Gurobi is taking too much time in converging the non-linear constraints in MIQCP problem
AnsweredHello everyone,
I have a MIQCP business problem, in which I am maximizing the Net Revenue which involves exponential and bilinear terms. Here, x, y, z are our decision variables to be found out after optimization. Since Gurobi can only take bilinear or quadratic terms as input, I have expanded the exp^x terms up to its x^8 terms which seems to be a great fit in our current scenarios.
obj(NR) : y+z+xy*exp^(x+c)+xz*exp^(x+c)
Now the problem is that I am creating many intermediate variables in between, and putting bounds on some variables. Currently, I have removed all the bounds and just creating those interim variables so that I could analyze why is it taking so much time in convergence. All of the variables have quadratic or bilinear terms except the two which are ratios of the two variables.
When I am putting non-ratio variables only, it is converging in no time and giving an objective value of 5,141,540. The corresponding logging is shown below :
Changed value of parameter TimeLimit to 1800.0
Prev: 100.0 Min: 0.0 Max: inf Default: inf
Parameter MIPGap unchanged
Value: 0.01 Min: 0.0 Max: inf Default: 0.0001
Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (linux64)
Thread count: 8 physical cores, 16 logical processors, using up to 16 threads
Optimize a model with 1124 rows, 2160 columns and 3696 nonzeros
Model fingerprint: 0xc1fe6050
Model has 988 quadratic constraints
Variable types: 2112 continuous, 48 integer (0 binary)
Coefficient statistics:
Matrix range [1e-01, 1e+01]
QMatrix range [1e-03, 1e+03]
QLMatrix range [5e-01, 8e+03]
Objective range [1e+00, 1e+00]
Bounds range [5e-01, 2e+01]
RHS range [1e+00, 3e+01]
QRHS range [5e+01, 3e+03]
MIP start from previous solve did not produce a new incumbent solution
MIP start from previous solve violates constraint A83_promo_constr by 2.000000000
Presolve removed 992 rows and 1778 columns
Presolve time: 0.16s
Presolved: 1654 rows, 512 columns, 4371 nonzeros
Presolved model has 400 bilinear constraint(s)
Variable types: 490 continuous, 22 integer (0 binary)
Root relaxation: objective 6.661247e+06, 788 iterations, 0.01 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 6661247.08 0 402 - 6661247.08 - - 0s
0 0 6528343.27 0 408 - 6528343.27 - - 0s
0 0 6483825.97 0 410 - 6483825.97 - - 0s
0 0 6421692.18 0 408 - 6421692.18 - - 0s
0 0 6395304.59 0 408 - 6395304.59 - - 0s
0 0 6386205.61 0 408 - 6386205.61 - - 0s
0 0 6386205.61 0 408 - 6386205.61 - - 0s
H 0 0 4647135.9070 6386205.61 37.4% - 0s
H 0 0 4666892.9139 6386205.61 36.8% - 0s
0 2 6386205.61 0 408 4666892.91 6386205.61 36.8% - 0s
H 68 80 4669936.7244 6349161.30 36.0% 5.4 0s
H 210 216 4758589.8062 6349161.30 33.4% 5.9 0s
H 312 320 4801959.8831 6349161.30 32.2% 6.2 0s
H 383 454 4918188.6883 6349161.30 29.1% 6.2 0s
H 393 454 5000515.0501 6349161.30 27.0% 6.2 0s
H 1534 1599 5094922.0706 6349161.30 24.6% 5.3 0s
H 1561 1238 5134542.1544 6349161.30 23.7% 5.2 0s
H 2123 1316 5141540.5112 6348414.51 23.5% 5.1 1s
Cutting planes:
RLT: 20
Explored 2349 nodes (13377 simplex iterations) in 1.26 seconds
Thread count was 16 (of 16 available processors)
Solution count 10: 5.14154e+06 5.13454e+06 5.09492e+06 ... 4.64714e+06
Optimal solution found (tolerance 1.00e-02)
Warning: max constraint violation (9.5522e-06) exceeds tolerance
Best objective 5.141540511209e+06, best bound 5.141540511209e+06, gap 0.0000%
But when I am creating one of the variables ratio terms, it is not converging in even one hour. Can you please tell me if I could reduce the time, as I have two such variable-ratio terms and many bounds to be given to intermediate variable which is making Gurobi very slower to solve my problem? MIP Logging for 30 minutes run is given below :
Changed value of parameter TimeLimit to 1800.0
Prev: 100.0 Min: 0.0 Max: inf Default: inf
Parameter MIPGap unchanged
Value: 0.01 Min: 0.0 Max: inf Default: 0.0001
Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (linux64)
Thread count: 8 physical cores, 16 logical processors, using up to 16 threads
Optimize a model with 1124 rows, 2161 columns and 3696 nonzeros
Model fingerprint: 0x6aedc2cf
Model has 989 quadratic constraints
Variable types: 2113 continuous, 48 integer (0 binary)
Coefficient statistics:
Matrix range [1e-01, 1e+01]
QMatrix range [1e-03, 1e+03]
QLMatrix range [5e-01, 8e+03]
Objective range [1e+00, 1e+00]
Bounds range [5e-01, 2e+01]
RHS range [1e+00, 3e+01]
QRHS range [5e+01, 3e+03]
