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

Ranking on PAR2 score (complete solver point of view)

WARNING: Parallel solvers do not appear in this ranking. Since in this ranking no specific limit is enforced by postprocessing, the PAR2 score of parallel solvers would be computed with their full CPU time. In other words, for parallel solvers, the limit is enforced on wall clock time, with is not the case for sequential solvers. The comparison between sequential and parallel solvers is not fair. Besides, the penalty of 2 times the CPU time limit wouldn't be significant.

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 "decision problem, linear constraints, no UNSAT certificate" (DEC-LIN): SAT+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: 492
Virtual Best Solver (VBS)--464183 SAT, 281 UNSAT94%100%82436.190.10177.66----
1Local-PB2026-05-14704,150.2399155 SAT, 244 UNSAT81%86%34550.220.6486.5934664.430.6486.881.00
2Hybrid-SynLSExact+CASHWMaxSATDisjComSv1745,046.8398158 SAT, 240 UNSAT81%86%68246.816.83171.4768510.586.96172.141.00
3roundingsat-satsuma-MIR2026-06-11746,148.3393144 SAT, 249 UNSAT80%85%33348.281.0684.8633484.741.0885.201.00
4roundingsat-satsuma-MIR2026-06-11 (cert)751,559.5392143 SAT, 5 UNSAT, 244 UNSATC80%84%31559.551.2280.5132005.391.3181.650.99
5Hybrid-SynLSExact+CASHWMaxSATDisjComSv2755,223.3397157 SAT, 240 UNSAT81%86%71223.276.79179.4071497.526.91180.091.00
6Hybrid-SynLSRS+CASHWMaxSATDisjComSv1765,389.1398159 SAT, 239 UNSAT81%86%88589.115.61222.5988934.595.72223.451.00
7Hybrid-SynLSRS+CASHWMaxSATDisjComSv2778,888.3397159 SAT, 238 UNSAT81%86%94888.264.92239.0195254.325.18239.941.00
8roundingsat-satsuma-liftedcover2026-06-11789,325.7389141 SAT, 248 UNSAT79%84%47725.731.34122.6947912.351.37123.171.00
9roundingsat-satsuma-liftedcover2026-06-11 (cert)791,936.7389141 SAT, 13 UNSAT, 235 UNSATC79%84%50336.681.65129.4051916.322.20133.460.97
10cpmpy_ortools (1 core)2026-05-18813,228.8383156 SAT, 227 UNSAT78%83%28428.772.4974.2328752.363.4775.070.99
11roundingsat-satsuma-saturation2026-06-11826,064.7383140 SAT, 243 UNSAT78%83%41264.711.04107.7441412.591.11108.131.00
12SynLSExact2026-06-06826,586.4383153 SAT, 230 UNSAT78%83%41786.436.19109.1041977.616.34109.601.00
13roundingsat-satsuma-saturation2026-06-11 (cert)832,519.4382139 SAT, 6 UNSAT, 237 UNSATC78%82%40519.431.21106.0741314.061.35108.150.98
14UWrMaxSat-SCIP2.0.4853,709.6383154 SAT, 229 UNSAT78%83%68909.628.50179.9269146.138.53180.541.00
15SCIP-NaPSscip-naps-1.00a2871,182.0385159 SAT, 226 UNSAT78%83%100782.0410.57261.77101138.5510.49262.701.00
16NaPS1.04878,202.9384158 SAT, 226 UNSAT78%83%100602.8711.57261.99100960.8111.64262.921.00
17SynLSRS2026-06-06882,090.1377149 SAT, 228 UNSAT77%81%54090.153.99143.4854320.014.07144.081.00
18Exact2026-06-14 (cert)982,664.2362140 SAT, 6 UNSAT, 216 UNSATC74%78%46664.230.97128.9147834.231.01132.140.98
19Exact2026-06-141,001,279.4359138 SAT, 221 UNSAT73%77%43679.440.72121.6743831.600.72122.091.00
20Exact_symbreak2026-06-141,013,752.0357133 SAT, 224 UNSAT73%77%41752.030.77116.9541893.330.78117.351.00
21Exact_symlocal2026-06-141,024,729.7355134 SAT, 221 UNSAT72%77%38329.720.68107.9738461.790.68108.341.00
