| Name | Type | Description | #Solved | #Total |
| Bin Packing | BPP | 1D Bin-Packing Problems from FALKENAUER (1996). | 160 | 160 |
| Scholl | BPP | 1D Bin-Packing Problems from SCHOLL/KLEIN/JUERGENS (1997). | 1210 | 1210 |
| Hard28 | BPP | The 28 VERY hard BPP instances of J. Schoenfield (with m from 140 to 200). | 28 | 28 |
| SCH/WAE | BPP | 1D Bin-Packing Problems from SCHWERIN/WAESCHER (1998). | 200 | 200 |
| WAE/GAU | BPP | 1D Bin-Packing Problems from WAESCHER/GAU (1996). | 17 | 17 |
| Cutting Stock | CSP | 1D Bin-Packing Problems from FALKENAUER (1996) [demand x 10^6]. | 160 | 160 |
| Cutgen | CSP | CUTGEN (Gau and Wascher, 1995). | 1800 | 1800 |
| Fiber | CSP | Instances taken from a real application in a paper tube industry in Japan. | 39 | 39 |
| Bin Packing Card | Card | Instances from FALKENAUER (1996) [with cardinality constraints]. | 720 | 720 |
| Scholl Card | Card | 1D Bin-Packing Problems from SCHOLL/KLEIN/JUERGENS (1997) [with cardinality constraints]. | 3748 | 3748 |
| Hard28 Card | Card | The 28 VERY hard BPP instances of J. Schoenfield (with m from 140 to 200) [with cardinality constraints]. | 56 | 56 |
| SCH/WAE Card | Card | 1D Bin-Packing Problems from SCHWERIN/WAESCHER (1998) [with cardinality constraints]. | 1000 | 1000 |
| WAE/GAU Card | Card | 1D Bin-Packing Problems from WAESCHER/GAU (1996) [with cardinality constraints]. | 131 | 131 |
| Cutting Stock Card | Card | Instances from FALKENAUER (1996) [demand x 10^6; with cardinality constraints]. | 320 | 320 |
| Cutgen Card | Card | CUTGEN (Gau and Wascher, 1995) [with cardinality constraints]. | 7299 | 7299 |
| Fiber Card | Card | Instances taken from a real applications in a paper tube industry in Japan [with cardinality constraints]. | 279 | 279 |
| Two-Constraint BPP | 2CBP | Two-Constraint Bin Packing instances of Spieksma/Caprara/Toth. | 320 | 400 |
|
| Label | Description |
| z | optimum objective value |
| lb_lp | arc flow linear relaxation lower bound |
| lb_sp | space lower bound |
| lb_crd | cardinality lower bound |
| lb_sp1 | space lower bound in the first dimension |
| lb_sp2 | space lower bound in the second dimension |
| lb_lp1 | arc flow linear relaxation lower bound in the first dimension |
| lb_lp2 | arc flow linear relaxation lower bound in the second dimension |
| W | bin capacity |
| C | cardinality limit |
| W1 | capacity of the first dimension |
| W2 | capacity of the second dimension |
| n | number of items |
| m | number of different item sizes |
| #vi | number of vertices in step i graph |
| #ai | number of arcs in step i graph (including the final loss arcs) |
| %v | ratio between the number of vertices after compression and the initial number of vertices |
| %a | ratio between the number of arcs after compression and the initial number of arcs |
| n_bb | number of nodes explored in the branch-and-bound procedure |
| t_pp | time spent in pre/post-processing (seconds) |
| t_lp | time spent in the linear relaxation of the root node (seconds) |
| t_ip | time spent in the branch and bound procedure (seconds) |
| tt | total run time (seconds) |
| op | number of open instances solved |
| ffd | first fit decreasing solution |
| bfd | best fit decreasing solution |
| a_* | absolute gap |h-z| |
| r_* | relative gap (h-z)/z |
| 2ffd | 2D first fit decreasing solution |
| 2bfd | 2D best fit decreasing solution [selecting the bin that minimizes s1/W1+s2/W2 where (s1,s2) is the currently available space (using decreasing lexicographic order in case of a tie)] |
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