An issue with duplicate bounds when solving a MILP

zoh...@gmail.com

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Jun 3, 2025, 5:07:13 PMJun 3

to mosek

The story:

https://github.com/yalmip/YALMIP/discussions/1485

Michal Adamaszek

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Jun 4, 2025, 3:35:34 AMJun 4

to mosek

LI bound X449 0
MI bound X449

Mosek writes this to indicate an unbounded integer. CPLEX will reject a file where a variable bound is defined twice, but Mosek accepts it. Strictly speaking you could claim that Mosek writes an illegal CPLEX MPS file, but that's how we do it now.

By removing the MI bound you have changed the variable from free integer to nonnegative integer, so you are solving a different problem after pruning. If you want to keep the variable as free you have to sue the INTORG section in the MPS file, which Mosek never writes.

You may want to experiment with the LP format instead.

Regarding the actual solve - it finds some integer point reasonably soon. We will investigate it more.

Michal

On Tuesday, June 3, 2025 at 11:07:13 PM UTC+2 zoh...@gmail.com wrote:

The story:

https://github.com/yalmip/YALMIP/discussions/1485

Michal Adamaszek

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Jun 4, 2025, 4:14:16 AMJun 4

to mosek

Regarding SCIP you write:

Therefore, limiting the number of solutions was crucial.

Of course you can do the same with Mosek:

https://docs.mosek.com/latest/capi/parameters.html#mosek.iparam.mio_max_num_solutions

With Mosek 11.0.21 I get the first solution after no more than a minute (will depend on the number of threads). I would use the latest 11.0 since there were some fixes in the MIP solver since the 11.0.8 you mention and they seem relevant here.

Michal

zoh...@gmail.com

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Jun 4, 2025, 5:46:32 AMJun 4

to mosek

"LI bound X449 0" says: X is integer and X >= 0.

"MI bound X449 0" says: X is integer and X >= -inf.

Are you saying that these aren't two constraints, but the first should be ignored, and the second overshadows it?

I'll consider .LP next time.

---

I also noted in my post how to limit the solutions in mosek and gurobi.

