Feasibility issue when widening bounds on a variable in .mps file

[yellowdrac]

Hi, and thank you for your work on HiGHS!

I'm working with two .mps files generated via h.writeModel(). These two models are nearly identical, with one key difference: the bounds on a specific variable (column) differ slightly between them.

Case A:
Variable has lower bound = -0.06

Variable has upper bound = -0.06 (i.e., fixed value)

This case produces a feasible solution (within reasonable solve time)

CaseB
Same variable now has lower bound = -0.3

Upper bound remains -0.06 (i.e., a wider feasible range)

This case results in an infeasible solution

My expectation was that, by allowing the variable more freedom (a wider range), the problem would remain feasible or even improve. However, the opposite occurs.

My question:

Why would relaxing the bounds on a variable (i.e., increasing the feasible region) cause infeasibility?

I'm sharing the mps files as .txt if helpful.

OBEN3-8COILS-IN METERS-24072-60sf.txt
OBEN3-8COILS-IN METERS-INF-300sf.txt

Thanks in advance for any guidance!

[jajhall]

These problems are nasty numerically

Coefficient ranges:
Matrix [6e-02, 3e+04]
Cost [1e+00, 3e+00]
Bound [1e+00, 2e+09]
RHS [1e+00, 2e+09]

In particular, you have dangerously large bounds. I've tested with a commercial solver, and it gets an optimal solution for OBEN3-8COILS-IN METERS-24072-60sf and OBEN3-8COILS-IN METERS-INF-300sf, but observes that integrality, as well as the variable and constraint bounds, are all violated by more than the default tolerances. Hence the problems may be close to being infeasible - or even infeasible - if the tolerances are to be respected.

Although the slightly relaxed problem (OBEN3-8COILS-IN METERS-INF-300sf) should be feasible if OBEN3-8COILS-IN METERS-24072-60sf is feasible, both problems are in the territory where there's a big chance of something going wrong when solving them.

[jajhall]

Interestingly, the commercial solver that reports all the tolerance violations gets an objective value of 24.072, whereas HiGHS on OBEN3-8COILS-IN METERS-24072-60sf claims optimality with an objective of 32.074, but no tolerance violations. It's clearly a nasty problem numerically.

Your question has exposed #2460 and, once I've fixed this, I should be able to experiment with your model using better scaling of the variables.

In the meantime, perhaps you could see whether you could change some of the units of variables/constraints in your model so that the bounds are reduced. It's should to improve solver performance, as well as reduce the chance of anomalies.

[odow]

Hi @yellowdrac, I wrote a tutorial for the JuMP documentation that you should read: https://jump.dev/JuMP.jl/stable/tutorials/getting_started/tolerances/

[yellowdrac]

Awesome, I'll check it out.