Download or read book Local Search for the Steiner Tree Problem in the Euclidean Plane written by Martin Zachariasen and published by . This book was released on 1997 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Most heuristics for the Steiner tree problem in the Euclidean plane perform a series of iterative improvements using the minimum spanning tree as an initial solution. We may therefore characterize them as local search heuristics. In this paper, we first give a survey of existing heuristic approaches from a local search perspective, by setting up solution spaces and neighbourhood structures. Secondly, we present a new general local search approach which is based on a list of full Steiner trees constructed in a preprocessing phase. This list defines a solution space on which three neighbourhood structures are proposed and evaluated. Computational results show that this new approach is very competitive from a cost-benefit point of view. Furthermore, it has the advantage of being easy to apply to the Steiner tree problem in other metric spaces and to obstacle avoiding variants."
Download or read book Rapport written by and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Steiner Tree Problem written by F.K. Hwang and published by Elsevier. This book was released on 1992-10-20 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues.This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most prolific research amongst the three areas. The Rectilinear Steiner Problem, introduced by Hanan in 1965, is discussed in the third part. Additionally, a forth section has been included, with chapters discussing areas where the body of results is still emerging.The collaboration of three authors with different styles and outlooks affords individual insights within a cohesive whole.
Download or read book Steiner Trees in Industry written by Xiuzhen Cheng and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles studying various Steiner tree prob lems with applications in industries, such as the design of electronic cir cuits, computer networking, telecommunication, and perfect phylogeny. The Steiner tree problem was initiated in the Euclidean plane. Given a set of points in the Euclidean plane, the shortest network interconnect ing the points in the set is called the Steiner minimum tree. The Steiner minimum tree may contain some vertices which are not the given points. Those vertices are called Steiner points while the given points are called terminals. The shortest network for three terminals was first studied by Fermat (1601-1665). Fermat proposed the problem of finding a point to minimize the total distance from it to three terminals in the Euclidean plane. The direct generalization is to find a point to minimize the total distance from it to n terminals, which is still called the Fermat problem today. The Steiner minimum tree problem is an indirect generalization. Schreiber in 1986 found that this generalization (i.e., the Steiner mini mum tree) was first proposed by Gauss.
Download or read book Advances in Steiner Trees written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2000-01-31 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an up-to-date set of contributions by the most influential authors on the Steiner Tree problem. The authors address the latest concerns of Steiner Trees for their computational complexity, design of algorithms, performance guaranteed heuristics, computational experimentation, and range of applications. Audience: The book is intended for advanced undergraduates, graduates and research scientists in Combinational Optimization and Computer Science. It is divided into two sections: Part I includes papers on the general geometric Steiner Tree problem in the plane and higher dimensions; Part II includes papers on the Steiner problem on graphs which has significant import to Steiner Tree applications.
Download or read book Local Search for the Steiner Tree Problem in the Euchlidean Plane written by Martin Zachariasen and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hybrid Evolutionary Algorithms written by Crina Grosan and published by Springer. This book was released on 2007-08-29 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume is targeted at presenting the latest state-of-the-art methodologies in "Hybrid Evolutionary Algorithms". The chapters deal with the theoretical and methodological aspects, as well as various applications to many real world problems from science, technology, business or commerce. Overall, the book has 14 chapters including an introductory chapter giving the fundamental definitions and some important research challenges. The contributions were selected on the basis of fundamental ideas/concepts rather than the thoroughness of techniques deployed.
