Gomory cuts revisited

In this paper, we investigate the use of Gomory's mixed integer cuts within a branch-and-cut framework. It has been argued in the literature that \a marriage of classical cutting planes and tree search is out of the question as far as the solution of large-scale combinatorial optimization problems is concerned" 16] because the cuts generated at one node of the search tree need not be valid at other nodes. We show in this paper that it is possible, using a simple lifting procedure, to make Gomory cuts generated in a node of the enumeration tree globally valid in the case of mixed 0-1 programs. Other issues addressed in this paper are of computational nature, such as strategies for generating the cutting planes, deciding between branching and cutting, etc. The result is a robust mixed integer program solver.