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Optimal Solution of Set Covering/Partitioning Problems Using Dual Heuristics

Optimal Solution of Set Covering/Partitioning Problems Using Dual Heuristics We present an algorithm for a mixed set covering/partitioning model that includes as special cases the well-known set covering problem and set partitioning problem. The novel feature of our algorithm is the use of continuous heuristics applied to the dual of the linear programming relaxation to provide lower bounds for a branch and bound algorithm. The heuristics are continuous adaptations of the well-known greedy and 3-opt methods that have been applied to a variety of combinatorial optimization problems. Our algorithm has outperformed the current best set covering algorithm of Balas and Ho (1980) by about a factor of 3, and appears to improve on the best existing set partitioning algorithm by more than an order of magnitude. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Management Science INFORMS

Optimal Solution of Set Covering/Partitioning Problems Using Dual Heuristics

Management Science , Volume 36 (6): 15 – Jun 1, 1990
16 pages

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Publisher
INFORMS
Copyright
Copyright © INFORMS
Subject
Research Article
ISSN
0025-1909
eISSN
1526-5501
DOI
10.1287/mnsc.36.6.674
Publisher site
See Article on Publisher Site

Abstract

We present an algorithm for a mixed set covering/partitioning model that includes as special cases the well-known set covering problem and set partitioning problem. The novel feature of our algorithm is the use of continuous heuristics applied to the dual of the linear programming relaxation to provide lower bounds for a branch and bound algorithm. The heuristics are continuous adaptations of the well-known greedy and 3-opt methods that have been applied to a variety of combinatorial optimization problems. Our algorithm has outperformed the current best set covering algorithm of Balas and Ho (1980) by about a factor of 3, and appears to improve on the best existing set partitioning algorithm by more than an order of magnitude.

Journal

Management ScienceINFORMS

Published: Jun 1, 1990

Keywords: Keywords : set covering ; set partitioning ; optimization ; Lagrangean relaxation

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