MIQP Model taking forever to compute
AnsweredHello!
I am trying to run an MIQP model with indicator constraints and it is taking forever to compute. I have already let it run for 4 days nonstop and still could not get it solved. Please find the .mps file on the following link: https://drive.google.com/file/d/1wcl_jurd4sbm4qCAi9PUjL67sYfe1yMT/view?usp=sharing
I understand that the model size is fairly large. It has:
Model has 5024 quadratic objective terms
Model has 4632 general constraints
Variable types: 3015 continuous, 1544 integer (1544 binary)
And the Objective function has bilinear terms.
However, the coefficient statistics do not look that bad:
Coefficient statistics:
Matrix range [9e06, 2e+01]
Objective range [2e04, 2e+02]
QObjective range [2e04, 2e+01]
Bounds range [1e+00, 2e+04]
RHS range [6e02, 5e+02]
GenCon rhs range [6e02, 1e+02]
GenCon coe range [9e06, 2e+01]
So, my question is: Is this issue a fundamental issue of scaling in which Gurobi can't really help OR am I getting this issue due to some numerical or modelling error. Any help would be appreciated.
P.S. One of the continuous variable is negative while others are nonnegative. If I make all of them nonnegative, then it is solved (although also in quite some time) but I would really need that variable to be negative.
P.S.2 Can you please let me know once you have accessed the .mps file. I will remove it from the link afterwards.

Hi,
The model numerics are not great mainly because the coefficient matrix spans over a wide range of 7 orders of magnitude. However, using Gurobi version 11.0.3 and NoRelHeurTime=60, the gap is around 8.4% in 2 minutes. Do you want to solve the model to optimality?
You can consider experimenting with different combinations of the parameters below:
 Increase the NoRelHeurTime parameter value
 Presolve=2
 PreSparsify=1
 ScaleFlag=2
 Cuts=23
 MIPFocus=2
Best regards,
Maliheh
0 
Hello Maliheh,
Thanks for the reply. The coefficient matrix only starts from 9e6 which is almost 1e5. Do you still think that it is a serious issue?
I have already experimented with NoRelHeurTime parameter. It does help in finding good feasible solutions but the optimality is not proved.
MIPFocus=2 also doesn't change a lot.I will try the other parameters.
The optimality gap of 8% does not really tell anything in this case. I will be needing something more like 0.1%. Is there anything more that can be done?
Thanks in advance!
RegardsGaurav
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The coefficient matrix only starts from 9e6 which is almost 1e5. Do you still think that it is a serious issue?
As explained in the Gurobi Numerical Guidelines section "Advanced User Scaling," we ideally prefer the matrix coefficient range to be within six orders of magnitude or less, specifically between 1e3 and 1e6. There is no warning message in the log indicating that this is causing a numerical issue. However, better model numerics typically lead to better performance.
Is there anything more that can be done?
Based on the runs I conducted, the bottleneck in closing the gap appears to be slow progress in improving the best bound. The parameters previously shared focus on model strengthening and generating cutting planes more aggressively. You can add the parameters VarBranch=3 and BranchDir=11 to the previous list to experiment with.
Other suggestions include:
 Define the tightest possible lower and upper bounds for all variables participating in the bilinear terms.
 Consider potential reformulation ideas, if possible, to reduce the number of bilinear terms.
Maliheh
0
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