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Re: [Help-glpk] Glpk Enhancement Request: Terminate on MIP gap tolerance

From: Stefan Vigerske
Subject: Re: [Help-glpk] Glpk Enhancement Request: Terminate on MIP gap tolerance
Date: Tue, 9 Oct 2007 22:25:52 +0400


but how do I terminate at a gap tolerance if I use the advanced B&B 
solver that does not support function callbacks (to my knowledge)?
You once replied this question 
by proposing to add a few lines of code into the B&B main loop, but then 
one have to recompile glpk everytime one wants to change the tolerance, 
and one would need to modify GLPK for every new release.

So I agree with Michael Drew (and others) that having a parameter for 
the relative mip gap would be a valuable feature. Setting TOLOBJ might 
by a way to do this (?), but there is a warning in the documentation 
that one shouldn't change it, and in the code you forbid to set it to a 
value larger than 0.001.
However, often, esp. when a MIP is solved as a subproblem (e.g., in a 
B&B or OA code for MINLPs), it is desirable to get quick some solution 
for a MIP that do not need to be very close to the global minimum (e.g., 
because the problem that is solved is just an approximation), so having 
a convenient way to run GLPK with a large mip gap tolerance (0.1, 0.5, 
or even 1) would make much sense.

Another (maybe related) question:
Is there a way to obtain the best lower bound (in a minimization sense) 
after GLPKs advanced B&B terminates?


Stefan Vigerske
Humboldt University Berlin, Numerical Mathematics

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