Benders Decomposition Approach to Set Covering Problems Satisfying Almost the Consecutive Ones Property

Abstract

Although in the actual phase, we are evaluating it, the algorithm pre- sented in this paper is designed for solving real world set covering instances arising from railway public transportation in Germany (Deutsche Bahn). These instances, with large sizes, are characterized by a special pattern. The binary matrices they exhibit, have “almost” consecutive ones prop- erty. Taking advantage of this nice structure, we present a decomposition of the SCP into a mixed linear-integer program, and we present a Benders- like algorithm. We end the paper with the computational experience where twenty randomly generated instances are run.