O( n log n) procedures for tightening cover inequalities

We present two procedures for tightening cover induced inequalities in 0-1 programs by using knapsack constraints plus some other information from the program. The tightening is obtained by solving successive knapsack problems with all 0-1 objective function coefficients, and using dominance criteri...

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Bibliographic Details
Published inEuropean journal of operational research Vol. 113; no. 3; pp. 676 - 687
Main Authors Escudero, L.F., Garı́n, A., Pérez, G.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 16.03.1999
Elsevier
Elsevier Sequoia S.A
SeriesEuropean Journal of Operational Research
Subjects
0-1 program
Applied sciences
Clique
Coefficient increase
Cover
Exact sciences and technology
Flows in networks. Combinatorial problems
Knapsack constraint
Knapsack problem
Lifting
Operational research and scientific management
Operational research. Management science
Probing
Studies
0-1 program
Cover
Probing
Clique
Coefficient increase
Lifting
Knapsack constraint
Coefficient
Zero one programming
Constraint
Dominance
Increase
Objective function
Inequality
Knapsack problem
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Summary:We present two procedures for tightening cover induced inequalities in 0-1 programs by using knapsack constraints plus some other information from the program. The tightening is obtained by solving successive knapsack problems with all 0-1 objective function coefficients, and using dominance criteria to avoid the explicit solving of some knapsack problems. The new constraints are 0-1 equivalent to and LP tighter than the original ones. Both procedures have O (n log n) complexity, where n is the number of variables with nonzero coefficients in the knapsack constraint, however one of them can strongly reduce the computational effort. Some computational experience is reported.
ISSN:0377-2217
1872-6860
DOI:10.1016/S0377-2217(98)00100-3