I updated mosek, and still no solution after 5min (see below). Is this a seed thing, and you got super lucky?

```

MOSEK Version 11.0.21 (Build date: 2025-5-28 08:02:29)
Copyright (c) MOSEK ApS, Denmark WWW: mosek.com
Platform: Windows/64-X86

Open file 'mosek_model.mps'
Reading started.
Using 'OBJ' as objective vector
Read 1488709 number of A nonzeros in 0.36 seconds.
Using 'rhs' as rhs vector
Using 'bound' as bound vector
Reading terminated. Time: 0.40

Read summary
Type : LO (linear optimization problem)
Objective sense : minimize
Scalar variables : 10465
Matrix variables : 0
Scalar constraints : 33550
Affine conic constraints : 0
Disjunctive constraints : 0
Cones : 0
Integers : 5536
Time : 0.4

Problem
Name :
Objective sense : minimize
Type : LO (linear optimization problem)
Constraints : 33550
Affine conic cons. : 0
Disjunctive cons. : 0
Cones : 0
Scalar variables : 10465
Matrix variables : 0
Integer variables : 5536

Optimizer started.
Mixed integer optimizer started.
Threads used: 6
Presolve started.
Presolve terminated. Time = 2.66, probing time = 1.66
Presolved problem: 4779 variables, 13650 constraints, 54037 non-zeros
Presolved problem: 14 general integer, 962 binary, 3803 continuous
Clique table size: 55487
BRANCHES RELAXS ACT_NDS DEPTH BEST_INT_OBJ BEST_RELAX_OBJ REL_GAP(%) TIME
0 0 1 0 NA NA NA 2.9
0 1 1 0 NA 1.3933649172e-11 NA 3.4
Root cut generation started.
0 1 1 0 NA 1.3933649265e-11 NA 4.6
0 2 1 0 NA -5.8451767475e-08 NA 6.1
Root cut generation terminated. Time = 1.74
6 13 7 3 NA 1.3933649265e-11 NA 7.8
20 30 21 7 NA 1.3933649265e-11 NA 8.7
38 53 39 10 NA 1.3933649265e-11 NA 9.0
74 91 75 16 NA 1.3933649265e-11 NA 9.3
146 163 147 28 NA 1.3933649265e-11 NA 9.8
290 307 291 52 NA 1.3933649265e-11 NA 10.9
480 497 481 77 NA 1.3933649265e-11 NA 12.4
715 732 716 118 NA 1.3933649265e-11 NA 13.9
855 872 856 144 NA 1.3933649265e-11 NA 15.1
1017 1032 1014 160 NA 1.3933649265e-11 NA 16.3
1165 1210 1152 198 NA 1.3933649265e-11 NA 17.6
1267 1331 1220 110 NA 1.3933649265e-11 NA 18.5
1311 1470 1256 139 NA 1.3933649265e-11 NA 20.2
1349 1604 1294 28 NA 1.3933649265e-11 NA 21.6
1389 1780 1334 80 NA 1.3933649265e-11 NA 22.7
1430 1923 1367 42 NA 1.3933649265e-11 NA 23.8
1485 2036 1422 138 NA 1.3933649265e-11 NA 24.8
1563 2184 1500 193 NA 1.3933649265e-11 NA 26.4
1672 2310 1605 158 NA 1.3933649265e-11 NA 27.8
1763 2447 1694 183 NA 1.3933649265e-11 NA 29.2
1826 2521 1755 185 NA 1.3933649265e-11 NA 30.2
1925 2638 1854 49 NA 1.3933649265e-11 NA 31.7
2023 2756 1950 75 NA 1.3933649265e-11 NA 33.0
2083 2868 2006 186 NA 1.3933649265e-11 NA 34.3
2169 2965 2088 144 NA 1.3933649265e-11 NA 35.6
2275 3141 2190 71 NA 1.3933649265e-11 NA 37.5
2378 3336 2289 14 NA 1.3933649265e-11 NA 39.2

Performed MIP restart 1.
Presolve started.
Presolve terminated. Time = 3.67, probing time = 2.51
Presolved problem: 4779 variables, 14011 constraints, 55406 non-zeros
Presolved problem: 14 general integer, 962 binary, 3803 continuous
Clique table size: 55221
BRANCHES RELAXS ACT_NDS DEPTH BEST_INT_OBJ BEST_RELAX_OBJ REL_GAP(%) TIME
2522 3578 1 0 NA 1.3933649265e-11 NA 42.1
Root cut generation started.
2522 3579 1 0 NA 1.3933649265e-11 NA 43.2
2522 3580 1 0 NA 1.3933649265e-11 NA 43.9
2522 3581 1 0 NA 1.3933649265e-11 NA 44.7
Root cut generation terminated. Time = 3.69
