Download or read book Heuristic Methods Applied to Difficult Graph Theory Problems written by Roqyah Alalqam and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graph Theory Heuristic Methods written by N.B. Singh and published by N.B. Singh. This book was released on with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Graph Theory: Heuristic Methods" explores the intersection of graph theory and heuristic algorithms, offering a comprehensive exploration of how these methodologies contribute to solving diverse real-world challenges in network design and optimization. Covering fundamental concepts, advanced applications, and emerging trends, this book serves as a vital resource for researchers, practitioners, and students seeking to leverage heuristic approaches for tackling complex problems across various domains."
Download or read book Optimization Problems in Graph Theory written by Boris Goldengorin and published by Springer. This book was released on 2018-09-27 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents open optimization problems in graph theory and networks. Each chapter reflects developments in theory and applications based on Gregory Gutin’s fundamental contributions to advanced methods and techniques in combinatorial optimization. Researchers, students, and engineers in computer science, big data, applied mathematics, operations research, algorithm design, artificial intelligence, software engineering, data analysis, industrial and systems engineering will benefit from the state-of-the-art results presented in modern graph theory and its applications to the design of efficient algorithms for optimization problems. Topics covered in this work include: · Algorithmic aspects of problems with disjoint cycles in graphs · Graphs where maximal cliques and stable sets intersect · The maximum independent set problem with special classes · A general technique for heuristic algorithms for optimization problems · The network design problem with cut constraints · Algorithms for computing the frustration index of a signed graph · A heuristic approach for studying the patrol problem on a graph · Minimum possible sum and product of the proper connection number · Structural and algorithmic results on branchings in digraphs · Improved upper bounds for Korkel--Ghosh benchmark SPLP instances
Download or read book Meta Heuristics written by Ibrahim H. Osman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meta-heuristics have developed dramatically since their inception in the early 1980s. They have had widespread success in attacking a variety of practical and difficult combinatorial optimization problems. These families of approaches include, but are not limited to greedy random adaptive search procedures, genetic algorithms, problem-space search, neural networks, simulated annealing, tabu search, threshold algorithms, and their hybrids. They incorporate concepts based on biological evolution, intelligent problem solving, mathematical and physical sciences, nervous systems, and statistical mechanics. Since the 1980s, a great deal of effort has been invested in the field of combinatorial optimization theory in which heuristic algorithms have become an important area of research and applications. This volume is drawn from the first conference on Meta-Heuristics and contains 41 papers on the state-of-the-art in heuristic theory and applications. The book treats the following meta-heuristics and applications: Genetic Algorithms, Simulated Annealing, Tabu Search, Networks & Graphs, Scheduling and Control, TSP, and Vehicle Routing Problems. It represents research from the fields of Operations Research, Management Science, Artificial Intelligence and Computer Science.
Download or read book Graph Theory written by Ralucca Gera and published by Springer. This book was released on 2018-10-26 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume in a two-volume series provides an extensive collection of conjectures and open problems in graph theory. It is designed for both graduate students and established researchers in discrete mathematics who are searching for research ideas and references. Each chapter provides more than a simple collection of results on a particular topic; it captures the reader’s interest with techniques that worked and failed in attempting to solve particular conjectures. The history and origins of specific conjectures and the methods of researching them are also included throughout this volume. Students and researchers can discover how the conjectures have evolved and the various approaches that have been used in an attempt to solve them. An annotated glossary of nearly 300 graph theory parameters, 70 conjectures, and over 600 references is also included in this volume. This glossary provides an understanding of parameters beyond their definitions and enables readers to discover new ideas and new definitions in graph theory. The editors were inspired to create this series of volumes by the popular and well-attended special sessions entitled “My Favorite Graph Theory Conjectures,” which they organized at past AMS meetings. These sessions were held at the winter AMS/MAA Joint Meeting in Boston, January 2012, the SIAM Conference on Discrete Mathematics in Halifax in June 2012, as well as the winter AMS/MAA Joint Meeting in Baltimore in January 2014, at which many of the best-known graph theorists spoke. In an effort to aid in the creation and dissemination of conjectures and open problems, which is crucial to the growth and development of this field, the editors invited these speakers, as well as other experts in graph theory, to contribute to this series.
