Comparison of optimization software by Benchmarks

2022-05-02
11 min read

Environment

Solver Version Machine
Gurobi Gurobi Optimizer version 9.5.0 build v9.5.0rc5 NEOS SERVER
AutoRoster RosterViewerDemo4.3.5 Branch and Price Ryzen 5800X 64GB
Cplex IBM(R) ILOG(R) CPLEX(R) Interactive Optimizer 20.1.0.0 NEOS SERVER
Schedule Nurse3 Algorithm3 Ryzen 5800X 64GB

Classical Benchmarks

References

  1. Asta, S., Özcan, E., and Curtois, T. A tensor based hyper-heuristic for nurse rostering. Knowledge-based systems, 2016. 98: p. 185-199.

  2. Burke E.K. and T. Curtois. New Approaches to Nurse Rostering Benchmark Instances. European Journal of Operational Research, 2014. 237(1): p. 71-81. pdf.

  3. Solos, Ioannis P., Ioannis X. Tassopoulos and Grigorios N. Beligiannis. A Generic Two-Phase Stochastic Variable Neighborhood Approach for Effectively Solving the Nurse Rostering Problem. Algorithms, 2013. 6: p. 278-308.

Speed Comparison

Optimality Proven Instances

Instance Name Cplex Gurobi AutoRoster ScheduleNurse3
QMC-1 2.95/2.25=1.3 2.25/2.25=1 - 8.5/2.25=3.8
SINTEF 1.89/0.78=2.4 0.78/0.78=1 9/0.78=11.5 1.15/0.78=1.5
ikegami-3Shift-DATA1.2 - 695/5.66=122.8 - 5.66/5.66=1
ikegami-3Shift-DATA1.1 6606/7.155=923.3 416/7.155=58.1 - 7.155/7.155=1
ikegami-3Shift-DATA1 1838/4=459.5 285/4=71.3 - 4/4=1
ikegami-2Shift-DATA1 9.23/0.14=65.9 0.14/0.14=1 11/0.14=78.6 1.94/0.14=13.9
GPOST-B 227/34=6.7 161/34=4.7 40/34=1.2 34/34=1
GPOST 124/2.8=44.3 22/2.8=7.9 17/2.8=6.1 2.8/2.8=1
Valouxis-1 - - - 37/37=1
WHPP - 4853/4=1213.3 17/4=4.3 4/4=1
BCDT-Sep - - - 140/140=1

Optimal Objective Reached Instances

Instance Name Cplex Gurobi AutoRoster ScheduleNurse3
QMC-1 2.95/2.25=1.3 2.25/2.25=1 140/2.25=62.2 8.5/2.25=3.8
SINTEF 1.89/0.78=2.4 0.78/0.78=1 9/0.78=11.5 1.146/0.78=1.5
ikegami-3Shift-DATA1.2 2573/4=643.3 184/4=46 - 4/4=1
ikegami-3Shift-DATA1.1 6606/3.94=1676.6 175/3.94=44.4 - 3.94/3.94=1
ikegami-3Shift-DATA1 1200/4=300 285/4=71.3 300/4=75 4/4=1
ikegami-2Shift-DATA1 9.23/0.14=65.9 0.14/0.14=1 11/0.14=78.6 1.94/0.14=13.9
GPOST-B 130/2.5=52 61/2.5=24.4 40/2.5=16 2.5/2.5=1
GPOST 124/2.3=53.9 22/2.3=9.6 17/2.3=7.4 2.3/2.3=1
Valouxis-1 663/3.91=170 224/3.91=57.3 9/3.91=2.3 3.91/3.91=1
WHPP - 4853/4=1213.3 17/4=4.3 4/4=1
BCDT-Sep - - - 140/140=1

Time - Number of Instances proven optimality

No. Instance Name
1 Millar-2Shift-DATA1.1
2 Millar-2Shift-DATA1
3 Ozkarahan
4 Musa
5 Azaiez
6 QMC-1
7 LLR
8 SINTEF
9 ikegami-3Shift-DATA1.2
10 ikegami-3Shift-DATA1.1
11 ikegami-3Shift-DATA1
12 ikegami-2Shift-DATA1
13 GPOST-B
14 BCV-4.13.1
15 GPOST
16 Valouxis-1
17 WHPP
18 BCDT-Sep