2527 3591 6 3 NA 1.3933649265e-11 NA 45.3
2545 3613 24 5 NA 1.3933649265e-11 NA 45.8
2569 3641 48 9 NA 1.3933649265e-11 NA 46.0
2613 3686 92 17 NA 1.3933649265e-11 NA 46.3
2703 3776 182 32 NA 1.3933649265e-11 NA 47.0
2866 3934 333 62 NA 1.3933649265e-11 NA 48.0
3045 4116 512 94 NA 1.3933649265e-11 NA 49.7
3228 4300 689 133 NA 1.3933649265e-11 NA 51.1
3418 4493 875 173 NA 1.3933649265e-11 NA 52.6
3544 4673 981 194 NA 1.3933649265e-11 NA 54.0
3695 4933 1114 197 NA 1.3933649265e-11 NA 55.6
3827 5187 1242 199 NA 1.3933649265e-11 NA 57.3
3957 5459 1358 202 NA 1.3933649265e-11 NA 59.0
4063 5766 1434 205 NA 1.3933649265e-11 NA 61.0
4172 6020 1525 172 NA 1.3933649265e-11 NA 63.1
4299 6309 1648 114 NA 1.3933649265e-11 NA 65.2
4379 6798 1728 171 NA 1.3933649265e-11 NA 67.2
4455 7139 1804 174 NA 1.3933649265e-11 NA 68.6
4527 7485 1868 177 NA 1.3933649265e-11 NA 70.3
4595 7759 1932 178 NA 1.3933649265e-11 NA 71.7
4717 7957 2050 188 NA 1.3933649265e-11 NA 73.2
4818 8167 2139 201 NA 1.3933649265e-11 NA 74.9
4978 8415 2295 177 NA 1.3933649265e-11 NA 76.7
5104 8623 2407 205 NA 1.3933649265e-11 NA 78.2
5168 8788 2463 180 NA 1.3933649265e-11 NA 80.1
5288 9021 2565 204 NA 1.3933649265e-11 NA 81.9
5403 9212 2660 194 NA 1.3933649265e-11 NA 83.6
5544 9449 2785 182 NA 1.3933649265e-11 NA 85.2
5642 9643 2859 159 NA 1.3933649265e-11 NA 87.0
5760 9848 2955 177 NA 1.3933649265e-11 NA 88.7
5902 10062 3075 124 NA 1.3933649265e-11 NA 90.6
6017 10257 3176 173 NA 1.3933649265e-11 NA 92.5
6158 10485 3265 176 NA 1.3933649265e-11 NA 94.3
6295 10710 3352 178 NA 1.3933649265e-11 NA 96.2
6425 10918 3424 184 NA 1.3933649265e-11 NA 97.9
6580 11160 3515 176 NA 1.3933649265e-11 NA 99.7
6741 11412 3600 199 NA 1.3933649265e-11 NA 101.3
6915 11672 3686 180 NA 1.3933649265e-11 NA 103.0
7070 11931 3813 177 NA 1.3933649265e-11 NA 104.8
7234 12192 3929 191 NA 1.3933649265e-11 NA 106.5
7408 12458 4039 116 NA 1.3933649265e-11 NA 108.3
7587 12719 4150 172 NA 1.3933649265e-11 NA 110.2
7745 12985 4266 198 NA 1.3933649265e-11 NA 111.8
7898 13245 4381 198 NA 1.3933649265e-11 NA 113.6
8050 13497 4517 199 NA 1.3933649265e-11 NA 115.2
8240 13727 4665 111 NA 1.3933649265e-11 NA 117.2
8427 13950 4822 156 NA 1.3933649265e-11 NA 119.0
8597 14169 4968 178 NA 1.3933649265e-11 NA 120.8
8771 14358 5128 206 NA 1.3933649265e-11 NA 122.7
8924 14558 5261 160 NA 1.3933649265e-11 NA 124.5
9036 14781 5349 162 NA 1.3933649265e-11 NA 126.6
9193 14949 5404 166 NA 1.3933649265e-11 NA 128.7
9371 15135 5490 171 NA 1.3933649265e-11 NA 130.5
9482 15278 5591 173 NA 1.3933649265e-11 NA 132.5
9585 15431 5664 172 NA 1.3933649265e-11 NA 134.4
9720 15605 5773 196 NA 1.3933649265e-11 NA 136.3
9871 15780 5872 176 NA 1.3933649265e-11 NA 138.4
9983 15948 5936 185 NA 1.3933649265e-11 NA 140.2
10135 16145 6040 185 NA 1.3933649265e-11 NA 142.1
10240 16296 6123 186 NA 1.3933649265e-11 NA 144.0
10391 16499 6250 188 NA 1.3933649265e-11 NA 145.7
10527 16750 6356 199 NA 1.3933649265e-11 NA 147.3
10724 17015 6501 205 NA 1.3933649265e-11 NA 149.1
10894 17209 6613 209 NA 1.3933649265e-11 NA 150.7
11091 17431 6764 100 NA 1.3933649265e-11 NA 152.4
11300 17651 6969 138 NA 1.3933649265e-11 NA 154.4
11516 17871 7185 175 NA 1.3933649265e-11 NA 156.2
11731 18107 7398 204 NA 1.3933649265e-11 NA 158.2
11906 18429 7569 208 NA 1.3933649265e-11 NA 161.7
