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Optimizing the Minimum Vertex Guard Set on Simple Polygons via a Genetic Algorithm

TL;DR: An approximation algorithm based on general metaheuristic genetic algorithms to solve the MVG problem concludes that on average the minimum number of vertex-guards needed to cover an arbitrary and an orthogonal polygon with n vertices is 38 n.
Abstract: The problem of minimizing the number of vertex-guards necessary to cover a given simple polygon (MINIMUM VERTEX GUARD (MVG) problem) is NP-hard. This computational complexity opens two lines of investigation: the development of algorithms that establish approximate solutions and the determination of optimal solutions for special classes of simple polygons. In this paper we follow the first line of investigation and propose an approximation algorithm based on general metaheuristic genetic algorithms to solve the MVG problem. Based on our algorithm, we conclude that on average the minimum number of vertex-guards needed to cover an arbitrary and an orthogonal polygon with n vertices is 38 n , respectively. We also conclude that this result is very satisfactory in the sense that it is always close to optimal (with an approximation ratio of 2, for arbitrary polygons; and with an approximation ratio of 1.9, for orthogonal polygons).

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Proceedings ArticleDOI
11 Jul 2015
TL;DR: The objective of the proposed model is to maximize WMSN reliability by considering communication range of the nodes and terrain specific characteristics like occlusions, threat zones, and importance of targets under a given budget constraint.
Abstract: One of the most important design considerations for Wireless Multimedia Sensor Networks (WMSNs) is the reliability which involves connectivity and coverage issues with sensor and relay node deployment strategies that affects the coverage performance of the network directly. This paper addresses synergies from combining exact algorithms and metaheuristics to solve relay node deployment problem so as to maximize the information gathering reliability. The objective of the proposed model is to maximize WMSN reliability by considering communication range of the nodes and terrain specific characteristics like occlusions, threat zones, and importance of targets under a given budget constraint. We also integrated a Branch&Bound (B&B) approach with a Hybrid Genetic Algorithm Based Matheuristic (HGABM) to find the exact orientations of the cameras, and a Mixed Integer Linear Programming (MILP) network flow model is used to find the exact deployment points of the relay nodes. Since the calculation of network reliabilities for each network is time consuming, a Parallel Monte Carlo (MC) simulation is also developed and performed on General Purpose Graphic Processing Unit (GPGPU). Experimental study and comparison is conducted on synthetically generated terrains with different characteristics in order to show the effectiveness of HGABM.

5 citations


Cites methods from "Optimizing the Minimum Vertex Guard..."

  • ...The approximate methods [3–6] and genetic algorithms [7, 8] are applicable for restricted versions of the problem....

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Proceedings ArticleDOI
11 Oct 2009
TL;DR: This paper proposes three metaheuristic approaches to the problem of stationing guards in vertices of a simple polygon in such a way that the whole polygon is guarded and the number of guards is minimum.
Abstract: We address the problem of stationing guards in vertices of a simple polygon in such a way that the whole polygon is guarded and the number of guards is minimum. This problem is NP-hard with relevant practical applications. In this paper we propose three metaheuristic approaches to this problem. Combined with the genetic algorithms strategy, which was proposed in [4], these four approximation algorithms have been implemented and compared. The experimental evaluation from the hybrid strategy shows significant improvement in the number of guards compared to theoretical bounds.

5 citations


Cites background or methods or result from "Optimizing the Minimum Vertex Guard..."

  • ...It is important to note that, using hybrid metaheuristics, we improved our previous results [4]....

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  • ...Combined with the genetic algorithms strategy, which was proposed in [4], these four approximation algorithms have...

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  • ...In [4], we concluded that the combination that best fits into our problem is to use the tournament selection method and a variant of the single point crossover, where the generated children cannot be clones of the parents, with a probability of pc = 80%....

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  • ...For more details on the method used to calculate this approximation ratio, please refer to [4]....

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  • ...Concerning the genetic operators selection and crossover, in [4], we conducted an experimental study using several choices for these operators....

