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Martin Furer - One of the best experts on this subject based on the ideXlab platform.
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approximation of k set cover by semi Local Optimization
Symposium on the Theory of Computing, 1997Co-Authors: Martin FurerAbstract:In this thesis a powerful new approximation technique called semi-Local Optimization is introduced. It provides very natural heuristics that are distinctly more effective than those based on Local Optimization. With an appropriate metric, semi-Local Optimization can still be viewed as a Local Optimization, but it has the advantage of making global changes to an approximate solution in polynomial time. Semi-Local Optimization generalizes recent heuristics of Halldorsson for the 3-Set Cover problem, the Color Saving problem, and the k-Set Cover problem. Greatly improved performance ratios of 4/3 for the 3-Set Cover problem and 6/5 for the Color Saving problem in graphs without independent sets of size 4 are obtained and shown to be the best possible with semi-Local Optimization. Also, based on the result for the 3-Set Cover problem and a restricted greedy phase for big sets, the performance ratio, for the k-Set Cover problem is correspondingly improved to ${\cal H}\sb{k}-1/2$. This result is also tight with the semi-Local Optimization technique. For larger values of k, further improvement better than ${\cal H}\sb{k}-1/2$ are also possible when the greedy selection of big sets is replaced by a Local Optimization selection. In the Color Saving problem, when larger independent sets exist, an improvement of the performance ratio to ${240}\over{193}$ for general graphs can be obtained.
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STOC - Approximation of k -set cover by semi-Local Optimization
Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC '97, 1997Co-Authors: Martin FurerAbstract:In this thesis a powerful new approximation technique called semi-Local Optimization is introduced. It provides very natural heuristics that are distinctly more effective than those based on Local Optimization. With an appropriate metric, semi-Local Optimization can still be viewed as a Local Optimization, but it has the advantage of making global changes to an approximate solution in polynomial time. Semi-Local Optimization generalizes recent heuristics of Halldorsson for the 3-Set Cover problem, the Color Saving problem, and the k-Set Cover problem. Greatly improved performance ratios of 4/3 for the 3-Set Cover problem and 6/5 for the Color Saving problem in graphs without independent sets of size 4 are obtained and shown to be the best possible with semi-Local Optimization. Also, based on the result for the 3-Set Cover problem and a restricted greedy phase for big sets, the performance ratio, for the k-Set Cover problem is correspondingly improved to ${\cal H}\sb{k}-1/2$. This result is also tight with the semi-Local Optimization technique. For larger values of k, further improvement better than ${\cal H}\sb{k}-1/2$ are also possible when the greedy selection of big sets is replaced by a Local Optimization selection. In the Color Saving problem, when larger independent sets exist, an improvement of the performance ratio to ${240}\over{193}$ for general graphs can be obtained.
David S Johnson - One of the best experts on this subject based on the ideXlab platform.
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the traveling salesman problem a case study in Local Optimization
2008Co-Authors: David S Johnson, Lyle A McgeochAbstract:This is a preliminary version of a chapter that appeared in the book Local Search in Combinatorial Optimization, E. H. L. Aarts and J. K. Lenstra (eds.), John Wiley and Sons, London, 1997, pp. 215-310. The traveling salesman problem (TSP) has been an early proving ground for many approaches to combinatorial Optimization, including classical Local Optimization techniques as well as many of the more recent variants on Local Optimization, such as simulated annealing, tabu search, neural networks, and genetic algorithms. This chapter discusses how these various approaches have been adapted to the TSP and evaluates their relative success in this perhaps atypical domain from both a theoretical and an experimental point of view.
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Local Optimization and the traveling salesman problem
International Colloquium on Automata Languages and Programming, 1990Co-Authors: David S JohnsonAbstract:The Traveling Salesman Problem (TSP) is often cited as the prototypical “hard” combinatorial Optimization problem. As such, it would seem to be an ideal candidate for nonstandard algorithmic approaches, such as simulated annealing, and, more recently, genetic algorithms. Both of these approaches can be viewed as variants on the traditional technique called Local Optimization. This paper surveys the state of the art with respect to the TSP, with emphasis on the performance of traditional Local Optimization algorithms and their new competitors, and on what insights complexity theory does, or does not, provide.
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ICALP - Local Optimization and the Traveling Salesman Problem
Automata Languages and Programming, 1990Co-Authors: David S JohnsonAbstract:The Traveling Salesman Problem (TSP) is often cited as the prototypical “hard” combinatorial Optimization problem. As such, it would seem to be an ideal candidate for nonstandard algorithmic approaches, such as simulated annealing, and, more recently, genetic algorithms. Both of these approaches can be viewed as variants on the traditional technique called Local Optimization. This paper surveys the state of the art with respect to the TSP, with emphasis on the performance of traditional Local Optimization algorithms and their new competitors, and on what insights complexity theory does, or does not, provide.
