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A nonlinear approach to a class of combinatorial optimization problems

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  • J. P. Warners

Abstract

A special class of combinatorial optimization problems is considered. We develop a compact nonconvex quadratic model for these problems that incorporates all inequality constraints in the objective function, and discuss two approximation algorithms for solving this model. One is inspired by Karmarkar's potential reduction algorithm for solving combinatorial optimization problems; the other is a variant of the reduced gradient method. The paper concludes with computational experiences with both real‐life and randomly generated instances of the frequency assignment problem. Large problems are satisfactorily solved in reasonable computation times.

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  • J. P. Warners, 1998. "A nonlinear approach to a class of combinatorial optimization problems," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(2), pages 162-184, June.
    • Handle: RePEc:bla:stanee:v:52:y:1998:i:2:p:162-184
    DOI: 10.1111/1467-9574.00076
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    Cited by:

    1. Karen Aardal & Cor Hurkens & Jan Karel Lenstra & Sergey Tiourine, 2002. "Algorithms for Radio Link Frequency Assignment: The Calma Project," Operations Research, INFORMS, vol. 50(6), pages 968-980, December.

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