Gurobi not making progress on the gap
Answered
Hello all,
I am trying to solve a relatively large energy system model that has a number of start-up constraints. Solving the model for a month only is no issue, but running the whole year has left me stuck at gurobi trying to close the gap.
I have tried a number of parameter settings. For everything I have tried, Gurobi usually found a solution but always had problems closing the branch-and-bound gap.
Do you might have any ideas on parameter settings that could bring me closer? Otherwise I see no choice but to reformulate my model and remove some constraints.
Thank you in advance.
Academic license - for non-commercial use only
Read LP format model from file C:\Users\xy
Reading time = 14.74 seconds
x613204: 534365 rows, 586924 columns, 31189041 nonzeros
Set parameter Threads to value 10
Set parameter Method to value 1
Set parameter Presolve to value 2
Set parameter NodefileStart to value 0.5
Set parameter NoRelHeurTime to value 600
Set parameter PreSparsify to value 1
Set parameter MIPGap to value 0.001
Set parameter MIPFocus to value 3
Set parameter TimeLimit to value 54000
Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (win64)
CPU model: 12th Gen Intel(R) Core(TM) i5-1235U, instruction set [SSE2|AVX|AVX2]
Thread count: 10 physical cores, 12 logical processors, using up to 10 threads
Optimize a model with 534365 rows, 586924 columns and 31189041 nonzeros
Model fingerprint: 0xa69b55dc
Variable types: 534363 continuous, 52561 integer (52561 binary)
Coefficient statistics:
Matrix range [7e-02, 2e+03]
Objective range [3e-01, 9e+03]
Bounds range [1e+00, 2e+03]
RHS range [1e+00, 7e+02]
Presolve removed 275600 rows and 367922 columns (presolve time = 6s) ...
Presolve removed 297800 rows and 377330 columns (presolve time = 12s) ...
Presolve removed 297800 rows and 377330 columns (presolve time = 15s) ...
Presolve removed 346329 rows and 377341 columns (presolve time = 21s) ...
Presolve removed 394868 rows and 425880 columns (presolve time = 25s) ...
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Presolve removed 412391 rows and 434640 columns (presolve time = 1035s) ...
Presolve removed 412391 rows and 434640 columns (presolve time = 1040s) ...
Sparsify removed 25833492 nonzeros (92%)
Presolve removed 412391 rows and 455652 columns (presolve time = 1046s) ...
Presolve removed 412391 rows and 413193 columns
Presolve time: 1046.22s
Presolved: 121974 rows, 173731 columns, 2382998 nonzeros
Variable types: 105099 continuous, 68632 integer (47185 binary)
Starting NoRel heuristic
Found heuristic solution: objective 3.009583e+07
Found heuristic solution: objective 2.836915e+07
Found heuristic solution: objective 2.836623e+07
Found heuristic solution: objective 2.494275e+07
Found heuristic solution: objective 2.356657e+07
Elapsed time for NoRel heuristic: 6s (best bound 1.48068e+06)
Found heuristic solution: objective 2.194842e+07
Found heuristic solution: objective 2.093745e+07
Found heuristic solution: objective 2.028350e+07
Found heuristic solution: objective 2.002779e+07
Found heuristic solution: objective 1.943139e+07
Found heuristic solution: objective 1.913917e+07
Found heuristic solution: objective 1.895433e+07
Found heuristic solution: objective 1.876361e+07
Found heuristic solution: objective 1.865674e+07
Found heuristic solution: objective 1.849013e+07
Found heuristic solution: objective 1.845184e+07
Elapsed time for NoRel heuristic: 12s (best bound 1.48068e+06)
Found heuristic solution: objective 1.841289e+07
Found heuristic solution: objective 1.840115e+07
Found heuristic solution: objective 1.830596e+07
Found heuristic solution: objective 1.824025e+07
Found heuristic solution: objective 1.810829e+07
Found heuristic solution: objective 1.800852e+07
Found heuristic solution: objective 1.791411e+07
Found heuristic solution: objective 1.788675e+07
Elapsed time for NoRel heuristic: 17s (best bound 1.48068e+06)
Found heuristic solution: objective 1.782456e+07
Found heuristic solution: objective 1.777042e+07
Found heuristic solution: objective 1.775810e+07
Found heuristic solution: objective 1.775625e+07
Found heuristic solution: objective 1.775585e+07
Found heuristic solution: objective 1.775421e+07
Found heuristic solution: objective 1.775421e+07
Found heuristic solution: objective 1.775003e+07
Found heuristic solution: objective 1.768950e+07
Found heuristic solution: objective 1.765825e+07
Elapsed time for NoRel heuristic: 24s (best bound 1.48068e+06)
Found heuristic solution: objective 1.761794e+07
