Mixed 0–1 programming by lift-and-project in a branch-and-cut framework

We investigate the computational issues that need to be addressed when incorporating general cutting planes for mixed 0–1 programs into a branch-and-cut framework. The cuts we use are of the lift-and-project variety. Some of the issues addressed have a theoretical answer, but others are of an experimental nature and are settled by comparing alternatives on a set of test problems. The resulting code is a robust solver for mixed 0–1 programs. We compare it with several existing codes. On a wide range of test problems it performs as well as, or better than, some of the best currently available mixed integer programming codes.