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An exact algorithm for the maximal covering problem
Author(s) -
Downs Brian T.,
Camm Jeffrey D.
Publication year - 1996
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/(sici)1520-6750(199604)43:3<435::aid-nav8>3.0.co;2-a
Subject(s) - heuristics , bounding overwatch , mathematical optimization , range (aeronautics) , heuristic , branch and bound , mathematics , relaxation (psychology) , algorithm , computer science , greedy algorithm , dual (grammatical number) , exact solutions in general relativity , artificial intelligence , psychology , social psychology , art , mathematical analysis , materials science , literature , composite material
This article develops a robust, exact algorithm for the maximal covering problem (MCP) using dual‐based solution methods and greedy heuristics in branch and bound. Based on tests using randomly generated problems with problem parameters similar to those in the existing literature, the hybrid approach developed in this work appears to be effective over a wide range of MCP model parameters. The method is further validated on problems constructed from three real‐world data sets. The extensive computational study compares the new method with other existing exact methods using problems that are as big, or larger than, those used in previous work on MCP. The results show that the proposed method is effective in most instances of MCP. In particular, it is shown that bounding schemes using Lagrangian relaxation are effective on MCP as a method of obtaining both exact and heuristic solutions. © 1996 John Wiley & Sons, Inc.