Time - Number of Instances reached optimal objective

No. Instance Name
1 Millar-2Shift-DATA1.1
2 Millar-2Shift-DATA1
3 Ozkarahan
4 Musa
5 Azaiez
6 QMC-1
7 LLR
8 SINTEF
9 ikegami-3Shift-DATA1.2
10 ikegami-3Shift-DATA1.1
11 ikegami-3Shift-DATA1
12 ikegami-2Shift-DATA1
13 GPOST-B
14 BCV-4.13.1
15 GPOST
16 Valouxis-1
17 WHPP
18 BCDT-Sep

Detail Data

Second International Nurse Rostering Competition Instances

References

  1. Second Nurse Scheduling Competition

  2. Second International Nurse Rostering Competition (INRC-II) — Problem Description and Rules —

  3. A rotation-based branch-and-price approach for the nurse scheduling problem

  4. Mathematical Models and a Late Acceptance Fix-and-Optimize Approach for a Nurse Rostering Problem (ufrgs.br)

  5. CESCHIA, S.; GUIDO, R.; SCHAERF, A. Solving the static inrc-ii nurse rostering problem by simulated annealing based on large neighborhoods. Annals of Operations Research, Springer, p. 1–19, 2020.

  6. GOMES, R. A.; TOFFOLO, T. A.; SANTOS, H. G. Variable neighborhood search accelerated column generation for the nurse rostering problem. Electronic Notes in Discrete Mathematics, Elsevier, v. 58, p. 31–38, 2017.

4weeks

Instance Weeks Employees Best known LB Best known UB Known Best Gap Schedule NurseⅢ LB Schedule NurseⅢ　UB Schedule Nurse Ⅲ　Gap Note
n030w4 1 6-2-9-1 4 30 1615 1685 4.33% 1670 1670 0.00%
n030w4 1 6-7-5-3 4 30 1740 1840 5.75% 1815 1815 0.00%
n035w4 0 1-7-1-8 4 35 1250 1415 13.20% 1360 1360 0.00%
n035w4 2 8-8-7-5 4 35 1045 1145 9.57% 1080 1080 0.00%
n040w4 0 2-0-6-1 4 40 1335 1640 22.85% 1565 1565 0.00%
n040w4 2 6-1-0-6 4 40 1570 1865 18.79% 1750 1750 0.00%
n050w4 0 0-4-8-7 4 50 1195 1445 20.92% 1320 1320 0.00%
n050w4 0 7-2-7-2 4 50 1200 1405 17.08% 1315 1315 0.00%
n060w4 1 6-1-1-5 4 60 2380 2465 3.57% 2455 2455 0.00%
n060w4 1 9-6-3-8 4 60 2615 2730 4.40% 2675 2675 0.00%
n070w4 0 3-6-5-1 4 70 2280 2430 6.58% 2380 2380 0.00%
n070w4 0 4-9-6-7 4 70 1990 2125 6.78% 2115 2115 0.00%
n080w4 2 4-3-3-3 4 80 3140 3320 5.73% 3300 3300 0.00%
n080w4 2 6-0-4-8 4 80 3045 3240 6.40% 3180 3190 0.31%
n100w4 0 1-1-0-8 4 100 1055 1230 16.59% 1170 1170 0.00%
n100w4 2 0-6-4-6 4 100 1470 1855 26.19% 1780 1780 0.00% SC3 shows UB=1790, while Verilator shows UB=1780
n110w4 0 1-4-2-8 4 110 2210 2390 8.14% 2330 2330 0.00%
n110w4 0 1-9-3-5 4 110 2255 2525 11.97% 2455 2455 0.00%
n120w4 1 4-6-2-6 4 120 1790 2165 20.95% 2020 2020 0.00% SC3 shows UB=2040, while Verilator shows UB=2020
n120w4 1 5-6-9-8 4 120 1820 2220 21.98% 2050 2050 0.00% SC3 shows UB=2090, while Verilator shows UB=2050.

