A Sequential Approach to the 0-1 Linear Programming Problem

The paper gives a method of minimizing a linear function of zero-one variables subject to linear constraints. The method is based on transforming an n-variable m-constraint problem into a sequence of n-variable 2-constraint problems which are easier to solve. The algorithm has been tested on test pr...

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Published in:SIAM journal on applied mathematics Vol. 31; no. 2; pp. 271 - 285
Main Authors: Christofides, Nicos, Trypia, Mary
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.09.1976
Subjects:
Algorithms
Dynamic programming
Integer programming
Integers
Iterative solutions
Linear programming
Methods
Objective functions
Optimal solutions
Tableaux
Variable coefficients
ISSN:0036-1399, 1095-712X
Online Access:Get full text
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Abstract The paper gives a method of minimizing a linear function of zero-one variables subject to linear constraints. The method is based on transforming an n-variable m-constraint problem into a sequence of n-variable 2-constraint problems which are easier to solve. The algorithm has been tested on test problems found in the literature and on a set of 80 random problems. Good results have been obtained, both in terms of the number of iterations involved in solving this sequence of subproblems, and in terms of the total computation time required to reach the final solution. The method is most effective when the coefficients of the problem are small integer numbers.
AbstractList The paper gives a method of minimizing a linear function of zero-one variables subject to linear constraints. The method is based on transforming an $n$-variable $m$-constraint problem into a sequence of $n$-variable 2-constraint problems which are easier to solve. The algorithm has been tested on test problems found in the literature and on a set of 80 random problems. Good results have been obtained, both in terms of the number of iterations involved in solving this sequence of subproblems, and in terms of the total computation time required to reach the final solution. The method is most effective when the coefficients of the problem are small integer numbers.
Author Christofides, Nicos
Trypia, Mary
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crossref_primary_10_1016_0377_2217_85_90033_5
Cites_doi 10.1287/opre.13.6.879
10.1137/1009031
10.1287/opre.17.4.638
10.6028/jres.069B.025
10.1287/mnsc.13.9.736
10.1093/comjnl/14.4.418
10.1287/mnsc.18.9.465
10.1287/mnsc.15.9.481
10.1287/opre.15.5.892
10.1287/opre.14.6.1045
10.2307/1910129
10.1287/opre.13.4.517
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Copyright Copyright 1976 Society for Industrial and Applied Mathematics
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Snippet The paper gives a method of minimizing a linear function of zero-one variables subject to linear constraints. The method is based on transforming an n-variable...
The paper gives a method of minimizing a linear function of zero-one variables subject to linear constraints. The method is based on transforming an...
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SubjectTerms Algorithms
Dynamic programming
Integer programming
Integers
Iterative solutions
Linear programming
Methods
Objective functions
Optimal solutions
Tableaux
Variable coefficients
Title A Sequential Approach to the 0-1 Linear Programming Problem
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