22cpmpy_highs (1 core)2026-07-051,172,469.9336132 SAT, 204 UNSAT68%72%49269.902.45146.6449590.893.22147.590.99
23AI448PBSolver2026-04-261,187,165.2331120 SAT, 211 UNSAT67%71%27965.200.2884.4928091.110.4684.871.00
24cpmpy_highs (1 core)2026-05-181,206,841.1330129 SAT, 201 UNSAT67%71%40441.072.60122.5540154.863.68121.681.01
25exact-printemps (1 core) (incomplete)2026-05-181,215,086.2326140 SAT, 186 UNSAT66%70%19886.162.5261.0019958.982.5461.221.00
26OR-Tools CP-SAT (1 core)2026-05-181,238,779.4324141 SAT, 183 UNSAT66%70%29179.370.9190.0629284.180.9190.381.00
27AY2026-07-11b1,343,662.9315120 SAT, 195 UNSAT64%68%69262.886.09219.8823329.152.1874.062.97
28Picat(kissat)2026-06-191,385,690.1307150 SAT, 157 UNSAT62%66%53690.063.32174.8953869.693.41175.471.00
29cpmpy_pindakaas_cadical2026-05-181,484,995.6294131 SAT, 163 UNSAT60%63%59395.639.24202.0359895.3210.62203.730.99
30scip-printemps (1 core) (incomplete)2026-06-281,512,417.4286127 SAT, 159 UNSAT58%62%29217.410.62102.1629314.800.64102.501.00
31AY-cert2026-07-13-certfix (cert)1,621,802.6273115 SAT, 158 UNSATC55%59%45002.631.49164.8444714.931.60163.791.01
32AY0.11.01,712,559.7289112 SAT, 177 UNSAT59%62%250959.70113.86868.37251780.07114.45871.211.00
33Sat4j Resolution2026-06-101,739,486.4258115 SAT, 143 UNSAT52%56%54686.433.05211.9654140.891.73209.851.01
34Sat4j Resolution CERT2026-05-20 (cert)1,743,730.6258115 SAT, 143 UNSATC52%56%58930.614.13228.4159291.602.10229.810.99
35Sat4j CuttingPlanes2026-06-102,002,352.221968 SAT, 151 UNSAT45%47%36752.254.58167.8235775.461.92163.361.03
36Sat4j CuttingPlanes CERT2026-06-10 (cert)2,002,704.021968 SAT, 151 UNSATC45%47%37103.994.90169.4236142.212.14165.031.03
37PRINTEMPS (1 core) (incomplete)2026-05-182,668,848.9124122 SAT, 2 UNSAT25%27%19248.921.71155.2319269.241.70155.401.00

Category "decision problem, non-linear constraints, no UNSAT certificate" (DEC-NLC): SAT+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: 10
Virtual Best Solver (VBS)--106 SAT, 4 UNSAT100%100%1061.240.15106.12----
1scip-printemps (1 core) (incomplete)2026-06-2815,099.286 SAT, 2 UNSAT80%80%699.190.2887.40701.420.2987.681.00
2exact-printemps (1 core) (incomplete)2026-05-1815,254.186 SAT, 2 UNSAT80%80%854.120.10106.76856.950.15107.121.00
3Picat(kissat)2026-06-1915,354.184 SAT, 4 UNSAT80%80%954.070.76119.26957.480.78119.681.00
4UWrMaxSat-SCIP2.0.418,131.384 SAT, 4 UNSAT80%80%3731.350.80466.423743.520.81467.941.00
5UWrMaxSat-SCIP2.0.318,219.584 SAT, 4 UNSAT80%80%3819.480.82477.433833.970.83479.251.00
6Exact_symbreak2026-06-1428,800.464 SAT, 2 UNSAT60%60%0.390.030.070.390.030.070.99
7Exact_symlocal2026-06-1428,800.464 SAT, 2 UNSAT60%60%0.380.030.060.390.030.070.98
8Exact2026-06-1428,800.464 SAT, 2 UNSAT60%60%0.370.030.060.370.030.060.99
9OR-Tools CP-SAT (1 core)2026-05-1828,803.364 SAT, 2 UNSAT60%60%3.330.240.563.350.240.560.99
10AY2026-07-11b28,835.164 SAT, 2 UNSAT60%60%35.114.175.8518.342.163.061.91
11AY0.11.028,855.264 SAT, 2 UNSAT60%60%55.162.489.1955.572.529.260.99
12PRINTEMPS (1 core) (incomplete)2026-05-1828,956.466 SAT60%60%156.390.7726.07156.550.6726.091.00
13Sat4j Resolution2026-06-1050,401.331 SAT, 2 UNSAT30%30%1.270.200.420.590.130.202.14
14Sat4j CuttingPlanes2026-06-1072,000.000%0%0.000.00-0.000.00--

