Supplementary results¶
Model size¶
Median number of variables and constraints of each method's model.
Final gap¶
Median final optimality gap of the tasks that were not proved. Every unproved task with a gap enters the median. The axis ends at 100 %; larger medians are drawn at the top edge as triangles, and the hover shows their value.
Big-M parameters and IOM master size¶
Certified parameters (median / maximum)
| method | size | κ median | κ max | M_z median | M_z max | regional M_z median |
|---|---|---|---|---|---|---|
| SSD | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.46e+04 |
| SSD | 60 | 1.64e+03 | 2.2e+03 | 1.47e+06 | 2.34e+06 | 4.21e+04 |
| ASD | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.46e+04 |
| ASD | 60 | 1.64e+03 | 2.2e+03 | 1.47e+06 | 2.34e+06 | 4.21e+04 |
| KKT-BigM | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.46e+04 |
| KKT-BigM | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 4.84e+04 |
| KKT-SOS1 | 10 | 376 | 865 | 1.26e+05 | 3.43e+05 | 1.45e+04 |
| KKT-SOS1 | 60 | 1.65e+03 | 2.45e+03 | 1.5e+06 | 2.34e+06 | 4.33e+04 |
| CB-SSD | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.19e+04 |
| CB-SSD | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 3.38e+04 |
| CB-ASD | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.19e+04 |
| CB-ASD | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 3.38e+04 |
| CB-KKT-BigM | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.19e+04 |
| CB-KKT-BigM | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 3.38e+04 |
| CB-KKT-SOS1 | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.19e+04 |
| CB-KKT-SOS1 | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 3.38e+04 |
IOM final master against the complete convex-block model
| method | size | tasks | final blocks (median) | complete blocks (median) | share (median) |
|---|---|---|---|---|---|
| IOM-All (SSD) | 10 | all | 4 | 7 | 67 % |
| IOM-All (SSD) | 10 | proved | 4 | 7 | 67 % |
| IOM-All (SSD) | 60 | all | 4 | 4 | 58 % |
| IOM-All (SSD) | 60 | proved | 4 | 4 | 60 % |
| IOM-All (ASD) | 10 | all | 4 | 7 | 67 % |
| IOM-All (ASD) | 10 | proved | 4 | 7 | 67 % |
| IOM-All (ASD) | 60 | all | 4 | 4 | 58 % |
| IOM-All (ASD) | 60 | proved | 4 | 4 | 67 % |
| IOM-All (KKT-BigM) | 10 | all | 4 | 7 | 67 % |
| IOM-All (KKT-BigM) | 10 | proved | 4 | 7 | 67 % |
| IOM-All (KKT-BigM) | 60 | all | 4 | 4 | 53 % |
| IOM-All (KKT-BigM) | 60 | proved | 2 | 4 | 67 % |
| IOM-All (KKT-SOS1) | 10 | all | 4 | 7 | 67 % |
| IOM-All (KKT-SOS1) | 10 | proved | 4 | 6 | 67 % |
| IOM-All (KKT-SOS1) | 60 | all | 4 | 4 | 56 % |
| IOM-All (KKT-SOS1) | 60 | proved | 2 | 4 | 100 % |
| IOM-All (MibS) | 10 | all | 4 | 7 | 67 % |
| IOM-All (MibS) | 10 | proved | 4 | 6 | 67 % |
| IOM-All (MibS) | 60 | all | 4 | 4 | 58 % |
| IOM-All (MibS) | 60 | proved | 4 | 4 | 58 % |
| IOM-Top1 (SSD) | 10 | all | 4 | 7 | 50 % |