12029 18675 7662 184 NA 1.3933649265e-11 NA 163.5
12216 18886 7823 75 NA 1.3933649265e-11 NA 165.7
12400 19096 7995 124 NA 1.3933649265e-11 NA 167.7
12601 19297 8196 160 NA 1.3933649265e-11 NA 169.0
12798 19560 8393 191 NA 1.3933649265e-11 NA 170.9
12869 19971 8464 194 NA 1.3933649265e-11 NA 173.4
12925 20284 8500 154 NA 1.3933649265e-11 NA 175.4
13061 20556 8624 108 NA 1.3933649265e-11 NA 177.9
13168 20760 8717 90 NA 1.3933649265e-11 NA 180.6
13274 21079 8801 118 NA 1.3933649265e-11 NA 185.6

Performed MIP restart 2.
Presolve started.
Presolve terminated. Time = 4.24, probing time = 2.95
Presolved problem: 4779 variables, 14100 constraints, 56523 non-zeros
Presolved problem: 14 general integer, 962 binary, 3803 continuous
Clique table size: 48955
BRANCHES RELAXS ACT_NDS DEPTH BEST_INT_OBJ BEST_RELAX_OBJ REL_GAP(%) TIME
13423 21285 1 0 NA 1.3933649265e-11 NA 189.2
Root cut generation started.
13423 21286 1 0 NA 1.3933649265e-11 NA 190.0
13423 21287 1 0 NA 1.3933649265e-11 NA 190.4
13423 21288 1 0 NA 1.3933649265e-11 NA 191.0
Root cut generation terminated. Time = 5.03
13428 21298 6 3 NA 1.3933649265e-11 NA 191.7
13446 21319 22 8 NA 1.3933649265e-11 NA 192.2
13464 21339 40 11 NA 1.3933649265e-11 NA 192.4
13500 21377 76 17 NA 1.3933649265e-11 NA 192.7
13572 21449 148 29 NA 1.3933649265e-11 NA 193.3
13709 21586 285 53 NA 1.3933649265e-11 NA 194.4
13972 21849 548 97 NA 1.3933649265e-11 NA 196.4
14081 22017 651 113 NA 1.3933649265e-11 NA 198.1
14131 22312 697 115 NA 1.3933649265e-11 NA 199.6
14166 22681 728 118 NA 1.3933649265e-11 NA 202.1
14186 23100 740 121 NA 1.3933649265e-11 NA 204.4
14211 23479 765 126 NA 1.3933649265e-11 NA 206.4
14238 23857 776 145 NA 1.3933649265e-11 NA 208.4
14252 24028 790 145 NA 1.3933649265e-11 NA 209.4
14277 24180 799 146 NA 1.3933649265e-11 NA 211.1
14342 24437 824 127 NA 1.3933649265e-11 NA 213.0
14422 24591 900 124 NA 1.3933649265e-11 NA 214.6
14499 24800 977 132 NA 1.3933649265e-11 NA 216.7
14563 24938 1041 131 NA 1.3933649265e-11 NA 218.2
14641 25093 1119 133 NA 1.3933649265e-11 NA 220.0
14720 25243 1198 134 NA 1.3933649265e-11 NA 221.6
14788 25391 1266 143 NA 1.3933649265e-11 NA 223.3
14860 25543 1334 146 NA 1.3933649265e-11 NA 225.3
14938 25684 1408 148 NA 1.3933649265e-11 NA 227.1
15031 25838 1483 138 NA 1.3933649265e-11 NA 229.0
15099 25955 1535 139 NA 1.3933649265e-11 NA 230.4
15171 26064 1587 138 NA 1.3933649265e-11 NA 232.2
15235 26181 1633 145 NA 1.3933649265e-11 NA 233.8
15315 26300 1687 145 NA 1.3933649265e-11 NA 235.5
15435 26436 1725 153 NA 1.3933649265e-11 NA 237.7
15542 26569 1786 163 NA 1.3933649265e-11 NA 239.8
15647 26704 1861 161 NA 1.3933649265e-11 NA 241.7
15713 26807 1909 162 NA 1.3933649265e-11 NA 243.1
15776 26894 1948 145 NA 1.3933649265e-11 NA 244.4
15853 27013 2007 146 NA 1.3933649265e-11 NA 246.2
15942 27133 2084 148 NA 1.3933649265e-11 NA 247.8
16034 27264 2162 134 NA 1.3933649265e-11 NA 249.1
16087 27388 2215 160 NA 1.3933649265e-11 NA 250.9
16185 27531 2295 141 NA 1.3933649265e-11 NA 252.9
16265 27682 2365 139 NA 1.3933649265e-11 NA 255.1
16349 27824 2443 163 NA 1.3933649265e-11 NA 256.8
16435 27941 2523 134 NA 1.3933649265e-11 NA 258.2
16519 28054 2589 138 NA 1.3933649265e-11 NA 259.4
16572 28133 2620 139 NA 1.3933649265e-11 NA 260.4
