ABSTRACT Proportional symbol map is a cartographic tool that employs symbols to represent data as... more ABSTRACT 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.
ABSTRACT Proportional symbol maps are a tool often used by cartographers and geoscience professio... more ABSTRACT Proportional symbol maps are a tool often used by cartographers and geoscience professionals to visualize geopositioned data associated with events and demographic statistics, such as earthquakes and population counts. Symbols are placed at specific locations on a map, and their areas are scaled to become proportional to the magnitudes of the data points they represent. We focus specifically on creating physically realizable drawings of symbols—opaque disks, in our case—by maximizing two quality metrics: the total and the minimum length of their visible borders. As these two maximization problems have been proven to be NP-hard, we provide integer programming formulations for their solution, along with decomposition techniques designed to decrease the size of input instances. Our computational experiments, which use real-life data sets, demonstrate the effectiveness of our approach and provide, for the first time, a number of optimal solutions to previously studied instances of this problem.
Brazilian petrobras is one of the world largest oil companies. Recurrently, it faces a very diffi... more Brazilian petrobras is one of the world largest oil companies. Recurrently, it faces a very difficult over-constrained planning challenge: how to operate a large pipeline network in order to adequately transport oil derivatives and biofuels from refineries to local markets. ...
2008 11th IEEE International Conference on Computational Science and Engineering, 2008
... Planning and Scheduling Problem Arnaldo V. Moura, Cid C. de Souza, Andre A. Cire, Tony MT Lop... more ... Planning and Scheduling Problem Arnaldo V. Moura, Cid C. de Souza, Andre A. Cire, Tony MT Lopes Institute of Computing - University of Campinas 13081-970, Campinas, SP {arnaldo, cid}@ic.unicamp.br, {andre.cire, tony.lopes}@gmail.com Abstract ...
Assume that a rectangle R is given on the Euclidean plane together with a finite set P of points ... more Assume that a rectangle R is given on the Euclidean plane together with a finite set P of points that are interior to R. A rectangular partition of R is a partition of the surface of R into smaller rectangles. The length of such a partition equals the sum of the lengths for the line ...
This paper studies the Orthogonal Milling with Turn Costs. An exact algorithm is proposed based o... more This paper studies the Orthogonal Milling with Turn Costs. An exact algorithm is proposed based on an Integer Programming formulation of the problem. To our knowledge, this is the first exact algorithm ever proposed for the problem. Besides, a simple heuristic is also presented and an unprecedented experimentation involving these two algorithms and an existing approximation algorithm is carried out.
Proceedings of the 2000 ACM symposium on Applied computing - SAC '00, 2000
In this article, we present a hybrid methodology for the exact solution of large scale real world... more In this article, we present a hybrid methodology for the exact solution of large scale real world crew scheduling problems. Our approach integrates mathematical programming and constraint satisfaction techniques, taking advantage of their particular abilities in modeling and solving specific parts of the problem. An Integer Programming framework was responsible for guiding the overall search process and for obtaining lower
ABSTRACT Proportional symbol map is a cartographic tool that employs symbols to represent data as... more ABSTRACT 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.
ABSTRACT Proportional symbol maps are a tool often used by cartographers and geoscience professio... more ABSTRACT Proportional symbol maps are a tool often used by cartographers and geoscience professionals to visualize geopositioned data associated with events and demographic statistics, such as earthquakes and population counts. Symbols are placed at specific locations on a map, and their areas are scaled to become proportional to the magnitudes of the data points they represent. We focus specifically on creating physically realizable drawings of symbols—opaque disks, in our case—by maximizing two quality metrics: the total and the minimum length of their visible borders. As these two maximization problems have been proven to be NP-hard, we provide integer programming formulations for their solution, along with decomposition techniques designed to decrease the size of input instances. Our computational experiments, which use real-life data sets, demonstrate the effectiveness of our approach and provide, for the first time, a number of optimal solutions to previously studied instances of this problem.
Brazilian petrobras is one of the world largest oil companies. Recurrently, it faces a very diffi... more Brazilian petrobras is one of the world largest oil companies. Recurrently, it faces a very difficult over-constrained planning challenge: how to operate a large pipeline network in order to adequately transport oil derivatives and biofuels from refineries to local markets. ...
2008 11th IEEE International Conference on Computational Science and Engineering, 2008
... Planning and Scheduling Problem Arnaldo V. Moura, Cid C. de Souza, Andre A. Cire, Tony MT Lop... more ... Planning and Scheduling Problem Arnaldo V. Moura, Cid C. de Souza, Andre A. Cire, Tony MT Lopes Institute of Computing - University of Campinas 13081-970, Campinas, SP {arnaldo, cid}@ic.unicamp.br, {andre.cire, tony.lopes}@gmail.com Abstract ...
Assume that a rectangle R is given on the Euclidean plane together with a finite set P of points ... more Assume that a rectangle R is given on the Euclidean plane together with a finite set P of points that are interior to R. A rectangular partition of R is a partition of the surface of R into smaller rectangles. The length of such a partition equals the sum of the lengths for the line ...
This paper studies the Orthogonal Milling with Turn Costs. An exact algorithm is proposed based o... more This paper studies the Orthogonal Milling with Turn Costs. An exact algorithm is proposed based on an Integer Programming formulation of the problem. To our knowledge, this is the first exact algorithm ever proposed for the problem. Besides, a simple heuristic is also presented and an unprecedented experimentation involving these two algorithms and an existing approximation algorithm is carried out.
Proceedings of the 2000 ACM symposium on Applied computing - SAC '00, 2000
In this article, we present a hybrid methodology for the exact solution of large scale real world... more In this article, we present a hybrid methodology for the exact solution of large scale real world crew scheduling problems. Our approach integrates mathematical programming and constraint satisfaction techniques, taking advantage of their particular abilities in modeling and solving specific parts of the problem. An Integer Programming framework was responsible for guiding the overall search process and for obtaining lower
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