Separation algorithms for 0-1 knapsack polytopes
Separation algorithms for 0-1 knapsack polytopes
Valid inequalities for 0-1 knapsack polytopes often prove useful
when tackling hard 0-1 Linear Programming problems. To generate
such inequalities, one needs separation algorithms for them, i.e., rou-
tines for detecting when they are violated. We present new exact
and heuristic separation algorithms for several classes of inequalities,
namely lifted cover, extended cover, weight and lifted pack inequalities.
Moreover, we show how to improve a recent separation algorithm for
the 0-1 knapsack polytope itself. Extensive computational results, on
MIPLIB and OR Library instances, show the strengths and limitations
of the inequalities and algorithms considered.
integer programming, knapsack problems, cutting planes
Kaparis, Konstantinos
29a564bc-2835-43ee-bf21-50e65e0a894a
Letchford, Adam
eec1a668-1726-43cf-bc4f-f8c90ddf9a9a
Kaparis, Konstantinos
29a564bc-2835-43ee-bf21-50e65e0a894a
Letchford, Adam
eec1a668-1726-43cf-bc4f-f8c90ddf9a9a
Kaparis, Konstantinos and Letchford, Adam
(2008)
Separation algorithms for 0-1 knapsack polytopes.
Mathematical Programming.
(In Press)
Abstract
Valid inequalities for 0-1 knapsack polytopes often prove useful
when tackling hard 0-1 Linear Programming problems. To generate
such inequalities, one needs separation algorithms for them, i.e., rou-
tines for detecting when they are violated. We present new exact
and heuristic separation algorithms for several classes of inequalities,
namely lifted cover, extended cover, weight and lifted pack inequalities.
Moreover, we show how to improve a recent separation algorithm for
the 0-1 knapsack polytope itself. Extensive computational results, on
MIPLIB and OR Library instances, show the strengths and limitations
of the inequalities and algorithms considered.
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Submitted date: 2008
Accepted/In Press date: 2008
Keywords:
integer programming, knapsack problems, cutting planes
Organisations:
Operational Research
Identifiers
Local EPrints ID: 68689
URI: http://eprints.soton.ac.uk/id/eprint/68689
ISSN: 0025-5610
PURE UUID: 723b60a3-de03-423e-8761-630d2435b196
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Date deposited: 16 Sep 2009
Last modified: 10 Dec 2021 16:18
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Contributors
Author:
Konstantinos Kaparis
Author:
Adam Letchford
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