Primal cutting plane algorithms revisited

Letchford, A. N. and Lodi, A. (2002) Primal cutting plane algorithms revisited. Mathematical Methods of Operational Research, 56 (1). pp. 67-81. ISSN 1432-2994

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Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutting planes is to enable a feasible solution to the original problem to be improved. Research on these algorithms has been almost non-existent. In this paper we argue for a re-examination of these primal methods. We describe a new primal algorithm for pure 0-1 problems based on strong valid inequalities and give some encouraging computational results. Possible extensions to the case of general mixed-integer programs are also discussed.

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Journal Article
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Mathematical Methods of Operational Research
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11 Jul 2011 18:02
Last Modified:
21 Nov 2022 21:01