Primal cutting plane algorithms revisited

Adam N. Letchford and Andrea Lodi

Mathematical Methods of Operations Research, 2002, vol. 56, issue 1, 67-81

Abstract: 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. Copyright Springer-Verlag Berlin Heidelberg 2002

Keywords: Key words: integer programming; cutting planes; primal algorithms (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/s001860200200

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