About how to optimize the solver's speed for large optimization.

I am running a large optimization problem for task scheduling. The ILP problem seems fine for 8-10 days of task scheduling. But when I run it for 31 days. It has taken so long, and still cannot reach any solution. Since I set a termination time, it just stops and reports no solution found yet. I used parameters

schedule_model.setParam('MIPGap', 0.1)
schedule_model.setParam('Timelimit', 100000)

I copy and pasted the solver's outcome below. Please let me know if there is any parameter we can set to expedite this process. Or should I simply wait for longer days for solutions? Many thanks!

Optimize a model with 4443771 rows, 17335093 columns and 151138704 nonzeros
Model fingerprint: 0xa20a9992
Variable types: 0 continuous, 17335093 integer (17335093 binary)
Coefficient statistics:
  Matrix range     [1e+00, 2e+04]
  Objective range  [6e-01, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+00, 2e+04]
Presolve removed 0 rows and 0 columns (presolve time = 13s) ...
Presolve removed 0 rows and 0 columns (presolve time = 16s) ...
Presolve removed 0 rows and 10743920 columns (presolve time = 23s) ...
Presolve removed 71629 rows and 10743920 columns (presolve time = 28s) ...
Presolve removed 71755 rows and 10744046 columns (presolve time = 40s) ...
Presolve removed 71755 rows and 10744046 columns (presolve time = 48s) ...
Presolve removed 71755 rows and 10744046 columns (presolve time = 50s) ...
Presolve removed 71755 rows and 10744046 columns (presolve time = 56s) ...
Presolve removed 71755 rows and 10744046 columns (presolve time = 68s) ...
Presolve removed 71755 rows and 10744046 columns (presolve time = 76s) ...
Presolve removed 71755 rows and 10744046 columns (presolve time = 97s) ...
Presolve removed 71755 rows and 10744046 columns (presolve time = 131s) ...
Presolve removed 71755 rows and 10744046 columns (presolve time = 139s) ...
Presolve removed 71755 rows and 10744046 columns (presolve time = 158s) ...
Presolve removed 156759 rows and 10744046 columns (presolve time = 164s) ...
Presolve removed 156759 rows and 10744046 columns (presolve time = 176s) ...
Presolve removed 156759 rows and 10744046 columns (presolve time = 188s) ...
Presolve removed 156759 rows and 10744046 columns (presolve time = 190s) ...
Presolve removed 156759 rows and 10744046 columns (presolve time = 206s) ...
Presolve removed 162713 rows and 10750000 columns (presolve time = 217s) ...
Presolve removed 239270 rows and 10826557 columns (presolve time = 230s) ...
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Presolve removed 311260 rows and 11334974 columns (presolve time = 770s) ...
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Presolve removed 311260 rows and 11512791 columns (presolve time = 1425s) ...
Presolve removed 506680 rows and 11514519 columns (presolve time = 1431s) ...
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Presolve removed 531785 rows and 11514521 columns (presolve time = 1536s) ...
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Presolve removed 575539 rows and 11541294 columns (presolve time = 1888s) ...
Presolve removed 572531 rows and 11538286 columns
Presolve time: 1888.52s
Presolved: 3871240 rows, 5796807 columns, 97758679 nonzeros
Variable types: 0 continuous, 5796807 integer (5795527 binary)
Deterministic concurrent LP optimizer: primal simplex, dual simplex, and barrier
Showing barrier log only...

Root barrier log...

Ordering time: 2.97s

Barrier statistics:
 Dense cols : 5652
 AA' NZ     : 3.619e+07
 Factor NZ  : 1.059e+08 (roughly 2.3 GB of memory)
 Factor Ops : 3.683e+11 (roughly 7 seconds per iteration)
 Threads    : 17