Download or read book Algorithms for Plane Steiner Tree Problems written by Martin Zachariasen and published by . This book was released on 1998 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Topological network design is the process of planning the layout of a network subject to constraints on topology. Applications include the design of transportation and communication networks where the construction costs typically are associated with the nodes and/or edges of the network. The Steiner tree problem is one of the fundamental topological network design problems. The problem is to interconnect (a subset of) the nodes such that there is a path between every pair of nodes while minimizing the total cost of selected edges. Originally, the Steiner tree problem was stated as a purely geometric problem: Given a set of points (terminals) in the plane, construct a tree interconnecting all terminals such that the total length of all line segments is minimized. In the Euclidean Steiner tree problem, the length of a line segment is the usual Euclidean (or L2) distance between the endpoints of the segment. Correspondingly, in the rectilinear Steiner tree problem distances are measured using the rectilinear (or L1) distance metric. This thesis is about algorithms for solving Euclidean and rectilinear Steiner tree problems. More precisely, new exact and heuristic algorithms for these problems are evaluated by performing extensive computational experiments. The thesis covers the full range of algorithms, in particular for the Euclidean problem: Fast greedy heuristics with an O(n log n) worst-case running time behaviour, powerful local search algorithms which provide near-optimal solutions quickly, and efficient exact algorithms which solve problem instances with more than 2000 terminals to optimality. The new heuristics provide better solutions faster than any other heuristic proposed in the literature and the new exact algorithm solves problem instances which are more than an order of magnitude larger than those previously solved. The efficiency of the proposed algorithms stems from a structural property of optimal solutions to these two problems. The optimal Steiner tree breaks into so-called full Steiner trees (FSTs) in which all terminals are leaves. These FSTs are typically very small (seldom span more than six terminals) and have many well-established properties that may be exploited efficiently by using geometric structures. The thesis is a collection of six research papers. Five of these are on the Euclidean and rectilinear Steiner tree problems, while the last one presents a tabu search algorithm for another geometric problem, the traveling salesman problem in the plane. The thesis begins with a short introduction to algorithms for plane Steiner tree problems."
Download or read book Knowledge Based Intelligent Information and Engineering Systems written by Bogdan Gabrys and published by Springer Science & Business Media. This book was released on 2006-09-27 with total page 1360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volume set LNAI 4251, LNAI 4252, and LNAI 4253 constitutes the refereed proceedings of the 10th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2006, held in Bournemouth, UK in October 2006. The 480 revised papers presented were carefully reviewed and selected from about 1400 submissions. The papers present a wealth of original research results from the field of intelligent information processing.
Download or read book Steiner Tree Problems in Computer Communication Networks written by Dingzhu Du and published by World Scientific. This book was released on 2008 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Steiner tree problem is one of the most important combinatorial optimization problems. It has a long history that can be traced back to the famous mathematician Fermat (1601-1665). This book studies three significant breakthroughs on the Steiner tree problem that were achieved in the 1990s, and some important applications of Steiner tree problems in computer communication networks researched in the past fifteen years. It not only covers some of the most recent developments in Steiner tree problems, but also discusses various combinatorial optimization methods, thus providing a balance between theory and practice.
Download or read book Approximate Solutions to the Steiner Tree Problem written by Albert Thomas Borchers and published by . This book was released on 1996 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Steiner Minimal Trees written by Dietmar Cieslik and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of "Shortest Connectivity", which is discussed here, has a long and convoluted history. Many scientists from many fields as well as laymen have stepped on its stage. Usually, the problem is known as Steiner's Problem and it can be described more precisely in the following way: Given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and is called a Steiner Minimal Tree (SMT). It may contain vertices different from the points which are to be connected. Such points are called Steiner points. Steiner's Problem seems disarmingly simple, but it is rich with possibilities and difficulties, even in the simplest case, the Euclidean plane. This is one of the reasons that an enormous volume of literature has been published, starting in 1 the seventeenth century and continuing until today. The difficulty is that we look for the shortest network overall. Minimum span ning networks have been well-studied and solved eompletely in the case where only the given points must be connected. The novelty of Steiner's Problem is that new points, the Steiner points, may be introduced so that an intercon necting network of all these points will be shorter. This also shows that it is impossible to solve the problem with combinatorial and geometric methods alone.
Download or read book Theoretical Aspects of Local Search written by Wil Michiels and published by Springer Science & Business Media. This book was released on 2007-01-17 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Local search has been applied successfully to a diverse collection of optimization problems. However, results are scattered throughout the literature. This is the first book that presents a large collection of theoretical results in a consistent manner. It provides the reader with a coherent overview of the achievements obtained so far, and serves as a source of inspiration for the development of novel results in the challenging field of local search.
