Logical Reduction Methods in Zero-One Programming—Minimal Preferred Variables

In the first part of this paper, the concept of logical reduction is presented Minimal preferred variable inequalities are introduced, and algorithms are given for their calculation. A simple illustrative example is carried along from the start, further examples are provided later. The second part of the paper describes certain properties of the generated logical inequalities. It then explains some of the decreases of computational effort which may be achieved by the use of minimal preferred inequalities and outlines a number of concrete applications with some numerical results. Finally, a number of more recent concepts and results are discussed, among them the notion of “probing” and a related zero-one enumeration code for large scale problems under the extended control language of MPSX/370.