MIP start from previous solve did not produce a new incumbent solution
MIP start from previous solve violates constraint A83_promo_constr by 2.000000000
Presolve removed 907 rows and 1600 columns
Presolve time: 0.01s
Presolved: 2200 rows, 716 columns, 6160 nonzeros
Presolved model has 519 bilinear constraint(s)
Variable types: 668 continuous, 48 integer (0 binary)
Root relaxation: objective 7.105256e+06, 1062 iterations, 0.01 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 7105255.71 0 489 - 7105255.71 - - 0s
0 0 6891785.83 0 505 - 6891785.83 - - 0s
0 0 6839510.32 0 507 - 6839510.32 - - 0s
0 0 6740966.32 0 496 - 6740966.32 - - 0s
0 0 6713222.06 0 498 - 6713222.06 - - 0s
0 0 6704123.08 0 498 - 6704123.08 - - 0s
0 0 6704123.08 0 498 - 6704123.08 - - 0s
0 2 6704123.08 0 498 - 6704123.08 - - 0s
* 1997 1918 151 4833859.1600 6667078.77 37.9% 12.4 0s
* 2211 2013 161 4837715.7655 6666628.96 37.8% 11.9 0s
H 3052 2676 4848395.8358 6662015.62 37.4% 11.1 1s
H 3085 2756 4851527.1307 6662015.62 37.3% 11.1 1s
H 7347 4941 4851527.1422 6660502.15 37.3% 8.9 2s
H15369 10076 4908338.8690 6645340.42 35.4% 7.9 4s
H16941 11332 4908338.8793 6643463.88 35.4% 7.8 4s
17227 11739 cutoff 111 4908338.88 6642632.63 35.3% 7.7 5s
*38967 27713 191 4961240.3774 6634174.88 33.7% 7.5 9s
40356 29854 5734247.16 62 340 4961240.38 6634174.88 33.7% 7.5 10s
*41011 28717 195 4988152.8006 6634174.88 33.0% 7.5 10s
*58689 43145 183 5002996.1532 6632494.49 32.6% 7.2 13s
65305 48369 5870725.43 50 327 5002996.15 6631358.37 32.5% 7.1 15s
89937 70169 5703952.44 63 382 5002996.15 6630297.26 32.5% 7.2 20s
H109435 83936 5010525.3133 6629834.97 32.3% 7.1 24s
113614 87529 5049405.18 114 307 5010525.31 6629635.11 32.3% 7.1 25s
H133045 104194 5013963.3260 6628989.15 32.2% 7.1 29s
138095 108023 5998568.14 55 384 5013963.33 6628946.44 32.2% 7.1 30s
161286 128191 5060434.88 118 214 5013963.33 6628219.27 32.2% 7.1 35s
H165050 130886 5013963.3334 6628091.22 32.2% 7.2 36s
184537 146939 6172350.60 43 428 5013963.33 6627244.62 32.2% 7.4 40s
H209724 165739 5013963.3402 6626511.98 32.2% 7.5 44s
210046 167479 5374423.12 94 375 5013963.34 6626511.98 32.2% 7.5 45s
233456 187634 5119625.68 115 280 5013963.34 6626045.61 32.2% 7.5 50s
257540 206537 6588035.99 38 432 5013963.34 6625397.39 32.1% 7.5 55s
282035 226804 5079349.95 100 285 5013963.34 6625020.67 32.1% 7.6 60s
306845 248090 6016481.62 47 411 5013963.34 6624552.91 32.1% 7.6 65s
331057 267643 5025209.18 88 263 5013963.34 6624303.36 32.1% 7.6 70s
353223 286587 5914721.95 52 377 5013963.34 6623989.26 32.1% 7.7 75s
377085 308461 5028635.22 140 225 5013963.34 6623989.26 32.1% 7.7 80s
403477 329347 5213165.27 82 222 5013963.34 6623561.72 32.1% 7.6 85s
426062 349614 5838118.44 43 346 5013963.34 6623435.13 32.1% 7.7 90s
453516 372537 5095937.64 120 314 5013963.34 6623118.56 32.1% 7.6 95s
476256 392855 6202281.30 45 424 5013963.34 6623033.76 32.1% 7.7 100s
499746 413135 5197113.81 81 224 5013963.34 6622843.06 32.1% 7.7 105s
522864 433233 5061124.63 67 116 5013963.34 6622650.74 32.1% 7.7 110s
547801 452770 5929883.26 46 374 5013963.34 6622407.50 32.1% 7.6 115s
572192 472690 infeasible 59 5013963.34 6622183.36 32.1% 7.7 120s
596710 494818 6616930.58 31 438 5013963.34 6622125.58 32.1% 7.7 125s
621633 515327 5205597.57 68 270 5013963.34 6621876.14 32.1% 7.7 130s
643487 535347 5368727.04 88 309 5013963.34 6621829.41 32.1% 7.8 135s
H657916 547211 5013963.3511 6621817.38 32.1% 7.8 138s
668019 557019 infeasible 31 5013963.35 6621742.31 32.1% 7.8 140s
691249 578326 5921775.36 41 355 5013963.35 6621654.69 32.1% 7.8 145s
714051 597573 5836013.60 43 325 5013963.35 6621526.21 32.1% 7.8 150s
740152 620388 5127616.28 114 320 5013963.35 6621394.70 32.1% 7.8 155s
765308 641069 5181706.06 109 316 5013963.35 6621376.95 32.1% 7.8 160s
790053 660720 6614059.13 32 430 5013963.35 6621012.06 32.1% 7.8 165s
813400 682075 5537602.19 74 379 5013963.35 6620938.17 32.0% 7.8 170s
837473 701606 cutoff 99 5013963.35 6620784.69 32.0% 7.8 175s
864252 723246 5925532.27 45 357 5013963.35 6620650.48 32.0% 7.8 180s
888304 742963 5264858.83 98 272 5013963.35 6620482.36 32.0% 7.8 185s
911894 763477 5531193.65 83 385 5013963.35 6620389.80 32.0% 7.8 190s
H928680 773091 5016118.3876 6620333.70 32.0% 7.8 193s
935636 778913 5592798.44 50 393 5016118.39 6620313.68 32.0% 7.8 195s
959914 798679 6580904.59 42 397 5016118.39 6620167.38 32.0% 7.8 200s
984148 818298 5385352.31 89 359 5016118.39 6620032.20 32.0% 7.8 205s
1007330 838475 5864875.57 52 412 5016118.39 6619982.81 32.0% 7.9 210s
