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Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining

Author: Hassan AbouEisha

Publisher: Springer

Published: 2018-05-22

Total Pages: 280

ISBN-13: 3319918397

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Dynamic programming is an efficient technique for solving optimization problems. It is based on breaking the initial problem down into simpler ones and solving these sub-problems, beginning with the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects. This book develops extensions of dynamic programming, enabling us to (i) describe the set of objects under consideration; (ii) perform a multi-stage optimization of objects relative to different criteria; (iii) count the number of optimal objects; (iv) find the set of Pareto optimal points for bi-criteria optimization problems; and (v) to study relationships between two criteria. It considers various applications, including optimization of decision trees and decision rule systems as algorithms for problem solving, as ways for knowledge representation, and as classifiers; optimization of element partition trees for rectangular meshes, which are used in finite element methods for solving PDEs; and multi-stage optimization for such classic combinatorial optimization problems as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths. The results presented are useful for researchers in combinatorial optimization, data mining, knowledge discovery, machine learning, and finite element methods, especially those working in rough set theory, test theory, logical analysis of data, and PDE solvers. This book can be used as the basis for graduate courses.

Book Synopsis Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining by : Hassan AbouEisha

Download or read book Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining written by Hassan AbouEisha and published by Springer. This book was released on 2018-05-22 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic programming is an efficient technique for solving optimization problems. It is based on breaking the initial problem down into simpler ones and solving these sub-problems, beginning with the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects. This book develops extensions of dynamic programming, enabling us to (i) describe the set of objects under consideration; (ii) perform a multi-stage optimization of objects relative to different criteria; (iii) count the number of optimal objects; (iv) find the set of Pareto optimal points for bi-criteria optimization problems; and (v) to study relationships between two criteria. It considers various applications, including optimization of decision trees and decision rule systems as algorithms for problem solving, as ways for knowledge representation, and as classifiers; optimization of element partition trees for rectangular meshes, which are used in finite element methods for solving PDEs; and multi-stage optimization for such classic combinatorial optimization problems as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths. The results presented are useful for researchers in combinatorial optimization, data mining, knowledge discovery, machine learning, and finite element methods, especially those working in rough set theory, test theory, logical analysis of data, and PDE solvers. This book can be used as the basis for graduate courses.

Combinatorial Data Analysis

Author: Lawrence Hubert

Publisher: SIAM

Published: 2001-01-01

Total Pages: 172

ISBN-13: 0898714788

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Combinatorial data analysis refers to methods for the study of data sets where the arrangement of objects is central.

Book Synopsis Combinatorial Data Analysis by : Lawrence Hubert

Download or read book Combinatorial Data Analysis written by Lawrence Hubert and published by SIAM. This book was released on 2001-01-01 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial data analysis refers to methods for the study of data sets where the arrangement of objects is central.

Data Correcting Approaches in Combinatorial Optimization

Author: Boris Goldengorin

Publisher: Springer Science & Business Media

Published: 2012-10-11

Total Pages: 124

ISBN-13: 1461452856

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Data Correcting Approaches in Combinatorial Optimization focuses on algorithmic applications of the well known polynomially solvable special cases of computationally intractable problems. The purpose of this text is to design practically efficient algorithms for solving wide classes of combinatorial optimization problems. Researches, students and engineers will benefit from new bounds and branching rules in development efficient branch-and-bound type computational algorithms. This book examines applications for solving the Traveling Salesman Problem and its variations, Maximum Weight Independent Set Problem, Different Classes of Allocation and Cluster Analysis as well as some classes of Scheduling Problems. Data Correcting Algorithms in Combinatorial Optimization introduces the data correcting approach to algorithms which provide an answer to the following questions: how to construct a bound to the original intractable problem and find which element of the corrected instance one should branch such that the total size of search tree will be minimized. The PC time needed for solving intractable problems will be adjusted with the requirements for solving real world problems.