Found heuristic solution: objective 1.756892e+07
Found heuristic solution: objective 1.751378e+07
Found heuristic solution: objective 1.747962e+07
Found heuristic solution: objective 1.746990e+07
Found heuristic solution: objective 1.739293e+07
Elapsed time for NoRel heuristic: 31s (best bound 1.48068e+06)
Found heuristic solution: objective 1.736338e+07
Found heuristic solution: objective 1.736260e+07
Found heuristic solution: objective 1.734071e+07
Found heuristic solution: objective 1.732879e+07
Elapsed time for NoRel heuristic: 37s (best bound 1.48068e+06)
Found heuristic solution: objective 1.731476e+07
Found heuristic solution: objective 1.730596e+07
Found heuristic solution: objective 1.729948e+07
Elapsed time for NoRel heuristic: 44s (best bound 1.48068e+06)
Found heuristic solution: objective 1.729815e+07
Found heuristic solution: objective 1.729797e+07
Found heuristic solution: objective 1.729740e+07
Found heuristic solution: objective 1.729581e+07
Found heuristic solution: objective 1.728467e+07
Found heuristic solution: objective 1.727977e+07
Elapsed time for NoRel heuristic: 51s (best bound 1.48068e+06)
Found heuristic solution: objective 1.727264e+07
Found heuristic solution: objective 1.726619e+07
Found heuristic solution: objective 1.726432e+07
Found heuristic solution: objective 1.726158e+07
Elapsed time for NoRel heuristic: 56s (best bound 1.48068e+06)
Found heuristic solution: objective 1.725931e+07
Found heuristic solution: objective 1.725713e+07
Found heuristic solution: objective 1.725628e+07
Found heuristic solution: objective 1.725421e+07
Elapsed time for NoRel heuristic: 61s (best bound 1.48068e+06)
Found heuristic solution: objective 1.725258e+07
Found heuristic solution: objective 1.724988e+07
Found heuristic solution: objective 1.724817e+07
Found heuristic solution: objective 1.724462e+07
Found heuristic solution: objective 1.717360e+07
Elapsed time for NoRel heuristic: 72s (best bound 1.48068e+06)
Found heuristic solution: objective 1.717306e+07
Elapsed time for NoRel heuristic: 79s (best bound 1.68053e+06)
Elapsed time for NoRel heuristic: 90s (best bound 1.68053e+06)
Elapsed time for NoRel heuristic: 105s (best bound 1.72259e+06)
Elapsed time for NoRel heuristic: 121s (best bound 1.72259e+06)
Found heuristic solution: objective 1.717280e+07
Found heuristic solution: objective 1.716888e+07
Found heuristic solution: objective 1.713004e+07
Elapsed time for NoRel heuristic: 157s (best bound 1.72259e+06)
Found heuristic solution: objective 1.712500e+07
Found heuristic solution: objective 1.711431e+07
Found heuristic solution: objective 1.709531e+07
Found heuristic solution: objective 1.706829e+07
Elapsed time for NoRel heuristic: 166s (best bound 1.75062e+06)
Found heuristic solution: objective 1.706584e+07
Found heuristic solution: objective 1.706361e+07
Found heuristic solution: objective 1.706344e+07
Found heuristic solution: objective 1.706196e+07
Found heuristic solution: objective 1.706162e+07
Elapsed time for NoRel heuristic: 183s (best bound 1.75062e+06)
Found heuristic solution: objective 1.706129e+07
Found heuristic solution: objective 1.706079e+07
Found heuristic solution: objective 1.706029e+07
Found heuristic solution: objective 1.705929e+07
Elapsed time for NoRel heuristic: 192s (best bound 1.75062e+06)
Found heuristic solution: objective 1.705912e+07
Found heuristic solution: objective 1.705912e+07
Elapsed time for NoRel heuristic: 198s (best bound 1.75062e+06)
Found heuristic solution: objective 1.705879e+07
Elapsed time for NoRel heuristic: 203s (best bound 1.75062e+06)
Elapsed time for NoRel heuristic: 210s (best bound 1.75062e+06)
Elapsed time for NoRel heuristic: 217s (best bound 1.81295e+06)
Elapsed time for NoRel heuristic: 224s (best bound 1.81295e+06)
Elapsed time for NoRel heuristic: 253s (best bound 1.81295e+06)
Elapsed time for NoRel heuristic: 307s (best bound 2.06142e+06)
Elapsed time for NoRel heuristic: 339s (best bound 2.21279e+06)
Elapsed time for NoRel heuristic: 371s (best bound 2.34799e+06)
Elapsed time for NoRel heuristic: 420s (best bound 2.61664e+06)
Elapsed time for NoRel heuristic: 453s (best bound 2.87185e+06)
Elapsed time for NoRel heuristic: 486s (best bound 3.06905e+06)
Elapsed time for NoRel heuristic: 517s (best bound 3.27374e+06)
Elapsed time for NoRel heuristic: 589s (best bound 3.61357e+06)
Elapsed time for NoRel heuristic: 620s (best bound 3.8728e+06)
Root relaxation presolve removed 42941 rows and 39769 columns (presolve time = 5s) ...