Download or read book Solving Hard Graph Problems with Combinatorial Computing and Optimization written by Alexander R. Lange and published by . This book was released on 2013 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Many problems arising in graph theory are difficult by nature, and finding solutions to large or complex instances of them often requires the use of computers. As some such problems are NP-hard or lie even higher in the polynomial hierarchy, it is unlikely that efficient, exact algorithms will solve them. Therefore, alternative computational methods are used. Combinatorial computing is a branch of mathematics and computer science concerned with these methods, where algorithms are developed to generate and search through combinatorial structures in order to determine certain properties of them. In this thesis, we explore a number of such techniques, in the hopes of solving specific problem instances of interest. Three separate problems are considered, each of which is attacked with different methods of combinatorial computing and optimization. The first, originally proposed by Erdös and Hajnal in 1967, asks to find the Folkman number Fe(3, 3; 4), defined as the smallest order of a K4-free graph that is not the union of two triangle-free graphs. A notoriously difficult problem associated with Ramsey theory, the best known bounds on it prior to this work were 19 [less than or equal to] Fe (3, 3; 4) [less than or equal to] 941. We improve the upper bound to Fe (3, 3; 4) [less than or equal to] 786 using a combination of known methods and the Goemans-Williamson semi-definite programming relaxation of MAX-CUT. The second problem of interest is the Ramsey number R(C4, Km), which is the smallest n such that any n-vertex graph contains a cycle of length four or an independent set of order m. With the help of combinatorial algorithms, we determine R(C4, K9) = 30 and R(C4, K10) = 36 using large-scale computations on the Open Science Grid. Finally, we explore applications of the well-known Lenstra-Lenstra-Lovász (LLL) algorithm, a polynomial-time algorithm that, when given a basis of a lattice, returns a basis for the same lattice with relatively short vectors. The main result of this work is an application to graph domination, where certain hard instances are solved using this algorithm as a heuristic."--Abstract.
Download or read book The Shortest Path Problem written by Hector Ortega-Arranz and published by Springer Nature. This book was released on 2022-05-31 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many applications in different domains need to calculate the shortest-path between two points in a graph. In this paper we describe this shortest path problem in detail, starting with the classic Dijkstra's algorithm and moving to more advanced solutions that are currently applied to road network routing, including the use of heuristics and precomputation techniques. Since several of these improvements involve subtle changes to the search space, it may be difficult to appreciate their benefits in terms of time or space requirements. To make methods more comprehensive and to facilitate their comparison, this book presents a single case study that serves as a common benchmark. The paper also compares the search spaces explored by the methods described, both from a quantitative and qualitative point of view, and including an analysis of the number of reached and settled nodes by different methods for a particular topology. Table of Contents: List of Figures / List of Tables / Acknowledgments / Introduction / Graph Theory Basics / Classical Algorithms / Hierarchical Preprocessing-Dependent Approaches / Non-Hierarchical Preprocessing-Dependent Approaches / Analysis and Comparison of Approaches / Conclusions / Bibliography / Authors' Biographies
Download or read book Design of Heuristic Algorithms for Hard Optimization written by Éric D. Taillard and published by Springer Nature. This book was released on 2022-10-29 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content.
Download or read book Graph Theory Binary Optimization written by N.B. Singh and published by N.B. Singh. This book was released on with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Graph Theory: Binary Optimization" introduces fundamental graph theory concepts and their practical applications in binary optimization. This beginner-friendly book explains how graphs model real-world problems like network design and scheduling, equipping readers with essential skills in optimization techniques.
Download or read book Algorithmics for Hard Problems written by Juraj Hromkovič and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the methods of designing algorithms for hard computing tasks, concentrating mainly on approximate, randomized, and heuristic algorithms, and on the theoretical and experimental comparison of these approaches according to the requirements of the practice. This is the first book to systematically explain and compare all the main possibilities of attacking hard computing problems. It also closes the gap between theory and practice by providing at once a graduate textbook and a handbook for practitioners dealing with hard computing problems.
