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On the exact separation of cover inequalities of maximum-depth

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
1862-4472
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, 1-21. (doi:10.1007/s11590-021-01741-0).

Record type: Article

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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More information

Accepted/In Press date: 15 April 2021
e-pub ahead of print date: 1 May 2021
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
ORCID for Stefano Coniglio: ORCID iD orcid.org/0000-0001-9568-4385

Catalogue record

Date deposited: 06 May 2021 16:33
Last modified: 26 Nov 2021 03:05

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Contributors

Author: Daniele Catanzaro
Author: Fabio Furini

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