Research Article
A Hybrid Demon Algorithm for the Two-Dimensional Orthogonal Strip Packing Problem
Table 4
Results obtained by GRASP, SVC, ISA, and HDA on NT.
| Instance | meanh | Gap | ā | | | LB | GRASP | SVC | ISA | HDA | GRASP | SVC | ISA | HDA |
| n1a | 17 | 200 | 200 | 200 | 202 | 200.0 | 200 | 0.0 | 1.0 | 0.0 | 0.0 | n1b | 17 | 200 | 200 | 209 | 200 | 211.2 | 200 | 4.5 | 0.0 | 5.6 | 0.0 | n1c | 17 | 200 | 200 | 200 | 200 | 200.0 | 200 | 0.0 | 0.0 | 0.0 | 0.0 | n1d | 17 | 200 | 200 | 200 | 200 | 200.0 | 200 | 0.0 | 0.0 | 0.0 | 0.0 | n1e | 17 | 200 | 200 | 200 | 200 | 200.0 | 200 | 0.0 | 0.0 | 0.0 | 0.0 |
| n2a | 25 | 200 | 200 | 206 | 205 | 204.0 | 201.3 | 3.0 | 2.5 | 2.0 | 0.7 | n2b | 25 | 200 | 200 | 206 | 209 | 209.4 | 210 | 3.0 | 4.5 | 4.7 | 5.0 | n2c | 25 | 200 | 200 | 208 | 209 | 208.5 | 206.3 | 4.0 | 4.5 | 4.3 | 3.2 | n2d | 25 | 200 | 200 | 209 | 207 | 207.8 | 205.9 | 4.5 | 3.5 | 3.9 | 3.0 | n2e | 25 | 200 | 200 | 206 | 205 | 206.7 | 206.1 | 3.0 | 2.5 | 3.3 | 3.1 |
| n3a | 29 | 200 | 200 | 209 | 208 | 206.1 | 206.3 | 4.5 | 4.0 | 3.1 | 3.2 | n3b | 29 | 200 | 200 | 208 | 207 | 209.0 | 208.9 | 4.0 | 3.5 | 4.5 | 4.5 | n3c | 29 | 200 | 200 | 205 | 207 | 206.1 | 205 | 2.5 | 3.5 | 3.1 | 2.5 | n3d | 29 | 200 | 200 | 207 | 208 | 204.3 | 204.5 | 3.5 | 4.0 | 2.2 | 2.3 | n3e | 29 | 200 | 200 | 207 | 207 | 208.0 | 208.1 | 3.5 | 3.5 | 4.0 | 4.1 |
| n4a | 49 | 200 | 200 | 206 | 205 | 206.0 | 205.9 | 3.0 | 2.5 | 3.0 | 3.0 | n4b | 49 | 200 | 200 | 207 | 205 | 205.0 | 204.7 | 3.5 | 2.5 | 2.5 | 2.3 | n4c | 49 | 200 | 200 | 205 | 205 | 206.0 | 205.3 | 2.5 | 2.5 | 3.0 | 2.7 | n4d | 49 | 200 | 200 | 206 | 205 | 204.8 | 204.9 | 3.0 | 2.5 | 2.4 | 2.5 | n4e | 49 | 200 | 200 | 205 | 205 | 206.0 | 206.1 | 2.5 | 2.5 | 3.0 | 3.1 |
| n5a | 73 | 200 | 200 | 205 | 204 | 205.1 | 205.5 | 2.5 | 2.0 | 2.6 | 2.8 | n5b | 73 | 200 | 200 | 204 | 204 | 203.6 | 203.1 | 2.0 | 2.0 | 1.8 | 1.6 | n5c | 73 | 200 | 200 | 206 | 204 | 204.4 | 204.5 | 3.0 | 2.0 | 2.2 | 2.3 | n5d | 73 | 200 | 200 | 204 | 205 | 205.0 | 204.7 | 2.0 | 2.5 | 2.5 | 2.3 | n5e | 73 | 200 | 200 | 206 | 205 | 204.7 | 204.9 | 3.0 | 2.5 | 2.3 | 2.5 |
| n6a | 97 | 200 | 200 | 204 | 203 | 202.8 | 202.7 | 2.0 | 1.5 | 1.4 | 1.3 | n6b | 97 | 200 | 200 | 204 | 204 | 203.0 | 202.9 | 2.0 | 2.0 | 1.5 | 1.5 | n6c | 97 | 200 | 200 | 204 | 204 | 203.6 | 203.2 | 2.0 | 2.0 | 1.8 | 1.6 | n6d | 97 | 200 | 200 | 204.1 | 202 | 203.8 | 203 | 2.1 | 1.0 | 1.9 | 1.5 | n6e | 97 | 200 | 200 | 204 | 203 | 203.5 | 203 | 2.0 | 1.5 | 1.8 | 1.5 |
| n7a | 199 | 200 | 200 | 202 | 202 | 201.0 | 201 | 1.0 | 1.0 | 0.5 | 0.5 | n7b | 199 | 200 | 200 | 203 | 202 | 202.0 | 201 | 1.5 | 1.0 | 1.0 | 0.5 | n7c | 199 | 200 | 200 | 203 | 202 | 201.9 | 201 | 1.5 | 1.0 | 1.0 | 0.5 | n7d | 199 | 200 | 200 | 203 | 202 | 201.9 | 201 | 1.5 | 1.0 | 1.0 | 0.5 | n7e | 199 | 200 | 200 | 203 | 202 | 201.9 | 201 | 1.5 | 1.0 | 1.0 | 0.5 |
