PB'26 competition WBO: ranking of solvers
All selected instances (including those not supported by some solvers)

Ranking on final answers (complete solver point of view)

This section presents the ranking of the different solvers. Solvers are ranked on the number of solved instances, i.e. where a final answer was given. Ties are broken by considering the minimum total solution time.

Solvers which gave a wrong answer in a category are excluded from the ranking in that category.

The Virtual Best Solver (VBS) is a theoretical construction which returns the best answer provided by one of the submitted solver. It corresponds to the 'Best result' column in the bench per bench view of the results. It can be considered as a meta solver which uses a perfect oracle to guess instantaneously which of the submitted solver will be the most efficient to solve the instance. Another way to look at it is to consider this VBS as a solver which would run all other solvers in parallel, bringing together all the solvers strenghs. This VBS is essentially the same notion as State Of The Art (SOTA) solver defined in "Evaluating general purpose automated theorem proving systems", Artificial Intelligence, Volume 131, Issues 1-2, September 2001, Pages 39-54 Geoff Sutcliffe, Christian Suttner. However, SOTA is a more general notion: the VBS can be seen as the least powerful SOTA solver.

Category "WBO, both soft and hard constraints, linear constraints" (PARTIAL-LIN): OPT+UNSAT answers

Rank SolverVersion PAR2 score Number of
solved instances
Detail % of all instances% of VBSCumulated CPU time
on solved instances
Median CPU timeAverage CPU time
per solved instance
Cumulated WC time
on solved instances
Median WC timeAverage WC time
per solved instance
CPU/WC
Total number of instances in the category: 208
Virtual Best Solver (VBS)--137136 MOPT, 1 UNSAT66%100%11208.750.8381.82----
1UWrMaxSat-SCIP2.0.5136,688.2179178 MOPT, 1 UNSAT86%131%10686.690.5159.7010716.070.5259.871.00
2OR-Tools CP-SAT2026-05-18168,089.9175175 MOPT84%128%16884.070.6196.485804.920.2833.172.91
3Exact2026-06-14221,024.2160159 MOPT, 1 UNSAT77%117%5739.620.1135.875764.140.1136.031.00
4Exact_symlocal2026-06-14222,208.5160159 MOPT, 1 UNSAT77%117%8364.340.1252.288393.130.1252.461.00
5Exact_symbreak2026-06-14220,039.9159158 MOPT, 1 UNSAT76%116%6140.450.1238.626162.090.1238.761.00
6scip-printemps (incomplete)2026-06-28273,163.9147146 MOPT, 1 UNSAT71%107%2536.960.6417.262550.720.6517.350.99
7exact-printemps (incomplete)2026-05-18272,066.7144143 MOPT, 1 UNSAT69%105%2037.860.2014.152049.010.2414.230.99
8NaPS1.04261,963.1140139 MOPT, 1 UNSAT67%102%11052.982.1278.9511096.332.2079.261.00
9Sat4j Resolution2026-06-10325,645.7130129 MOPT, 1 UNSAT63%95%5231.551.1840.245100.160.4439.231.03
10AY2026-07-11b524,248.69292 MOPT44%67%35873.6821.36389.9336010.8021.50391.421.00
11PRINTEMPS (incomplete)2026-05-18759,991.600%0%0.000.00-0.000.00--

Category "WBO, both soft and hard constraints, linear constraints" (PARTIAL-LIN): OPT answers

Rank SolverVersion PAR2 score Number of
solved instances
% of all instances% of VBSCumulated CPU time
on solved instances
Median CPU timeAverage CPU time
per solved instance
Cumulated WC time
on solved instances
Median WC timeAverage WC time
per solved instance
CPU/WC
Total number of instances in the category: 208
Virtual Best Solver (VBS)--13665%100%11207.920.0082.41----
1UWrMaxSat-SCIP2.0.5136,688.217886%131%10685.860.4960.0310715.240.5060.201.00
2OR-Tools CP-SAT2026-05-18168,089.917584%129%16884.070.6196.485804.920.2833.172.91
3Exact2026-06-14221,024.215976%117%5725.540.1136.015750.000.1136.161.00
4Exact_symlocal2026-06-14222,208.515976%117%8342.740.1252.478371.440.1252.651.00
5Exact_symbreak2026-06-14220,039.915876%116%6119.970.1238.736141.530.1238.871.00
6scip-printemps (incomplete)2026-06-28273,163.914670%107%2509.380.6317.192522.990.6417.280.99
7exact-printemps (incomplete)2026-05-18272,066.714369%105%2013.360.2014.082024.410.2414.160.99
8NaPS1.04261,963.113967%102%11047.122.1079.4811090.352.1879.791.00
9Sat4j Resolution2026-06-10325,645.712962%95%5193.711.1740.265064.170.4439.261.03
10AY2026-07-11b524,248.69244%68%35873.6821.36389.9336010.8021.50391.421.00
11PRINTEMPS (incomplete)2026-05-18759,991.600%0%0.000.00-0.000.00--