Category "optimization problem, linear constraints, no OPT/UNSAT certificate" (OPT-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: 585
Virtual Best Solver (VBS)--444425 OPT, 19 UNSAT76%100%296414.900.47667.60----
1Local-PB2026-05-141,607,474.2369353 OPT, 16 UNSAT63%83%52274.200.70141.6652448.220.70142.141.00
2UWrMaxSat-SCIP2.0.41,758,090.3348331 OPT, 17 UNSAT59%78%51690.293.12148.5451859.633.13149.021.00
3SCIP-NaPSscip-naps-1.00a21,854,662.9340323 OPT, 17 UNSAT58%77%90662.903.98266.6690993.144.33267.631.00
4UWrMaxSat-SCIP2.0.31,855,028.5334317 OPT, 17 UNSAT57%75%47828.462.59143.2047984.732.60143.671.00
5AutoAdaptRoundingSat2026-06-081,894,517.1331317 OPT, 14 UNSAT57%75%65717.0861.13198.5465960.4661.56199.281.00
6Hybrid-CASHWMaxSATDisjComS-AdaptRoundingSatv21,911,915.3354338 OPT, 16 UNSAT61%80%248715.30127.02702.59249586.79127.57705.051.00
7WMaxCDCL-S92026-05-171,919,247.6333319 OPT, 14 UNSAT57%75%104847.635.37314.86105213.465.61315.961.00
8Hybrid-CASHWMaxSATDisjComS-AdaptExactv11,924,261.2331315 OPT, 16 UNSAT57%75%95461.172.82288.4095834.333.11289.531.00
9Hybrid-CASHWMaxSATDisjComS-AdaptExactv21,926,803.6331315 OPT, 16 UNSAT57%75%98003.612.83296.0898374.273.05297.201.00
10Hybrid-CASHWMaxSATDisjComS-AdaptRoundingSatv11,927,025.3351335 OPT, 16 UNSAT60%79%242225.27110.19690.10243065.35110.60692.491.00
11Qiuqi (1 core)2026-06-151,928,385.5328313 OPT, 15 UNSAT56%74%77985.5371.21237.7678259.5471.45238.601.00
12roundingsat-satsuma-opt2026-06-111,935,528.2322309 OPT, 13 UNSAT55%73%41928.221.43130.2142077.581.49130.681.00
13roundingsat-opt2026-06-111,944,047.8321308 OPT, 13 UNSAT55%72%43247.801.07134.7343408.421.11135.231.00
14NaPS1.041,945,753.8323306 OPT, 17 UNSAT55%73%59353.822.77183.7659574.022.80184.441.00
15roundingsat-satsuma-opt2026-06-11 (cert)1,954,918.031911 OPT, 295 OPTC, 13 UNSATC55%72%39718.041.76124.5141340.591.84129.590.96
16roundingsat-opt2026-06-11 (cert)1,963,255.13181 OPT, 304 OPTC, 13 UNSATC54%72%40855.101.16128.4841943.061.70131.900.97
17Exact2026-06-142,024,347.0311296 OPT, 15 UNSAT53%70%51547.021.22165.7551723.421.22166.311.00
18Exact_symlocal2026-06-142,033,160.1310295 OPT, 15 UNSAT53%70%53160.071.44171.4853337.461.45172.061.00
19HitPBO2026-06-222,046,728.9308299 OPT, 9 UNSAT53%69%52328.881.13169.9052500.281.15170.461.00
20Exact_symbreak2026-06-142,049,355.2307292 OPT, 15 UNSAT52%69%47755.161.62155.5547918.931.62156.091.00
21AutoAdaptRoundingSatv22,052,434.7327313 OPT, 14 UNSAT56%74%194834.69600.70595.82195428.96602.72597.641.00
22AdaptExact2026-06-082,060,955.7306291 OPT, 15 UNSAT52%69%52155.741.80170.4452365.891.98171.131.00
23AdaptExactv22,061,389.3306291 OPT, 15 UNSAT52%69%52589.271.81171.8652811.221.96172.591.00
24Exact2026-06-14 (cert)2,125,312.229735 OPT, 247 OPTC, 15 UNSATC51%67%51712.211.90174.1252886.052.10178.070.98
25cpmpy_ortools (1 core)2026-07-142,172,999.0289276 OPT, 13 UNSAT49%65%41798.992.08144.6343364.6110.07150.050.96
26cpmpy_ortools (1 core)2026-05-182,187,296.7287274 OPT, 13 UNSAT49%65%41696.652.10145.2842029.763.13146.450.99
27roundingsat-ihs2026-06-112,209,592.6283270 OPT, 13 UNSAT48%64%35192.621.10124.3635313.061.16124.781.00
28roundingsat-ihs2026-06-11 (cert)2,214,194.22831 OPT, 269 OPTC, 1 UNSAT, 12 UNSATC48%64%39794.201.26140.6242143.421.37148.920.94
