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Extracting Embedded Generalized Networks from Linear Programming Problems

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Author
Brown, Gerald G.
McBride, Richard D.
Wood, R. Kevin
Date
1985
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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.
Description
Mathematical Programming, 32, pp. 11-31.
Rights
defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
URI
http://hdl.handle.net/10945/38134
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    Extracting Embedded Generalized Networks from Linear Programming Problems 

    Brown, Gerald G.; McBride, Richard D.; Wood, R. Kevin (Monterey, California: Naval Postgraduate School, 1984-09); NPS55-84-020
    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 ...
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    Automatic identification of embedded network rows in large-scale optimization models 

    Brown, Gerald G.; Wright, William G. (Springer, 1984);
    The solution of a large-scale linear, integer, or mixed integer programming problem is often facilitated by the exploitation of special structure in the model. This paper presents heuristic algorithms for identifying ...
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    Automatic identification of embedded network rows in large-scale optimization models 

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    The solution of a contemporary large-scale linear, integer, or mixed-integer programming problem is often facilitated by the exploitation of intrinsic special structure in the model. This paper deals with the problem of ...
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