1031662 859705 5323253.28 65 228 5016118.39 6619891.03 32.0% 7.9 215s
H1037009 863512 5016118.3901 6619872.07 32.0% 7.9 216s
1056060 878484 6015658.03 43 418 5016118.39 6619767.78 32.0% 7.9 220s
1080142 897774 5262324.29 72 235 5016118.39 6619642.50 32.0% 7.9 225s
*1098600 752924 185 5078888.6196 6619572.15 30.3% 7.9 228s
1104247 758791 5154464.98 103 320 5078888.62 6619541.09 30.3% 7.9 230s
1130470 780130 6602674.21 39 425 5078888.62 6619431.55 30.3% 7.9 235s
1154797 797953 5831918.39 46 319 5078888.62 6619305.68 30.3% 7.9 240s
1178712 818050 5404065.48 94 380 5078888.62 6619226.55 30.3% 7.9 245s
1203919 838132 cutoff 95 5078888.62 6619158.73 30.3% 7.9 250s
1226143 855440 5929898.16 47 352 5078888.62 6619073.90 30.3% 7.9 255s
1252467 875985 5080456.21 90 273 5078888.62 6618951.07 30.3% 8.0 260s
1276898 894359 cutoff 90 5078888.62 6618866.90 30.3% 8.0 265s
1301203 912728 cutoff 93 5078888.62 6618759.67 30.3% 8.0 270s
1325205 931146 cutoff 90 5078888.62 6618667.33 30.3% 8.0 275s
1351459 950701 5463464.82 74 378 5078888.62 6618540.47 30.3% 8.0 280s
1375710 969893 5856126.15 49 268 5078888.62 6618469.59 30.3% 8.0 285s
1401864 988750 5160303.86 52 210 5078888.62 6618329.32 30.3% 8.0 290s
1425744 1007103 5887288.03 33 361 5078888.62 6618242.78 30.3% 8.0 295s
1452229 1027066 5133240.65 85 245 5078888.62 6618140.84 30.3% 8.0 300s
1476301 1048170 5319018.85 94 346 5078888.62 6618082.14 30.3% 8.0 305s
1500065 1067046 6591563.46 42 400 5078888.62 6618019.27 30.3% 8.0 310s
1526380 1088417 5790134.96 56 376 5078888.62 6617933.72 30.3% 8.0 315s
1550619 1108026 5135713.44 112 315 5078888.62 6617883.90 30.3% 8.1 320s
1574490 1127153 5932278.37 44 351 5078888.62 6617815.07 30.3% 8.1 325s
1600978 1146674 5939622.81 39 357 5078888.62 6617715.97 30.3% 8.1 330s
1624681 1165677 5538521.74 67 339 5078888.62 6617640.57 30.3% 8.1 335s
1648931 1184480 5627505.37 64 260 5078888.62 6617585.28 30.3% 8.1 340s
1675510 1205021 6595435.94 41 422 5078888.62 6617502.40 30.3% 8.1 345s
1699119 1224577 6602305.04 30 437 5078888.62 6617440.60 30.3% 8.1 350s
1723259 1242009 6614176.62 32 433 5078888.62 6617340.58 30.3% 8.1 355s
1749484 1262678 5826586.58 53 414 5078888.62 6617262.69 30.3% 8.1 360s
1773693 1281203 5301182.99 76 227 5078888.62 6617203.29 30.3% 8.1 365s
1797568 1299101 5315368.31 67 360 5078888.62 6617115.51 30.3% 8.1 370s
1821735 1318603 cutoff 99 5078888.62 6617080.34 30.3% 8.1 375s
1847908 1339539 5885149.31 42 321 5078888.62 6617016.23 30.3% 8.1 380s
1871923 1358697 5381635.95 95 375 5078888.62 6616982.97 30.3% 8.1 385s
1895957 1376646 cutoff 67 5078888.62 6616918.91 30.3% 8.1 390s
1919552 1396933 cutoff 35 5078888.62 6616890.91 30.3% 8.2 395s
1941558 1413330 5083085.42 91 314 5078888.62 6616836.80 30.3% 8.2 400s
H1961180 1426597 5079562.6682 6616787.35 30.3% 8.2 404s
1965544 1429515 5928381.93 51 365 5079562.67 6616780.38 30.3% 8.2 405s
1991691 1449653 5355805.89 54 227 5079562.67 6616728.25 30.3% 8.2 410s
2016013 1468187 5079672.29 110 285 5079562.67 6616671.80 30.3% 8.2 415s
2039987 1487106 5833353.48 55 370 5079562.67 6616604.60 30.3% 8.2 420s
2066206 1508071 5230800.19 82 226 5079562.67 6616566.05 30.3% 8.2 425s
2090453 1525142 5653599.95 57 324 5079562.67 6616496.57 30.3% 8.2 430s
2112630 1542658 5399487.79 63 229 5079562.67 6616453.09 30.3% 8.2 435s
H2117924 1539632 5082095.2660 6616435.41 30.2% 8.2 436s
H2121086 1540288 5082450.2573 6616427.56 30.2% 8.2 437s
2134271 1551049 5155430.55 87 329 5082450.26 6616392.84 30.2% 8.2 440s
H2143236 1554699 5082979.5614 6616368.07 30.2% 8.2 441s
2158252 1567720 5807049.68 50 394 5082979.56 6616345.41 30.2% 8.2 445s
2182487 1585751 5885128.75 43 363 5082979.56 6616293.88 30.2% 8.2 450s
2206477 1604498 5249606.51 72 238 5082979.56 6616247.26 30.2% 8.2 455s
2232711 1624229 5846498.54 45 263 5082979.56 6616193.90 30.2% 8.2 460s
H2253735 1640040 5083106.7970 6616162.03 30.2% 8.2 464s
2256721 1643322 5852840.54 41 321 5083106.80 6616158.62 30.2% 8.2 465s
2278058 1658657 5600075.62 65 264 5083106.80 6616111.97 30.2% 8.2 470s
H2290585 1667134 5083181.2431 6616075.85 30.2% 8.2 472s
H2291885 1667022 5083218.8619 6616074.40 30.2% 8.2 472s
2302217 1676607 5832068.46 55 253 5083218.86 6616059.39 30.2% 8.2 475s
2326408 1697070 5327642.74 96 336 5083218.86 6616023.51 30.2% 8.2 480s
2350341 1716452 5109367.37 142 242 5083218.86 6615994.77 30.2% 8.2 485s
2374294 1735325 5085933.74 67 367 5083218.86 6615941.11 30.2% 8.2 490s
2400853 1755175 5146166.64 106 281 5083218.86 6615887.19 30.2% 8.2 495s