29cpmpy_highs (1 core)2026-07-052,281,374.7277266 OPT, 11 UNSAT47%62%63774.722.64230.2364115.663.41231.460.99
30scip-printemps (1 core) (incomplete)2026-06-282,314,974.4264249 OPT, 15 UNSAT45%59%3774.390.5714.303801.740.8114.400.99
31cpmpy_highs (1 core)2026-07-142,321,452.8270259 OPT, 11 UNSAT46%61%53452.842.60197.9754153.514.47200.570.99
32WMaxCDCL2026-05-172,414,370.4258248 OPT, 10 UNSAT44%58%59970.366.10232.4460183.786.15233.271.00
33exact-printemps (1 core) (incomplete)2026-05-182,438,733.3247233 OPT, 14 UNSAT42%56%5133.261.4920.785152.831.5020.861.00
34HitPBO-PL2026-06-22 (cert)2,467,609.024814 OPT, 220 OPTC, 14 UNSATC42%56%41208.960.83166.1741894.660.87168.930.98
35OR-Tools CP-SAT (1 core)2026-05-182,588,680.5230215 OPT, 15 UNSAT39%52%32680.550.24142.0932798.430.24142.601.00
36Picat(kissat)2026-06-192,592,555.9235220 OPT, 15 UNSAT40%53%72555.878.59308.7572779.248.63309.701.00
37AY2026-07-11b2,632,332.9226214 OPT, 12 UNSAT39%51%47532.909.58210.3219630.263.2586.862.42
38Sat4j Resolution2026-06-103,131,532.8153141 OPT, 12 UNSAT26%34%21132.781.49138.1220957.800.57136.981.01
39Sat4j Resolution CERT2026-05-20 (cert)3,136,626.21523 OPT, 137 OPTC, 12 UNSATC26%34%19026.211.69125.1719159.450.78126.050.99
40Sat4j CuttingPlanes2026-06-103,166,250.6148137 OPT, 11 UNSAT25%33%19850.592.40134.1319378.000.97130.931.02
41Sat4j CuttingPlanes CERT2026-06-10 (cert)3,166,727.8148137 OPTC, 11 UNSATC25%33%20327.832.41137.3520034.651.58135.371.01
42AY0.11.03,226,223.9150138 OPT, 12 UNSAT26%34%94223.927.16628.1694552.087.20630.351.00
43AY-cert2026-07-13-certfix (cert)4,140,000.31010 UNSATC2%2%0.320.040.030.470.050.050.67
44PRINTEMPS (1 core) (incomplete)2026-05-184,140,001.81010 UNSAT2%2%1.810.210.180.950.110.091.91
45DivingFalconSolver (1 core)2026-06-124,179,606.055 OPT1%1%3606.021.34721.203621.923.36724.381.00

Category "optimization problem, non-linear constraints, no OPT/UNSAT certificate" (OPT-NLC): 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: 64
Virtual Best Solver (VBS)--3636 OPT56%100%70860.230.051968.34----
1UWrMaxSat-SCIP2.0.3224,927.63333 OPT52%92%1727.620.2052.351733.220.2052.521.00
2UWrMaxSat-SCIP2.0.4224,929.13333 OPT52%92%1729.050.2052.401734.860.2152.571.00
3scip-printemps (1 core) (incomplete)2026-06-28244,897.73030 OPT47%83%97.680.353.2698.690.373.290.99
4OR-Tools CP-SAT (1 core)2026-05-18259,274.12828 OPT44%78%74.090.052.6574.380.052.661.00
5Exact_symlocal2026-06-14259,455.42828 OPT44%78%255.420.309.12256.320.319.151.00
6Exact_symbreak2026-06-14259,533.02828 OPT44%78%333.010.2511.89334.070.2511.931.00
7Exact2026-06-14259,544.32828 OPT44%78%344.310.2412.30345.590.2412.341.00
8exact-printemps (1 core) (incomplete)2026-05-18259,633.92828 OPT44%78%433.900.1615.50435.980.2215.571.00
9Picat(kissat)2026-06-19260,816.92828 OPT44%78%1616.930.0657.751622.580.0957.951.00
10Sat4j Resolution2026-06-10281,553.32525 OPT39%69%753.354.4230.13719.652.8628.791.05
11AY0.11.0327,892.32020 OPT31%56%11092.26720.77554.6111123.54722.70556.181.00
12Sat4j CuttingPlanes2026-06-10339,778.71717 OPT27%47%1378.692.6381.101331.510.9178.321.04
13AY2026-07-11b396,235.91010 OPT16%28%7435.94724.91743.597461.48727.23746.151.00
14PRINTEMPS (1 core) (incomplete)2026-05-18460,800.000%0%0.000.00-0.000.00--