Surrogate-RLT cuts for zero–one integer programs

Abstract

In this paper, we consider the class of 0---1 integer problems and develop an effective cutting plane algorithm that gives valid inequalities called surrogate-RLT cuts (SR cuts). Here we implement the surrogate constraint analysis along with the reformulation---linearization technique (RLT) to generate strong valid inequalities. In this approach, we construct a tighter linear relaxation by augmenting SR cuts to the problem. The level-$$d$$d SR closure of a 0---1 integer program is the polyhedron obtained by intersecting all the SR cuts obtained from RLT polyhedron formed over each set of $$d$$d variables with its initial formulation. We present an algorithm for approximately optimizing over the SR closure. Finally, we present the computational result of SR cuts for solving 0---1 integer programming problems of well-known benchmark instances from MIPLIB 3.0.