Category "WBO, both soft and hard constraints, linear constraints" (PARTIAL-LIN): UNSAT answers

Rank SolverVersion PAR2 score Number of
solved instances
% of all instances% of VBSCumulated CPU time
on solved instances
Median CPU timeAverage CPU time
per solved instance
Cumulated WC time
on solved instances
Median WC timeAverage WC time
per solved instance
CPU/WC
Total number of instances in the category: 208
Virtual Best Solver (VBS)--10%100%0.830.830.83----
1UWrMaxSat-SCIP2.0.5136,688.210%100%0.830.830.830.840.840.841.00
2NaPS1.04261,963.110%100%5.865.865.865.985.985.980.98
3Exact2026-06-14221,024.210%100%14.0814.0814.0814.1314.1314.131.00
4Exact_symbreak2026-06-14220,039.910%100%20.4820.4820.4820.5620.5620.561.00
5Exact_symlocal2026-06-14222,208.510%100%21.6021.6021.6021.6921.6921.691.00
6exact-printemps (incomplete)2026-05-18272,066.710%100%24.5024.5024.5024.6024.6024.601.00
7scip-printemps (incomplete)2026-06-28273,163.910%100%27.5727.5727.5727.7327.7327.730.99
8Sat4j Resolution2026-06-10325,645.710%100%37.8437.8437.8435.9835.9835.981.05
9OR-Tools CP-SAT2026-05-18168,089.900%0%0.000.00-0.000.00--
10PRINTEMPS (incomplete)2026-05-18759,991.600%0%0.000.00-0.000.00--
11AY2026-07-11b524,248.600%0%0.000.00-0.000.00--

Category "WBO, only soft constraints, linear constraints" (SOFT-LIN): OPT+UNSAT answers

Rank SolverVersion PAR2 score Number of
solved instances
Detail % of all instances% of VBSCumulated CPU time
on solved instances
Median CPU timeAverage CPU time
per solved instance
Cumulated WC time
on solved instances
Median WC timeAverage WC time
per solved instance
CPU/WC
Total number of instances in the category: 60
Virtual Best Solver (VBS)--4747 MOPT78%100%776.150.0016.51----
1Exact_symbreak2026-06-14941.76060 MOPT100%128%941.650.3215.69947.090.3215.780.99
2Exact2026-06-141,048.86060 MOPT100%128%1048.770.4517.481053.700.4617.561.00
3Exact_symlocal2026-06-141,116.26060 MOPT100%128%1116.200.3818.601127.490.3918.790.99
4OR-Tools CP-SAT2026-05-181,797.66060 MOPT100%128%1797.560.7429.96623.760.3510.402.88
5UWrMaxSat-SCIP2.0.52,209.96060 MOPT100%128%2209.902.9336.832218.052.9436.971.00
6UWrMaxSat-SCIP2.0.32,212.46060 MOPT100%128%2212.402.3336.872220.622.3437.011.00
7UWrMaxSat-SCIP2.0.42,220.16060 MOPT100%128%2220.112.8837.002227.692.8937.131.00
8scip-printemps (incomplete)2026-06-2834,281.05151 MOPT85%109%1883.370.8336.931893.250.8437.120.99
9exact-printemps (incomplete)2026-05-1862,328.14343 MOPT72%91%1124.300.6526.151130.370.7026.290.99
10Sat4j Resolution2026-06-1065,928.14242 MOPT70%89%1123.376.0326.751059.954.1725.241.06
11NaPS1.0471,663.74141 MOPT68%87%4507.7437.25109.944525.6637.50110.381.00
12AY2026-07-11b86,034.24040 MOPT67%85%14288.3623.73357.2114340.0623.87358.501.00
13AY0.11.0124,660.53535 MOPT58%74%6090.0619.13174.006115.0419.25174.721.00
14PRINTEMPS (incomplete)2026-05-18215,998.000%0%0.000.00-0.000.00--

