How does the "ScaleFlag" option work?

Answered

Fabio David

May 15, 2023 13:50

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Using grbtune to analyze my problem, it suggested using the option ScaleFlag=1. This significantly reduced the execution time for solving it.

Looking at the documentation on Gurobi site, it was not clear to me what exactly this option does, nor the difference when setting other values different from 1.

Where can I find more detailed documentation?

Thanks in advance,
Fabio

Related to

• Scaling

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  Maliheh Aramon

  • Gurobi Staff

  May 15, 2023 22:32

  Hi Fabio, 

  The available settings of the ScaleFlag parameter briefly means:

  • -1: Auto
  • 0: No scaling
  • 1: equilibrium scaling (First scale each row to make its largest nonzero entry to be magnitude one, then scale each column to max-norm 1)
  • 2: geometric scaling
  • 3: multi-pass equilibrium scaling

  You can learn more about different strategies for scaling linear optimization problems in the paper titled "Scaling linear optimization problems priori to application of the simplex method". 

  We intentionally do not include extensive details in the documentation because it may confuse a general user or it may be hard to explain the effect of each option precisely on the solver performance. 

  Best regards,

  Maliheh

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  Fabio David

  May 16, 2023 13:13

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  Hi Maliheh,

  Thank you for your quick response. I had checked out this option on https://www.gurobi.com/documentation/9.5/refman/scaleflag.html. However, the reference documentation for version 10.0 is much more complete.

  Thanks again, I will read the suggested article.

  Regards,
  Fabio

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  jake roth

  October 17, 2023 17:43

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  Thanks for the detail on how the `equilibrium scaling` option works! Are you able to share a high-level overview of the geometric mean scaling (option = 2)?

  --Jake

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  Robert Fourer

  October 19, 2023 18:53

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  In J.A. Tomlin, "On Scaling Linear Programming Problems," Mathematical Programming Study 4 (1975) 146-166, geometric mean scaling is defined as follows:

  

  Gurobi may be doing something of this sort. Computing the actual geometric mean of all the magnitudes in a row or column would introduce some time-consuming complications.

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