T. Sakamoto - One of the best experts on this subject based on the ideXlab platform.
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2‐D cutting‐stock algorithms based on Local Optimization
Electronics and Communications in Japan Part Iii-fundamental Electronic Science, 2007Co-Authors: T. SakamotoAbstract:This paper proposes the two-dimensional (2-D) cutting-stock algorithm based on the Local Optimization. First, it is intended to eliminate the combinational process for the rectangular parts in the traditional system. The search operation is defined as the one-to-one mapping of the rectangular parts to the partial rectangular regions generated by the divide operation. A stack is used to store the data for the partial rectangular regions, and the merge operation is introduced as a new concept of operation in the stack. The algorithm is constructed recursively using the following four operations, i.e., search, divide, merge, and stack. Through an application example, it is verified that the proposed algorithm can realize nearly the same layout efficiency as the traditional method by the dynamic programming.
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Numerical experiment on the 2D cutting-stock algorithms based on Local Optimization
System Modelling and Optimization, 1996Co-Authors: T. SakamotoAbstract:A numerical experiment on the computational complexity and the efficiency of layout is reported for the 2D cutting-stock algorithms based on Local Optimization. The time and the space complexity are respectively found to be O(n 2) and better than O(e 0) by the regression analysis, where n is the number of rectangular parts and e 0 is the edge length of square sheets. The efficiency of layout is also discussed with respect to the aspect ratio of rectangular sheets.
Shigeru Obayashi - One of the best experts on this subject based on the ideXlab platform.
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Multi-Stage Aerodynamic Design of Multi-Body Geometries via Global and Local Optimization Methods
46th AIAA Aerospace Sciences Meeting and Exhibit, 2008Co-Authors: Shigeru ObayashiAbstract:*† ‡ § An efficient and high-fidelity design approach is proposed by combining global and Local Optimization methods for wing planform and surface design. For enhanced design results, aerodynamic shape Optimization process is carried out via 2-stage with different Optimization strategy. In the first stage, global Optimization techniques are applied to planform design with a few geometric design variables. In the second stage, Local Optimization techniques are used for wing surface design with a lot of design variables to maintain a sufficient design space with high DOF (Degree of Freedom) geometric change. For global Optimization, meta-modeling techniques such as RS (Response Surface) and Kriging methods are used in conjunction with Genetic Algorithm (GA). For Local Optimization, a discrete adjoint variable method is used. By the successive combination of global and Local Optimization techniques, drag minimization is performed for a multi-body aircraft configuration while maintaining the baseline lift and the wing weight at the same time. Through the design process, performances of the test models are remarkably improved in comparison with the single stage design approach. The capability of proposed design framework including wing planform design variables can be evaluated by the drag decomposition method which can provide improvement of induced drag and wave drag, respectively.
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Multi-stage aerodynamic design of multi-body geometries via global and Local Optimization methods
46th AIAA Aerospace Sciences Meeting and Exhibit, 2008Co-Authors: Jinwoo Yim, Space Engineering, Byung Joon Lee, Corresponding Author, Shigeru Obayashi, Chulsoo KimAbstract:An efficient and high-fidelity design approach is proposed by combining global and Local Optimization methods for wing planform and surface design. For enhanced design results, aerodynamic shape Optimization process is carried out via 2-stage with different Optimization strategy. In the first stage, global Optimization techniques are applied to planform design with a few geometric design variables. In the second stage, Local Optimization techniques are used for wing surface design with a lot of design variables to maintain a sufficient design space with high DOF (Degree of Freedom) geometric change. For global Optimization, meta-modeling techniques such as RS (Response Surface) and Kriging methods are used in conjunction with Genetic Algorithm (GA). For Local Optimization, a discrete adjoint variable method is used. By the successive combination of global and Local Optimization techniques, drag minimization is performed for a multi-body aircraft configuration while maintaining the baseline lift and the wing weight at the same time. Through the design process, performances of the test models are remarkably improved in comparison with the single stage design approach. The capability of proposed design framework including wing planform design variables can be evaluated by the drag decomposition method which can provide improvement of induced drag and wave drag, respectively. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc.
Ghassan Hamarneh - One of the best experts on this subject based on the ideXlab platform.
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Local Optimization based segmentation of spatially recurring multi region objects with part configuration constraints
IEEE Transactions on Medical Imaging, 2014Co-Authors: Masoud S Nosrati, Ghassan HamarnehAbstract:: Incorporating prior knowledge into image segmentation algorithms has proven useful for obtaining more accurate and plausible results. Two important constraints, containment and exclusion of regions, have gained attention in recent years mainly due to their descriptive power. In this paper, we augment the level set framework with the ability to handle these two intuitive geometric relationships, containment and exclusion, along with a distance constraint between boundaries of multi-region objects. Level set's important property of automatically handling topological changes of evolving contours/surfaces enables us to segment spatially-recurring objects (e.g., multiple instances of multi-region cells in a large microscopy image) while satisfying the two aforementioned constraints. In addition, the level set approach gives us a very simple and natural way to compute the distance between contours/surfaces and impose constraints on it. The downside, however, is a Local Optimization framework in which the final segmentation solution depends on the initialization. In fact, here, we sacrifice the optimizability (Local instead of global solution) in exchange for lower space complexity (less memory usage) and faster runtime (especially for large microscopic images) as well as no grid artifacts. Nevertheless, the result from validating our method on several biomedical applications showed the utility and advantages of this augmented level set framework (even with rough initialization that is distant from the desired boundaries). We also compared our framework with its counterpart methods in the discrete domain and reported the pros and cons of each of these methods in terms of metrication error and efficiency in memory usage and runtime.