Download or read book Graph Theory Approximation Methods written by N.B. Singh and published by N.B. Singh. This book was released on with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore the fascinating realm of graph theory through the lens of approximation methods in this comprehensive guide, Graph Theory: Approximation Methods . From fundamental concepts to advanced algorithms, this book delves into strategies for solving complex optimization problems in networks, offering insights and techniques essential for both students and researchers in the field. Discover practical applications, theoretical foundations, and cutting-edge developments that shape the future of graph theory and its computational applications.
Download or read book Meta Heuristics written by Stefan Voß and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimizations comprises a carefully refereed selection of extended versions of the best papers presented at the Second Meta-Heuristics Conference (MIC 97). The selected articles describe the most recent developments in theory and applications of meta-heuristics, heuristics for specific problems, and comparative case studies. The book is divided into six parts, grouped mainly by the techniques considered. The extensive first part with twelve papers covers tabu search and its application to a great variety of well-known combinatorial optimization problems (including the resource-constrained project scheduling problem and vehicle routing problems). In the second part we find one paper where tabu search and simulated annealing are investigated comparatively and two papers which consider hybrid methods combining tabu search with genetic algorithms. The third part has four papers on genetic and evolutionary algorithms. Part four arrives at a new paradigm within meta-heuristics. The fifth part studies the behavior of parallel local search algorithms mainly from a tabu search perspective. The final part examines a great variety of additional meta-heuristics topics, including neural networks and variable neighbourhood search as well as guided local search. Furthermore, the integration of meta-heuristics with the branch-and-bound paradigm is investigated.
Download or read book Graph Theory NP Problems written by N.B. Singh and published by N.B. Singh. This book was released on with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Graph Theory: NP Problems" offers a comprehensive exploration of complex computational challenges through the lens of graph theory. From fundamental concepts to advanced applications, this book delves into NP problems—examining their theoretical foundations, practical implications, and algorithmic solutions. Whether you're a student, researcher, or practitioner, discover how graphs serve as powerful models to unravel intricate problems in computer science and beyond, providing essential insights into the nature of computational complexity and efficient problem-solving strategies.
Download or read book Handbook of Graph Theory written by Jonathan L. Gross and published by CRC Press. This book was released on 2003-12-29 with total page 1200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approach
Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 2410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air line crew scheduling, corporate planning, computer-aided design and man ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi tion, linear programming relaxations are often the basis for many approxi mation algorithms for solving NP-hard problems (e.g. dual heuristics).
Download or read book Utilizing Information Technology Systems Across Disciplines Advancements in the Application of Computer Science written by Abu-Taieh, Evon M. O. and published by IGI Global. This book was released on 2009-03-31 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides original material concerned with all aspects of information resources management, managerial and organizational applications, as well as implications of information technology.
Download or read book Multi Objective Combinatorial Optimization Problems and Solution Methods written by Mehdi Toloo and published by Academic Press. This book was released on 2022-02-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Objective Combinatorial Optimization Problems and Solution Methods discusses the results of a recent multi-objective combinatorial optimization achievement that considered metaheuristic, mathematical programming, heuristic, hyper heuristic and hybrid approaches. In other words, the book presents various multi-objective combinatorial optimization issues that may benefit from different methods in theory and practice. Combinatorial optimization problems appear in a wide range of applications in operations research, engineering, biological sciences and computer science, hence many optimization approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic and algebraic techniques. This book covers this important topic as computational optimization has become increasingly popular as design optimization and its applications in engineering and industry have become ever more important due to more stringent design requirements in modern engineering practice. Presents a collection of the most up-to-date research, providing a complete overview of multi-objective combinatorial optimization problems and applications Introduces new approaches to handle different engineering and science problems, providing the field with a collection of related research not already covered in the primary literature Demonstrates the efficiency and power of the various algorithms, problems and solutions, including numerous examples that illustrate concepts and algorithms
