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On Disjunctive Cuts for Combinatorial Optimization

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  • Adam N. Letchford

    (Lancaster University)

Abstract

In the successful branch-and-cut approach to combinatorial optimization, linear inequalities are used as cutting planes within a branch-and-bound framework. Although researchers often prefer to use facet-inducing inequalities as cutting planes, good computational results have recently been obtained using disjunctive cuts, which are not guaranteed to be facet-inducing in general. A partial explanation for the success of the disjunctive cuts is given in this paper. It is shown that, for six important combinatorial optimization problems (the clique partitioning, max-cut, acyclic subdigraph, linear ordering, asymmetric travelling salesman and set covering problems), certain facet-inducing inequalities can be obtained by simple disjunctive techniques. New polynomial-time separation algorithms are obtained for these inequalities as a by-product. The disjunctive approach is then compared and contrasted with some other ‘general-purpose’ frameworks for generating cutting planes and some conclusions are made with respect to the potential and limitations of the disjunctive approach.

Suggested Citation

  • Adam N. Letchford, 2001. "On Disjunctive Cuts for Combinatorial Optimization," Journal of Combinatorial Optimization, Springer, vol. 5(3), pages 299-315, September.
    • Handle: RePEc:spr:jcomop:v:5:y:2001:i:3:d:10.1023_a:1011493126498
    DOI: 10.1023/A:1011493126498
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    References listed on IDEAS

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    Cited by:

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    2. Jamie Fairbrother & Adam N. Letchford & Keith Briggs, 2018. "A two-level graph partitioning problem arising in mobile wireless communications," Computational Optimization and Applications, Springer, vol. 69(3), pages 653-676, April.
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