New INRC2 4weeks Data

Schedule Nurse 3 (Ryzen5800X 64GB Win10) Mathematical Models and a Late Acceptance Fix-and-Optimize Approach for a Nurse Rostering Problem (ufrgs.br)
Legrain et al. (2019) Gomes et al. (2017) Ceschia et al. (2020) LAFO
LB=A Validator(SC3) UB Validator(SC3) Optimality Proven Time(sec) UB reached time(sec) GAP( (obj-A)/A*100)[%] UB Time GAP( (obj-A)/A*100)[%] UB Time GAP( (obj-A)/A*100)[%] UB Time GAP( (obj-A)/A*100)[%] UB Time GAP( (obj-A)/A*100)[%]
staff=35 n035w4_2_8-8-7-5 1080 1080 275 275 0 1,145 1,803 6.0 1,085 5,586 0.5 1,151 1,317 6.6 1,237.00 5,160 14.5
n035w4_0_1-7-1-8 1360 1360 471 471 0 1,415 1,803 4.0 1,425 3,269 4.8 1,455 1,317 7.0 1,565.90 5,160 15.1
n035w4_0_4-2-1-6 1605 1605 203 103 0 1,705 1,803 6.2 1,615 5,124 0.6 1,663 1,317 3.6 1,760.50 5,160 9.7
n035w4_0_5-9-5-6 1500 1500 5188 241 0 1,575 1,803 5.0 1,540 6,872 2.7 1,544 1,317 2.9 1,628.30 5,160 8.6
n035w4_0_9-8-7-7 1335 1335 2460 1110 0 1,430 1,803 7.1 1,365 4,475 2.2 1,421 1,317 6.4 1,500.00 5,160 12.4
n035w4_1_0-6-9-2 1300 1300 361 361 0 1,375 1,803 5.8 1,385 5,359 6.5 1,391 1,317 7.0 1,487.00 5,160 14.4
n035w4_2_8-6-7-1 1080 1080 287 287 0 1,425 1,803 31.9 1,335 6,453 23.6 1,340 1,317 24.1 1,455.50 5,160 34.8
n035w4_2_9-2-2-6 1080 1080 294 294 0 1,595 1,803 47.7 1,525 6,204 41.2 1,577 1,317 46.0 1,696.50 5,160 57.1
n035w4_2_9-7-2-2 1080 1080 291 291 0 1,550 1,803 43.5 1,480 12,340 37.0 1,539 1,317 42.5 1,624.00 5,160 50.4
n035w4_2_9-9-2-1 1080 1080 284 284 0 1,540 1,803 42.6 1509 1,317 39.7 1,651.50 5,160 52.9
staff=70 n070w4_0_3-6-5-1 2380 2380 35125 480 0 2,430 3,206 2.1 2,460 3,640 3 2,455.00 2,342 3 2,842.50 5,160 19.4
n070w4_0_4-9-6-7 2115 2115 593 593 0 2,125 3,206 0.5 2,330 4,943 10.2 2,190.00 2,342 3.5 2,535.50 5,160 19.9
n070w4_0_4-9-7-6 2140 2140 914 914 0 2,210 3,206 3.3 2,315 9,465 8.2 2,229.00 2,342 4.2 2,587.00 5,160 20.9
n070w4_0_8-6-0-8 2285 2285 10433 659 0 2,320 3,206 1.5 2,400 1,795 5.0 2,345.50 2,342 2.6 2,668.50 5,160 16.8
n070w4_0_9-1-7-5 2080 2080 425 425 0 2,100 2,342 1.0 2,225 3,395 7.0 2,147.00 2,342 3.2 2,448.30 5,160 17.7
n070w4_1_1-3-8-8 2080 2080 425 425 0 2,530 2,342 21.6 2,615 3,457 25.7 2,582.50 2,342 24.2 2,915.40 5,160 40.2
n070w4_2_0-5-6-8 2270 2280 4665 4665 0 2,360 3,206 4.0 2,415 2,990 6.4 2,365.00 2,342 4.2 2,688.40 5,160 18.4
n070w4_2_3-5-8-2 2325 2335 525 525 0 2,380 2,342 2.4 2,405 5,032 3.4 2,424.50 2,342 4.3 2,690.00 5,160 15.7
n070w4_2_5-8-2-5 2290 2295 513 513 0 2,345 3,206 2.4 2,390 7,580 4.4 2,366.50 2,342 3.3 2,653.40 5,160 15.9
n070w4_2_9-5-6-5 2355 2365 426 426 0 2,465 3,206 4.7 2,480 2,495 5.3 2,416.00 2,342 2.6 2,764.50 5,160 17.4
staff=110 n110w4_0_1-4-2-8 2330 2330 25537 760 0 2,390 4,809 2.6 2,560 13,084 9.9 2,387.50 3,513 2.5 3,020.00 5,160 29.6
n110w4_0_1-9-3-5 2455 2455 402 402 0 2,525 4,809 2.9 2,640 9,624 7.5 2,566.50 3,513 4.5 3,205.50 5,160 30.6
n110w4_1_0-1-6-4 2530 2530(2785) 305 305 0 2,680 4,809 5.9 2,690 24,585 6.3 2,609.00 3,513 3.1 3,241.00 5,160 28.1
n110w4_1_0-5-8-8 2470 2475 415 0.2 2,625 4,809 6.3 2,705 12,838 9.5 2,596.00 3,513 5.1 3,254.00 5,160 31.7
n110w4_1_2-9-2-0 2870 2875 1641 0 2,975 3,513 3.7 3,170 11,570 10.5 3,032.00 3,513 5.6 3,646.00 5,160 27.0
n110w4_1_4-8-7-2 2430 2430 4740 2147 0 2,570 4,809 5.8 2,630 8,350 8.2 2,545.50 3,513 4.8 3,217.50 5,160 32.4
n110w4_2_0-2-7-0 2640 2640 7212 2193 0 2,780 4,809 5.3 2,960 10,882 12.1 2,763.50 3,513 4.7 3,388.50 5,160 28.4
n110w4_2_5-1-3-0 2640 2640 604 604 0 2,700 4,809 2.3 2,770 9,079 4.9 2,719.00 3,513 3.0 3,285.50 5,160 24.5
n110w4_2_8-9-9-2 2855 2860 4454 0.2 2,980 3,513 4.4 3,140 15,184 10.0 3,049.00 3,513 6.8 3,720.90 5,160 30.3
n110w4_2_9-8-4-9 2695 2700 1274 0.2 2,775 3,513 3.0 3,005 11,311 11.5 2,834.00 3,513 5.2 3,449.00 5,160 28.0