Category "WBO, only soft constraints, linear constraints" (SOFT-LIN): OPT answers

Rank SolverVersion PAR2 score Number of
solved instances
% of all instances% of VBSCumulated CPU time
on solved instances
Median CPU timeAverage CPU time
per solved instance
Cumulated WC time
on solved instances
Median WC timeAverage WC time
per solved instance
CPU/WC
Total number of instances in the category: 60
Virtual Best Solver (VBS)--4778%100%776.150.0016.51----
1Exact_symbreak2026-06-14941.760100%128%941.650.3215.69947.090.3215.780.99
2Exact2026-06-141,048.860100%128%1048.770.4517.481053.700.4617.561.00
3Exact_symlocal2026-06-141,116.260100%128%1116.200.3818.601127.490.3918.790.99
4OR-Tools CP-SAT2026-05-181,797.660100%128%1797.560.7429.96623.760.3510.402.88
5UWrMaxSat-SCIP2.0.52,209.960100%128%2209.902.9336.832218.052.9436.971.00
6UWrMaxSat-SCIP2.0.32,212.460100%128%2212.402.3336.872220.622.3437.011.00
7UWrMaxSat-SCIP2.0.42,220.160100%128%2220.112.8837.002227.692.8937.131.00
8scip-printemps (incomplete)2026-06-2834,281.05185%109%1883.370.8336.931893.250.8437.120.99
9exact-printemps (incomplete)2026-05-1862,328.14372%91%1124.300.6526.151130.370.7026.290.99
10Sat4j Resolution2026-06-1065,928.14270%89%1123.376.0326.751059.954.1725.241.06
11NaPS1.0471,663.74168%87%4507.7437.25109.944525.6637.50110.381.00
12AY2026-07-11b86,034.24067%85%14288.3623.73357.2114340.0623.87358.501.00
13AY0.11.0124,660.53558%74%6090.0619.13174.006115.0419.25174.721.00
14PRINTEMPS (incomplete)2026-05-18215,998.000%0%0.000.00-0.000.00--

Category "WBO, only soft constraints, linear constraints" (SOFT-LIN): UNSAT answers

Rank SolverVersion PAR2 score Number of
solved instances
% of all instances% of VBSCumulated CPU time
on solved instances
Median CPU timeAverage CPU time
per solved instance
Cumulated WC time
on solved instances
Median WC timeAverage WC time
per solved instance
CPU/WC
Total number of instances in the category: 60
Virtual Best Solver (VBS)--00%-0.000.00-----
1UWrMaxSat-SCIP2.0.32,212.400%-0.000.00-0.000.00--
2scip-printemps (incomplete)2026-06-2834,281.000%-0.000.00-0.000.00--
3AY0.11.0124,660.500%-0.000.00-0.000.00--
4Exact_symbreak2026-06-14941.700%-0.000.00-0.000.00--
5Exact_symlocal2026-06-141,116.200%-0.000.00-0.000.00--
6Exact2026-06-141,048.800%-0.000.00-0.000.00--
7OR-Tools CP-SAT2026-05-181,797.600%-0.000.00-0.000.00--
8Sat4j Resolution2026-06-1065,928.100%-0.000.00-0.000.00--
9UWrMaxSat-SCIP2.0.42,220.100%-0.000.00-0.000.00--
10exact-printemps (incomplete)2026-05-1862,328.100%-0.000.00-0.000.00--
11PRINTEMPS (incomplete)2026-05-18215,998.000%-0.000.00-0.000.00--
12UWrMaxSat-SCIP2.0.52,209.900%-0.000.00-0.000.00--
13AY2026-07-11b86,034.200%-0.000.00-0.000.00--
14NaPS1.0471,663.700%-0.000.00-0.000.00--

Ranking on the number of best answers found (incomplete solver point of view)

Number of best answers found with no further time limit

This section presents the ranking of the different solvers. Solvers are ranked on the number of instances for which they were able to find the best solution obtained by one the solvers within the global time limit. Ties are broken using the cumulated T1 time.

