Computers and Operations Research
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
GRASP for Seam Drawing in Mosaicking of Aerial Photographic Maps
Journal of Heuristics
Grasp and Path Relinking for 2-Layer Straight Line Crossing Minimization
INFORMS Journal on Computing
Parallel GRASP with path-relinking for job shop scheduling
Parallel Computing - Special issue: Parallel computing in numerical optimization
A Hybrid Heuristic for the p-Median Problem
Journal of Heuristics
A greedy randomized adaptive search procedure for the point-feature cartographic label placement
Computers & Geosciences
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
GRASP and path relinking for the max-min diversity problem
Computers and Operations Research
A probabilistic heuristic for a computationally difficult set covering problem
Operations Research Letters
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
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Proportional symbol map is a cartographic tool that employs symbols to represent data associated with specific locations. Each symbol is drawn at the location of an event and its size is proportional to the numerical data collected at that point on the map. The symbols considered here are opaque disks. When two or more disks overlap, part of their boundaries may not be visible and it might be difficult to gauge their size. Therefore, the order in which the disks are drawn affects the visual quality of a map. In this work, we focus on stacking drawings, i.e., a drawing that corresponds to the disks being stacked up, in sequence, starting from the one at the bottom of the stack. We address the Max-Total problem, which consists in maximizing the total visible boundary of all disks. We propose a sophisticated heuristic based on GRASP that includes most of the advanced techniques described in the literature for this procedure. We tested both sequential and parallel implementations on benchmark instances and the comparison against optimal solutions confirms the high quality of our heuristic. To the best of our knowledge, this is the first time a metaheuristic is applied to this problem.