# Kernel solve report

Generated by `bench/report-solve.ps1` from commit `8e2eb85`.

- Toolchain: `moon 0.1.20261016 (1af328f 2026-10-16) ~\.moon-0.10.16\bin\moon.exe | moonc v0.10.16+b1a0e846e (2026-10-16) ~\.moon-0.10.16\bin\moonc.exe | moonrun 0.1.20261016 (1af328f 2026-10-16) ~\.moon-0.10.16\bin\moonrun.exe |  | Feature flags enabled: rr_moon_mod,rr_moon_pkg`
- Instances: MIPLIB 2017 (<https://miplib.zib.de>), fetched by `bench/fetch-instances.ps1`.
- Mode: LP relaxation (integer columns treated as continuous), row limit 2500, pivot limit 20000, presolve on. An instance whose pivots column equals the pivot limit stopped there: the limit is part of the result, and two runs at different limits are not comparable.
- The script writes nothing unless the kernel exited zero, reported every manifest entry, and every reconstructed solution passed the row, bound and objective checks against the original model.

## Summary

| metric | value |
| --- | --- |
| instances in manifest | 32 |
| solved to optimality | 28 |
| skipped (row count over the limit) | 3 |
| refused (kernel problem over the sparse-LU row limit) | 0 |
| other outcomes | 1 |
| solved instances run through the reduction | 29 |
| reconstructions verified against the original model | 28 |
| runs that needed the Bland recovery | 1 |
| pivot iterations (total) | 36010 |
| largest solved model (rows) | 4497 |

Outcomes other than optimal are listed verbatim below; a numerical failure is a
measured verdict from the kernel's own residual check, not a silent wrong answer.

The `presolve` column is per instance: rows and variables before and after the
reduction, then the counters. The `check` column is the reconstructed solution
measured against the **original** model - worst row and bound violation, and the
objective recomputed from the original model's own cost vector. A run whose
reconstruction disagrees on the objective is not published at all.