| IOM-Top1 (SSD) | 10 | proved | 4 | 7 | 50 % |
| IOM-Top1 (SSD) | 60 | all | 2 | 4 | 39 % |
| IOM-Top1 (SSD) | 60 | proved | 2 | 4 | 50 % |
| IOM-Top1 (ASD) | 10 | all | 4 | 7 | 50 % |
| IOM-Top1 (ASD) | 10 | proved | 4 | 7 | 50 % |
| IOM-Top1 (ASD) | 60 | all | 2 | 4 | 39 % |
| IOM-Top1 (ASD) | 60 | proved | 2 | 4 | 50 % |
| IOM-Top1 (KKT-BigM) | 10 | all | 4 | 7 | 50 % |
| IOM-Top1 (KKT-BigM) | 10 | proved | 4 | 7 | 50 % |
| IOM-Top1 (KKT-BigM) | 60 | all | 2 | 4 | 50 % |
| IOM-Top1 (KKT-BigM) | 60 | proved | 2 | 4 | 50 % |
| IOM-Top1 (KKT-SOS1) | 10 | all | 4 | 7 | 50 % |
| IOM-Top1 (KKT-SOS1) | 10 | proved | 4 | 7 | 50 % |
| IOM-Top1 (KKT-SOS1) | 60 | all | 2 | 4 | 33 % |
| IOM-Top1 (KKT-SOS1) | 60 | proved | 2 | 4 | 50 % |
| IOM-Top1 (MibS) | 10 | all | 4 | 7 | 50 % |
| IOM-Top1 (MibS) | 10 | proved | 4 | 8 | 50 % |
| IOM-Top1 (MibS) | 60 | all | 2 | 4 | 39 % |
| IOM-Top1 (MibS) | 60 | proved | 2 | 4 | 39 % |
Branch-and-bound nodes (median over all tasks with a count)
| method | median nodes |
|---|---|
| SSD | 351 |
| ASD | 506 |
| KKT-BigM | 4.67e+03 |
| KKT-SOS1 | 1.03e+04 |
| CB-SSD | 510 |
| CB-ASD | 578 |
| CB-KKT-BigM | 3.88e+03 |
| CB-KKT-SOS1 | 6.35e+03 |
Certified parameters (median / maximum)
| method | size | κ median | κ max | M_z median | M_z max | regional M_z median |
|---|---|---|---|---|---|---|
| SSD | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| SSD | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.85e+03 |
| SSD | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| SSD | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| SSD | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| SSD | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| ASD | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| ASD | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.85e+03 |
| ASD | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| ASD | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| ASD | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| ASD | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| KKT-BigM | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| KKT-BigM | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.85e+03 |
| KKT-BigM | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| KKT-BigM | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| KKT-BigM | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| KKT-BigM | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| KKT-SOS1 | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| KKT-SOS1 | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.85e+03 |
| KKT-SOS1 | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| KKT-SOS1 | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| KKT-SOS1 | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| KKT-SOS1 | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| CB-SSD | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| CB-SSD | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.84e+03 |
