Download or read book Multicriteria shortest paths and related geometric problems written by Antonin Lentz and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cette thèse s'intéresse au calcul de plus courts chemins multicritères approché. Dans un contexte multicritère, le calcul des ensembles de Pareto, c'est-à-dire de toutes les solutions optimales, est souvent prohibitif. De nombreuses approches consistent à n'en calculer que des sous-ensembles. Certaines offrent des temps de calcul raisonnables mais aucune garantie quant à la représentabilité, c'est-à-dire la distribution du sous-ensemble calculé dans l'ensemble de Pareto complet. D'autres méthodes garantissent une certaine représentabilité et des complexités intéressantes, mais elles sont généralement inutilisables en pratique. Un autre problème est que ces deux approches ne garantissent généralement pas que la sortie est réellement un sous-ensemble de l'ensemble de Pareto : elle peut donc contenir des chemins non optimaux.Tout d'abord, nous proposons deux optimisations de méthodes exactes classiques : MC DIJKSTRA 2D pour le cas bicritère et BUCKET pour toute dimension. Ensuite, nous proposons des algorithmes d'approximation avec des garanties théoriques intéressantes. Plusieurs d'entre eux, SECTOR, SSECTOR et QSSECTOR, fonctionnent en dimension quelconque et leur complexité en fonction de la taille de la sortie est intéressante. Cette dernière étant incomparable à la taille de l'ensemble de Pareto, nous proposons une optimisation 2D, FRAME, qui garantit que la sortie n'est constituée que de chemins optimaux. Nous déduisons que la complexité de FRAME est inférieure ou égale à celle du meilleur algorithme de calcul exact connu. Afin d'évaluer la capacité d'élagage de FRAME, nous menons une étude expérimentale. Cette étude montre que notre algorithme est intéressant lorsque la taille des ensembles de Pareto est grande.Afin d'améliorer nos algorithmes d'approximation en 3D, nous étudions les Thêta-graphes. Nous proposons des algorithmes efficaces pour la maintenance dynamique de ces graphes. Ensuite, nous étudions une requête de proximité, utilisant un Thêta-graphe pour trouver les plus proches voisins dans une direction donnée. Enfin, nous détaillons comment appliquer nos algorithmes de Thêta-graphes pour le calcul de plus court chemins tricritères.
Download or read book Handbook of Computational Geometry written by J.R. Sack and published by Elsevier. This book was released on 1999-12-13 with total page 1087 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.
Download or read book Integration of Constraint Programming Artificial Intelligence and Operations Research written by Bistra Dilkina and published by Springer Nature. This book was released on with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Constrained Shortest Paths in Terrains and Graphs written by Mustaq Ahmed and published by . This book was released on 2009 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finding a shortest path is one of the most well-studied optimization problems. In this thesis we focus on shortest paths in geometric and graph theoretic settings subject to different feasibility constraints that arise in practical applications of such paths. One of the most fundamental problems in computational geometry is finding shortest paths in terrains, which has many applications in robotics, computer graphics and Geographic Information Systems (GISs). There are many variants of the problem in which the feasibility of a path is determined by some geometric property of the terrain. One such variant is the shortest descending path (SDP) problem, where the feasible paths are those that always go downhill. We need to compute an SDP, for example, for laying a canal of minimum length from the source of water at the top of a mountain to fields for irrigation purpose, and for skiing down a mountain along a shortest route. The complexity of finding SDPs is open. We give a full characterization of the bend angles of an SDP, showing that they follow a generalized form of Snell's law of refraction of light. We also reduce the SDP problem to the problem of finding an SDP through a given sequence of faces, by adapting the sequence tree approach of Chen and Han for our problem. Our results have two implications. First, we isolate the difficult aspect of SDPs. The difficulty is not in deciding which face sequence to use, but in finding the SDP through a given face sequence. Secondly, our results help us identify some classes of terrains for which the SDP problem is solvable in polynomial time. We give algorithms for two such classes. The difficulty of finding an exact SDP motivates the study of approximation algorithms for the problem. We devise two approximation algorithms for SDPs in general terrains---these are the first two algorithms to handle the SDP problem in such terrains. The algorithms are robust and easy-to-implement. We also give two approximation algorithms for the case when a face sequence is given. The first one solves the problem by formulating it as a convex optimization problem. The second one uses binary search together with our characterization of the bend angles of an SDP to locate an approximate path. We introduce a generalization of the SDP problem, called the shortest gently descending path (SGDP) problem, where a path descends but not too steeply. The additional constraint to disallow a very steep descent makes the paths more realistic in practice. For example, a vehicle cannot follow a too steep descent---this is why a mountain road has hairpin bends. We give two easy-to-implement approximation algorithms for SGDPs, both using the Steiner point approach. Between a pair of points there can be many SGDPs with different number of bends. In practice an SGDP with fewer bends or smaller total turn-angle is preferred. We show using a reduction from 3-SAT that finding an SGDP with a limited number of bends or a limited total turn-angle is hard. The hardness result applies to a generalization of the SGDP problem called the shortest anisotropic path problem, which is a well-studied computational geometry problem with many practical applications (e.g., robot motion planning), yet of unknown complexity.
Download or read book Shortest Paths Help Solve Geometric Optimization Problems on Planar Regions written by DIMACS (GROUP) and published by . This book was released on 1990 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: These same optimization techniques can be applied to splinegons (curved polygons). To do so, we first develop a decomposition technique for curved polygons which we substitute for triangulation in creating equally efficient curved versions of the algorithms for the shortest-path tree, ray-shooting and two-point shortest path problems."
Download or read book Multi criteria Shortest Paths in 3D Among Vertical Obstacles written by Nguyet Tran and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multicriteria Optimization written by Matthias Ehrgott and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Life is about decisions. Decisions, no matter if made by a group or an indi vidual, involve several conflicting objectives. The observation that real world problems have to be solved optimally according to criteria, which prohibit an "ideal" solution - optimal for each decision-maker under each of the criteria considered - has led to the development of multicriteria optimization. From its first roots, which where laid by Pareto at the end of the 19th century the discipline has prospered and grown, especially during the last three decades. Today, many decision support systems incorporate methods to deal with conflicting objectives. The foundation for such systems is a mathematical theory of optimization under multiple objectives. Fully aware of the fact that there have been excellent textbooks on the topic before, I do not claim that this is better text, but it has a has a consid erably different focus. Some of the available books develop the mathematical background in great depth, such as [SNT85, GN90, Jah86). Others focus on a specific structure of the problems covered as [Zel74, Ste85, Mie99) or on methodology [Yu85, CH83a, HM79). Finally there is the area of multicriteria decision aiding [Roy96, Vin92, KR93), the main goal of which is to help deci sion makers find the final solution (among many "optimal" ones) eventually to be implemented.
Download or read book Shortest Path Problems written by Zachary Clawson and published by . This book was released on 2017 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal path problems arise in many applications and several efficient methods are widely used for solving them on the whole domain. However, practitioners are often only interested in the solution at one specific source point, i.e. the shortest path to the exit-set from a particular starting location. This thesis will focus on three separate, but related, problems of this form. We employ solution methods that discretize the computational domain and recover an approximate solution to the shortest path problem. These methods either solve the problem on a geometrically embedded graph or approximate the viscosity solution to a static Hamilton-Jacobi PDE. Such paths can be viewed as characteristics of static Hamilton-Jacobi equations, so we restrict the computations to a neighborhood of the characteristic. We explain how heuristic under/over-estimate functions can be used to obtain a {\em causal} domain restriction, significantly decreasing the computational work without sacrificing convergence under mesh refinement. The discussed techniques are inspired by an alternative version of the classical A* algorithm on graphs. We illustrate the advantages of our approach on continuous isotropic examples in 2D and 3D. We compare its efficiency and accuracy to previous domain restriction techniques and analyze the behavior of errors under the grid refinement. However, if the heuristic functions used are very inaccurate this can lead to A*-type methods providing little to no restriction. One solution is to scale-up the underestimate functions used so that they become more accurate on parts of the domain. However, this will cause the algorithm to recover suboptimal, albeit locally optimal, solutions. These algorithms quickly produce an initial suboptimal solution that is iteratively improved. This ensures early availability of a good suboptimal path before the completion of the search for a globally optimal path. We illustrate the algorithm on examples where previous A*-FMM algorithms are unable to provide significant savings due to the poor quality of the heuristics. Finally we present a related algorithm for finding optimal paths on graphs with respect to two criteria simultaneously. Our approach is based on augmenting the state space to keep track of the ``budget'' remaining to satisfy the constraints on secondary cost. The resulting augmented graph is acyclic and the primary cost can be then minimized by a simple upward sweep through budget levels. The efficiency and accuracy of our algorithm is tested on Probabilistic Roadmap graphs to minimize the distance of travel subject to a constraint on the overall threat exposure to enemy observers. ...
Download or read book Automation and Robotics written by Juan-Manuel Ramos-Arreguin and published by BoD – Books on Demand. This book was released on 2008-05-01 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, a set of relevant, updated and selected papers in the field of automation and robotics are presented. These papers describe projects where topics of artificial intelligence, modeling and simulation process, target tracking algorithms, kinematic constraints of the closed loops, non-linear control, are used in advanced and recent research.
Download or read book A Multi Objective Programming Approach to Solve Integer Valued Neutrosophic Shortest Path Problems written by Ranjan Kumar and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic (NS) set hypothesis gives another way to deal with the vulnerabilities of the shortest path problems (SPP). Several researchers have worked on fuzzy shortest path problem (FSPP) in a fuzzy graph with vulnerability data and completely different applications in real world eventualities. However, the uncertainty related to the inconsistent information and indeterminate information isn't properly expressed by fuzzy set. The neutrosophic set deals these forms of uncertainty. This paper presents a model for shortest path problem with various arrangements of integer-valued trapezoidal neutrosophic (INVTpNS) and integer-valued triangular neutrosophic (INVTrNS). We characterized this issue as Neutrosophic Shortest way problem (NSSPP). The established linear programming (LP) model solves the classical SPP that consists of crisp parameters. To the simplest of our data, there's no multi objective applied mathematics approach in literature for finding the Neutrosophic shortest path problem (NSSPP).
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 Integer Programming and Related Areas written by R.v. Randow and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Constrained Shortest Paths and Related Problems written by Mark Ziegelmann and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Unobstructed Shortest Paths in Polyhedral Environments written by Varol Akman and published by . This book was released on 2014-01-15 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Combinatorial Optimization written by Ding-Zhu Du and published by Springer Nature. This book was released on 2022-09-26 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields. There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems. Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization. Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, such as greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer. Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.
Download or read book A novel method for solving the fully neutrosophic linear programming problems written by Mohamed Abdel-Basset and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most widely used technique for solving and optimizing a real-life problem is linear programming (LP), due to its simplicity and efficiency. However, in order to handle the impreciseness in the data, the neutrosophic set theory plays a vital role which makes a simulation of the decision-making process of humans by considering all aspects of decision (i.e., agree, not sure and disagree). By keeping the advantages of it, in the present work, we have introduced the neutrosophic LP models where their parameters are represented with a trapezoidal neutrosophic numbers and presented a technique for solving them. The presented approach has been illustrated with some numerical examples and shows their superiority with the state of the art by comparison. Finally, we conclude that proposed approach is simpler, efficient and capable of solving the LP models as compared to other methods.
Download or read book GIS written by Michael F. Worboys and published by CRC Press. This book was released on 2004-05-11 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: GIS: A Computing Perspective, Second Edition, provides a full, up-to-date overview of GIS, both Geographic Information Systems and the study of Geographic Information Science. Analyzing the subject from a computing perspective, the second edition explores conceptual and formal models needed to understand spatial information, and examines the representations and data structures needed to support adequate system performance. This volume also covers the special-purpose interfaces and architectures required to interact with and share spatial information, and explains the importance of uncertainty and time. The material on GIS architectures and interfaces as well as spatiotemporal information systems is almost entirely new. The second edition contains substantial new information, and has been completely reformatted to improve accessibility. Changes include: A new chapter on spatial uncertainty Complete revisions of the bibliography, index, and supporting diagrams Supplemental material is offset at the top of the page, as are references and links for further study Definitions of new terms are in the margins of pages where they appear, with corresponding entries in the index