Root relaxation presolve removed 42941 rows and 39769 columns (presolve time = 10s) ...
Root relaxation presolve removed 43157 rows and 39769 columns
Root relaxation presolved: 78817 rows, 134178 columns, 2283943 nonzeros
Root simplex log...
Iteration Objective Primal Inf. Dual Inf. Time
0 1.4408404e+06 8.736923e+04 0.000000e+00 1682s
25983 6.6216873e+06 2.021800e+05 0.000000e+00 1685s
40390 7.1457690e+06 5.726619e+04 0.000000e+00 1690s
48264 7.1971862e+06 1.210260e+05 0.000000e+00 1695s
55887 7.1977635e+06 6.321890e+04 0.000000e+00 1700s
Warning: Markowitz tolerance tightened to 0.0625
64230 7.3254270e+06 1.144022e+07 0.000000e+00 1705s
69393 7.3606411e+06 8.703603e+04 0.000000e+00 1710s
72273 7.3642578e+06 1.320236e+05 0.000000e+00 1715s
74513 7.3643420e+06 5.576702e+04 0.000000e+00 1720s
77073 7.3643891e+06 4.865423e+04 0.000000e+00 1725s
79473 7.3676351e+06 2.691312e+04 0.000000e+00 1730s
82353 7.3773648e+06 1.823674e+04 0.000000e+00 1735s
85233 7.3780662e+06 1.548992e+04 0.000000e+00 1740s
88113 7.3851088e+06 2.292992e+04 0.000000e+00 1745s
90513 7.3960382e+06 1.951552e+04 0.000000e+00 1750s
92273 7.3960551e+06 3.617315e+05 0.000000e+00 1755s
94193 7.3961473e+06 1.006320e+04 0.000000e+00 1760s
95943 7.4027889e+06 7.948342e+03 0.000000e+00 1765s
97543 7.4116809e+06 5.452327e+04 0.000000e+00 1770s
99143 7.4117267e+06 1.693707e+04 0.000000e+00 1775s
100903 7.4150966e+06 1.000090e+04 0.000000e+00 1780s
102503 7.4213874e+06 1.164586e+04 0.000000e+00 1785s
104263 7.4216349e+06 7.158157e+03 0.000000e+00 1790s
105863 7.4330180e+06 2.049030e+04 0.000000e+00 1795s
107623 7.4420647e+06 9.693165e+03 0.000000e+00 1800s
109223 7.4430936e+06 1.530564e+04 0.000000e+00 1805s
110823 7.4510618e+06 5.057497e+04 0.000000e+00 1811s
112103 7.4510772e+06 1.726800e+04 0.000000e+00 1815s
113543 7.4511787e+06 3.256365e+04 0.000000e+00 1820s
114823 7.4512506e+06 2.211874e+04 0.000000e+00 1825s
116263 7.4514030e+06 4.169719e+04 0.000000e+00 1831s
117703 7.4592767e+06 1.215550e+04 0.000000e+00 1835s
119143 7.4593614e+06 2.414930e+04 0.000000e+00 1840s
120423 7.4604247e+06 1.909527e+04 0.000000e+00 1845s
121703 7.4630317e+06 1.284191e+05 0.000000e+00 1850s
123143 7.4630507e+06 1.543057e+04 0.000000e+00 1855s
124583 7.4657003e+06 7.221221e+03 0.000000e+00 1860s
125703 7.4675025e+06 9.361682e+03 0.000000e+00 1865s
127303 7.4697760e+06 1.812158e+06 0.000000e+00 1871s
128743 7.4698276e+06 2.949619e+04 0.000000e+00 1875s
130183 7.4698571e+06 2.005990e+04 0.000000e+00 1880s
132263 7.4699287e+06 1.721648e+05 0.000000e+00 1885s
134343 7.4699646e+06 6.624768e+04 0.000000e+00 1890s
136583 7.4700359e+06 2.970284e+04 0.000000e+00 1895s
138663 7.4701131e+06 3.230538e+04 0.000000e+00 1900s
140903 7.4701421e+06 1.192831e+05 0.000000e+00 1905s
142983 7.4702241e+06 1.629243e+05 0.000000e+00 1910s
145223 7.4703312e+06 1.555199e+05 0.000000e+00 1915s
147303 7.4703621e+06 5.078687e+04 0.000000e+00 1920s
149223 7.4705393e+06 3.791616e+05 0.000000e+00 1926s
150823 7.4705885e+06 1.961377e+04 0.000000e+00 1930s
152583 7.4707796e+06 5.350040e+05 0.000000e+00 1935s
154663 7.4708473e+06 2.460007e+04 0.000000e+00 1940s
156423 7.4708769e+06 1.223090e+05 0.000000e+00 1945s
