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Row generation techniques for approximate solution of linear programming problems
Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 69-77.In this study, row generation techniques are applied on general linear programming
problems with a very large number of constraints with respect to the problem
dimension. A lower bound is obtained for the change in the objective value
caused by the generation of a specific row. To achieve row selection that results
in a large shift in the feasible region and the objective value at each row generation
iteration, the lower bound is used in the comparison of row generation
candidates. For a warm-start to the solution procedure, an effective selection of
the subset of constraints that constitutes the initial LP is considered. Several
strategies are discussed to form such a small subset of constraints so as to obtain
an initial solution close to the feasible region of the original LP. Approximation
schemes are designed and compared to make possible the termination of row generation
at a solution in the proximity of an optimal solution of the input LP.
The row generation algorithm presented in this study, which is enhanced with
a warm-start strategy and an approximation scheme is implemented and tested
for computation time and the number of rows generated. Two efficient primal
simplex method variants are used for benchmarking computation times, and the
row generation algorithm appears to perform better than at least one of them
especially when number of constraints is large.Paç, A BurakM.S