## Instances

| instance | vars | cons | nonzeros | integer vars | solve | objective | pivots | presolve | check | note |
| --- | ---: | ---: | ---: | ---: | --- | ---: | ---: | --- | --- | --- |
| flugpl | 18 | 18 | 64 | 11 | optimal | 1167185.7255925296 | 15 | rows 18 -> 15, vars 18 -> 15 (empty=0 redundant=1 singleton=1 tightened=14 fixed=2 empty-cols=0 rounds=4) | rows 18 vars, worst row violation 2.5614993855140804e-13, worst bound violation 0, objective 1167185.7255925296 (agrees with the reported 1167185.7255925296) (feasible) |  |
| blend2 | 353 | 274 | 1497 | 264 | optimal | 6.915675114033675 | 297 | rows 274 -> 169, vars 353 -> 319 (empty=0 redundant=79 singleton=9 tightened=110 fixed=17 empty-cols=0 rounds=3) | rows 353 vars, worst row violation 3.968518720876972e-9, worst bound violation 3.69160257916748e-12, objective 6.915675114033675 (agrees with the reported 6.915675114033675) (feasible) |  |
| cap6000 | 6000 | 2176 | 54238 | 6000 | optimal | -2451537.325025615 | 1150 | rows 2176 -> 2095, vars 6000 -> 5911 (empty=0 redundant=5 singleton=0 tightened=0 fixed=13 empty-cols=0 rounds=2) | rows 6000 vars, worst row violation 1.135684139321937e-12, worst bound violation 1.3700152123855663e-12, objective -2451537.325025615 (agrees with the reported -2451537.325025615) (feasible) |  |
| danoint | 521 | 664 | 3233 | 56 | optimal | 62.637280418466226 | 1907 | rows 664 -> 664, vars 521 -> 521 (empty=0 redundant=0 singleton=0 tightened=466 fixed=0 empty-cols=0 rounds=2) | rows 521 vars, worst row violation 6.862600789228876e-12, worst bound violation 1.2697620732621794e-12, objective 62.637280418466226 (agrees with the reported 62.637280418466226) (feasible) |  |
| dcmulti | 548 | 290 | 1833 | 75 | optimal | 183975.53969341915 | 483 | rows 290 -> 272, vars 548 -> 548 (empty=0 redundant=0 singleton=18 tightened=533 fixed=0 empty-cols=0 rounds=3) | rows 548 vars, worst row violation 9.164654395667723e-12, worst bound violation 0, objective 183975.53969341915 (agrees with the reported 183975.53969341915) (feasible) |  |
| dsbmip | 1886 | 1233 | 8536 | 192 | optimal | -305.1981750092895 | 1361 | rows 1233 -> 1185, vars 1886 -> 1775 (empty=4 redundant=20 singleton=0 tightened=3267 fixed=87 empty-cols=0 rounds=8) | rows 1886 vars, worst row violation 3.338243752931639e-8, worst bound violation 1.3700660928038633e-12, objective -305.1981750092895 (agrees with the reported -305.1981750092895) (feasible) |  |
| fiber | 1298 | 363 | 4198 | 1254 | optimal | 156082.51760020375 | 604 | rows 363 -> 295, vars 1298 -> 1230 (empty=0 redundant=0 singleton=15 tightened=61 fixed=15 empty-cols=0 rounds=3) | rows 1298 vars, worst row violation 1.2130625391598227e-10, worst bound violation 2.3882007482654704e-12, objective 156082.51760020375 (agrees with the reported 156082.51760020375) (feasible) |  |
| gt2 | 188 | 29 | 468 | 188 | optimal | 13460.233074418948 | 35 | rows 29 -> 28, vars 188 -> 173 (empty=0 redundant=1 singleton=0 tightened=12 fixed=15 empty-cols=0 rounds=2) | rows 188 vars, worst row violation 7.900347043226373e-13, worst bound violation 1.3699263945435965e-12, objective 13460.233074418948 (agrees with the reported 13460.233074418948) (feasible) |  |
| khb05250 | 1350 | 101 | 3973 | 24 | optimal | 95919464.00013639 | 442 | rows 101 -> 100, vars 1350 -> 1299 (empty=1 redundant=0 singleton=0 tightened=2596 fixed=51 empty-cols=0 rounds=3) | rows 1350 vars, worst row violation 1.4833187067785634e-12, worst bound violation 2.2204460492503126e-16, objective 95919464.00013639 (agrees with the reported 95919464.00013639) (feasible) |  |
| markshare1 | 62 | 6 | 324 | 50 | optimal | 0 | 33 | rows 6 -> 6, vars 62 -> 56 (empty=0 redundant=0 singleton=0 tightened=6 fixed=6 empty-cols=0 rounds=2) | rows 62 vars, worst row violation 5.928131022403401e-13, worst bound violation 0, objective 0 (agrees with the reported 0) (feasible) |  |
