Extracting Embedded Generalized Networks from Linear Programming Problems
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Authors
Brown, Gerald G.
McBride, Richard D.
Wood, R. Kevin
Subjects
Linear Programming
Generalized Networks
Basis Factorization
Computational Complexity
Heuristic Algorithms
Generalized Networks
Basis Factorization
Computational Complexity
Heuristic Algorithms
Advisors
Date of Issue
1985
Date
1985
Publisher
Language
Abstract
If a linear program tLP) possesses a large generalized network (GN) submatrix, this structure
can be exploited to decrease solution time. The problems of finding maximum sets of GN
constraint s and finding maximum embedded GN sub matrices are shown to be NP-complete,
indicating that reliable, efficient solution of these problems is difficult. Therefore, efficient heuristic
algorithms are developed for identifying such structure and are tested on a selection of twenty-three
real-world problems. The best of four algorithms for identifying GN constraint sets finds a set
which is maximum in twelve cases and averages 99.1% of maximum. On average, the GN
constraints identified comprise more than 62.3% of the total constraints in these problems. The
algorithm for identifying embedded GN submatrices finds submatrices whose sizes, rows plus
columns, average 96.8% of an LP upper bound. Over 91.3% of the total constraint matrix was
identified as a GN submatrix in these problems, on average.
Type
Article
Description
Mathematical Programming, 32, pp. 11-31.
Series/Report No
Department
Operations Research (OR)
Organization
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NPS Report Number
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Citation
Brown, G.G., McBride, R., and Wood, R.K., 1985, “Extracting Embedded Generalized Networks from Linear Programming Problems,” Mathematical Programming, 32, pp. 11-31.
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defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.