Simultaneously lifting sets of binary variables into cover inequalities for knapsack polytopes

Authors:
Todd Easton;Kevin Hooker
Affiliations:
237 Durland Hall, School of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66501, United States;237 Durland Hall, School of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66501, United States
Venue:
Discrete Optimization
Year:
2008

Citing 7
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Abstract

Cover inequalities are commonly used cutting planes for the 0-1 knapsack problem. This paper describes a linear-time algorithm (assuming the knapsack is sorted) to simultaneously lift a set of variables into a cover inequality. Conditions for this process to result in valid and facet-defining inequalities are presented. In many instances, the resulting simultaneously lifted cover inequality cannot be obtained by sequentially lifting over any cover inequality. Some computational results demonstrate that simultaneously lifted cover inequalities are plentiful, easy to find and can be computationally beneficial.