2425061 1773016 5089895.24 63 281 5083218.86 6615840.60 30.2% 8.2 500s
2449049 1790392 5921998.03 39 359 5083218.86 6615776.28 30.1% 8.2 505s
2475628 1810104 5911924.39 42 326 5083218.86 6615722.61 30.1% 8.2 510s
2499372 1828213 6601739.74 34 429 5083218.86 6615674.75 30.1% 8.2 515s
H2524820 1846553 5083293.3081 6615630.27 30.1% 8.2 520s
H2531318 1849767 5084053.0533 6615622.42 30.1% 8.2 521s
2547081 1861981 5956890.19 42 400 5084053.05 6615605.22 30.1% 8.2 525s
2571189 1880001 6598425.71 35 432 5084053.05 6615556.71 30.1% 8.2 530s
2597360 1899772 5646414.69 65 380 5084053.05 6615511.91 30.1% 8.2 535s
2621365 1918120 5926225.67 39 355 5084053.05 6615476.37 30.1% 8.2 540s
2645863 1936936 5895283.15 42 351 5084053.05 6615427.53 30.1% 8.2 545s
2672274 1957332 5455544.88 53 397 5084053.05 6615387.45 30.1% 8.2 550s
H2682371 1963985 5084435.9813 6615378.88 30.1% 8.2 552s
2696205 1975220 cutoff 65 5084435.98 6615357.84 30.1% 8.2 555s
2718558 1994484 5091019.15 89 233 5084435.98 6615336.35 30.1% 8.3 560s
2743818 2014430 5782645.21 53 358 5084435.98 6615311.79 30.1% 8.3 565s
2768166 2033234 5091103.05 96 255 5084435.98 6615277.79 30.1% 8.3 570s
2792131 2053598 5086067.06 121 309 5084435.98 6615258.36 30.1% 8.3 575s
2818602 2073222 5242917.67 79 247 5084435.98 6615204.04 30.1% 8.3 580s
2842517 2091510 6590585.87 38 423 5084435.98 6615166.71 30.1% 8.3 585s
2868787 2111371 5100604.60 117 313 5084435.98 6615135.39 30.1% 8.3 590s
2892464 2130538 5553842.21 65 405 5084435.98 6615103.68 30.1% 8.3 595s
2916422 2148263 5786593.17 63 361 5084435.98 6615056.18 30.1% 8.3 600s
2943180 2167448 cutoff 89 5084435.98 6615019.90 30.1% 8.3 605s
2967157 2185182 5924574.70 39 355 5084435.98 6614987.97 30.1% 8.3 610s
2993915 2207873 5096611.63 102 321 5084435.98 6614962.07 30.1% 8.3 615s
3017662 2224881 5485877.51 84 349 5084435.98 6614934.38 30.1% 8.3 620s
3041613 2244035 5095011.92 63 277 5084435.98 6614905.82 30.1% 8.3 625s
3065011 2264302 6614782.94 32 435 5084435.98 6614889.87 30.1% 8.3 630s
3091721 2286935 cutoff 98 5084435.98 6614866.28 30.1% 8.3 635s
3115761 2306063 5099555.64 114 302 5084435.98 6614840.91 30.1% 8.3 640s
3139983 2323679 5092843.43 57 174 5084435.98 6614806.63 30.1% 8.3 645s
3163953 2342988 5759924.30 56 364 5084435.98 6614771.44 30.1% 8.3 650s
3190470 2363819 5432106.85 94 380 5084435.98 6614741.40 30.1% 8.3 655s
3214493 2382130 5877875.23 39 330 5084435.98 6614714.65 30.1% 8.3 660s
3240635 2402125 5593082.64 70 395 5084435.98 6614679.94 30.1% 8.3 665s
3264623 2421118 5354268.61 99 378 5084435.98 6614651.23 30.1% 8.3 670s
3288274 2440186 cutoff 86 5084435.98 6614629.78 30.1% 8.3 675s
3312913 2460066 5826228.16 47 263 5084435.98 6614610.90 30.1% 8.3 680s
3336648 2478900 5291368.20 93 345 5084435.98 6614576.45 30.1% 8.3 685s
3360665 2496933 5919320.82 45 314 5084435.98 6614543.19 30.1% 8.3 690s
3387055 2518557 6171413.04 38 423 5084435.98 6614512.67 30.1% 8.3 695s
3408460 2537095 5276434.81 102 316 5084435.98 6614497.39 30.1% 8.3 700s
*3421890 2544151 185 5085055.2150 6614486.16 30.1% 8.3 702s
3432100 2554125 6081684.76 40 428 5085055.22 6614479.33 30.1% 8.3 705s
H3436222 2554213 5085518.7046 6614479.33 30.1% 8.3 706s
3454003 2570412 6592078.38 37 424 5085518.70 6614457.42 30.1% 8.3 710s
3478225 2588722 5523261.74 60 286 5085518.70 6614421.73 30.1% 8.3 715s
3504102 2610246 5234770.03 107 320 5085518.70 6614396.50 30.1% 8.4 720s
3528510 2628009 5918739.91 47 366 5085518.70 6614356.82 30.1% 8.4 725s
3554749 2648156 5222323.68 54 169 5085518.70 6614321.85 30.1% 8.4 730s
3578725 2665017 5095184.32 64 286 5085518.70 6614274.15 30.1% 8.4 735s
3602634 2683066 5236797.84 65 233 5085518.70 6614238.18 30.1% 8.4 740s
3629406 2703606 5802639.96 56 249 5085518.70 6614206.07 30.1% 8.4 745s
3653318 2722429 5130145.38 113 316 5085518.70 6614182.50 30.1% 8.4 750s
3677074 2740821 cutoff 93 5085518.70 6614160.61 30.1% 8.4 755s
3699702 2761470 5525054.18 70 354 5085518.70 6614143.75 30.1% 8.4 760s
3726991 2782132 5593814.48 59 278 5085518.70 6614124.17 30.1% 8.4 765s
3751199 2800307 6610933.10 35 427 5085518.70 6614094.25 30.1% 8.4 770s
3775581 2818511 6614026.18 38 428 5085518.70 6614064.44 30.1% 8.4 775s
3801737 2838626 5526087.18 77 373 5085518.70 6614035.85 30.1% 8.4 780s
3825624 2856790 5132567.91 94 270 5085518.70 6614004.61 30.1% 8.4 785s
3852039 2876328 6605110.53 39 425 5085518.70 6613973.31 30.1% 8.4 790s
3876293 2893589 5287203.79 38 361 5085518.70 6613941.45 30.1% 8.4 795s
3900242 2912020 5927086.97 46 395 5085518.70 6613915.52 30.1% 8.4 800s