Note: New best objective function values by a validator are available per the following links.

https://github.com/sugawara-system/Schedule_Nurse3_Gallery/tree/main/English/Benchmarks/INRC2/4weeks

Detail Data

8weeks

Instance Weeks Employees Best known LB Best known UB Known Best Gap Schedule NurseⅢ LB Schedule NurseⅢ　UB Schedule Nurse Ⅲ　Gap Note
n030w8 1 2-7-0-9-3-6-0-6  8 30 1920 2070 7.81% 1994 2010 0.80% 　
n030w8 1 6-7-5-3-5-6-2-9  8 30 1620 1735 7.10% 1710 1730 1.17% 　
n035w8 0 6-2-9-8-7-7-9-8  8 35 2330 2555 9.66% 2408 2445 1.54%
n035w8 1 0-8-1-6-1-7-2-0  8 35 2180 2305 5.73% 2153 2245 4.27%
n040w8 0 0-6-8-9-2-6-6-4  8 40 2340 2620 11.97% 2464 2540 3.08%
n040w8 2 5-0-4-8-7-1-7-2  8 40 2205 2420 9.75% 2285 2315 1.31%
n050w8 1 1-7-8-5-7-4-1-8  8 50 4625 4900 5.95% 4778 4825 0.98%
n050w8 1 9-7-5-3-8-8-3-1  8 50 4530 4925 8.72% 4744 4770 0.55%
n060w8 0 6-2-9-9-0-8-1-3  8 60 1970 2345 19.04% 2099 2155 2.67%
n060w8 2 1-0-3-4-0-3-9-1  8 60 2260 2590 14.60% 2394 2440 1.92%
n070w8 0 3-3-9-2-3-7-5-2  8 70 4400 4595 4.43% 4475 4540 1.45%
n070w8 0 9-3-0-7-2-1-1-0  8 70 4540 4760 4.85% 4637 4675 0.82%
n080w8 1 4-4-9-9-3-6-0-5  8 80 3775 4180 10.73% 3942 4015 1.85%
n080w8 2 0-4-0-9-1-9-6-2  8 80 4125 4450 7.88% 4287 4325 0.89%
n100w8 0 0-1-7-8-9-1-5-4  8 100 2005 2125 5.99% 2026 2045 0.94%
n100w8 1 2-4-7-9-3-9-2-8  8 100 2125 2210 4.00% 2153 2170 0.79%
n110w8 0 2-1-1-7-2-6-4-7  8 110 3870 4010 3.62% 3990 3990 0.00% SC3 shows UB=4050, while Verilator shows UB=3990
n110w8 0 3-2-4-9-4-1-3-7  8 110 3375 3560 5.48% 3450 3450 0.00% SC3 shows UB=3510, while Verilator shows UB=3450
n120w8 0 0-9-9-4-5-1-0-3  8 120 2295 2600 13.29% 2485 2490 0.20%
n120w8 1 7-2-6-4-5-2-0-2  8 120 2535 3095 22.09% 2912 2920 0.27%

Detail Data

Nurse Rostering Benchmark Instances

References

  1. Nurse Rostering Benchmark Instances

  2. computational_results_on_new_staff_scheduling_benchmark_instances

  3. Burke E.K. and T. Curtois. New Approaches to Nurse Rostering Benchmark Instances. European Journal of Operational Research, 2014. 237(1): p. 71-81. pdf.

