Extracting Embedded Generalized Networks from Linear Programming Problems.
Abstract
If a linear program (LP) possesses a large generalized network (GN) submatrix, this structure can be exploited to decrease solution time. The problems of definding maximum sets of GN constraints and finding maximum embedded GN submatrices 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 average 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. Originator supplied keywords include: embedded networks, computational complexity, and large-scale optimization.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1984
- Accession Number
- ADA147565
Entities
People
- Graham G. Brown
- R. D. Mcbride
- R. Kevin Wood
Organizations
- Naval Postgraduate School