2022/03/06 by Alberto Del Pia, Del Pia, Alberto, Jeff Linderoth +3
Engineering · Computer Science · #Optimization and Packing Problems #Advanced Manufacturing and Logistics Optimization #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.2203.02873
The complementarity knapsack problem (CKP) is a knapsack problem with real-valued variables and complementarity conditions between pairs of its variables. We extend the polyhedral studies of De Farias et al. for CKP, by proposing three new families of cutting-planes that are all obtained from a combinatorial concept known as a pack. Sufficient conditions for these inequalities to be facet-defining, based on the concept of a maximal switching pack, are also provided. Moreover, we answer positively a conjecture by de Farias et~al.~about the separation complexity of the inequalities introduced in their work, and propose efficient separation algorithms for our newly defined cutting-planes.