| markshare2 | 74 | 7 | 448 | 60 | optimal | 0 | 43 | rows 7 -> 7, vars 74 -> 67 (empty=0 redundant=0 singleton=0 tightened=7 fixed=7 empty-cols=0 rounds=2) | rows 74 vars, worst row violation 6.117301587473878e-13, worst bound violation 0, objective 0 (agrees with the reported 0) (feasible) |  |
| misc07 | 260 | 212 | 8620 | 259 | optimal | 1414.9999960700861 | 905 | rows 212 -> 212, vars 260 -> 254 (empty=0 redundant=0 singleton=0 tightened=2 fixed=6 empty-cols=0 rounds=2) | rows 260 vars, worst row violation 7.77715823155801e-9, worst bound violation 0, objective 1414.9999960700861 (agrees with the reported 1414.9999960700861) (feasible) |  |
| mitre | 10724 | 2054 | 49028 | 10724 | optimal | 114740.51848158274 | 2141 | rows 2054 -> 1662, vars 10724 -> 10724 (empty=0 redundant=392 singleton=0 tightened=0 fixed=0 empty-cols=0 rounds=2) | rows 10724 vars, worst row violation 6.1104936353212675e-12, worst bound violation 2.2531976284716782e-12, objective 114740.51848158274 (agrees with the reported 114740.51848158274) (feasible) |  |
| mod010 | 2655 | 146 | 13858 | 2655 | optimal | 6532.083391108283 | 3455 | rows 146 -> 146, vars 2655 -> 2655 (empty=0 redundant=0 singleton=0 tightened=0 fixed=0 empty-cols=0 rounds=1) | rows 2655 vars, worst row violation 1.2874287703095415e-8, worst bound violation 5.743014949187969e-10, objective 6532.083391108283 (agrees with the reported 6532.083391108283) (feasible) |  |
| mod011 | 10958 | 4497 | 30759 | 96 | optimal | -62121982.55190222 | 10177 | rows 4497 -> 2402, vars 10958 -> 8057 (empty=1 redundant=17 singleton=0 tightened=9676 fixed=824 empty-cols=0 rounds=5) | rows 10958 vars, worst row violation 7.184789971869119e-10, worst bound violation 0, objective -62121982.55190222 (agrees with the reported -62121982.55190222) (feasible) | recovered from a numerical failure by restarting with Bland's rule (basis became numerically singular) |
| noswot | 128 | 182 | 760 | 100 | optimal | -43.000000000044004 | 131 | rows 182 -> 182, vars 128 -> 127 (empty=0 redundant=0 singleton=0 tightened=155 fixed=1 empty-cols=0 rounds=2) | rows 128 vars, worst row violation 1.3699999999939026e-12, worst bound violation 1.1846079672749017e-13, objective -43.000000000044004 (agrees with the reported -43.000000000044004) (feasible) |  |
| p0201 | 201 | 133 | 2124 | 201 | optimal | 6875.000016026327 | 307 | rows 133 -> 133, vars 201 -> 201 (empty=0 redundant=0 singleton=0 tightened=6 fixed=0 empty-cols=0 rounds=2) | rows 201 vars, worst row violation 5.66809107283705e-9, worst bound violation 1.1851630787859499e-12, objective 6875.000016026327 (agrees with the reported 6875.000016026327) (feasible) |  |
| pk1 | 86 | 45 | 916 | 55 | optimal | 1e-12 | 85 | rows 45 -> 45, vars 86 -> 86 (empty=0 redundant=0 singleton=0 tightened=0 fixed=0 empty-cols=0 rounds=1) | rows 86 vars, worst row violation 6.854624713203607e-13, worst bound violation 0, objective 1e-12 (agrees with the reported 1e-12) (feasible) |  |
| qiu | 840 | 1192 | 3744 | 48 | optimal | -931.6388451940545 | 2163 | rows 1192 -> 1192, vars 840 -> 840 (empty=0 redundant=0 singleton=0 tightened=804 fixed=0 empty-cols=0 rounds=3) | rows 840 vars, worst row violation 3.172441696317061e-10, worst bound violation 0, objective -931.6388451940545 (agrees with the reported -931.6388451940545) (feasible) |  |
| rout | 556 | 291 | 2432 | 315 | optimal | 981.8642857314371 | 432 | rows 291 -> 291, vars 556 -> 556 (empty=0 redundant=0 singleton=0 tightened=242 fixed=0 empty-cols=0 rounds=2) | rows 556 vars, worst row violation 4.521095486990477e-11, worst bound violation 1.0530243343853799e-11, objective 981.8642857314371 (agrees with the reported 981.8642857314371) (feasible) |  |
| 22433 | 429 | 198 | 3409 | 231 | optimal | 21240.526170816112 | 1035 | rows 198 -> 198, vars 429 -> 429 (empty=0 redundant=0 singleton=0 tightened=0 fixed=0 empty-cols=0 rounds=1) | rows 429 vars, worst row violation 3.291293163924598e-12, worst bound violation 2.9575231152902073e-12, objective 21240.526170816112 (agrees with the reported 21240.526170816112) (feasible) |  |
| 30n20b8 | 18380 | 576 | 109708 | 18380 | optimal | 1.5664076455147433 | 568 | rows 576 -> 493, vars 18380 -> 11098 (empty=0 redundant=83 singleton=0 tightened=4053 fixed=7282 empty-cols=0 rounds=2) | rows 18380 vars, worst row violation 1.9836935164370356e-12, worst bound violation 1.3001420271354856e-14, objective 1.5664076455147433 (agrees with the reported 1.5664076455147433) (feasible) |  |
| 50v-10 | 2013 | 233 | 4392 | 1647 | optimal | 2879.065686853283 | 290 | rows 233 -> 233, vars 2013 -> 2013 (empty=0 redundant=0 singleton=0 tightened=366 fixed=0 empty-cols=0 rounds=2) | rows 2013 vars, worst row violation 8.988609375797898e-10, worst bound violation 0, objective 2879.065686853283 (agrees with the reported 2879.065686853283) (feasible) |  |
| aflow40b | 2728 | 1442 | 8147 | 1364 | optimal | 1005.6648165142183 | 1133 | rows 1442 -> 1442, vars 2728 -> 2728 (empty=0 redundant=0 singleton=0 tightened=0 fixed=0 empty-cols=0 rounds=1) | rows 2728 vars, worst row violation 1.3699999999981231e-12, worst bound violation 2.7176779345383806e-12, objective 1005.6648165142183 (agrees with the reported 1005.6648165142183) (feasible) |  |
| 2club200v15p5scn | 200 | 17013 | 105011 | 200 | skipped |  |  |  |  | rows=17013 reduced from 17013 > 2500 |
| bc1 | 1751 | 1913 | 276843 | 252 | optimal | 0.7828368234202856 | 3170 | rows 1913 -> 1913, vars 1751 -> 1751 (empty=0 redundant=0 singleton=0 tightened=5791 fixed=0 empty-cols=0 rounds=3) | rows 1751 vars, worst row violation 1.2651022887748349e-11, worst bound violation 0, objective 0.7828368234202856 (agrees with the reported 0.7828368234202856) (feasible) |  |
| bienst1 | 505 | 576 | 2185 | 28 | optimal | 11.72413793105124 | 629 | rows 576 -> 576, vars 505 -> 505 (empty=0 redundant=0 singleton=0 tightened=448 fixed=0 empty-cols=0 rounds=3) | rows 505 vars, worst row violation 1.177411109784615e-12, worst bound violation 0, objective 11.72413793105124 (agrees with the reported 11.72413793105124) (feasible) |  |
| bienst2 | 505 | 576 | 2185 | 35 | optimal | 11.72413793105124 | 629 | rows 576 -> 576, vars 505 -> 505 (empty=0 redundant=0 singleton=0 tightened=448 fixed=0 empty-cols=0 rounds=3) | rows 505 vars, worst row violation 1.177411109784615e-12, worst bound violation 0, objective 11.72413793105124 (agrees with the reported 11.72413793105124) (feasible) |  |
| blp-ar98 | 16021 | 1128 | 200602 | 15806 | optimal | 5891.226580303744 | 2390 | rows 1128 -> 1128, vars 16021 -> 16017 (empty=0 redundant=0 singleton=0 tightened=82 fixed=4 empty-cols=0 rounds=2) | rows 16021 vars, worst row violation 5.896858758832458e-12, worst bound violation 1.4935830350259924e-12, objective 5891.226580303744 (agrees with the reported 5891.226580303744) (feasible) |  |
| core2536-691 | 15293 | 2539 | 193032 | 15284 | skipped |  |  |  |  | rows=2505 reduced from 2539 > 2500 |
| dano3_3 | 13873 | 3202 | 79656 | 69 | skipped |  |  |  |  | rows=3202 reduced from 3202 > 2500 |
| fast0507 | 63009 | 507 | 472358 | 63009 | iteration-limit | - | 20000 | rows 507 -> 489, vars 63009 -> 63001 (empty=0 redundant=10 singleton=8 tightened=7 fixed=8 empty-cols=1 rounds=3) |  | iteration limit reached before optimality was proven (kernel objective 164.252869961398 after 20000 pivots) |