3926581 2932268 6610399.37 36 433 5085518.70 6613885.99 30.1% 8.4 805s
3950570 2950770 cutoff 61 5085518.70 6613866.45 30.1% 8.4 810s
3974499 2969532 5112079.29 105 320 5085518.70 6613848.58 30.1% 8.4 815s
4001055 2991063 6605954.85 35 428 5085518.70 6613820.55 30.1% 8.4 820s
4024753 3007183 5877478.84 51 273 5085518.70 6613786.91 30.1% 8.4 825s
4048754 3025335 5651482.79 68 394 5085518.70 6613764.48 30.1% 8.4 830s
4072740 3044412 5353810.65 96 288 5085518.70 6613742.54 30.1% 8.4 835s
4097189 3063572 5310086.92 92 359 5085518.70 6613712.53 30.0% 8.4 840s
4123626 3083610 cutoff 91 5085518.70 6613688.74 30.0% 8.4 845s
4147197 3101865 5108263.18 121 264 5085518.70 6613663.92 30.0% 8.4 850s
4173769 3123259 5341648.05 99 330 5085518.70 6613644.26 30.0% 8.4 855s
4197696 3141570 5102191.19 113 273 5085518.70 6613613.10 30.0% 8.4 860s
4221924 3160720 5632990.06 65 400 5085518.70 6613592.84 30.0% 8.4 865s
4245744 3179832 5089447.18 90 289 5085518.70 6613570.59 30.0% 8.4 870s
4272586 3199548 5896038.33 40 349 5085518.70 6613550.01 30.0% 8.4 875s
4296284 3217578 5097360.59 109 309 5085518.70 6613528.05 30.0% 8.4 880s
4322713 3238592 5421432.21 91 380 5085518.70 6613495.76 30.0% 8.4 885s
4346697 3257492 6609051.61 34 436 5085518.70 6613480.99 30.0% 8.4 890s
4370547 3277305 5105591.07 91 271 5085518.70 6613464.49 30.0% 8.4 895s
4393307 3295052 5797062.25 43 365 5085518.70 6613445.20 30.0% 8.4 900s
4417723 3315089 5846355.78 55 260 5085518.70 6613430.85 30.0% 8.4 905s
4442529 3332801 cutoff 55 5085518.70 6613400.99 30.0% 8.4 910s
4469019 3351069 5113117.90 83 217 5085518.70 6613371.64 30.0% 8.4 915s
4493095 3369438 5134782.47 80 212 5085518.70 6613348.58 30.0% 8.4 920s
4517235 3387457 5244528.87 73 212 5085518.70 6613322.20 30.0% 8.4 925s
4543433 3407678 5280717.64 51 288 5085518.70 6613297.72 30.0% 8.4 930s
4567022 3425964 5417822.48 81 365 5085518.70 6613277.17 30.0% 8.4 935s
4594055 3447048 5435201.24 90 380 5085518.70 6613250.67 30.0% 8.4 940s
4617765 3465003 5557341.78 79 387 5085518.70 6613226.98 30.0% 8.4 945s
4641911 3484004 5373149.75 69 280 5085518.70 6613208.52 30.0% 8.4 950s
4665807 3503032 5104670.25 117 310 5085518.70 6613188.26 30.0% 8.4 955s
4692443 3523527 5115563.40 104 320 5085518.70 6613164.33 30.0% 8.4 960s
4716365 3541634 5777290.14 42 367 5085518.70 6613142.95 30.0% 8.4 965s
4743086 3561630 5201030.24 103 319 5085518.70 6613120.02 30.0% 8.4 970s
4767064 3579356 5558582.43 57 266 5085518.70 6613098.01 30.0% 8.4 975s
4792911 3600434 5388040.03 69 348 5085518.70 6613075.09 30.0% 8.4 980s
4817141 3619074 cutoff 91 5085518.70 6613058.24 30.0% 8.4 985s
4841512 3638606 6599512.18 36 427 5085518.70 6613034.04 30.0% 8.4 990s
4867459 3659458 5806336.88 57 397 5085518.70 6613016.46 30.0% 8.4 995s
4891667 3677678 5600390.04 69 398 5085518.70 6612994.77 30.0% 8.4 1000s
4915911 3696184 5368462.68 97 357 5085518.70 6612978.12 30.0% 8.4 1005s
4939654 3715173 infeasible 30 5085518.70 6612957.56 30.0% 8.4 1010s
4965959 3735773 5349187.61 80 335 5085518.70 6612938.93 30.0% 8.4 1015s
4989761 3754952 5089798.93 88 264 5085518.70 6612923.15 30.0% 8.4 1020s
5014344 3773285 5360499.92 81 225 5085518.70 6612902.34 30.0% 8.4 1025s
5040935 3793150 5363154.79 65 234 5085518.70 6612879.82 30.0% 8.4 1030s
5064825 3811897 5087526.02 116 272 5085518.70 6612867.31 30.0% 8.4 1035s
5091129 3832148 5259545.52 101 320 5085518.70 6612841.62 30.0% 8.4 1040s
5114829 3851297 5603430.40 66 369 5085518.70 6612824.37 30.0% 8.4 1045s
5138692 3871060 5116518.78 112 316 5085518.70 6612810.11 30.0% 8.4 1050s
5163293 3888732 cutoff 43 5085518.70 6612786.60 30.0% 8.4 1055s
5189194 3909506 5290028.38 72 306 5085518.70 6612762.05 30.0% 8.4 1060s
5213461 3928075 5395565.35 95 374 5085518.70 6612749.81 30.0% 8.4 1065s
5237073 3948237 5738735.35 51 349 5085518.70 6612735.36 30.0% 8.4 1070s
5261566 3966019 6358019.49 39 428 5085518.70 6612711.68 30.0% 8.4 1075s
5285823 3985853 5813371.15 47 373 5085518.70 6612702.10 30.0% 8.4 1080s
5309767 4003309 5190962.37 88 231 5085518.70 6612678.09 30.0% 8.4 1085s
5336566 4022336 5515432.71 67 319 5085518.70 6612652.53 30.0% 8.4 1090s
5360270 4040279 5206742.28 69 218 5085518.70 6612635.58 30.0% 8.4 1095s
5386594 4060344 5211770.19 58 302 5085518.70 6612611.86 30.0% 8.4 1100s
5409760 4079633 6598714.50 38 430 5085518.70 6612595.36 30.0% 8.4 1105s
5434222 4099708 5763948.73 55 419 5085518.70 6612583.69 30.0% 8.4 1110s
5458270 4119326 5113875.70 92 211 5085518.70 6612572.16 30.0% 8.4 1115s
5482614 4136952 5929644.61 41 360 5085518.70 6612551.15 30.0% 8.4 1120s