| CB-SSD | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| CB-SSD | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| CB-SSD | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| CB-SSD | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| CB-ASD | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| CB-ASD | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.84e+03 |
| CB-ASD | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| CB-ASD | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| CB-ASD | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| CB-ASD | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| CB-KKT-BigM | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| CB-KKT-BigM | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.84e+03 |
| CB-KKT-BigM | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| CB-KKT-BigM | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| CB-KKT-BigM | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| CB-KKT-BigM | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| CB-KKT-SOS1 | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| CB-KKT-SOS1 | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.84e+03 |
| CB-KKT-SOS1 | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| CB-KKT-SOS1 | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| CB-KKT-SOS1 | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| CB-KKT-SOS1 | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
IOM final master against the complete convex-block model
| method | size | tasks | final blocks (median) | complete blocks (median) | share (median) |
|---|---|---|---|---|---|
| IOM-All (SSD) | 30 | all | 4 | 5 | 88 % |
| IOM-All (SSD) | 30 | proved | 4 | 5 | 88 % |
| IOM-All (SSD) | 35 | all | 5 | 7 | 88 % |
| IOM-All (SSD) | 35 | proved | 5 | 7 | 88 % |
| IOM-All (SSD) | 40 | all | 4 | 5.5 | 67 % |
| IOM-All (SSD) | 40 | proved | 4 | 5.5 | 67 % |
| IOM-All (SSD) | 45 | all | 5 | 6 | 88 % |
| IOM-All (SSD) | 45 | proved | 5 | 6 | 88 % |
| IOM-All (SSD) | 50 | all | 5 | 6 | 88 % |
| IOM-All (SSD) | 50 | proved | 5 | 6 | 88 % |
| IOM-All (SSD) | 55 | all | 7 | 8 | 100 % |
| IOM-All (SSD) | 55 | proved | 7 | 8 | 100 % |
| IOM-All (ASD) | 30 | all | 4 | 5 | 88 % |
| IOM-All (ASD) | 30 | proved | 4 | 4 | 100 % |
| IOM-All (ASD) | 35 | all | 5 | 7 | 88 % |
| IOM-All (ASD) | 35 | proved | 3.5 | 4 | 100 % |
| IOM-All (ASD) | 40 | all | 4 | 5.5 | 67 % |
| IOM-All (ASD) | 40 | proved | 3 | 4 | 67 % |
| IOM-All (ASD) | 45 | all | 5 | 6 | 71 % |
| IOM-All (ASD) | 45 | proved | 3 | 4 | 100 % |
| IOM-All (ASD) | 50 | all | 5 | 6 | 71 % |
| IOM-All (ASD) | 50 | proved | 3.5 | 4 | 100 % |
| IOM-All (ASD) | 55 | all | 7 | 8 | 88 % |
