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Efficiency of solving LP relaxation

up vote 14 down vote favorite

I'm building a mixed-integer programming model, and the solver is experiencing a very long run time. So I tried to solve the LP relaxation to the MIP, and I get a similarly long solve time, which surprises me. I was wondering what might make an LP take a long time to solve, without any integrality constraints.

2 Answers

up vote 4 down vote accept

If LP takes a long time to solve, you can check a couple of things:

1) How large is the problem? Large LPs (>1 million variables/constraints on a ballpark) can take a long time.

2) How large is the range of coefficients in the objective function and constraints? Having a large range of the coefficients typically hurts computational performance.

up vote 3 down vote

Highly degenerate LP's can be very hard to solve using the simplex method and much easier to solve using an interior point method. It's possible that your LP relaxation has this issue.


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Efficiency of solving LP relaxation

up vote 14 down vote

I'm building a mixed-integer programming model, and the solver is experiencing a very long run time. So I tried to solve the LP relaxation to the MIP, and I get a similarly long solve time, which surprises me. I was wondering what might make an LP take a long time to solve, without any integrality constraints.


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up vote 9 down vote

If LP takes a long time to solve, you can check a couple of things:

1) How large is the problem? Large LPs (>1 million variables/constraints on a ballpark) can take a long time.

2) How large is the range of coefficients in the objective function and constraints? Having a large range of the coefficients typically hurts computational performance.

edit

I'd add 3) how dense is the problem? Size alone is not that big of a problem, if the constraint matrix is sparse. - Michael Feldmeier Jun 18 at 17:25

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