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01 Jan 2013
TL;DR: An approximate and polynomial solution based on metaheuristic genetic algorithms that can be applied to general 3D environments without any restriction and, therefore, applicable in shooter games and also real-world environments is presented.
Abstract: The Art Gallery Problem consists in determining th e minimum number of observers required to cover an environment such that each point is seen by at least one observer. This is a NP-Hard problem well known in the field of computational geometry. In the literature, several restrictions are applied to 2D and 3D environments to study and solve the problem in polynomial time, for example the use of simple polygons, orthogonal and planar environments, etc. In this paper we present an approximate and polynomial solution based on metaheuristic genetic algorithms that can be applied to general 3D environments without any restriction and, therefore, applicable in shooter games and also real-world environments. The solution uses the techniques of (i) computer graphics to generate sample points in the environment, (ii) ray-mesh intersection test to generate a graph of visibility between the samples and (iii) genetic algorithms to find and optimize the minimum set of observers. The maps of the game Counter-Strike were used to analyze the placement of small groups of observers in complex environments with obstacles. The game engines Half- Life and Irrlicht were used to apply the ray-mesh intersection test in 3D environments. A series of experiments were performed and the results show that our methodology is capable of obtaining a good coverage of space with a small number of agents observing. Keywords—art gallery problem; co mputational geometry; visibility; natural computation; computer graphics; shooter games

5 citations

Journal ArticleDOI
TL;DR: A new information gathering network reliability definition is made for WMSNs, and a mixed integer linear programming (MILP) network flow-based model is added into the initial population generation procedure of the HGA, and HGA outperforms the other algorithms.
Abstract: Network reliability has vital importance for designing wireless multimedia sensor networks (WMSNs). The definition of network reliability for WMSNs differentiates from the traditional communication network types which simultaneously involves node deployment, connectivity and coverage issues. Therefore, in this study, a new information gathering network reliability definition is made for WMSNs. The information gathering network reliability is maximized under a given total budget constraint by including node and terrain characteristics. The model is developed to get surveillance from an enemy zone. Since the reliable WMSN design considering node deployment, connectivity and coverage has NP-hard complexity, new hybrid methods are proposed with hybridization of exact methods with nature-inspired metaheuristics. Five algorithms are generated. Firstly, problem-specific simulated annealing (SA) and genetic algorithm (GA) are developed, then branch and bound (B&B) is embedded into the SA and GA named as hybrid SA (HSA) and hybrid GA (HGA). The B&B method optimizes the orientations of the sensor nodes. Additionally, an HGA-based matheuristic (HGABM) is proposed. In HGABM, a mixed integer linear programming (MILP) network flow-based model is added into the initial population generation procedure of the HGA. The MILP model finds the exact deployment points of the relay nodes. In experimental study, it is noticed that the main time-consuming parts of the algorithms are network reliability calculations. Thence, a parallel Monte Carlo (MC) simulation is developed and the MC runs are made in multiple general purpose graphics processing units (GPGPUs). Full-factorial experimental design and Taguchi design approaches are preferred to tune the parameters, to generate the problem sets and to make the experiments. The experimental study is performed on synthetically generated terrains with different terrain and device-based scenarios. Statistical methods are used to compare the performances of the algorithms. In conclusion, for small-sized sets HGABM and for moderate- and large-sized sets, HGA outperforms the other algorithms. The algorithms are coded in MATLAB and the MILP model is solved with CPLEX.

4 citations

Proceedings ArticleDOI
27 Aug 2020
TL;DR: This approach uses convolutional neural networks to classify materials by performing semantic segmentation on images captured in the VE, allowing a significant reduction in manual material tagging.
Abstract: This paper presents the ongoing work on an approach to material information retrieval in virtual environments (VEs). Our approach uses convolutional neural networks to classify materials by performing semantic segmentation on images captured in the VE. Class maps obtained are then re-projected onto the environment. We use transfer learning and fine-tune a pretrained segmentation model on images captured in our VEs. The geometry and semantic information can then be used to create mappings between objects in the VE and acoustic absorption coefficients. This can then be input for physically-based audio renderers, allowing a significant reduction in manual material tagging.

4 citations


Cites background from "Optimizing the Minimum Vertex Guard..."

  • ...extrapolate materials tagged to the entire scene, solutions to the Art Gallery problem would optimise the number of predictions required [24], [25]....