5508766 4156940 5889591.12 35 362 5085518.70 6612529.30 30.0% 8.4 1125s
5532840 4176092 5125244.61 88 205 5085518.70 6612513.94 30.0% 8.4 1130s
5557074 4193687 6004211.50 41 427 5085518.70 6612490.27 30.0% 8.4 1135s
5583343 4214433 5941360.38 48 412 5085518.70 6612473.67 30.0% 8.4 1140s
5609494 4236326 5354012.36 93 323 5085518.70 6612460.11 30.0% 8.4 1145s
H5631149 4251147 5085871.7440 6612443.34 30.0% 8.4 1150s
5655026 4270818 5884354.86 43 366 5085871.74 6612431.61 30.0% 8.4 1155s
H5671464 4281066 5086006.9364 6612421.72 30.0% 8.4 1159s
5674863 4284605 5243659.44 47 344 5086006.94 6612415.81 30.0% 8.4 1160s
H5679871 4282729 5087095.6545 6612411.68 30.0% 8.4 1161s
5695946 4295631 6606995.64 30 438 5087095.65 6612402.96 30.0% 8.4 1165s
5720001 4313967 5098150.52 90 219 5087095.65 6612386.36 30.0% 8.4 1170s
5744296 4330417 5637013.04 59 368 5087095.65 6612365.66 30.0% 8.4 1175s
5770862 4350488 cutoff 85 5087095.65 6612343.30 30.0% 8.4 1180s
5794796 4368169 6611598.24 32 411 5087095.65 6612325.06 30.0% 8.4 1185s
5818382 4387038 5255909.95 57 300 5087095.65 6612309.37 30.0% 8.4 1190s
5845128 4407005 cutoff 92 5087095.65 6612290.61 30.0% 8.4 1195s
5868775 4427302 5262727.35 74 296 5087095.65 6612278.06 30.0% 8.4 1200s
H5887082 4438923 5087390.5077 6612271.97 30.0% 8.4 1204s
5890113 4443084 5755015.97 57 362 5087390.51 6612268.07 30.0% 8.4 1205s
5914426 4461329 6604135.96 35 428 5087390.51 6612251.46 30.0% 8.4 1210s
H5929158 4467210 5088375.8137 6612242.94 29.9% 8.4 1213s
5935684 4473639 5743925.04 48 373 5088375.81 6612237.42 29.9% 8.4 1215s
5959576 4493052 5678580.96 64 397 5088375.81 6612228.41 29.9% 8.4 1220s
5983659 4511903 5357486.35 81 289 5088375.81 6612212.69 29.9% 8.5 1225s
6007712 4531400 5683051.39 66 396 5088375.81 6612197.42 29.9% 8.5 1230s
H6008335 4529220 5088763.1180 6612197.42 29.9% 8.5 1230s
6030177 4545704 6604271.59 46 420 5088763.12 6612185.12 29.9% 8.5 1235s
6054113 4563562 5384305.27 87 381 5088763.12 6612171.40 29.9% 8.5 1240s
6078008 4582622 5854737.44 52 259 5088763.12 6612156.46 29.9% 8.5 1245s
6104308 4604219 5191444.94 76 228 5088763.12 6612141.77 29.9% 8.5 1250s
6125774 4622152 6608263.64 31 443 5088763.12 6612131.63 29.9% 8.5 1255s
6152415 4642629 5127099.92 105 311 5088763.12 6612115.32 29.9% 8.5 1260s
6176317 4662634 5353433.00 95 380 5088763.12 6612106.64 29.9% 8.5 1265s
6200381 4681079 5925650.25 40 359 5088763.12 6612090.90 29.9% 8.5 1270s
6224662 4699801 6605070.87 37 431 5088763.12 6612073.23 29.9% 8.5 1275s
6250746 4720039 5090258.67 100 253 5088763.12 6612056.21 29.9% 8.5 1280s
6275214 4738412 5564061.72 72 392 5088763.12 6612042.09 29.9% 8.5 1285s
6298788 4756421 5102326.02 66 266 5088763.12 6612025.58 29.9% 8.5 1290s
6322730 4775812 6610801.97 29 442 5088763.12 6612015.06 29.9% 8.5 1295s
6346987 4794212 cutoff 96 5088763.12 6612001.81 29.9% 8.5 1300s
6373479 4815180 6590481.44 34 413 5088763.12 6611989.00 29.9% 8.5 1305s
6397655 4832433 5095612.29 63 273 5088763.12 6611972.31 29.9% 8.5 1310s
6423968 4852519 5396204.43 61 271 5088763.12 6611952.37 29.9% 8.5 1315s
6447640 4871268 5931798.04 40 355 5088763.12 6611939.14 29.9% 8.5 1320s
6472036 4889960 6179996.52 35 432 5088763.12 6611918.63 29.9% 8.5 1325s
6498373 4909158 5148304.23 56 216 5088763.12 6611902.72 29.9% 8.5 1330s
6522290 4925720 6606471.54 31 438 5088763.12 6611886.20 29.9% 8.5 1335s
6546602 4943652 6021451.83 36 434 5088763.12 6611869.05 29.9% 8.5 1340s
6572802 4964408 5139767.23 106 316 5088763.12 6611856.54 29.9% 8.5 1345s
6596560 4983581 6611118.87 31 414 5088763.12 6611843.77 29.9% 8.5 1350s
6618021 5001828 5283409.36 47 299 5088763.12 6611838.17 29.9% 8.5 1355s
6641137 5020095 5885134.14 58 363 5088763.12 6611825.32 29.9% 8.5 1360s
6666100 5039684 6611132.15 37 405 5088763.12 6611809.95 29.9% 8.5 1365s
6689779 5058651 5930224.04 47 371 5088763.12 6611796.13 29.9% 8.5 1370s
6716850 5079005 5269945.79 92 350 5088763.12 6611779.44 29.9% 8.5 1375s
6740685 5096577 5191237.35 106 320 5088763.12 6611763.97 29.9% 8.5 1380s
6763209 5117274 5111150.65 107 315 5088763.12 6611755.95 29.9% 8.5 1385s
6788048 5136749 cutoff 86 5088763.12 6611749.02 29.9% 8.5 1390s
6812000 5155706 5362841.49 73 222 5088763.12 6611736.59 29.9% 8.5 1395s
6836282 5174141 5237880.72 76 223 5088763.12 6611722.10 29.9% 8.5 1400s
6860489 5192863 6598790.10 33 432 5088763.12 6611712.26 29.9% 8.5 1405s
6884603 5211613 5666317.23 46 372 5088763.12 6611695.86 29.9% 8.5 1410s
6910512 5230153 cutoff 58 5088763.12 6611679.51 29.9% 8.5 1415s