  4. Strandmark, P., Qu, Y. and Curtois, T. First-order linear programming in a column generation-based heuristic approach to the nurse rostering problem. Computers & Operations Research, 2020. 120, p. 104945. (pdf)

  5. Demirović, E., Musliu, N., and Winter, F. Modeling and solving staff scheduling with partial weighted maxSAT. Annals of Operations Research, 2019. 275(1): p. 79-99.

  6. Smet P. Constraint reformulation for nurse rostering problems, in: PATAT 2018 twelfth international conference on the practice and theory of automated timetabling, Vienna, August, 2018, p. 69-80.

  7. Rahimian, E., Akartunalı, K., and Levine, J. A hybrid integer programming and variable neighbourhood search algorithm to solve nurse rostering problems. European Journal of Operational Research, 2017. 258(2): p. 411-423.

Speed Comparison

Optimality Proven Instances

Instance Name Cplex Gurobi AutoRoster ScheduleNurse3
Instance4 4.4/0.6=7.3 4/0.6=6.7 6/0.6=10 0.6/0.6=1
Instance5 29/2.4=12.1 16/2.4=6.7 - 2.4/2.4=1
Instance6 7/1.6=4.4 5/1.6=3.1 - 1.6/1.6=1
Instance7 61/6.2=9.8 20/6.2=3.2 - 6.2/6.2=1
Instance8 4623/50=92.5 931/50=18.6 - 50/50=1
Instance9 - - - -
Instance10 41/13=3.2 20/13=1.5 660/13=50.8 13/13=1
Instance11 45/18=2.5 18/18=1 71/18=3.9 37/18=2.1
Instance12 260/54=4.8 185/54=3.4 660/54=12.2 54/54=1
Instance13 - 12115/572=21.2 - 572/572=1
Instance14 690/4.3=160.5 205/4.3=47.7 - 4.3/4.3=1
Instance15 - - - -
Instance16 937/4.3=217.9 78/4.3=18.1 - 4.3/4.3=1
Instance17 4022/4.8=837.9 143/4.8=29.8 10000/4.8=2083.3 4.8/4.8=1
Instance18 21387/135=158.4 787/135=5.8 - 135/135=1
Instance19 - 3006/3006=1 - 5285/3006=1.8
Instance20 - 3665/678=5.4 - 678/678=1

Optimal Objective Reached Instances

|

Instance Name Cplex Gurobi AutoRoster ScheduleNurse3
Instance4 4.4/0.5=8.8 4/0.5=8 6/0.5=12 0.5/0.5=1
Instance5 29/2.4=12.1 16/2.4=6.7 11/2.4=4.6 2.4/2.4=1
Instance6 7/1.6=4.4 5/1.6=3.1 - 1.6/1.6=1
Instance7 61/6.2=9.8 20/6.2=3.2 - 6.2/6.2=1
Instance8 4623/50=92.5 931/50=18.6 - 50/50=1
Instance9 - - - -
Instance10 41/13=3.2 20/13=1.5 660/13=50.8 13/13=1
Instance11 45/18=2.5 18/18=1 71/18=3.9 37/18=2.1
Instance12 260/54=4.8 185/54=3.4 660/54=12.2 54/54=1
Instance13 - 12115/572=21.2 - 572/572=1
Instance14 690/4.3=160.5 205/4.3=47.7 - 4.3/4.3=1
Instance15 - - - -
Instance16 937/4.3=217.9 78/4.3=18.1 - 4.3/4.3=1
Instance17 4022/4.8=837.9 143/4.8=29.8 10000/4.8=2083.3 4.8/4.8=1
Instance18 21387/135=158.4 787/135=5.8 - 135/135=1
Instance19 - 3006/3006=1 - 5285/3006=1.8
Instance20 - 3665/678=5.4 - 678/678=1

