Title:
Topics in group methods for integer programming
Topics in group methods for integer programming
Author(s)
Chen, Kenneth
Advisor(s)
Cook, William J.
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Abstract
In 2003, Gomory and Johnson gave two different three-slope T-space
facet constructions, both of which shared a slope with the corresponding
Gomory mixed-integer cut. We give a new three-slope facet
which is independent of the GMIC and also give a four-slope
T-space facet construction, which to our knowledge, is the first
four-slope construction.
We describe an enumerative framework for the discovery of T-space
facets.
Using an algorithm by Harvey for computing integer hulls in the
plane, we give a heuristic for quickly computing lattice-free
triangles.
Given two rows of the tableau, we derive how to exactly calculate
lattice-free triangles and quadrilaterals in the plane which can be
used to derive facet-defining inequalities of the integer hull.
We then present computational results using these derivations where
non-basic integer variables are strengthened using Balas-Jeroslow lifting.
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Date Issued
2011-06-15
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Text
Resource Subtype
Dissertation