                  Objective                Residual
Iter       Primal          Dual         Primal    Dual     Compl     Time
   0   3.88467558e+03 -6.75909235e+04  6.10e+04 2.19e-01  1.07e+02  2220s
   1   2.46095013e+03 -2.20866878e+06  3.35e+04 5.88e-01  5.76e+01  2224s
   2   1.53019190e+03 -3.08473758e+06  1.67e+04 2.65e-01  2.86e+01  2227s
   3   1.16580986e+03 -3.09383474e+06  1.02e+04 1.13e-01  1.75e+01  2230s
   4   6.61563010e+02 -2.43557956e+06  1.44e+03 1.03e-01  2.70e+00  2235s
   5   4.82038853e+02 -1.44432898e+06  7.05e+02 4.51e-02  1.26e+00  2238s
   6   3.57552891e+02 -1.02838037e+06  2.60e+02 2.87e-02  5.38e-01  2242s
   7   3.26000950e+02 -3.41486603e+05  1.01e+02 1.41e-02  1.86e-01  2245s
   8   3.19061986e+02 -1.15607495e+05  3.72e+01 3.73e-03  6.43e-02  2248s
   9   3.34097824e+02 -9.30188749e+04  1.67e+01 2.89e-03  3.62e-02  2252s
  10   3.46336249e+02 -4.58373903e+04  1.03e+01 1.27e-03  1.97e-02  2255s
  11   3.47558388e+02 -2.48572482e+04  5.68e+00 6.04e-04  1.06e-02  2259s
  12   3.26685305e+02 -9.76206900e+03  1.14e+00 2.07e-04  2.95e-03  2262s
  13   2.97099999e+02 -7.72477620e+03  5.85e-01 1.69e-04  2.03e-03  2265s

  14   2.86528601e+02 -5.67219772e+03  4.74e-01 1.28e-04  1.55e-03  2269s
  15   2.65563962e+02 -5.20397088e+03  3.43e-01 1.18e-04  1.33e-03  2273s

Barrier performed 15 iterations in 2273.13 seconds (1359.74 work units)
Barrier solve interrupted - model solved by another algorithm

Concurrent spin time: 96.89s (can be avoided by choosing Method=3)

Solved with dual simplex

Root simplex log...

Iteration    Objective       Primal Inf.    Dual Inf.      Time
  106708    1.7308972e+02   0.000000e+00   0.000000e+00   2277s

Use crossover to convert LP symmetric solution to basic solution...

Root crossover log...

   20770 DPushes remaining with DInf 1.6431239e-04              2289s
    2035 DPushes remaining with DInf 1.3947156e-04              2291s
       0 DPushes remaining with DInf 1.3947156e-04              2292s

   33190 PPushes remaining with PInf 0.0000000e+00              2293s
   14421 PPushes remaining with PInf 6.1546377e-05              2295s
       0 PPushes remaining with PInf 5.0968885e-05              2299s

  Push phase complete: Pinf 5.0968885e-05, Dinf 1.2611250e+02   2300s


Root simplex log...

Iteration    Objective       Primal Inf.    Dual Inf.      Time
  159549    1.7308972e+02   0.000000e+00   1.261125e+02   2305s
  159982    1.7308972e+02   5.096889e-05   0.000000e+00   2310s
  159996    1.7308972e+02   0.000000e+00   0.000000e+00   2317s
  159996    1.7308972e+02   0.000000e+00   0.000000e+00   2328s

Root relaxation: objective 1.730897e+02, 159996 iterations, 361.60 seconds (165.25 work units)
Total elapsed time = 2336.71s
Total elapsed time = 2423.60s
Total elapsed time = 2482.18s
Total elapsed time = 2522.27s
Total elapsed time = 2566.19s

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0  173.08972    0 8385          -  173.08972      -     - 3112s
     0     0  325.50076    0 21525          -  325.50076      -     - 29949s
     0     0  325.50076    0 21039          -  325.50076      -     - 30025s
     0     0  325.50076    0 20915          -  325.50076      -     - 30066s

Cutting planes:
  Learned: 1149
  Gomory: 61
  Cover: 936
  Clique: 3182
  MIR: 8
  Flow cover: 357
  GUB cover: 478
  Zero half: 211
  RLT: 10
  Relax-and-lift: 11
  BQP: 74

Explored 1 nodes (702894 simplex iterations) in 100004.53 seconds (78595.89 work units)
Thread count was 20 (of 40 available processors)

Solution count 0

Time limit reached
Best objective -, best bound 3.255250000000e+02, gap -
CPU times: total: 1d 11h 13min 4s
Wall time: 1d 3h 46min 44s

Jaromił Najman

Gurobi Staff

April 24, 2023 07:20

Which version of Gurobi did you use? Please always use the latest version (currently 10.0.1).