| IOM-All (ASD) | 55 | proved | 3 | 4 | 100 % |
| IOM-All (KKT-BigM) | 30 | all | 1 | 5 | 21 % |
| IOM-All (KKT-BigM) | 35 | all | 1 | 7 | 25 % |
| IOM-All (KKT-BigM) | 35 | proved | 4 | 4 | 100 % |
| IOM-All (KKT-BigM) | 40 | all | 1 | 5.5 | 33 % |
| IOM-All (KKT-BigM) | 40 | proved | 2 | 3.5 | 83 % |
| IOM-All (KKT-BigM) | 45 | all | 1 | 6 | 17 % |
| IOM-All (KKT-BigM) | 50 | all | 1 | 6 | 29 % |
| IOM-All (KKT-BigM) | 50 | proved | 2 | 4 | 100 % |
| IOM-All (KKT-BigM) | 55 | all | 1 | 8 | 12 % |
| IOM-All (KKT-SOS1) | 30 | all | 1 | 5 | 21 % |
| IOM-All (KKT-SOS1) | 35 | all | 1 | 7 | 19 % |
| IOM-All (KKT-SOS1) | 40 | all | 1 | 5.5 | 22 % |
| IOM-All (KKT-SOS1) | 40 | proved | 1 | 4.5 | 39 % |
| IOM-All (KKT-SOS1) | 45 | all | 1 | 6 | 17 % |
| IOM-All (KKT-SOS1) | 50 | all | 1 | 6 | 25 % |
| IOM-All (KKT-SOS1) | 55 | all | 1 | 8 | 12 % |
| IOM-All (MibS) | 30 | all | 0 | 5 | 0 % |
| IOM-All (MibS) | 35 | all | 0 | 7 | 0 % |
| IOM-All (MibS) | 40 | all | 0 | 5.5 | 0 % |
| IOM-All (MibS) | 45 | all | 0 | 6 | 0 % |
| IOM-All (MibS) | 50 | all | 0 | 6 | 0 % |
| IOM-All (MibS) | 55 | all | 0 | 8 | 0 % |
| IOM-Top1 (SSD) | 30 | all | 4 | 5 | 75 % |
| IOM-Top1 (SSD) | 30 | proved | 4 | 5 | 75 % |
| IOM-Top1 (SSD) | 35 | all | 5 | 7 | 75 % |
| IOM-Top1 (SSD) | 35 | proved | 5 | 7 | 75 % |
| IOM-Top1 (SSD) | 40 | all | 4 | 5.5 | 67 % |
| IOM-Top1 (SSD) | 40 | proved | 4 | 5.5 | 67 % |
| IOM-Top1 (SSD) | 45 | all | 5 | 6 | 71 % |
| IOM-Top1 (SSD) | 45 | proved | 5 | 6 | 71 % |
| IOM-Top1 (SSD) | 50 | all | 5 | 6 | 71 % |
| IOM-Top1 (SSD) | 50 | proved | 5 | 6 | 71 % |
| IOM-Top1 (SSD) | 55 | all | 6 | 8 | 100 % |
| IOM-Top1 (SSD) | 55 | proved | 6 | 8 | 100 % |
| IOM-Top1 (ASD) | 30 | all | 4 | 5 | 75 % |
| IOM-Top1 (ASD) | 30 | proved | 4 | 4 | 100 % |
| IOM-Top1 (ASD) | 35 | all | 5 | 7 | 75 % |
| IOM-Top1 (ASD) | 35 | proved | 3.5 | 4 | 100 % |
| IOM-Top1 (ASD) | 40 | all | 4 | 5.5 | 67 % |
| IOM-Top1 (ASD) | 40 | proved | 3.5 | 4 | 67 % |
| IOM-Top1 (ASD) | 45 | all | 5 | 6 | 71 % |
| IOM-Top1 (ASD) | 45 | proved | 3 | 4 | 100 % |
| IOM-Top1 (ASD) | 50 | all | 5 | 6 | 71 % |
| IOM-Top1 (ASD) | 50 | proved | 4 | 4 | 100 % |
| IOM-Top1 (ASD) | 55 | all | 6 | 8 | 88 % |
| IOM-Top1 (ASD) | 55 | proved | 3 | 4 | 100 % |
| IOM-Top1 (KKT-BigM) | 30 | all | 1 | 5 | 21 % |
| IOM-Top1 (KKT-BigM) | 35 | all | 1 | 7 | 25 % |
| IOM-Top1 (KKT-BigM) | 35 | proved | 4 | 4 | 100 % |
| IOM-Top1 (KKT-BigM) | 40 | all | 1 | 5.5 | 28 % |
| IOM-Top1 (KKT-BigM) | 40 | proved | 2 | 4 | 67 % |
| IOM-Top1 (KKT-BigM) | 45 | all | 1 | 6 | 17 % |
| IOM-Top1 (KKT-BigM) | 50 | all | 1 | 6 | 25 % |
| IOM-Top1 (KKT-BigM) | 50 | proved | 2 | 4 | 100 % |
| IOM-Top1 (KKT-BigM) | 55 | all | 1 | 8 | 12 % |
| IOM-Top1 (KKT-SOS1) | 30 | all | 1 | 5 | 21 % |
| IOM-Top1 (KKT-SOS1) | 35 | all | 1 | 7 | 17 % |
| IOM-Top1 (KKT-SOS1) | 40 | all | 1 | 5.5 | 21 % |
