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Re: [Help-glpk] Multiobjective problem

From: Andrew Makhorin
Subject: Re: [Help-glpk] Multiobjective problem
Date: Fri, 28 Aug 2009 06:08:35 +0400

> I'm trying to face a multiobjective problem with lexicographic goals. The
> approach I'm implementing is to optimize the first goal, fix the columns
> involved in this goal, and proceed to the following goal.
> This works well. The problem is that subsequently I need to reoptimize: so I
> have to free the previously fixed variables. But these columns (being fixed)
> were out of basis, whereas when freed they should stay in basis (they were
> fixed to values > 0) to keep the current solution feasible. The simplex
> takes a lot of iterations to bring back the solution to a feasible status.

> Which is the best way to avoid this?

If the current basic solution is optimal and you free some previously
fixed variables, the solution cannot become primal infeasible; it may
become only non-optimal (dual infeasible). Or I misunderstand something?

Andrew Makhorin

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