Time - Number of Instances proven optimality

Time - Number of Instances reached optimal objective

Detail Data

First International Nurse Rostering Competition Instances

References

  1. First Nurse Scheduling Competition 2010

  2. Nurse Rostering Problem

Medium Instances

Speed Comparison

Optimality Proven Instances
Instance Name Cplex Gurobi ScheduleNurse3
medium-early01 44/3=14.7 3/3=1 47/3=15.7
medium-early02 24/6.8=3.5 45/6.8=6.6 6.8/6.8=1
medium-early03 20/6=3.3 6/6=1 9.3/6=1.6
medium-early04 8/8=1 15/8=1.9 47/8=5.9
medium-early05 21/9.9=2.1 15/9.9=1.5 9.9/9.9=1
medium-hidden01 - - -
medium-hidden02 - - -
medium-hidden03 - - 38/38=1
medium-hidden04 - - 78/78=1
medium-hidden05 - - 3390/3390=1
medium-late01 - 2682/175=15.3 175/175=1
medium-late02 3152=851.9 211/3.7=57.0 3.7/3.7=1
medium-late03 - 2503/13=192.5 13/13=1
medium-late04 12350/5=2470 165/5=33 5/5=1
medium-late05 - 790/139=5.7 139/139=1
Optimal Objective Reached Instances
Instance Name Cplex Gurobi ScheduleNurse3
medium-early01 44/3=14.7 3/3=1 47/3=15.7
medium-early02 24/6.8=3.5 45/6.8=6.6 6.8/6.8=1
medium-early03 20/6=3.3 6/6=1 9.3/6=1.6
medium-early04 8/8=1 15/8=1.9 47/8=5.9
medium-early05 21/9.9=2.1 15/9.9=1.5 9.9/9.9=1
medium-hidden01 - - -
medium-hidden02 - - -
medium-hidden03 - - 38/38=1
medium-hidden04 - - 78/78=1
medium-hidden05 - - 3390/3390=1
medium-late01 - 918/175=5.2 175/175=1
medium-late02 3152/3.3=955.2 211/3.3=63.9 3.3/3.3=1
medium-late03 - 508/13=39.1 13/13=1
medium-late04 2393/5=478.6 165/5=33 5/5=1
medium-late05 - 790/139=5.7 139/139=1

Time - Number of Instances proven optimality

Time - Number of Instances reached optimal objective

Detail Data

Long Instances

Optimality Proven Instances
Instance Name Cplex Gurobi ScheduleNurse3
long-early01 3/2=1.5 2/2=1 11/2=5.5
long-early02 15/14=1.1 14/14=1 82/14=6
long-early03 3/1=3 1/1=1 44/1=44
long-early04 4/2=2 2/2=1 71/2=35.5
long-early05 4/2=2 2/2=1 81/2=40.5
long-hidden01 - - 168/168=1
long-hidden02 - - 98/98=1
long-hidden03 - 27097/49=553 49/49=1
long-hidden04 - 9775/13=751.9 13/13=1
long-hidden05 - 2223/35=63.5 35/35=1
long-late01 - 3585/130=27.6 130/130=1
long-late02 - 5481/141=38.9 141/141=1
long-late03 - - 3740/3740=1
long-late04 - 6550/146=44.9 146/146=1
long-late05 - 550/75=7.3 75/75=1
Optimal Objective Reached Instances
Instance Name Cplex Gurobi ScheduleNurse3
long-early01 3/2=1.5 2/2=1 10/2=5
long-early02 15/14=1.1 14/14=1 82/14=6
long-early03 3/1=3 1/1=1 44/1=44
long-early04 4/2=2 2/2=1 71/2=35.5
long-early05 4/2=2 2/2=1 81/2=40.5
long-hidden01 - 3737/168=22.2 168/168=1
long-hidden02 - 586/98=6.0 98/98=1
long-hidden03 - 3392/48=70.7 48/48=1
long-hidden04 2662/13=204.8 488/13=37.5 13/13=1
long-hidden05 6979/35=199.4 518/35=14.8 35/35=1
long-late01 - 1529/130=11.8 130/130=1
long-late02 - 5481/141=38.9 141/141=1
long-late03 12668/135=93.8 6154/135=45.6 135/135=1
long-late04 - 1277/146=8.7 146/146=1
long-late05 1592/75=21.2 550/75=7.3 75/75=1

Time - Number of Instances proven optimality

Time - Number of Instances reached optimal objective

Detail Data

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