| IOM-Top1 (KKT-SOS1) | 40 | proved | 1 | 4.5 | 28 % |
| IOM-Top1 (KKT-SOS1) | 45 | all | 1 | 6 | 17 % |
| IOM-Top1 (KKT-SOS1) | 50 | all | 1 | 6 | 25 % |
| IOM-Top1 (KKT-SOS1) | 55 | all | 1 | 8 | 12 % |
| IOM-Top1 (MibS) | 30 | all | 0 | 5 | 0 % |
| IOM-Top1 (MibS) | 35 | all | 0 | 7 | 0 % |
| IOM-Top1 (MibS) | 40 | all | 0 | 5.5 | 0 % |
| IOM-Top1 (MibS) | 45 | all | 0 | 6 | 0 % |
| IOM-Top1 (MibS) | 50 | all | 0 | 6 | 0 % |
| IOM-Top1 (MibS) | 55 | all | 0 | 8 | 0 % |
Branch-and-bound nodes (median over all tasks with a count)
| method | median nodes |
|---|---|
| SSD | 232 |
| ASD | 7.9e+03 |
| KKT-BigM | 4.3e+03 |
| KKT-SOS1 | 1.08e+06 |
| CB-SSD | 131 |
| CB-ASD | 7.32e+03 |
| CB-KKT-BigM | 1.22e+04 |
| CB-KKT-SOS1 | 2.12e+06 |
Certified parameters (median / maximum)
| method | size | κ median | κ max | M_z median | M_z max | regional M_z median |
|---|---|---|---|---|---|---|
| SSD | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.46e+04 |
| SSD | 60 | 1.64e+03 | 2.2e+03 | 1.47e+06 | 2.34e+06 | 4.21e+04 |
| ASD | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.46e+04 |
| ASD | 60 | 1.64e+03 | 2.2e+03 | 1.47e+06 | 2.34e+06 | 4.21e+04 |
| KKT-BigM | 10 | 376 | 865 | 1.26e+05 | 3.43e+05 | 1.45e+04 |
| KKT-BigM | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 4.84e+04 |
| KKT-SOS1 | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.46e+04 |
| KKT-SOS1 | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 4.84e+04 |
| CB-SSD | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.19e+04 |
| CB-SSD | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 3.38e+04 |
| CB-ASD | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.19e+04 |
| CB-ASD | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 3.38e+04 |
| CB-KKT-BigM | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.19e+04 |
| CB-KKT-BigM | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 3.38e+04 |
| CB-KKT-SOS1 | 10 | 380 | 865 | 1.26e+05 | 3.43e+05 | 1.19e+04 |
| CB-KKT-SOS1 | 60 | 1.65e+03 | 2.55e+03 | 1.52e+06 | 2.71e+06 | 3.38e+04 |
IOM final master against the complete convex-block model
| method | size | tasks | final blocks (median) | complete blocks (median) | share (median) |
|---|---|---|---|---|---|
| IOM-All (SSD) | 10 | all | 4 | 7 | 67 % |
| IOM-All (SSD) | 10 | proved | 4 | 4 | 71 % |
| IOM-All (SSD) | 60 | all | 1 | 4 | 30 % |
| IOM-All (SSD) | 60 | proved | 1 | 4 | 29 % |
| IOM-All (ASD) | 10 | all | 4 | 7 | 67 % |
| IOM-All (ASD) | 10 | proved | 2 | 4 | 100 % |
| IOM-All (ASD) | 60 | all | 1 | 4 | 25 % |
| IOM-All (ASD) | 60 | proved | 1 | 4 | 25 % |
| IOM-All (KKT-BigM) | 10 | all | 4 | 7 | 67 % |
| IOM-All (KKT-BigM) | 10 | proved | 4 | 7 | 67 % |
| IOM-All (KKT-BigM) | 60 | all | 4 | 4 | 50 % |
| IOM-All (KKT-BigM) | 60 | proved | 2 | 4 | 50 % |
| IOM-All (KKT-SOS1) | 10 | all | 4 | 7 | 67 % |
