Heuristics for cartographic label placement problems

The cartographic label placement problem is an important task in automated cartography and Geographical Information Systems. Positioning the texts requires that overlap among texts should be avoided, that cartographic conventions and preference should be obeyed. This paper examines the point-feature cartographic label placement problem (PFCLP) as an optimization problem. We formulate the PFCLP considering the minimization of existing overlaps and labeling of all points on a map. This objective improves legibility when all points must be placed even if overlaps are inevitable. A new mathematical formulation of binary integer linear programming that allows labeling of all points is presented, followed by some Lagrangean relaxation heuristics. The computational tests considered instances proposed in the literature up to 1000 points, and the relaxations provided good lower and upper bounds.