An Application of Machine Learning Tools to Predict the Number of Solutions for a Minimum Cardinality Set Covering Problem

The minimum cardinality set covering problem (MCSCP) is an NP-hard combinatorial optimization problem in which a set must be covered by a minimum number of subsets selected from a specified collection of subsets of the given set. It is well documented in the literature that the MCSCP has numerous, varied, and important industrial applications. For some of these applications, it would be useful to know if there are alternative optimums and the qualitative number of alternative optimums. In this article, both classification trees and neural networks are employed to qualitatively (small, medium, or large) predict the number of optimal solutions to a MCSCP. Results show that both model types have an accuracy in the low to mid 80%, with the neural network slightly outperforming the classification tree. Sensitivity and positive predictive value (PPV) are used to describe more detailed information.