Set covering algorithms using cutting planes, heuristics, and subgradient optimization: A computational study

Abstract

We report on the implementation and computational testing of several versions of a set covering algorithm, based on the family of cutting planes from conditional bounds discussed in the companion paper [2]. The algorithm uses a set of heuristics to find prime covers, another set of heuristics to find feasible solutions to the dual linear program which are needed to generate cuts, and subgradient optimization to find lower bounds. It also uses implicit enumeration with some new branching rules. Each of the ingredients was implemented and tested in several versions. The variant of the algorithm that emerged as best was run on 55 randomly generated test problems (20 of them from the literature), with up to 200 constraints and 2000 variables. The results show the algorithm to be more reliable and efficient than earlier procedures on large, sparse set covering problems.

Research supported by the National Science Foundation under grant MCS76-12026 A02 and the Office of Naval Research under contract N00014-75-C-0621 NR 047-048.