| IOM-All (KKT-SOS1) | 10 | proved | 4 | 6 | 67 % |
| IOM-All (KKT-SOS1) | 60 | all | 4 | 4 | 50 % |
| IOM-All (KKT-SOS1) | 60 | proved | 2 | 4 | 50 % |
| IOM-Top1 (SSD) | 10 | all | 3 | 7 | 50 % |
| IOM-Top1 (SSD) | 10 | proved | 2 | 4 | 50 % |
| IOM-Top1 (SSD) | 60 | all | 1 | 4 | 25 % |
| IOM-Top1 (SSD) | 60 | proved | 1 | 4 | 25 % |
| IOM-Top1 (ASD) | 10 | all | 3 | 7 | 45 % |
| IOM-Top1 (ASD) | 10 | proved | 2 | 4 | 50 % |
| IOM-Top1 (ASD) | 60 | all | 1 | 4 | 25 % |
| IOM-Top1 (ASD) | 60 | proved | 1 | 4 | 25 % |
| IOM-Top1 (KKT-BigM) | 10 | all | 3 | 7 | 50 % |
| IOM-Top1 (KKT-BigM) | 10 | proved | 3 | 7 | 50 % |
| IOM-Top1 (KKT-BigM) | 60 | all | 2 | 4 | 30 % |
| IOM-Top1 (KKT-BigM) | 60 | proved | 1 | 4 | 33 % |
| IOM-Top1 (KKT-SOS1) | 10 | all | 3 | 7 | 50 % |
| IOM-Top1 (KKT-SOS1) | 10 | proved | 3 | 7 | 50 % |
| IOM-Top1 (KKT-SOS1) | 60 | all | 2 | 4 | 28 % |
| IOM-Top1 (KKT-SOS1) | 60 | proved | 1 | 4 | 33 % |
Branch-and-bound nodes (median over all tasks with a count)
| method | median nodes |
|---|---|
| SSD | 7.31e+03 |
| ASD | 4.28e+03 |
| KKT-BigM | 3.35e+03 |
| KKT-SOS1 | 1.17e+04 |
| CB-SSD | 1.1e+04 |
| CB-ASD | 1.03e+04 |
| CB-KKT-BigM | 1.47e+03 |
| CB-KKT-SOS1 | 3.91e+03 |
Certified parameters (median / maximum)
| method | size | κ median | κ max | M_z median | M_z max | regional M_z median |
|---|---|---|---|---|---|---|
| SSD | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| SSD | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.85e+03 |
| SSD | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| SSD | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| SSD | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| SSD | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| ASD | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| ASD | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.85e+03 |
| ASD | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| ASD | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| ASD | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| ASD | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| KKT-BigM | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| KKT-BigM | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.85e+03 |
| KKT-BigM | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| KKT-BigM | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| KKT-BigM | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| KKT-BigM | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| KKT-SOS1 | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| KKT-SOS1 | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.85e+03 |
| KKT-SOS1 | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| KKT-SOS1 | 45 | 2.53e+03 | 4.17e+03 | 8.43e+05 | 1.49e+06 | 2.4e+03 |
| KKT-SOS1 | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| KKT-SOS1 | 55 | 3.15e+03 | 4.85e+03 | 1.17e+06 | 2e+06 | 2.9e+03 |
