Innovative Applications of O.R. A Clustering Search metaheuristic for the Point-Feature Cartographic Label Placement Problem Rômulo Louzada Rabello a , Geraldo Regis Mauri a,⇑ , Glaydston Mattos Ribeiro b , Luiz Antonio Nogueira Lorena c a Federal University of Espírito Santo – UFES, Alegre, ES 29500-000, Brazil b Federal University of Rio de Janeiro – UFRJ, Rio de Janeiro, RJ 21945-970, Brazil c National Institute for Space Research – INPE, São José dos Campos, SP 12227-010, Brazil article info Article history: Received 24 December 2012 Accepted 8 October 2013 Available online 18 October 2013 Keywords: Metaheuristics Combinatorial optimization Clustering Search Point-Feature Cartographic Label Placement abstract The Point-Feature Cartographic Label Placement (PFCLP) problem consists of placing text labels to point features on a map avoiding overlaps to improve map visualization. This paper presents a Clustering Search (CS) metaheuristic as a new alternative to solve the PFCLP problem. Computational experiments were performed over sets of instances with up to 13,206 points. These instances are the same used in sev- eral recent and important researches about the PFCLP problem. The results enhance the potential of CS by finding optimal solutions (proven in previous works) and improving the best-known solutions for instances whose optimal solutions are unknown so far. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction The Point-Feature Cartographic Label Placement (PFCLP) prob- lem has a great importance for applications which use computa- tional resources to generate maps, as for example, georeferencing systems, web applications, etc. The PFCLP problem is classified in the literature as NP – Hard (Marks & Shieber, 1991) and according to Ribeiro and Lorena (2008b), it consists in organizing points on maps avoiding overlaps of labels and providing clarity in viewing and understanding of the map. The labels contain information of objects to be displayed in cartographic maps, networks, graphs or diagrams (Wolff, 1999). Fig. 1 shows a map of São Paulo State (Brazil) with districts and roadways. The labels indicate the name of the districts and the gray districts indicate that their labels are overlapped. One way to improve the map view is moving the labels to spe- cific positions close to their respective points which are known as ‘‘candidate positions’’. The candidate positions represent the possi- ble locations where the label of a point can be placed, respecting a cartographic pattern. Fig. 2 illustrates the cartographic pattern proposed by Christensen, Marks, and Shieber (1995). This pattern is one of the most known and used in the literature. The regions 1–8 indicate the candidate positions for labeling the point. Each position has a number indicating its cartographic preference, and position 1 is the most suitable, i.e. the smallest number indicates the best posi- tion. Starting from this pattern, the point-labeling problem can be defined as a combinatorial problem which must select candidate positions to label the points. In the PFCLP problem, overlapping labels may be accepted or not. When overlaps are not accepted, we can keep the size of the labels and label the greatest number of points without overlapping. In this case, the PFCLP problem is a special case of the traditional Maximum Independent Set Problem (Ribeiro, Mauri, & Lorena, 2011; Strijk, Verweij, & Aardal, 2000; Zoraster, 1990). We also may decrease the size of the labels such that all of them fit without overlap. Here, the objective is to find the maximum scale factor for the label size such that a labeling without conflict is generated (Klau & Mutzel, 2003). Overlaps are allowed in several papers about the PFCLP problem, and so, all points must necessarily be labeled. Conse- quently, two approaches are identified: minimize the number of conflicts (Ribeiro & Lorena, 2008a, 2008b) and maximize the number of conflict-free labels (Alvim & Taillard, 2009; Mauri, Ribeiro, & Lorena, 2010). In this paper, we consider that last ap- proach for which a mathematical model is available in Mauri et al. (2010). This paper aims to present a new alternative to solve the PFCLP problem. A Clustering Search (CS) metaheuristic is proposed using a Simulated Annealing algorithm as part of its structure. 0377-2217/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ejor.2013.10.021 ⇑ Corresponding author. Tel.: +55 28 3552 8902; fax: +55 28 3552 8903. E-mail addresses: romulo_louzada@hotmail.com (R.L. Rabello), mauri@cca. ufes.br (G.R. Mauri), glaydston@pet.coppe.ufrj.br (G.M. Ribeiro), lorena@lac. inpe.br (L.A.N. Lorena). European Journal of Operational Research 234 (2014) 802–808 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor