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[Help-glpk] [Fwd: primal and dual simplex solves multiobjective problems
[Help-glpk] [Fwd: primal and dual simplex solves multiobjective problems]
Mon, 07 Dec 2015 18:48:36 +0300
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Subject: primal and dual simplex solves multiobjective problems
Date: Mon, 07 Dec 2015 15:34:33 +0100
The attached patch against version 4.57 implements a kind of "multiobjective"
optimization. Given the "main" objective c_1,...,c_n and "auxiliary"
objectives <e_11,...e_1n>, <e_21,...,e_2n>,...<e_p1,...,e_pn>, find
the optimal value of the "main" objective, then within the solution
space minimize (maximize) the first auxiliary objective, within the
solution space minimize (maximize) the second auxiliary objective,
etc. It is a kind of generalization of asking the lexicographically
minimal optimal solution of the LP problem.
Please consider this patch as a tentative contribution to the package;
use it as you like. I would be happy to receive comments what I did
The following new api functions are added:
sets the number of auxiliary objectives; set to zero to delete
set the objno-th auxiliary objective coefficient
retrieve the coefficient
A new parameter in glp_smcp is parm->mobj, which should be set to
GLP_ON to do multiobjective optimization.
All added lines are between #ifdef CSL and #endif; there is only one
disabled line which checks the consistency of bound flags in the dual
In the primal/dual algorithm, primal_simplex()/dual_simplex() is
called repeatedly after calling next_objective() which goes over all
non-basic variables and fixes the value of those which have active
bound (by making the lower and upper bounds the same), and then
replaces the objective values with the next objective.
It is not clear whether csa->phase has to be set to zero in the dual
problem; and whether the when PSE pricing is on, whether it should be
invalidated from one invocation to the next.
Alfred Renyi Mathematical Institute
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