| t1a | 17 | 200 | 200 | 200 | 200 | 200.0 | 200 | 0.0 | 0.0 | 0.0 | 0.0 | t1b | 17 | 200 | 200 | 200 | 211 | 200.0 | 200 | 0.0 | 5.5 | 0.0 | 0.0 | t1c | 17 | 200 | 200 | 200 | 210 | 200.0 | 200 | 0.0 | 5.0 | 0.0 | 0.0 | t1d | 17 | 200 | 200 | 200 | 200 | 211.8 | 200 | 0.0 | 0.0 | 5.9 | 0.0 | t1e | 17 | 200 | 200 | 200 | 209 | 200.0 | 200 | 0.0 | 4.5 | 0.0 | 0.0 |
| t2a | 25 | 200 | 200 | 204 | 207 | 207.0 | 206.3 | 2.0 | 3.5 | 3.5 | 3.2 | t2b | 25 | 200 | 200 | 208 | 205 | 207.0 | 205.8 | 4.0 | 2.5 | 3.5 | 2.9 | t2c | 25 | 200 | 200 | 208 | 206 | 206.0 | 207.4 | 4.0 | 3.0 | 3.0 | 3.7 | t2d | 25 | 200 | 200 | 206 | 207 | 209.3 | 204.4 | 3.0 | 3.5 | 4.7 | 2.2 | t2e | 25 | 200 | 200 | 206 | 207 | 207.4 | 205.9 | 3.0 | 3.5 | 3.7 | 3.0 |
| t3a | 29 | 200 | 200 | 207 | 208 | 209.0 | 209 | 3.5 | 4.0 | 4.5 | 4.5 | t3b | 29 | 200 | 200 | 209 | 207 | 208.1 | 207.9 | 4.5 | 3.5 | 4.1 | 4.0 | t3c | 29 | 200 | 200 | 206 | 207 | 206.6 | 206.3 | 3.0 | 3.5 | 3.3 | 3.2 | t3d | 29 | 200 | 200 | 207 | 208 | 206.4 | 206.4 | 3.5 | 4.0 | 3.2 | 3.2 | t3e | 29 | 200 | 200 | 208 | 206 | 205.0 | 205 | 4.0 | 3.0 | 2.5 | 2.5 |
| t4a | 49 | 200 | 200 | 205 | 205 | 205.0 | 204.7 | 2.5 | 2.5 | 2.5 | 2.3 | t4b | 49 | 200 | 200 | 205 | 205 | 206.1 | 205.9 | 2.5 | 2.5 | 3.1 | 3.0 | t4c | 49 | 200 | 200 | 206 | 205 | 204.9 | 204.7 | 3.0 | 2.5 | 2.5 | 2.3 | t4d | 49 | 200 | 200 | 206 | 205 | 205.7 | 205.4 | 3.0 | 2.5 | 2.8 | 2.7 | t4e | 49 | 200 | 200 | 207 | 205 | 205.2 | 205.5 | 3.5 | 2.5 | 2.6 | 2.8 |
| t5a | 73 | 200 | 200 | 206 | 204 | 204.4 | 204.5 | 3.0 | 2.0 | 2.2 | 2.3 | t5b | 73 | 200 | 200 | 204 | 204 | 204.0 | 204.4 | 2.0 | 2.0 | 2.0 | 2.2 | t5c | 73 | 200 | 200 | 205 | 204 | 205.0 | 205.5 | 2.5 | 2.0 | 2.5 | 2.8 | t5d | 73 | 200 | 200 | 204 | 205 | 204.9 | 204.7 | 2.0 | 2.5 | 2.5 | 2.3 | t5e | 73 | 200 | 200 | 204 | 204 | 204.0 | 204.7 | 2.0 | 2.0 | 2.0 | 2.3 |
| t6a | 97 | 200 | 200 | 204 | 204 | 203.2 | 203.7 | 2.0 | 2.0 | 1.6 | 1.8 | t6b | 97 | 200 | 200 | 204 | 202 | 203.4 | 203.2 | 2.0 | 1.0 | 1.7 | 1.6 | t6c | 97 | 200 | 200 | 204 | 204 | 203.0 | 202.7 | 2.0 | 2.0 | 1.5 | 1.3 | t6d | 97 | 200 | 200 | 204 | 204 | 203.5 | 203.7 | 2.0 | 2.0 | 1.8 | 1.8 | t6e | 97 | 200 | 200 | 205 | 204 | 203.5 | 203.5 | 2.5 | 2.0 | 1.8 | 1.8 |
| t7a | 199 | 200 | 200 | 203 | 201 | 201.2 | 201 | 1.5 | 0.5 | 0.6 | 0.5 | t7b | 199 | 200 | 200 | 203 | 202 | 201.0 | 201 | 1.5 | 1.0 | 0.5 | 0.5 | t7c | 199 | 200 | 200 | 204 | 202 | 201.0 | 201 | 2.0 | 1.0 | 0.5 | 0.5 | t7d | 199 | 200 | 200 | 202 | 202 | 202.0 | 201 | 1.0 | 1.0 | 1.0 | 0.5 | t7e | 199 | 200 | 200 | 203 | 202 | 201.7 | 201 | 1.5 | 1.0 | 0.8 | 0.5 |
| Average | 204.64 | 204.54 | 204.48 | 203.83 | 2.32 | 2.27 | 2.24 | 1.91 |
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