| CB-SSD | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| CB-SSD | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.84e+03 |
| CB-SSD | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| CB-SSD | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| CB-SSD | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| CB-SSD | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| CB-ASD | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| CB-ASD | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.84e+03 |
| CB-ASD | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| CB-ASD | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| CB-ASD | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| CB-ASD | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| CB-KKT-BigM | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| CB-KKT-BigM | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.84e+03 |
| CB-KKT-BigM | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| CB-KKT-BigM | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| CB-KKT-BigM | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| CB-KKT-BigM | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
| CB-KKT-SOS1 | 30 | 1.9e+04 | 3.75e+04 | 1.47e+08 | 2.88e+08 | 1.46e+04 |
| CB-KKT-SOS1 | 35 | 2.07e+03 | 3.81e+03 | 6.76e+05 | 1.63e+06 | 1.84e+03 |
| CB-KKT-SOS1 | 40 | 2.38e+03 | 4.07e+03 | 1.28e+06 | 2.52e+06 | 2.09e+03 |
| CB-KKT-SOS1 | 45 | 2.59e+03 | 4.4e+03 | 8.89e+05 | 1.77e+06 | 2.41e+03 |
| CB-KKT-SOS1 | 50 | 2.88e+03 | 4.96e+03 | 1.35e+06 | 3.38e+06 | 2.65e+03 |
| CB-KKT-SOS1 | 55 | 3.18e+03 | 4.85e+03 | 1.27e+06 | 2.27e+06 | 2.91e+03 |
IOM final master against the complete convex-block model
| method | size | tasks | final blocks (median) | complete blocks (median) | share (median) |
|---|---|---|---|---|---|
| IOM-All (SSD) | 30 | all | 4 | 5 | 88 % |
| IOM-All (SSD) | 30 | proved | 3 | 4 | 100 % |
| IOM-All (SSD) | 35 | all | 6 | 7 | 100 % |
| IOM-All (SSD) | 35 | proved | 4.5 | 5 | 100 % |
| IOM-All (SSD) | 40 | all | 2 | 5.5 | 47 % |
| IOM-All (SSD) | 40 | proved | 2 | 4 | 67 % |
| IOM-All (SSD) | 45 | all | 4 | 6 | 90 % |
| IOM-All (SSD) | 45 | proved | 4 | 4 | 100 % |
| IOM-All (SSD) | 50 | all | 4 | 6 | 71 % |
| IOM-All (SSD) | 50 | proved | 3.5 | 4 | 100 % |
| IOM-All (SSD) | 55 | all | 1 | 8 | 22 % |
| IOM-All (SSD) | 55 | proved | 15 | 20 | 75 % |
| IOM-All (ASD) | 30 | all | 2.5 | 5 | 67 % |
| IOM-All (ASD) | 30 | proved | 1 | 1 | 100 % |
| IOM-All (ASD) | 35 | all | 4 | 7 | 75 % |
| IOM-All (ASD) | 35 | proved | 1 | 1 | 100 % |
| IOM-All (ASD) | 40 | all | 2 | 5.5 | 50 % |
| IOM-All (ASD) | 40 | proved | 2.5 | 2.5 | 100 % |
| IOM-All (ASD) | 45 | all | 3.5 | 6 | 47 % |
| IOM-All (ASD) | 50 | all | 4 | 6 | 50 % |
| IOM-All (ASD) | 55 | all | 1 | 8 | 18 % |