6934529 5250536 5143159.36 106 323 5088763.12 6611674.59 29.9% 8.5 1420s
6958694 5269773 5107799.14 95 255 5088763.12 6611662.27 29.9% 8.5 1425s
6982742 5289772 infeasible 48 5088763.12 6611652.83 29.9% 8.5 1430s
7006632 5309119 5176630.17 88 217 5088763.12 6611639.82 29.9% 8.5 1435s
7030903 5327222 5119169.84 85 280 5088763.12 6611626.05 29.9% 8.5 1440s
7054817 5345513 5518157.90 69 381 5088763.12 6611613.08 29.9% 8.5 1445s
7081186 5365269 6079989.99 38 431 5088763.12 6611598.01 29.9% 8.5 1450s
7104983 5385116 5402374.01 58 268 5088763.12 6611589.78 29.9% 8.5 1455s
7129266 5404090 5531227.79 70 349 5088763.12 6611577.22 29.9% 8.5 1460s
7153130 5422317 5248511.98 70 281 5088763.12 6611562.07 29.9% 8.5 1465s
H7172426 5435071 5089221.4226 6611551.22 29.9% 8.5 1470s
7196468 5454480 cutoff 51 5089221.42 6611541.23 29.9% 8.5 1475s
7222769 5475030 5105245.97 115 315 5089221.42 6611525.81 29.9% 8.5 1480s
7246729 5494229 5926202.58 49 410 5089221.42 6611511.54 29.9% 8.5 1485s
7270524 5511371 5996393.91 40 362 5089221.42 6611497.63 29.9% 8.5 1490s
7294390 5531649 cutoff 61 5089221.42 6611488.69 29.9% 8.5 1495s
7318326 5549935 5662565.00 49 338 5089221.42 6611475.46 29.9% 8.5 1500s
7342806 5569244 5460249.44 87 384 5089221.42 6611466.80 29.9% 8.5 1505s
7368916 5589875 6608298.12 30 435 5089221.42 6611454.67 29.9% 8.5 1510s
7392903 5609281 cutoff 85 5089221.42 6611443.53 29.9% 8.5 1515s
7417025 5625585 cutoff 88 5089221.42 6611426.93 29.9% 8.5 1520s
7441008 5645674 5932438.10 42 355 5089221.42 6611419.05 29.9% 8.5 1525s
7464874 5664604 5923168.95 42 363 5089221.42 6611407.34 29.9% 8.5 1530s
7491191 5684335 5803235.75 48 374 5089221.42 6611393.42 29.9% 8.5 1535s
7515342 5704215 5357166.69 97 352 5089221.42 6611385.05 29.9% 8.5 1540s
7539305 5722889 5158347.82 90 245 5089221.42 6611370.65 29.9% 8.5 1545s
7563506 5742109 cutoff 114 5089221.42 6611360.22 29.9% 8.5 1550s
7587437 5760261 5275353.18 96 309 5089221.42 6611345.62 29.9% 8.5 1555s
7613918 5780042 6039735.41 41 404 5089221.42 6611331.03 29.9% 8.5 1560s
7638231 5800269 5310201.51 93 363 5089221.42 6611324.60 29.9% 8.5 1565s
7662024 5817519 5634566.23 50 352 5089221.42 6611310.70 29.9% 8.5 1570s
7685773 5836266 5483316.92 39 374 5089221.42 6611299.07 29.9% 8.5 1575s
7709992 5854873 5093625.39 68 277 5089221.42 6611286.52 29.9% 8.5 1580s
7734517 5872112 5920146.24 38 355 5089221.42 6611271.51 29.9% 8.5 1585s
7760858 5890743 5347425.74 70 238 5089221.42 6611253.40 29.9% 8.5 1590s
7784238 5908006 5099116.78 90 210 5089221.42 6611235.42 29.9% 8.5 1595s
7808498 5927888 5119577.43 121 198 5089221.42 6611231.47 29.9% 8.5 1600s
7832733 5946106 5136452.27 61 283 5089221.42 6611214.37 29.9% 8.5 1605s
7856408 5965581 5451867.96 69 230 5089221.42 6611205.56 29.9% 8.6 1610s
7882689 5983450 5096127.62 71 272 5089221.42 6611185.24 29.9% 8.6 1615s
7906624 6003756 cutoff 94 5089221.42 6611180.90 29.9% 8.6 1620s
7930743 6023700 5575893.82 47 358 5089221.42 6611171.76 29.9% 8.6 1625s
7954703 6041905 5096840.84 97 293 5089221.42 6611161.64 29.9% 8.6 1630s
7978706 6058075 5210437.14 75 239 5089221.42 6611148.02 29.9% 8.6 1635s
8002800 6074875 6611090.87 33 435 5089221.42 6611132.74 29.9% 8.6 1640s
8029288 6092880 5274957.59 65 261 5089221.42 6611112.29 29.9% 8.6 1645s
8053341 6111365 5860070.35 48 268 5089221.42 6611101.99 29.9% 8.6 1650s
8076933 6129600 5590678.91 67 262 5089221.42 6611091.15 29.9% 8.6 1655s
8100860 6149207 5602308.37 71 397 5089221.42 6611084.49 29.9% 8.6 1660s
8124739 6168313 5324193.34 79 293 5089221.42 6611069.63 29.9% 8.6 1665s
8149026 6186609 cutoff 88 5089221.42 6611057.36 29.9% 8.6 1670s
8175480 6207264 5308455.81 73 245 5089221.42 6611046.57 29.9% 8.6 1675s
8199852 6226202 5093774.01 115 300 5089221.42 6611036.22 29.9% 8.6 1680s
8223160 6244681 5840771.46 62 242 5089221.42 6611025.15 29.9% 8.6 1685s
8247687 6262773 infeasible 32 5089221.42 6611010.66 29.9% 8.6 1690s
8273813 6283574 5286060.70 50 353 5089221.42 6610998.73 29.9% 8.6 1695s
8297935 6302031 6601539.04 44 422 5089221.42 6610985.16 29.9% 8.6 1700s
8321944 6320214 6609714.71 36 428 5089221.42 6610971.92 29.9% 8.6 1705s
8348021 6341342 5323549.94 69 366 5089221.42 6610960.88 29.9% 8.6 1710s
8369903 6359884 cutoff 118 5089221.42 6610953.28 29.9% 8.6 1715s
8393925 6376831 5452481.11 68 238 5089221.42 6610944.00 29.9% 8.6 1720s
8420228 6398002 5111598.08 87 216 5089221.42 6610936.03 29.9% 8.6 1725s
8444452 6417497 5403115.89 73 320 5089221.42 6610923.49 29.9% 8.6 1730s
8468351 6437420 5797608.42 44 420 5089221.42 6610915.17 29.9% 8.6 1735s
