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[Help-glpk] Solve subproblem then use sol'n in larger problem

From: Joey Rios
Subject: [Help-glpk] Solve subproblem then use sol'n in larger problem
Date: Fri, 8 Feb 2008 12:19:34 -0800


For my particular problem, I have a method for obtaining a feasible, sub-optimal solution using GLPK.  I do this by creating a subproblem that optimizes the 'tricky' parts of the problem.  It's usually within 10-20% of optimal and can be found 10-20X faster than solving the larger problem optimally.  What I would like to start doing is using this solution as a starting point for the larger optimization problem.   Basically, I am asking here if it sounds as if I am thinking about my approach correctly.

All of the variables in the subproblem will have the same name in the larger problem.  The variables that are missing from the subproblem that are present in the larger problem will have known values that keep the problem feasible (essentially all of the binary vars would be '1' if they weren't in the subproblem). 

So what I am thinking I should do is the following:

1)  Read in MathProg model and data for subproblem.
2)  Solve subproblem.
3)  Read in MathProg model and data for larger problem.
4)  For each column in larger problem, set value according to subproblem solution (since variable names are same in both problems, I think this will be easy?).
5)  Solve larger problem.

Based upon my sketchy description, is my approach reasonable?  Are there any red flags I should worry about?  I would gladly provide further details if helpful.  Just want to save some programming headaches in case there is a major flaw in this plan.

Thanks in advance.

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