16674 28282 2700 164 NA 1.3933649265e-11 NA 262.1
16767 28396 2777 163 NA 1.3933649265e-11 NA 263.9
16826 28477 2798 163 NA 1.3933649265e-11 NA 265.0
16929 28643 2895 131 NA 1.3933649265e-11 NA 266.6
17007 28789 2959 139 NA 1.3933649265e-11 NA 268.0
17093 28931 3023 143 NA 1.3933649265e-11 NA 269.8
17195 29084 3101 138 NA 1.3933649265e-11 NA 271.5
17325 29243 3185 132 NA 1.3933649265e-11 NA 273.4
17415 29358 3239 137 NA 1.3933649265e-11 NA 274.7
17492 29449 3282 149 NA 1.3933649265e-11 NA 275.8
17575 29553 3345 155 NA 1.3933649265e-11 NA 277.2
17678 29662 3416 163 NA 1.3933649265e-11 NA 278.5
17754 29742 3456 141 NA 1.3933649265e-11 NA 279.5
17822 29814 3486 146 NA 1.3933649265e-11 NA 281.0
17908 29944 3552 136 NA 1.3933649265e-11 NA 282.7
18031 30092 3647 138 NA 1.3933649265e-11 NA 284.4
18140 30231 3738 162 NA 1.3933649265e-11 NA 286.2
18232 30346 3802 136 NA 1.3933649265e-11 NA 288.0
18353 30498 3891 161 NA 1.3933649265e-11 NA 289.6
18468 30643 3982 145 NA 1.3933649265e-11 NA 291.4
18564 30781 4058 133 NA 1.3933649265e-11 NA 293.5
18676 30923 4118 163 NA 1.3933649265e-11 NA 295.9
18770 31041 4178 138 NA 1.3933649265e-11 NA 297.6
18855 31159 4239 133 NA 1.3933649265e-11 NA 299.3
18934 31249 4298 158 NA 1.3933649265e-11 NA 300.2
19039 31391 4383 132 NA 1.3933649265e-11 NA 301.9
19141 31528 4463 156 NA 1.3933649265e-11 NA 303.3
19251 31678 4543 167 NA 1.3933649265e-11 NA 305.4
19366 31817 4608 163 NA 1.3933649265e-11 NA 307.1
19446 31917 4644 133 NA 1.3933649265e-11 NA 308.6
19555 32060 4717 157 NA 1.3933649265e-11 NA 310.5
19667 32178 4799 169 NA 1.3933649265e-11 NA 311.9
19820 32346 4896 164 NA 1.3933649265e-11 NA 313.9
19929 32496 4973 160 NA 1.3933649265e-11 NA 316.1
20009 32593 5005 135 NA 1.3933649265e-11 NA 317.4
20091 32691 5045 127 NA 1.3933649265e-11 NA 318.8
20168 32776 5070 92 NA 1.3933649265e-11 NA 320.1
20276 32910 5146 96 NA 1.3933649265e-11 NA 322.2
20427 33132 5277 103 NA 1.3933649265e-11 NA 324.5
20516 33425 5350 127 NA 1.3933649265e-11 NA 329.0
20558 33897 5392 130 NA 1.3933649265e-11 NA 331.4
20578 34304 5410 133 NA 1.3933649265e-11 NA 333.1
CTRLC-C has been pressed.

Objective of best integer solution : Not available.
Best objective bound : 1.393364926477e-11
Initial feasible solution objective: Undefined
Construct solution objective : Not employed
User objective cut value : Not employed
Number of cuts generated : 5068
Number of Gomory cuts : 575
Number of CMIR cuts : 1074
Number of clique cuts : 2230
Number of implied bound cuts : 1186
Number of knapsack_cover cuts : 3
Number of branches : 20578
Number of relaxations solved : 34304
Number of interior point iterations: 26
Number of simplex iterations : 683173
Time spend presolving the root : 4.24
Time spend optimizing the root : 0.70
Mixed integer optimizer terminated. Time: 333.11

Optimizer terminated. Time: 333.17

Integer solution solution summary
Problem status : UNKNOWN
Solution status : UNKNOWN
Primal. obj: 0.0000000000e+00 nrm: 0e+00 Viol. con: 3e+03 var: 0e+00 itg: 0e+00

Optimizer summary
Optimizer - time: 333.17
Interior-point - iterations : 26 time: 0.49
Simplex - iterations : 2138977 time: 0.00
Mixed integer - relaxations: 34304 time: 333.11

Open file 'mosek_model.int'
Writing started.
Writing terminated. Time: 0.06
Return code - 100007 [MSK_RES_TRM_USER_CALLBACK]

