On the exact separation of cover inequalities of maximum-depth
On the exact separation of cover inequalities of maximum-depth
We investigate the problem of separating cover inequalities of maximum-depth exactly. We propose a pseudopolynomial-time dynamic-programming algorithm for its solution, thanks to which we show that this problem is weakly NP-hard (similarly to the problem of separating cover inequalities of maximum violation). We carry out extensive computational experiments on instances of the knapsack and the multi-dimensional knapsack problems with and without conflict constraints. The results show that, with a cutting-plane generation method based on the maximum-depth criterion, we can optimize over the cover-inequality closure by generating a number of cuts smaller than when adopting the standard maximum-violation criterion. We also introduce the Point-to-Hyperplane Distance Knapsack Problem (PHD-KP), a problem closely related to the separation problem for maximum-depth cover inequalities, and show how the proposed dynamic programming algorithm can be adapted for effectively solving the PHD-KP as well.
Cover inequalities, Cutting plane generation, Dynamic programming, Knapsack problem, Mixed integer nonlinear programming
1-21
Catanzaro, Daniele
0614e487-58f2-42e2-ab98-5cbc58932e1d
Coniglio, Stefano
03838248-2ce4-4dbc-a6f4-e010d6fdac67
Furini, Fabio
0bf78b98-3255-4fa0-aff7-699d8f8bb292
Catanzaro, Daniele
0614e487-58f2-42e2-ab98-5cbc58932e1d
Coniglio, Stefano
03838248-2ce4-4dbc-a6f4-e010d6fdac67
Furini, Fabio
0bf78b98-3255-4fa0-aff7-699d8f8bb292
Catanzaro, Daniele, Coniglio, Stefano and Furini, Fabio
(2021)
On the exact separation of cover inequalities of maximum-depth.
Optimization Letters, .
(doi:10.1007/s11590-021-01741-0).
Abstract
We investigate the problem of separating cover inequalities of maximum-depth exactly. We propose a pseudopolynomial-time dynamic-programming algorithm for its solution, thanks to which we show that this problem is weakly NP-hard (similarly to the problem of separating cover inequalities of maximum violation). We carry out extensive computational experiments on instances of the knapsack and the multi-dimensional knapsack problems with and without conflict constraints. The results show that, with a cutting-plane generation method based on the maximum-depth criterion, we can optimize over the cover-inequality closure by generating a number of cuts smaller than when adopting the standard maximum-violation criterion. We also introduce the Point-to-Hyperplane Distance Knapsack Problem (PHD-KP), a problem closely related to the separation problem for maximum-depth cover inequalities, and show how the proposed dynamic programming algorithm can be adapted for effectively solving the PHD-KP as well.
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Accepted/In Press date: 15 April 2021
e-pub ahead of print date: 1 May 2021
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Funding Information:
Acknowledgements The authors are grateful to two anonymous referees and to the associate editor for their comments, which helped to improve the quality of the paper. The first author acknowledges support from the Université Catholique de Louvain via the “Fonds Spéciaux de Recherche” (FSR) 2017-2021, and the Fondation Louvain via the research grant COALESCENS.
Publisher Copyright:
© 2021, The Author(s).
Keywords:
Cover inequalities, Cutting plane generation, Dynamic programming, Knapsack problem, Mixed integer nonlinear programming
Identifiers
Local EPrints ID: 448845
URI: http://eprints.soton.ac.uk/id/eprint/448845
ISSN: 1862-4472
PURE UUID: 95e8a3d9-c86c-482a-8f22-67b90702014a
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Date deposited: 06 May 2021 16:33
Last modified: 17 Mar 2024 03:40
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Author:
Daniele Catanzaro
Author:
Fabio Furini
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