8492166 6457164 5362649.23 97 342 5089221.42 6610908.25 29.9% 8.6 1740s
8516146 6476102 5541467.69 73 376 5089221.42 6610899.58 29.9% 8.6 1745s
8540477 6494621 5123183.54 116 323 5089221.42 6610895.68 29.9% 8.6 1750s
8563795 6514372 5747451.13 54 361 5089221.42 6610880.01 29.9% 8.6 1755s
8588374 6532903 6610191.65 31 410 5089221.42 6610869.22 29.9% 8.6 1760s
8612299 6551841 5524424.18 45 374 5089221.42 6610860.57 29.9% 8.6 1765s
8636205 6570921 5868627.25 49 265 5089221.42 6610850.20 29.9% 8.6 1770s
8662910 6590253 5220589.89 77 254 5089221.42 6610835.48 29.9% 8.6 1775s
8687381 6607593 6605403.46 33 430 5089221.42 6610818.78 29.9% 8.6 1780s
8711343 6625584 5892958.89 45 363 5089221.42 6610806.76 29.9% 8.6 1785s
8737335 6645359 5090362.09 117 318 5089221.42 6610793.69 29.9% 8.6 1790s
8761398 6663894 5147252.73 60 285 5089221.42 6610784.34 29.9% 8.6 1795s
8785590 6680985 5212066.66 74 255 5089221.42 6610774.06 29.9% 8.6 1800s
Cutting planes:
RLT: 160
Explored 8786601 nodes (75475054 simplex iterations) in 1800.01 seconds
Thread count was 16 (of 16 available processors)
Solution count 10: 5.08922e+06 5.08876e+06 5.08838e+06 ... 5.08444e+06
Time limit reached
Best objective 5.089221422599e+06, best bound 6.610772926519e+06, gap 29.8975%
-
Official comment
This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?. -
Hi Onam,
Could you elaborate on how exactly the two models differ? If I understood correctly, you are adding \(x^8\) terms in the second model currently without bounds on \(x\) or the respective auxiliary variable, is this correct?
Note that tight variable bounds are essential when working with non-linear functions. Especially, when working with high degree polynomials. This is due to the fact, that Gurobi uses a piecewise linear approximation of the nonlinear terms, which is highly dependent on variable bounds.
Best regards,
Jaromił0 -
Hi Jaromil Najman,
Thank you very much for this reply. Both models are actually the same, both having up to x^8 terms in their objective function. The only difference is that in the second model I have a variable ratio term which isn't present in the first model. Also, I am keeping bounds on all the decision variables.
Actually, I am creating few intermediate variables which are quadratic in nature. In the main problem I need to keep bounds on those intermediate variables but currently, I am not doing so. I am just creating those variables to check if creating those variables takes more time which is consequently increasing convergence time. What I found out is that If all the interim variables involve quadratic(or bilinear) terms only, the code is converging in no time but if I am creating a variables ratio term the code is taking too much time(Not converging in even one hour). So, the first code is the result of without variable-ratio term, and the second is the output of what I got when I used variable-ratio term. I want to reduce the time of convergence in the second code.
0 -
Hi Onam,
Could you explicitly state the variable ratio terms that you are adding or in best case all terms that differ between the 2 problems? You can also provide the MPS/LP files as described in Posting to the Community Forum in order to make the issue reproducible for the Community.
It is also possible that your problem is prone to optimization path variability. You can check this by running hte model for different values of the Seed parameter and see whether the 1st model is always solved so fast and whether the 2nd model is always solved so slow.
Best regards,
Jaromił0 -
Let me give you a brief introduction to the problem. I have three different ways of selling any product, their corresponding prices are what needs to be found out after optimizing the objective variable. Let us name them x, y, z.
f(x) .. Linear function of x.
f(e^x) .. exponential function of x, which I have expanded.
c1, c2, c3 are constant values given from the file.Net Revenue(NR) = f(e^x)*(52-y-z) + f(e^x) * y * (1-f(x)) + f(e^x)*z*(1-f(x))
Gross Margin(GM) = f(e^x)* (52-y-z)*(1-c1) + f(e^x) * y * (1-f(x))*(1-c2) + f(e^x)*z*(1-f(x))*(1-c3)
I have other intermediate variables also which I am keeping in both the models. But GM/NR is created only in the second model which is a ratio of the variables. My question is why this variable creation taking so much time and is there anyways how we can make the second model run faster? My objective variable is NR(maximization problem).Best regards,
Onam0
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