```

zoh...@gmail.com

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Jun 4, 2025, 7:47:52 AMJun 4

to mosek

I tried to save a .lp the same way I saved a .mps:

mosekopt( 'write(mosek_model.lp)', prob, param )

I got an error:

Mosek error: MSK_RES_ERR_WRITE_LP_INVALID_VAR_NAMES (Invalid variable name. Cannot write valid LP file.)

I attached the data from yalmip.

I also noted in the doc: "The LP format is not a completely well-defined standard and hence different optimization packages may interpret the same LP file in slightly different ways."

I don't understand how people benchmark problems if there isn't even a proper standard.

mosek_model.mat

Michal Adamaszek

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Jun 4, 2025, 7:57:05 AMJun 4

to mosek

It is possible that my run was more lucky in the MIP path taken.

There is a parameter to write the files with generic names, it should write the file when you set it https://docs.mosek.com/latest/capi/parameters.html#mosek.iparam.write_generic_names

As you can see the standard is only a standard until one gets to the rare corner cases and the interpretations of the standard also differ. Additionally vendors have their own extensions to the standards.

I will write with any suggestions we have from running your model later.

Michal

Michal Adamaszek

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Jun 10, 2025, 2:40:35 AMJun 10

to mosek

Better late than never: You can get an MPS file compatible with CPLEX by setting the parameter

https://docs.mosek.com/latest/capi/parameters.html#mosek.iparam.write_mps_format

zoh...@gmail.com

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Jun 11, 2025, 5:10:44 PMJun 11

to mosek

Thanks for the tip, but I moved to .LP, per your advice, which seems more consistent, and I'm happy with it so far.

However, I'm less happy about mosek performance on my MILP problems. But I guess its forte is SOCP rather than MI.

Erling D. Andersen

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Jun 12, 2025, 5:17:17 AMJun 12

to mosek

We are investing a significant amount of resources in improving the MIP optimizer. However, as we say in Europe:

Rome was not built in one day.

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