158023 7.4710746e+06 1.382798e+04 0.000000e+00 1950s
159463 7.4712986e+06 2.784949e+04 0.000000e+00 1955s
160903 7.4713067e+06 9.010117e+03 0.000000e+00 1960s
162503 7.4753147e+06 9.372160e+04 0.000000e+00 1965s
163783 7.4779685e+06 1.024664e+04 0.000000e+00 1970s
165223 7.4784959e+06 6.708829e+03 0.000000e+00 1975s
166503 7.4786631e+06 1.256998e+05 0.000000e+00 1981s
167463 7.4786736e+06 4.367342e+04 0.000000e+00 1985s
168743 7.4787035e+06 1.334288e+05 0.000000e+00 1991s
170183 7.4787344e+06 7.140629e+03 0.000000e+00 1995s
171623 7.4791792e+06 1.004817e+04 0.000000e+00 2000s
173063 7.4792811e+06 6.341849e+03 0.000000e+00 2005s
174503 7.4797263e+06 1.307112e+04 0.000000e+00 2010s
176103 7.4801528e+06 1.224069e+06 0.000000e+00 2015s
177543 7.4801612e+06 5.499356e+04 0.000000e+00 2020s
179143 7.4802213e+06 4.951459e+03 0.000000e+00 2025s
181543 7.4806184e+06 1.140811e+06 0.000000e+00 2030s
184035 7.4810977e+06 7.883726e+05 0.000000e+00 2035s
186433 7.4811834e+06 1.277964e+05 0.000000e+00 2040s
188513 7.4812180e+06 4.392845e+04 0.000000e+00 2045s
190753 7.4814987e+06 2.437729e+03 0.000000e+00 2050s
192993 7.4815933e+06 1.301937e+04 0.000000e+00 2055s
195233 7.4816816e+06 5.943953e+03 0.000000e+00 2060s
197313 7.4816958e+06 2.128212e+05 0.000000e+00 2065s
199553 7.4817372e+06 7.321225e+03 0.000000e+00 2070s
201633 7.4817521e+06 9.416018e+03 0.000000e+00 2075s
204193 7.4818773e+06 4.167227e+03 0.000000e+00 2080s
206433 7.4819632e+06 1.863947e+04 0.000000e+00 2085s
208836 7.4825440e+06 1.133435e+04 0.000000e+00 2090s
211556 7.4830168e+06 3.852471e+04 0.000000e+00 2095s
214960 7.4835902e+06 0.000000e+00 0.000000e+00 2098s
217300 7.4835044e+06 0.000000e+00 3.076134e+06 2100s
222760 7.4832633e+06 0.000000e+00 9.534599e+05 2105s
228415 7.4830124e+06 0.000000e+00 1.179661e+05 2110s
230147 7.4835902e+06 0.000000e+00 0.000000e+00 2112s
Extra simplex iterations after uncrush: 15187
Root relaxation: objective 7.483590e+06, 230147 iterations, 441.99 seconds (773.96 work units)
Total elapsed time = 2150.70s
Total elapsed time = 2485.23s
Total elapsed time = 2505.77s
Total elapsed time = 2540.50s
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 7483590.20 0 21164 1.7059e+07 7483590.20 56.1% - 2551s
0 0 7489125.86 0 21045 1.7059e+07 7489125.86 56.1% - 3247s
H 0 0 1.079487e+07 7489125.86 30.6% - 3293s
0 0 7490019.95 0 19061 1.0795e+07 7490019.95 30.6% - 3398s
0 0 7494669.25 0 17687 1.0795e+07 7494669.25 30.6% - 3608s
0 0 7494880.88 0 17810 1.0795e+07 7494880.88 30.6% - 3743s
0 0 7494898.17 0 18144 1.0795e+07 7494898.17 30.6% - 3816s
0 0 7494901.34 0 18928 1.0795e+07 7494901.34 30.6% - 3859s
0 0 7494901.87 0 18531 1.0795e+07 7494901.87 30.6% - 3886s
0 0 7495087.98 0 18811 1.0795e+07 7495087.98 30.6% - 4506s
0 0 7495147.33 0 18439 1.0795e+07 7495147.33 30.6% - 4751s
0 0 7495166.42 0 19622 1.0795e+07 7495166.42 30.6% - 4916s
0 0 7495170.40 0 19739 1.0795e+07 7495170.40 30.6% - 4987s
0 0 7495170.97 0 20106 1.0795e+07 7495170.97 30.6% - 5032s
0 0 7495218.02 0 19752 1.0795e+07 7495218.02 30.6% - 5602s
0 0 7495229.01 0 21024 1.0795e+07 7495229.01 30.6% - 5788s
0 0 7495231.47 0 21199 1.0795e+07 7495231.47 30.6% - 5921s