Book Synopsis Data Correcting Approaches in Combinatorial Optimization by : Boris Goldengorin

Download or read book Data Correcting Approaches in Combinatorial Optimization written by Boris Goldengorin and published by Springer Science & Business Media. This book was released on 2012-10-11 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data Correcting Approaches in Combinatorial Optimization focuses on algorithmic applications of the well known polynomially solvable special cases of computationally intractable problems. The purpose of this text is to design practically efficient algorithms for solving wide classes of combinatorial optimization problems. Researches, students and engineers will benefit from new bounds and branching rules in development efficient branch-and-bound type computational algorithms. This book examines applications for solving the Traveling Salesman Problem and its variations, Maximum Weight Independent Set Problem, Different Classes of Allocation and Cluster Analysis as well as some classes of Scheduling Problems. Data Correcting Algorithms in Combinatorial Optimization introduces the data correcting approach to algorithms which provide an answer to the following questions: how to construct a bound to the original intractable problem and find which element of the corrected instance one should branch such that the total size of search tree will be minimized. The PC time needed for solving intractable problems will be adjusted with the requirements for solving real world problems.

Combinatorial Optimization Techniques in Data Mining

Author: Stanislav Busygin

Publisher:

Published: 2007

Total Pages:

ISBN-13:

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Next, I discuss the prominent role of graph models in data analysis with the emphasis on data analysis applications of the maximum clique/independent set problem. The great variety of real-world problems that can be tackled with the graph-based models is surveyed along with the employed methodologies of information retrieval. Finally, I present a practically efficient maximum clique heuristic QUALEX-MS. It utilizes a new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem. This generalization, representing quite a significant theoretical result itself, maximally preserves the form of the original Motzkin-Straus formulation and is proved directly, without the use of mathematical induction. QUALEX-MS employs a new trust region heuristic based upon this new quadratic programming formulation. In contrast to usual trust region methods, it takes into account not only the global optimum of a quadratic objective over a sphere, but also a set of other stationary points. The developed method has complexity O(n3), where n is the number of vertices of the graph. Computational experiments indicate that QUALEX-MS is exact on small graphs and very efficient on the DIMACS benchmark graphs and various random maximum weight clique problem instances. QUALEX-MS was utilized for optimization of classification and regression trees of databases.

Book Synopsis Combinatorial Optimization Techniques in Data Mining by : Stanislav Busygin

Download or read book Combinatorial Optimization Techniques in Data Mining written by Stanislav Busygin and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Next, I discuss the prominent role of graph models in data analysis with the emphasis on data analysis applications of the maximum clique/independent set problem. The great variety of real-world problems that can be tackled with the graph-based models is surveyed along with the employed methodologies of information retrieval. Finally, I present a practically efficient maximum clique heuristic QUALEX-MS. It utilizes a new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem. This generalization, representing quite a significant theoretical result itself, maximally preserves the form of the original Motzkin-Straus formulation and is proved directly, without the use of mathematical induction. QUALEX-MS employs a new trust region heuristic based upon this new quadratic programming formulation. In contrast to usual trust region methods, it takes into account not only the global optimum of a quadratic objective over a sphere, but also a set of other stationary points. The developed method has complexity O(n3), where n is the number of vertices of the graph. Computational experiments indicate that QUALEX-MS is exact on small graphs and very efficient on the DIMACS benchmark graphs and various random maximum weight clique problem instances. QUALEX-MS was utilized for optimization of classification and regression trees of databases.

Analysis and Design of Algorithms for Combinatorial Problems

Author: G. Ausiello

Publisher: Elsevier

Published: 1985-05-01

Total Pages: 318

ISBN-13: 9780080872209

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Combinatorial problems have been from the very beginning part of the history of mathematics. By the Sixties, the main classes of combinatorial problems had been defined. During that decade, a great number of research contributions in graph theory had been produced, which laid the foundations for most of the research in graph optimization in the following years. During the Seventies, a large number of special purpose models were developed. The impressive growth of this field since has been strongly determined by the demand of applications and influenced by the technological increases in computing power and the availability of data and software. The availability of such basic tools has led to the feasibility of the exact or well approximate solution of large scale realistic combinatorial optimization problems and has created a number of new combinatorial problems.

