 0 | W20.6 | | 492 | 464 | 14.27 | 479 | 0.40 | −2.65 | 479 | −2.24 | 0.41 |
| W30.1 | 2235 | 147 | 139 | 161.56 | 144 | 0.81 | −2.04 | 144 | −2.04 | 0 | W30.3 | 1305 | 566 | 521 | 140.12 | 550 | 0.97 | −2.83 | 550 | −2.30 | 0.53 | W30.6 | | 1181 | 1101 | 94.93 | 1151 | 0.92 | −2.54 | 1151 | −2.03 | 0.51 |
| W45.1 | 5040 | 675 | 594 | 202.48 | 605 | 0.92 | −10.38 | 612 | −9.33 | 1.05 | W45.3 | 2970 | 1300 | 1147 | 211.72 | 1192 | 1.02 | −8.31 | 1300 | −7.15 | 1.16 | W45.6 | | 2441 | 2272 | 217.57 | 2313 | 1.02 | −5.25 | 2350 | −3.73 | 1.52 |
| W60.1 | 8970 | 1069 | 918 | 256.35 | 965 | 2.14 | −9.73 | 981 | −8.23 | 1.50 | W60.3 | 5310 | 2494 | 2228 | 256.57 | 2301 | 3.13 | −7.74 | 2332 | −6.50 | 1.24 | W60.6 | | 4403 | 4054 | 266.68 | 4213 | 2.48 | −4.32 | 4307 | −2.18 | 2.14 |
| W80.1 | 15960 | 1567 | 1357 | 537.58 | 1415 | 5.82 | −9.71 | 1438 | −8.23 | 1.48 | W80.3 | 9480 | 4094 | 3666 | 546.23 | 3801 | 7.35 | −7.16 | 3912 | −4.45 | 2.71 | W80.6 | | 7746 | 7328 | 495.34 | 7423 | 6.31 | −4.17 | 7481 | −3.42 | 0.75 |
| W100.1 | 24950 | 2526 | 2149 | 893.52 | 2262 | 12.73 | −10.46 | 2302 | −8.87 | 1.60 | W100.3 | 14850 | 6418 | 5814 | 882.73 | 6010 | 12.66 | −6.36 | 6113 | −4.75 | 1.61 | W100.6 | | 11956 | 11212 | 865.28 | 11391 | 11.99 | −4.73 | 11422 | −4.47 | 0.26 |
| W120.1 | 33990 | 3746 | 3222 | 1476.54 | 3335 | 34.07 | −10.98 | 3392 | −9.45 | 1.53 | W120.3 | 21420 | 9173 | 8266 | 1498.18 | 8575 | 35.41 | −6.52 | 8623 | −6.00 | 0.52 | W120.6 | | 16748 | 15596 | 1567.43 | 16056 | 43.80 | −4.14 | 16114 | −3.79 | 0.35 |
| W150.1 | 56175 | 5821 | 5020 | 2618.11 | 5208 | 69.20 | −10.54 | 5257 | −9.69 | 0.85 | W150.3 | 33525 | 14432 | 13209 | 3021.87 | 13543 | 70.60 | −6.15 | 13607 | −5.72 | 0.43 | W150.6 | | 26310 | 25076 | 3172.22 | 25405 | 74.46 | −3.44 | 25517 | −3.01 | 0.43 |
| W180.05 | 80910 | 4303 | 3578 | 9043.25 | 3726 | 133.10 | −13.41 | 3812 | −11.41 | 1.20 | W180.1 | 48330 | 7236 | 6328 | 10225.54 | 6481 | 130.07 | −10.44 | 6547 | −9.52 | 0.92 | W180.3 | | 20147 | 18436 | 9887.36 | 19031 | 132.14 | −5.54 | 19213 | −4.64 | 0.90 | W180.6 | | 37292 | 35386 | 10004.11 | 35949 | 102.77 | −3.61 | 36124 | −3.13 | 0.48 |
| W200.05 | 99900 | 5174 | 4306 | 25872.33 | 4484 | 71.90 | −13.40 | 4509 | −12.85 | 0.55 | W200.1 | 59700 | 9271 | 8092 | 29003.28 | 8799 | 149.50 | −5.10 | 8853 | −4.51 | 0.59 | W200.5 | | 38831 | 36481 | 28774.17 | 37477 | 200.16 | −3.49 | 37552 | −3.29 | 0.20 |
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