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From: | Joey Rios |
Subject: | RE: [Help-glpk] Using branch and cut starting with relaxed solution |
Date: | Fri, 19 Dec 2008 11:04:18 -0800 |
Hi Michael, > If the relaxed solution found is known to be basic, > the LP can be greatly reduced for the purpose of finding the basis. > Simply remove every constraint that is known to not be tight. > When you put them back, every added variable will be basic. I don't know that the relaxed solution is basic. In fact, I'm pretty sure it isn't. If I run my regular monolithic (non-decomposed) version of the problem I can (usually) get an integer solution from the glp_simplex call. When I run the decomposed version, I get the same optimal value, but a non-integer solution. > > Finding a basis is trickier if the relaxed solution is not known to be basic. > Degeneracy and near degeneracy often present the > problem of how to tell something small from zero. > It's not always solvable. > Reduced costs can help. > If an optimal reduced cost is known to be nonzero, > the corresponding constraint must be tight. > If there is no optimal solution for which a constraint is tight, > that constraint may be dropped. > I'm not sure how to use the tools you are talking about here. How can I say anything about reduced costs if I don't have a basis yet? > If the factor of 100 persists in the B&B subproblems, > you might want to consider rolling your own > so that you can take advantage of decomposition. At this point, I am probably just going to implement a rounding heuristic on the variables and see which constraints I 'break'. I may end up being OK with a few unsatisfied constraints given the computational efficiency of my decompostion. Joey Its the same Hotmail®. If by same you mean up to 70% faster. Get your account now. |
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