You could try telling Gurobi to focus more on feasible points via the parameters MIPFocus=1 and by using the No Relaxation heuristic controlled by the NoRelHeurTime parameter. From the log, I would try setting NoRelHeurTime=3600 as a first experiment. You could also have a look at the list of Most important parameters for MIPs.

Please note that your model is really huge with over 17 million binary variables. Thus, it is somewhat expected that solution will take more that usual. Anyway, there is one thing which is suspicious. The big gap without any log output

  0     0  173.08972    0 8385          -  173.08972      -     - 3112s
                                             27k seconds without log output
  0     0  325.50076    0 21525          -  325.50076      -     - 29949s
[...]
  0     0  325.50076    0 20915          -  325.50076      -     - 30066s
-> jump to time limit of 100k seconds, i.e., 70k seconds no output.

Could you please share this model such that I could have a closer look? Note that uploading files in the Community Forum is not possible but we discuss an alternative in Posting to the Community Forum.

Best regards,
Jaromił

whwhwh55

April 24, 2023 12:00

Thank you! Let me first make a saved model to . mps file as soon as I can and then figure out how to share it to community with your link.

April 26, 2023 03:12

Do you expect to see the .mps model or the code to generate the model? The .mps model is 5.5GB. If it is too large, I have to schedule a shorter period so that you may just scan it for potential problems..

April 26, 2023 06:43

If you can reproduce the behavior where there is no output for a very long period of time with a smaller model, then a smaller model would definitely suffice.

Otherwise, you could just compress the .mps file. Size of the model is not a problem on my side as long as I can reproduce the issue, so you don't have to share your code.

April 27, 2023 01:14

Great. the zipped file is around 550MB. I hope I can upload from here.

April 27, 2023 15:55

The mode is uploaded to this dropbox link:

https://www.dropbox.com/s/yujwy4h6oyu9xzd/workindv_model.zip?dl=0

Many thanks

April 28, 2023 07:22

Unfortunately, I am not able to expand the file. I get the error

Unable to expand "workindv_model.zip" into "Downloads"
(Error 79 - inappropriate file type or format.)

Also automatic extracting in dropbox results in an error

1 file couldn't be automatically unzipped.

Could you please try again?

April 28, 2023 14:08

I apologize for the inconvenience. I put an unzip version and please see if it works. I also set the Dropbox access permission for anyone beyond our university scope.

https://www.dropbox.com/s/a1c8khi9nw5c6rz/workindv_model.mps?dl=0

Thank you so much for the great patience with me!

May 02, 2023 07:41

I was able to reproduce the issue on my side and am investigating. Unfortunately, at this point I cannot tell whether it is an actual bug or just expected behavior due to the model size. I will let you know here, when I find something.

It definitely looks like finding a first feasible point is a big issue for this model. You could try running NoRelHeurTime=20000 which will run a special heuristic before solving the root node relaxation for 20k seconds (1/5th of your overall time). Maybe the heuristic is able to find a first feasible solution and the overall optimization run is then better.

Thomas Leveringhaus

May 02, 2023 09:52

Reading this topic, it came to my mind that lazy constraints or the partition heuristic might help address the problem?

May 02, 2023 15:14

Thank you, Jaromil, I will try the heuristics.

Thoms, do you have any guidance tuning the lazy constraints and partition heuristic?

May 02, 2023 16:28

Hi whwhwh55,
besides the official gurobi articels I don't have additional guidance:

Lazy constraints:
https://support.gurobi.com/hc/en-us/articles/360013197972
https://www.gurobi.com/documentation/10.0/refman/lazy.html#attr:Lazy
Since your problem has a lot of (linear) constraints, some of them might be inactive and may remain in the lazy constraint pool, for example constraints for rare special cases of your task scheduling. But this is just a guess - I don't know your problem.

Partition Heuristic:
https://www.gurobi.com/documentation/10.0/refman/partition.html
I don't know your problem, so I don't know if your vars can be splitted into different groups.

Maybe spending more time for presolve could also help:
https://www.gurobi.com/documentation/10.0/refman/presolve.html#parameter:Presolve

May 02, 2023 17:47

Thank you!

About how to optimize the solver's speed for large optimization.

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