0 0 7495250.00 0 19890 1.0795e+07 7495250.00 30.6% - 6385s
0 0 7495259.82 0 20106 1.0795e+07 7495259.82 30.6% - 6600s
0 0 7495264.24 0 21385 1.0795e+07 7495264.24 30.6% - 6750s
0 0 7495265.55 0 21767 1.0795e+07 7495265.55 30.6% - 6871s
0 0 7495281.74 0 20686 1.0795e+07 7495281.74 30.6% - 7354s
0 0 7495281.74 0 20685 1.0795e+07 7495281.74 30.6% - 7473s
H 0 0 1.004149e+07 7495281.74 25.4% - 7933s
H 0 0 9902820.0667 7495281.74 24.3% - 7997s
H 0 0 9902764.5364 7495281.74 24.3% - 7999s
0 2 7495281.75 0 20685 9902764.54 7495281.75 24.3% - 8067s
1 4 7495281.78 1 20561 9902764.54 7495281.75 24.3% 1289 8291s
3 8 7495305.63 2 20783 9902764.54 7495281.78 24.3% 36426 10465s
7 14 7495322.05 3 23059 9902764.54 7495305.63 24.3% 88182 14818s
15 24 7495334.47 4 24143 9902764.54 7495322.05 24.3% 99160 23556s
25 29 7499560.32 5 25797 9902764.54 7495334.47 24.3% 131341 54000s
Cutting planes:
Learned: 2
Gomory: 61
Lift-and-project: 3
Cover: 20645
Implied bound: 780
Clique: 10878
MIR: 14810
StrongCG: 4459
Flow cover: 37856
GUB cover: 19
Zero half: 1978
RLT: 5676
Relax-and-lift: 546
BQP: 1
PSD: 39
Explored 32 nodes (5644331 simplex iterations) in 54003.53 seconds (59248.71 work units)
Thread count was 10 (of 12 available processors)
Solution count 10: 9.90276e+06 9.90282e+06 1.00415e+07 ... 1.70608e+07
Time limit reached
Best objective 9.902764536428e+06, best bound 7.495334474667e+06, gap 24.3107%
07:59:53-WARNING-Loading a SolverResults object with an 'aborted' status, but containing a solution
0
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Hi Sophie,
This is a huge model!
Some comments on your current parameter settings:
- The combination of Presolve=2 PreSparsify=1 looks like a very good choice because presolve is able to greatly reduce the size of your model (especially the nonzeros) in little more than 1000s, so I would definitely keep these parameters.
- Method=1: this forces Gurobi to use dual simplex to solve the root node. I would rather keep this one as default or use Method=3 in order to run primal simplex, dual simplex and barrier at the same time.
- MIPFocus=3: this makes Gurobi focus on improving the bound. I can see that the bound improves very slowly, but it is also possible that the bound is very good and doesn't have to be improved that much (depending on the formulation). Do you have an idea of what needs to be improved, whether the incumbent or the bound? If the bound is already very good, then I would rather use MIPFocus=1. Maybe you can guess which needs to be improved (incumbent or bound) from running your monthly model and applying the results to your yearly model.
The NoRel heuristic seems to be very successful, but you may improve the incumbent even more by increasing NoRelHeurTime.
Some other parameters I would test:
- DegenMoves=0. Because of the "Total elapsed time" messages after solving the root relaxation.
- NodeMethod=2. The number of iterations per node (column It/Node) is huge. Trying barrier for the nodes might help decrease this.
You can try our automatic tuner on one of your smaller models to find parameters and apply them to your larger model.
Best regards,
Elisabeth
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