| IOM-All (KKT-BigM) | 30 | all | 1 | 5 | 21 % |
| IOM-All (KKT-BigM) | 35 | all | 3 | 7 | 50 % |
| IOM-All (KKT-BigM) | 35 | proved | 2 | 2 | 100 % |
| IOM-All (KKT-BigM) | 40 | all | 1 | 5.5 | 50 % |
| IOM-All (KKT-BigM) | 40 | proved | 3.5 | 3.5 | 100 % |
| IOM-All (KKT-BigM) | 45 | all | 1 | 6 | 25 % |
| IOM-All (KKT-BigM) | 50 | all | 2 | 6 | 40 % |
| IOM-All (KKT-BigM) | 50 | proved | 2 | 2 | 100 % |
| IOM-All (KKT-BigM) | 55 | all | 1 | 8 | 12 % |
| IOM-All (KKT-SOS1) | 30 | all | 1 | 5 | 21 % |
| IOM-All (KKT-SOS1) | 35 | all | 1 | 7 | 21 % |
| IOM-All (KKT-SOS1) | 40 | all | 1 | 5.5 | 29 % |
| IOM-All (KKT-SOS1) | 40 | proved | 2 | 3 | 100 % |
| IOM-All (KKT-SOS1) | 45 | all | 1 | 6 | 17 % |
| IOM-All (KKT-SOS1) | 50 | all | 1 | 6 | 25 % |
| IOM-All (KKT-SOS1) | 55 | all | 1 | 8 | 12 % |
| IOM-Top1 (SSD) | 30 | all | 3 | 5 | 88 % |
| IOM-Top1 (SSD) | 30 | proved | 2.5 | 2.5 | 100 % |
| IOM-Top1 (SSD) | 35 | all | 5.5 | 7 | 100 % |
| IOM-Top1 (SSD) | 35 | proved | 4 | 4 | 100 % |
| IOM-Top1 (SSD) | 40 | all | 2 | 5.5 | 42 % |
| IOM-Top1 (SSD) | 40 | proved | 2 | 4 | 67 % |
| IOM-Top1 (SSD) | 45 | all | 4 | 6 | 65 % |
| IOM-Top1 (SSD) | 45 | proved | 3.5 | 3.5 | 100 % |
| IOM-Top1 (SSD) | 50 | all | 4 | 6 | 50 % |
| IOM-Top1 (SSD) | 50 | proved | 3 | 4 | 100 % |
| IOM-Top1 (SSD) | 55 | all | 1 | 8 | 20 % |
| IOM-Top1 (ASD) | 30 | all | 2 | 5 | 33 % |
| IOM-Top1 (ASD) | 30 | proved | 1 | 1 | 100 % |
| IOM-Top1 (ASD) | 35 | all | 2 | 7 | 39 % |
| IOM-Top1 (ASD) | 35 | proved | 1 | 1 | 100 % |
| IOM-Top1 (ASD) | 40 | all | 2 | 5.5 | 50 % |
| IOM-Top1 (ASD) | 40 | proved | 2 | 2 | 100 % |
| IOM-Top1 (ASD) | 45 | all | 2 | 6 | 29 % |
| IOM-Top1 (ASD) | 50 | all | 2 | 6 | 40 % |
| IOM-Top1 (ASD) | 55 | all | 1 | 8 | 12 % |
| IOM-Top1 (KKT-BigM) | 30 | all | 1 | 5 | 21 % |
| IOM-Top1 (KKT-BigM) | 35 | all | 2 | 7 | 50 % |
| IOM-Top1 (KKT-BigM) | 35 | proved | 2 | 2 | 100 % |
| IOM-Top1 (KKT-BigM) | 40 | all | 1 | 5.5 | 37 % |
| IOM-Top1 (KKT-BigM) | 40 | proved | 3.5 | 3.5 | 100 % |
| IOM-Top1 (KKT-BigM) | 45 | all | 1 | 6 | 21 % |
| IOM-Top1 (KKT-BigM) | 50 | all | 1.5 | 6 | 38 % |
| IOM-Top1 (KKT-BigM) | 50 | proved | 2 | 2 | 100 % |
| IOM-Top1 (KKT-BigM) | 55 | all | 1 | 8 | 12 % |
| IOM-Top1 (KKT-SOS1) | 30 | all | 1 | 5 | 21 % |
| IOM-Top1 (KKT-SOS1) | 35 | all | 1 | 7 | 17 % |
| IOM-Top1 (KKT-SOS1) | 40 | all | 1 | 5.5 | 25 % |
| IOM-Top1 (KKT-SOS1) | 40 | proved | 2 | 3 | 100 % |
| IOM-Top1 (KKT-SOS1) | 45 | all | 1 | 6 | 17 % |
| IOM-Top1 (KKT-SOS1) | 50 | all | 1 | 6 | 25 % |
| IOM-Top1 (KKT-SOS1) | 55 | all | 1 | 8 | 12 % |
Branch-and-bound nodes (median over all tasks with a count)
| method | median nodes |
|---|---|
| SSD | 1.37e+04 |
| ASD | 2.63e+05 |
| KKT-BigM | 6.07e+03 |
| KKT-SOS1 | 5.91e+05 |
| CB-SSD | 2.35e+04 |
| CB-ASD | 5.38e+05 |
| CB-KKT-BigM | 2.51e+04 |
| CB-KKT-SOS1 | 1.22e+06 |