Mixed-Integer Programming Subject to Uncertain Data
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Sprache:Englisch
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Beschreibung
Produktdetails
Einband
Paperback
Erscheinungsdatum
04.10.2012
Verlag
Cuvillier, ESeitenzahl
138
Maße (L/B/H)
21/14,8/0,8 cm
Gewicht
189 g
Auflage
1. Auflage
Sprache
Englisch
ISBN
978-3-95404-239-5
In the first part of this thesis, robust problems with uncertainty in the cost vector are investigated. Here, the emphasis lies on considering simply structured uncertainties that allow the reduction of a problem with uncertainty to a series of problems of the same type but without uncertainty. It is known from the literature that this is possible for robust 0-1 programs and the robust minimum-cost flow problem if the uncertainty is a (higher dimensional) interval where the upper bound corner is cut off by a single cardinality constraint; this constraint permits control over the amount of robustness in the problem. In this thesis, it is demonstrated that this is still possible for uncertainties where the upper bound is cut off by arbitrarily many knapsack constraints with non-negative coefficients, which permits more detailed control. For the robust minimum-cost flow problem, a subgradient optimization approach is proposed; this is more practical than the binary search method proposed in literature.
The second part of this thesis is concerned with more general uncertainties, mainly polyhedral ones, and robust and generalized mixed-integer programs. Reformulations of these problems as mixed-integer programs are discussed, and some useful tools known from linear programming, like duality and Farkas’ lemma, are reviewed for linear programs with uncertainty. With help of these, it is shown that lattice-free cuts for robust mixed-integer programs are generated by generalized linear programs while lattice-free cuts for generalized mixed-integer programs are generated by robust linear programs. Strengthening procedures, known from literature for the non-uncertain case, and, finally, problems with uncertainties described by convex conic sets are investigated.
The performance of the lattice-free cuts for robust mixed-integer programs is assessed in terms of the amount of gap closed and the time spent for cut generation by a computational study.
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