Solvers which gave a wrong answer in a category are excluded from the ranking in that category.

The Virtual Best Solver (VBS) is a theoretical construction which returns the best answer provided by one of the submitted solver. It corresponds to the 'Best result' column in the bench per bench view of the results. It can be considered as a meta solver which uses a perfect oracle to guess instantaneously which of the submitted solver will be the most efficient to solve the instance. Another way to look at it is to consider this VBS as a solver which would run all other solvers in parallel, bringing together all the solvers strenghs. This VBS is essentially the same notion as State Of The Art (SOTA) solver defined in "Evaluating general purpose automated theorem proving systems", Artificial Intelligence, Volume 131, Issues 1-2, September 2001, Pages 39-54 Geoff Sutcliffe, Christian Suttner. However, SOTA is a more general notion: the VBS can be seen as the least powerful SOTA solver.

Number of best answers found within 2 times the VBS time

This section presents the ranking of the different solvers. Solvers are ranked on the number of instances for which they were able to find the best solution obtained by one the solvers within 2 times the VBS time. Ties are broken using the cumulated T1 time.

Solvers which gave a wrong answer in a category are excluded from the ranking in that category.

The Virtual Best Solver (VBS) is a theoretical construction which returns the best answer provided by one of the submitted solver. It corresponds to the 'Best result' column in the bench per bench view of the results. It can be considered as a meta solver which uses a perfect oracle to guess instantaneously which of the submitted solver will be the most efficient to solve the instance. Another way to look at it is to consider this VBS as a solver which would run all other solvers in parallel, bringing together all the solvers strenghs. This VBS is essentially the same notion as State Of The Art (SOTA) solver defined in "Evaluating general purpose automated theorem proving systems", Artificial Intelligence, Volume 131, Issues 1-2, September 2001, Pages 39-54 Geoff Sutcliffe, Christian Suttner. However, SOTA is a more general notion: the VBS can be seen as the least powerful SOTA solver.

Number of best answers found within 4 times the VBS time

This section presents the ranking of the different solvers. Solvers are ranked on the number of instances for which they were able to find the best solution obtained by one the solvers within 4 times the VBS time. Ties are broken using the cumulated T1 time.

Solvers which gave a wrong answer in a category are excluded from the ranking in that category.

The Virtual Best Solver (VBS) is a theoretical construction which returns the best answer provided by one of the submitted solver. It corresponds to the 'Best result' column in the bench per bench view of the results. It can be considered as a meta solver which uses a perfect oracle to guess instantaneously which of the submitted solver will be the most efficient to solve the instance. Another way to look at it is to consider this VBS as a solver which would run all other solvers in parallel, bringing together all the solvers strenghs. This VBS is essentially the same notion as State Of The Art (SOTA) solver defined in "Evaluating general purpose automated theorem proving systems", Artificial Intelligence, Volume 131, Issues 1-2, September 2001, Pages 39-54 Geoff Sutcliffe, Christian Suttner. However, SOTA is a more general notion: the VBS can be seen as the least powerful SOTA solver.

Number of best answers found within 8 times the VBS time

This section presents the ranking of the different solvers. Solvers are ranked on the number of instances for which they were able to find the best solution obtained by one the solvers within 8 times the VBS time. Ties are broken using the cumulated T1 time.

Solvers which gave a wrong answer in a category are excluded from the ranking in that category.

The Virtual Best Solver (VBS) is a theoretical construction which returns the best answer provided by one of the submitted solver. It corresponds to the 'Best result' column in the bench per bench view of the results. It can be considered as a meta solver which uses a perfect oracle to guess instantaneously which of the submitted solver will be the most efficient to solve the instance. Another way to look at it is to consider this VBS as a solver which would run all other solvers in parallel, bringing together all the solvers strenghs. This VBS is essentially the same notion as State Of The Art (SOTA) solver defined in "Evaluating general purpose automated theorem proving systems", Artificial Intelligence, Volume 131, Issues 1-2, September 2001, Pages 39-54 Geoff Sutcliffe, Christian Suttner. However, SOTA is a more general notion: the VBS can be seen as the least powerful SOTA solver.