An OR Practitioner's Solution Approach for the Set Covering Problem

The set covering problem (SCP) is an NP-complete problem that has many important industrial applications. Since industrial applications are typically large in scale, exact solution algorithms are not feasible for operations research (OR) practitioners to use when called on to solve real-world problems involving SCPs. However, the best performing heuristics for the SCP reported in the literature are not usually straightforward to implement. Additionally, these heuristics usually require the fine-tuning of several parameters. In contrast, simple greedy or even randomized greedy heuristics typically do not give as good results as the more sophisticated heuristics. In this paper, the authors present a compromise; a straightforward to implement, population-based solution approach for the SCP. It uses a randomized greedy approach to generate an initial population and then uses a genetic-based two phase approach to improve the population solutions. This two-phase approach uses transformation equations based on a Teaching-Learning based optimization approach developed by Rao, Savsani and Vakharia (2011, 2012) for continuous nonlinear optimization problems. Empirical results using set covering problems from Beasley's OR-library demonstrate the competitiveness of this approach both in terms of solution quality and execution time. The advantage to this approach is its relative simplicity for the practitioner to implement.