Download or read book Computational Intelligence Optimization and Inverse Problems with Applications in Engineering written by Gustavo Mendes Platt and published by Springer. This book was released on 2018-09-25 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on metaheuristic methods and its applications to real-world problems in Engineering. The first part describes some key metaheuristic methods, such as Bat Algorithms, Particle Swarm Optimization, Differential Evolution, and Particle Collision Algorithms. Improved versions of these methods and strategies for parameter tuning are also presented, both of which are essential for the practical use of these important computational tools. The second part then applies metaheuristics to problems, mainly in Civil, Mechanical, Chemical, Electrical, and Nuclear Engineering. Other methods, such as the Flower Pollination Algorithm, Symbiotic Organisms Search, Cross-Entropy Algorithm, Artificial Bee Colonies, Population-Based Incremental Learning, Cuckoo Search, and Genetic Algorithms, are also presented. The book is rounded out by recently developed strategies, or hybrid improved versions of existing methods, such as the Lightning Optimization Algorithm, Differential Evolution with Particle Collisions, and Ant Colony Optimization with Dispersion – state-of-the-art approaches for the application of computational intelligence to engineering problems. The wide variety of methods and applications, as well as the original results to problems of practical engineering interest, represent the primary differentiation and distinctive quality of this book. Furthermore, it gathers contributions by authors from four countries – some of which are the original proponents of the methods presented – and 18 research centers around the globe.
Download or read book Experimental Algorithms written by Andrew V. Goldberg and published by Springer. This book was released on 2016-05-31 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th International Symposium on Experimental Algorithms, SEA 2016, held in St. Petersburg, Russia, in June 2016. The 25 revised full papers presented were carefully reviewed and selected from 54 submissions. The main theme of the symposium is the role of experimentation and of algorithm engineering techniques in the design and evaluation of algorithms and data structures. SEA covers a wide range of topics in experimental algorithmics, bringing together researchers from algorithm engineering, mathematical programming, and combinatorial optimization communities.
Download or read book Exact and Heuristic Algorithms for the Euclidean Steiner Tree Problem written by Jon William Van Laarhoven and published by . This book was released on 2010 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study the Euclidean Steiner tree problem (ESTP) which arises in the field of combinatorial optimization. The ESTP asks for a network of minimal total edge length spanning a set of given terminal points in Rd with the ability to add auxiliary connecting points (Steiner points) to decrease the overall length of the network. The graph theory literature contains extensive studies of exact, approximation, and heuristic algorithms for ESTP in the plane, but less is known in higher dimensions. The contributions of this thesis include a heuristic algorithm and enhancements to an exact algorithm for solving the ESTP. We present a local search heuristic for the ESTP in Rd for d [gt or eq] 2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to create a network on the inserted points, and second order cone programming to optimize the locations of Steiner points. Unlike other ESTP heuristics relying on the Delaunay triangulation, the algorithm inserts Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. The algorithm extends effectively into higher dimensions, and we present computational results on benchmark test problems in Rd for 2 [lt eq] d [lt eq] 5. We develop new geometric conditions derived from properties of Steiner trees which bound below the number of Steiner points on paths between terminals in the Steiner minimal tree. We describe conditions for trees with a Steiner topology and show how these conditions relate to the Voronoi diagram. We describe more restrictive conditions for trees with a full Steiner topology and their implementation into the algorithm of Smith (1992). We present computational results on benchmark test problems in Rd for 2 [lt eq] d [lt eq] 5.
Download or read book Combinatorial Optimization written by Bruno Simeone and published by Springer. This book was released on 2006-11-14 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The C.I.M.E. Summer School at Como in 1986 was the first in that series on the subject of combinatorial optimization. Situated between combinatorics, computer science and operations research, the subject draws on a variety of mathematical methods to deal with problems motivated by real-life applications. Recent research has focussed on the connections to theoretical computer science, in particular to computational complexity and algorithmic issues. The Summer School's activity centered on the 4 main lecture courses, the notes of which are included in this volume:
