On Merging Cover Inequalities for Multiple Knapsack Problems

Hickman, Randal; Easton, Todd

doi:10.4236/ojop.2015.44014

Cited by 4 publications

(1 citation statement)

References 42 publications

(47 reference statements)

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“…The 0-1 knapsack polyhedron as the most basic relaxation of a 0-1 integer program (IP) has attracted attention of many researchers over the years. In particular, developing facets for the 0-1 knapsack polyhedron has been extensively addressed over the past several decades see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] among many others. Most of the work in this direction has been focused on characterization of facets arising from lifting of the so-called minimal cover inequalities.…”

Section: Introductionmentioning

confidence: 99%

A very fast method for guaranteed generation of one facet for 0-1 knapsack polyhedron

Kianfar

Kianfar²,

Rafiee

2022

Scientia Iranica

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The 0-1 knapsack polyhedron as the most basic relaxation of a 0-1 integer program has attracted attention of many researchers over the years. We present a very fast method that is guaranteed to generate one facet for the 0-1 knapsack polyhedron. Unlike lifting of cover inequities, our method does not require an initial minimal cover or a predetermined lifting sequencing, and its worst-case complexity is linear in number of variables. Therefore, with minimal computational burden, it can be used to generate a potentially strong valid inequality based on any 0-1 relaxation of a general (mixed) integer program (M)IP. Such valid inequalities can be added to the (M)IP problem prior to solving, or given their low computational cost, can be generated during solving the (M)IP, checked to see if they separate the incumbent fractional solution, and added to the problem if they do.

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