A new mathematical model and a Lagrangean decomposition for the point-feature cartographic label placement problem

This paper proposes a 0-1 integer linear programming model for the point-feature cartographic label placement problem based on labeling of the largest number of free labels. In addition, one non-trivial valid inequality is presented to strengthen this proposed model. Even with the strengthened model, a commercial solver was not able to solve a representative sample of known instances presented in the literature. Thus, we also present a Lagrangean decomposition technique based on graph partitioning. Our added approaches established optimal solutions for practically all the used instances and the results significantly improved the ones presented in recent studies concerning the problem.