Research Article
A Hybrid Demon Algorithm for the Two-Dimensional Orthogonal Strip Packing Problem
Table 7
Results obtained by GRASP, SVC, ISA, and HDA on BWMV.
| | Instances | meanh | Gap | | | | | LB | GRASP | SVC | ISA | HDA | GRASP | SVC | ISA | HDA |
| | C01 | 20 | 10 | 60.3 | 61.4 | 61.4 | 61.3 | 61.3 | 1.8 | 1.8 | 1.7 | 1.7 | | 40 | 10 | 121.6 | 121.9 | 122 | 121.8 | 121.8 | 0.2 | 0.3 | 0.2 | 0.2 | | 60 | 10 | 187.4 | 188.6 | 188.6 | 188.6 | 188.6 | 0.6 | 0.6 | 0.6 | 0.6 | | 80 | 10 | 262.2 | 262.6 | 262.6 | 262.6 | 262.6 | 0.2 | 0.2 | 0.2 | 0.2 | | 100 | 10 | 304.4 | 305 | 304.9 | 304.9 | 304.9 | 0.2 | 0.2 | 0.2 | 0.2 |
| | C02 | 20 | 30 | 19.7 | 19.8 | 19.8 | 19.9 | 19.8 | 0.5 | 0.5 | 1.0 | 0.5 | | 40 | 30 | 39.1 | 39.1 | 39.1 | 39.1 | 39.1 | 0.0 | 0.0 | 0.0 | 0.0 | | 60 | 30 | 60.1 | 60.3 | 60.1 | 60.1 | 60.1 | 0.3 | 0.0 | 0.0 | 0.0 | | 80 | 30 | 83.2 | 83.3 | 83.2 | 83.2 | 83.2 | 0.1 | 0.0 | 0.0 | 0.0 | | 100 | 30 | 100.5 | 100.6 | 100.5 | 100.5 | 100.5 | 0.1 | 0.0 | 0.0 | 0.0 |
| | C03 | 20 | 40 | 157.4 | 163.5 | 164.6 | 164.0 | 163.7 | 3.9 | 4.6 | 4.2 | 4.0 | | 40 | 40 | 328.8 | 334.2 | 333.9 | 333.8 | 333.8 | 1.6 | 1.6 | 1.5 | 1.5 | | 60 | 40 | 500 | 506.6 | 506.9 | 505.8 | 505.9 | 1.3 | 1.4 | 1.2 | 1.2 | | 80 | 40 | 701.7 | 709.7 | 710.1 | 709.2 | 709.5 | 1.1 | 1.2 | 1.1 | 1.1 | | 100 | 40 | 832.7 | 840.2 | 839.9 | 837.8 | 838.4 | 0.9 | 0.9 | 0.6 | 0.7 |
| | C04 | 20 | 100 | 61.4 | 63.3 | 63.8 | 63.9 | 63.4 | 3.1 | 3.9 | 4.1 | 3.3 | | 40 | 100 | 123.9 | 126.2 | 126.2 | 126.1 | 125.8 | 1.9 | 1.9 | 1.8 | 1.5 | | 60 | 100 | 193 | 196.6 | 195.6 | 195.5 | 195.5 | 1.9 | 1.3 | 1.3 | 1.3 | | 80 | 100 | 267.2 | 272 | 270.5 | 269.8 | 270.1 | 1.8 | 1.2 | 1.0 | 1.1 | | 100 | 100 | 322 | 327.3 | 325.3 | 324.6 | 324.6 | 1.6 | 1.0 | 0.8 | 0.8 |
| | C05 | 20 | 100 | 512.2 | 533.9 | 537.9 | 534.6 | 534.1 | 4.2 | 5.0 | 4.4 | 4.3 | | 40 | 100 | 1053.8 | 1074.4 | 1076.4 | 1073.6 | 1073.5 | 2.0 | 2.1 | 1.9 | 1.9 | | 60 | 100 | 1614 | 1645.5 | 1647.6 | 1643.4 | 1644.0 | 2.0 | 2.1 | 1.8 | 1.9 | | 80 | 100 | 2268.4 | 2290.5 | 2288.9 | 2289.0 | 2289.3 | 1.0 | 0.9 | 0.9 | 0.9 | | 100 | 100 | 2617.4 | 2651.1 | 2653.5 | 2644.4 | 2646.4 | 1.3 | 1.4 | 1.0 | 1.1 |
