Article ID: | iaor20032516 |
Country: | Germany |
Volume: | 56 |
Issue: | 1 |
Start Page Number: | 67 |
End Page Number: | 81 |
Publication Date: | Jan 2002 |
Journal: | Mathematical Methods of Operations Research (Heidelberg) |
Authors: | Letchford A.N., Lodi A. |
Keywords: | programming: branch and bound, programming: fractional |
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.