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References
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Book
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17,039 citations

Proceedings ArticleDOI
05 Jul 1995
TL;DR: C Culling is near optimal for this problem, highly noise tolerant, and the best known a~~roach in some regimes, and some new large deviation bounds on this submartingale enable us to determine the running time of the algorithm.
Abstract: We analyze the performance of a Genetic Type Algorithm we call Culling and a variety of other algorithms on a problem we refer to as ASP. Culling is near optimal for this problem, highly noise tolerant, and the best known a~~roach . . in some regimes. We show that the problem of learning the Ising perception is reducible to noisy ASP. These results provide an example of a rigorous analysis of GA’s and give insight into when and how C,A’s can beat competing methods. To analyze the genetic algorithm, we view it as a special type of submartingale. We prove some new large deviation bounds on this submartingale w~ich enable us to determine the running time of the algorithm.

4,520 citations

Journal ArticleDOI
TL;DR: A survey of the nowadays most important metaheuristics from a conceptual point of view and introduces a framework, that is called the I&D frame, in order to put different intensification and diversification components into relation with each other.
Abstract: The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behavior of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

3,287 citations


"Optimizing the Minimum Vertex Guard..." refers methods in this paper

  • ...A metaheuristic is a general algorithmic framework which can be adapted to different optimization problems with minor adjustments (see [7, 11] for a comprehensive survey on the subject)....

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Book
01 Jan 2003
TL;DR: This book discusses Metaheuristic Class Libraries, Hyper-Heuristics, and Artificial Neural Networks for Combinatorial Optimization, which are concerned withMetaheuristic Algorithms and their applications in Search Technology.
Abstract: List of Contributing Authors. Preface. 1. Scatter Search and Path Relinking: Advances and Applications F. Glover, et al. 2. An Introduction to Tabu Search M. Grenreau. 3. Genetic Algorithms C. Reeves. 4. Genetic Programming 5. A Gentle Introduction to Memetic Algorithms P. Moscato, C. Cotta. 6. Variable Neighborhood Search P. Hansen, N. Mladenovic. 7. Guided Local Search C. Voudouris, E. Tsang. 8. Greedy Randomized Adaptive Search Procedures M. Resende, C. Ribeiro. 9. The Ant Colony Optimization Metaheuristic: Algorithms, Applications, and Advances M. Doringo, T. Stutzle. 10. The Theory and Practice of Simulated Annealing D. Henderson, et al. 11. Iterated Local Search H. Lourenco, et al. 12. Multi-Start Methods R. Marti 13. Local Search and Constraint Programming F. Focacci, et al. 14. Constraint Satisfaction E. Freuder, M. Wallace. 15. Artificial Neural Networks for Combinatorial Optimization J.-Y. Potvin, K. Smith. 16. Hyper-Heuristics: An Emerging Direction in Modern Search Technology E. Burke, et al. 17. Parallel Strategies for Meta-Heuristics T.G. Crainic, M. Toulouse. 18. Metaheuristic Class Libraries A. Fink, et al. 19. Asynchronous Teams S. Talukdar, et al. Index.

2,284 citations

BookDOI
TL;DR: The Handbook now includes updated chapters on the best known metaheuristics, including simulated annealing, tabu search, variable neighborhood search, scatter search and path relinking, genetic algorithms, memetic algorithms, genetic programming, ant colony optimization, and multi-start methods.
Abstract: The first edition of the Handbook of Metaheuristics was published in 2003 under the editorship of Fred Glover and Gary A. Kochenberger. Given the numerous developments observed in the field of metaheuristics in recent years, it appeared that the time was ripe for a second edition of the Handbook. When Glover and Kochenberger were unable to prepare this second edition, they suggested that Michel Gendreau and Jean-Yves Potvin should take over the editorship, and so this important new edition is now available. Through its 21 chapters, this second edition is designed to provide a broad coverage of the concepts, implementations and applications in this important field of optimization. Original contributors either revised or updated their work, or provided entirely new chapters. The Handbook now includes updated chapters on the best known metaheuristics, including simulated annealing, tabu search, variable neighborhood search, scatter search and path relinking, genetic algorithms, memetic algorithms, genetic programming, ant colony optimization, multi-start methods, greedy randomized adaptive search procedure, guided local search, hyper-heuristics and parallel metaheuristics. It also contains three new chapters on large neighborhood search, artificial immune systems and hybrid metaheuristics. The last four chapters are devoted to more general issues related to the field of metaheuristics, namely reactive search, stochastic search, fitness landscape analysis and performance comparison.

1,208 citations


"Optimizing the Minimum Vertex Guard..." refers methods in this paper

  • ...A metaheuristic is a general algorithmic framework which can be adapted to different optimization problems with minor adjustments (see [7, 11] for a comprehensive survey on the subject)....

    [...]