Trilinear terms in objective function
AnsweredHi,
I try to model a network where the users' heat demand is (m * t) = q. q is negtive and shall be minimized.
Bounds of m are [10, 0] and bounds of t are [350, 270].
Bounds of q are [-10000, 0].
m, t and q are continuous variables.
Additionally, there shall be a minimum pressure(p) at the inlet of the users edge which shall be not below the value p_min.
p - p_min >= 0. Logically, the constraint m * (p - p_min) >= 0 should force m to be zero if p < p_min?
My objective function is min (sum(q)).
Somehow, gurobi throws an infeasible at once. I am sure my bounds are correct and the rest of the model, as well. The model is running to optimality if I leave out the constraint of m * (p - p_min) >= 0.
I also tried to define a binary ind_p [0,1] with the bigM approach. ind_p is 1 if p >= p_min and 0 if p < p_min.
Therefore, I changed the objective function to
min (sum(q * ind_p))
and deleted the constraint m * (p - p_min) >= 0.
This also leads to infeasibility. I wonder if gurobi is able to optimize "trilinear" terms as m * t * ind_p = q and if not how to relax the problem to make it work.
Thank's.
Cheers Johannes
Ps.: Example .mps for the first approach is in sp70rp50 - m_(p-pmin).mps
Example .mps for the second approach is in sp70rp50 q_ind_p.mps
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Hi Johannes,
The Knowledge Base article How do I determine why my model is infeasible? and How do I model multilinear terms in Gurobi? should be helpful.
Best regards,
Jaromił0 -
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Dear Jaromił,
thank you for your comment. I have used the approach of "How do I model multilinear terms in Gurobi" where it was meaningful, so far.
The results of computeIIS() show that my bounds should not be the problems. However, I can not determine the infeasibility through it.
I added two links to a minimal network maybe that can help to find a solution for the problem.
Best regards,
Johannes
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When working with nonconvex models, you should provide tight bounds to all variables participating in nonconvex terms. So it is best to set a tight lower bound for all \(\texttt{div_F0XXX_to_F0XXX}\) variables.
If the iis is not too big, could you pelase post it or attach it as you did with your other files?
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Hi,
changing the bounds on "div" will also not lead to a feasibility.
Here you will find the computeIIS() *.ilp files:
sp70rp50 - m_(p-pmin).ilp = https://cloud.hawk.de/index.php/s/TGraNz885HFajzX
sp70rp50 - q_ind_p.ilp = https://cloud.hawk.de/index.php/s/cE2aiqLqQ9B4QDN
I also added the problem without included p-restrictions to show that the bounds on p are correct. The following model is just calculating the pressures losses without including them in the objective function nor in any restricting constraints.
sp70rp50.mps = https://cloud.hawk.de/index.php/s/NSSHanoWSqFS6id
sp70rp50.sol = https://cloud.hawk.de/index.php/s/NkoReWbnENdmepT
Best regards,
Johannes
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Hi Johannes,
Did you try the feasRelax approach, cf. How do I determine why my model is infeasible? Maybe this gives a simpler hint of what is going wrong.
Best regards,
Jaromił0 -
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Dear Jaromil,
Thank you for helping! It turned out that changing m^2 that occurres in one constraint to a new variable m2=m*m solved the issue. However the inequality constraint still does not work. I will go with the binary formulation and the m2 approach.
Cheers,
Johannes0 -
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