| | C06 | 20 | 10 | 159.9 | 167.2 | 169.6 | 169.6 | 168.7 | 4.6 | 6.1 | 6.1 | 5.5 | | 40 | 10 | 323.5 | 333.4 | 332.6 | 334.0 | 333.2 | 3.1 | 2.8 | 3.2 | 3.0 | | 60 | 10 | 505.1 | 519.9 | 517.2 | 519.0 | 518.5 | 2.9 | 2.4 | 2.8 | 2.6 | | 80 | 10 | 699.7 | 718.4 | 714.7 | 715.5 | 715.4 | 2.7 | 2.1 | 2.3 | 2.2 | | 100 | 10 | 843.8 | 865.1 | 860.6 | 861.1 | 861.2 | 2.5 | 2.0 | 2.1 | 2.1 |
| | C07 | 20 | 30 | 490.4 | 501.9 | 501.9 | 501.9 | 501.9 | 2.3 | 2.3 | 2.3 | 2.3 | | 40 | 30 | 1049.7 | 1059 | 1059.9 | 1059.0 | 1059.4 | 0.9 | 1.0 | 0.9 | 0.9 | | 60 | 30 | 1515.9 | 1529.6 | 1530 | 1529.6 | 1529.6 | 0.9 | 0.9 | 0.9 | 0.9 | | 80 | 30 | 2206.1 | 2222.2 | 2222.1 | 2222.1 | 2222.1 | 0.7 | 0.7 | 0.7 | 0.7 | | 100 | 30 | 2627 | 2644 | 2644 | 2645.4 | 2644.1 | 0.6 | 0.6 | 0.7 | 0.7 |
| | C08 | 20 | 40 | 434.6 | 458.3 | 461.2 | 458.6 | 458.0 | 5.5 | 6.1 | 5.5 | 5.4 | | 40 | 40 | 922 | 954.3 | 956.5 | 951.9 | 951.8 | 3.5 | 3.7 | 3.2 | 3.2 | | 60 | 40 | 1360.9 | 1405 | 1403.5 | 1399.4 | 1403.1 | 3.2 | 3.1 | 2.8 | 3.1 | | 80 | 40 | 1909.3 | 1971.5 | 1965 | 1954.7 | 1960.9 | 3.3 | 2.9 | 2.4 | 2.7 | | 100 | 40 | 2362.8 | 2436.8 | 2425 | 2410.8 | 2418.3 | 3.1 | 2.6 | 2.0 | 2.4 |
| | C09 | 20 | 100 | 1106.8 | 1106.8 | 1106.8 | 1106.8 | 1106.8 | 0.0 | 0.0 | 0.0 | 0.0 | | 40 | 100 | 2189.2 | 2190.6 | 2190.6 | 2190.6 | 2191.1 | 0.1 | 0.1 | 0.1 | 0.1 | | 60 | 100 | 3410.4 | 3410.4 | 3410.4 | 3410.4 | 3410.4 | 0.0 | 0.0 | 0.0 | 0.0 | | 80 | 100 | 4578.6 | 4588.1 | 4588.1 | 4588.1 | 4588.1 | 0.2 | 0.2 | 0.2 | 0.2 | | 100 | 100 | 5430.5 | 5434.9 | 5434.9 | 5434.9 | 5434.9 | 0.1 | 0.1 | 0.1 | 0.1 |
| | C10 | 20 | 100 | 337.8 | 350.5 | 351.5 | 350.4 | 350.1 | 3.8 | 4.1 | 3.7 | 3.6 | | 40 | 100 | 642.8 | 664.4 | 667 | 664.0 | 663.7 | 3.4 | 3.8 | 3.3 | 3.3 | | 60 | 100 | 911.1 | 934.7 | 936.6 | 933.1 | 933.2 | 2.6 | 2.8 | 2.4 | 2.4 | | 80 | 100 | 1177.6 | 1209.9 | 1212.4 | 1204.1 | 1205.2 | 2.7 | 3.0 | 2.3 | 2.3 | | 100 | 100 | 1476.5 | 1512.3 | 1514 | 1504.2 | 1506.5 | 2.4 | 2.5 | 1.9 | 2.0 |
| | Average | 1043.34 | 1043.19 | 1041.53 | 1041.92 | 1.77 | 1.80 | 1.66 | 1.63 |
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