Book Synopsis Analysis and Design of Algorithms for Combinatorial Problems by : G. Ausiello

Download or read book Analysis and Design of Algorithms for Combinatorial Problems written by G. Ausiello and published by Elsevier. This book was released on 1985-05-01 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial problems have been from the very beginning part of the history of mathematics. By the Sixties, the main classes of combinatorial problems had been defined. During that decade, a great number of research contributions in graph theory had been produced, which laid the foundations for most of the research in graph optimization in the following years. During the Seventies, a large number of special purpose models were developed. The impressive growth of this field since has been strongly determined by the demand of applications and influenced by the technological increases in computing power and the availability of data and software. The availability of such basic tools has led to the feasibility of the exact or well approximate solution of large scale realistic combinatorial optimization problems and has created a number of new combinatorial problems.

Dynamic Programming Multi-Objective Combinatorial Optimization

Author: Michal Mankowski

Publisher: Springer Nature

Published: 2021-02-08

Total Pages: 213

ISBN-13: 3030639207

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This book introduces a fairly universal approach to the design and analysis of exact optimization algorithms for multi-objective combinatorial optimization problems. It proposes the circuits without repetitions representing the sets of feasible solutions along with the increasing and strictly increasing cost functions as a model for such problems. The book designs the algorithms for multi-stage and bi-criteria optimization and for counting the solutions in the framework of this model. As applications, this book studies eleven known combinatorial optimization problems: matrix chain multiplication, global sequence alignment, optimal paths in directed graphs, binary search trees, convex polygon triangulation, line breaking (text justification), one-dimensional clustering, optimal bitonic tour, segmented least squares, optimization of matchings in trees, and 0/1 knapsack problem. The results presented are useful for researchers in combinatorial optimization. This book is also useful as the basis for graduate courses.

Book Synopsis Dynamic Programming Multi-Objective Combinatorial Optimization by : Michal Mankowski

Download or read book Dynamic Programming Multi-Objective Combinatorial Optimization written by Michal Mankowski and published by Springer Nature. This book was released on 2021-02-08 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a fairly universal approach to the design and analysis of exact optimization algorithms for multi-objective combinatorial optimization problems. It proposes the circuits without repetitions representing the sets of feasible solutions along with the increasing and strictly increasing cost functions as a model for such problems. The book designs the algorithms for multi-stage and bi-criteria optimization and for counting the solutions in the framework of this model. As applications, this book studies eleven known combinatorial optimization problems: matrix chain multiplication, global sequence alignment, optimal paths in directed graphs, binary search trees, convex polygon triangulation, line breaking (text justification), one-dimensional clustering, optimal bitonic tour, segmented least squares, optimization of matchings in trees, and 0/1 knapsack problem. The results presented are useful for researchers in combinatorial optimization. This book is also useful as the basis for graduate courses.

Nonlinear Combinatorial Optimization

Author: Ding-Zhu Du

Publisher: Springer

Published: 2019-06-14

Total Pages: 0

ISBN-13: 9783030161934

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Graduate students and researchers in applied mathematics, optimization, engineering, computer science, and management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization. Nonlinear combinatorial optimization is a new research area within combinatorial optimization and includes numerous applications to technological developments, such as wireless communication, cloud computing, data science, and social networks. Theoretical developments including discrete Newton methods, primal-dual methods with convex relaxation, submodular optimization, discrete DC program, along with several applications are discussed and explored in this book through articles by leading experts.

Book Synopsis Nonlinear Combinatorial Optimization by : Ding-Zhu Du

Download or read book Nonlinear Combinatorial Optimization written by Ding-Zhu Du and published by Springer. This book was released on 2019-06-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate students and researchers in applied mathematics, optimization, engineering, computer science, and management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization. Nonlinear combinatorial optimization is a new research area within combinatorial optimization and includes numerous applications to technological developments, such as wireless communication, cloud computing, data science, and social networks. Theoretical developments including discrete Newton methods, primal-dual methods with convex relaxation, submodular optimization, discrete DC program, along with several applications are discussed and explored in this book through articles by leading experts.

