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A column generation approach for the maximal covering location problem
Author(s) -
Pereira Marcos Antonio,
Lorena Luiz Antonio Nogueira,
Senne Edson Luiz França
Publication year - 2007
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/j.1475-3995.2007.00593.x
Subject(s) - column generation , column (typography) , mathematical optimization , selection (genetic algorithm) , mathematics , degeneracy (biology) , multiplier (economics) , computer science , algorithm , artificial intelligence , geometry , bioinformatics , macroeconomics , connection (principal bundle) , economics , biology
This article presents a column generation algorithm to calculate new improved lower bounds to the solution of maximal covering location problems formulated as a p ‐median problem. This reformulation leads to instances that are difficult for column generation methods. The traditional column generation method is compared with the new approach, where the reduced cost criterion used at the column selection is modified by a Lagrangean/surrogate multiplier. The efficiency of the new approach is tested with real data, where computational tests were conducted and showed the impact of sparsity and degeneracy on column generation‐based methods.