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Separation algorithms for 0-1 knapsack polytopes

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
0025-5610
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)

Record type: Article

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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More information

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: 12 Jun 2020 16:35

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Contributors

Author: Konstantinos Kaparis
Author: Adam Letchford

University divisions

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