Intelligence Science III

Author: Zhongzhi Shi

Publisher: Springer Nature

Published: 2021-04-14

Total Pages: 317

ISBN-13: 303074826X

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This book constitutes the refereed post-conference proceedings of the 4th International Conference on Intelligence Science, ICIS 2020, held in Durgapur, India, in February 2021 (originally November 2020). The 23 full papers and 4 short papers presented were carefully reviewed and selected from 42 submissions. One extended abstract is also included. They deal with key issues in brain cognition; uncertain theory; machine learning; data intelligence; language cognition; vision cognition; perceptual intelligence; intelligent robot; and medical artificial intelligence.

Book Synopsis Intelligence Science III by : Zhongzhi Shi

Download or read book Intelligence Science III written by Zhongzhi Shi and published by Springer Nature. This book was released on 2021-04-14 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-conference proceedings of the 4th International Conference on Intelligence Science, ICIS 2020, held in Durgapur, India, in February 2021 (originally November 2020). The 23 full papers and 4 short papers presented were carefully reviewed and selected from 42 submissions. One extended abstract is also included. They deal with key issues in brain cognition; uncertain theory; machine learning; data intelligence; language cognition; vision cognition; perceptual intelligence; intelligent robot; and medical artificial intelligence.

Advanced Computing and Intelligent Technologies

Author: Monica Bianchini

Publisher: Springer Nature

Published: 2021-07-21

Total Pages: 649

ISBN-13: 9811621640

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This book gathers selected high-quality research papers presented at International Conference on Advanced Computing and Intelligent Technologies (ICACIT 2021) held at NCR New Delhi, India, during March 20–21, 2021, jointly organized by Galgotias University, India, and Department of Information Engineering and Mathematics Università Di Siena, Italy. It discusses emerging topics pertaining to advanced computing, intelligent technologies, and networks including AI and machine learning, data mining, big data analytics, high-performance computing network performance analysis, Internet of things networks, wireless sensor networks, and others. The book offers a valuable asset for researchers from both academia and industries involved in advanced studies.

Book Synopsis Advanced Computing and Intelligent Technologies by : Monica Bianchini

Download or read book Advanced Computing and Intelligent Technologies written by Monica Bianchini and published by Springer Nature. This book was released on 2021-07-21 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers selected high-quality research papers presented at International Conference on Advanced Computing and Intelligent Technologies (ICACIT 2021) held at NCR New Delhi, India, during March 20–21, 2021, jointly organized by Galgotias University, India, and Department of Information Engineering and Mathematics Università Di Siena, Italy. It discusses emerging topics pertaining to advanced computing, intelligent technologies, and networks including AI and machine learning, data mining, big data analytics, high-performance computing network performance analysis, Internet of things networks, wireless sensor networks, and others. The book offers a valuable asset for researchers from both academia and industries involved in advanced studies.

Artificial Intelligence and Soft Computing

Author: Leszek Rutkowski

Publisher: Springer

Published: 2019-05-27

Total Pages: 712

ISBN-13: 3030209156

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The two-volume set LNCS 11508 and 11509 constitutes the refereed proceedings of of the 18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019, held in Zakopane, Poland, in June 2019. The 122 revised full papers presented were carefully reviewed and selected from 333 submissions. The papers included in the first volume are organized in the following five parts: neural networks and their applications; fuzzy systems and their applications; evolutionary algorithms and their applications; pattern classification; artificial intelligence in modeling and simulation. The papers included in the second volume are organized in the following five parts: computer vision, image and speech analysis; bioinformatics, biometrics, and medical applications; data mining; various problems of artificial intelligence; agent systems, robotics and control.

Book Synopsis Artificial Intelligence and Soft Computing by : Leszek Rutkowski

Download or read book Artificial Intelligence and Soft Computing written by Leszek Rutkowski and published by Springer. This book was released on 2019-05-27 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 11508 and 11509 constitutes the refereed proceedings of of the 18th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2019, held in Zakopane, Poland, in June 2019. The 122 revised full papers presented were carefully reviewed and selected from 333 submissions. The papers included in the first volume are organized in the following five parts: neural networks and their applications; fuzzy systems and their applications; evolutionary algorithms and their applications; pattern classification; artificial intelligence in modeling and simulation. The papers included in the second volume are organized in the following five parts: computer vision, image and speech analysis; bioinformatics, biometrics, and medical applications; data mining; various problems of artificial intelligence; agent systems, robotics and control.