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[Help-glpk] Using branch and cut starting with relaxed solution

From: Joey Rios
Subject: [Help-glpk] Using branch and cut starting with relaxed solution
Date: Wed, 17 Dec 2008 09:37:25 -0800

I know this has been asked in different ways, but I haven't gotten a clear sense of what to do from those previous posts.

I have a relaxed solution to a binary integer program.  In most of my cases, well over 90% of the variables are already binary.  I'd like to use the branch and bound/cut code already in GLPK to get to an integer solution.

The main problem I have is that I didn't arrive at the relaxed solution through a standard glp_simplex() call, so I don't have a basis ready, else I'd just call glp_intopt() and see what happens.

So I guess I have a few questions:

1.  What would be the method for creating a basis in this case?  I assume all of the binary variables with non-binary values would need to be basic, but after that how do I decide which other variables are basic just given their values from my relaxed solution?

2.  I have the reference manual for version 4.34 in front of me.  Should/can I just use the branch-and-cut API directly somehow?  If so, how should I go about using my relaxed solution as a starting point?

3.  Given what I've described, is there something else I should try?

Any advice appreciated.  I can provide further details if they'd be helpful.  Thanks.

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