Generalized Network Design Problems
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Generalized Network Design Problems
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Author : Petrica C. Pop
language : en
Publisher: Walter de Gruyter
Release Date : 2012-10-30
Generalized Network Design Problems written by Petrica C. Pop and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.
Combinatorial optimization is a fascinating topic. Combinatorial optimization problems arise in a wide variety of important fields such as transportation, telecommunications, computer networking, location, planning, distribution problems, etc. Important and significant results have been obtained on the theory, algorithms and applications over the last few decades. In combinatorial optimization, many network design problems can be generalized in a natural way by considering a related problem on a clustered graph, where the original problem's feasibility constraints are expressed in terms of the clusters, i.e., node sets instead of individual nodes. This class of problems is usually referred to as generalized network design problems (GNDPs) or generalized combinatorial optimization problems. The express purpose of this monograph is to describe a series of mathematical models, methods, propositions, algorithms developed in the last years on generalized network design problems in a unified manner. The book consists of seven chapters, where in addition to an introductory chapter, the following generalized network design problems are formulated and examined: the generalized minimum spanning tree problem, the generalized traveling salesman problem, the railway traveling salesman problem, the generalized vehicle routing problem, the generalized fixed-charge network design problem and the generalized minimum vertex-biconnected network problem. The book will be useful for researchers, practitioners, and graduate students in operations research, optimization, applied mathematics and computer science. Due to the substantial practical importance of some presented problems, researchers in other areas will find this book useful, too.
Generalized Network Design Problems
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Author : Labbé, Martine
language : en
Publisher: Montréal : Centre for Research on Transportation = Centre de recherche sur les transports (C.R.T.)
Release Date : 2002
Generalized Network Design Problems written by Labbé, Martine and has been published by Montréal : Centre for Research on Transportation = Centre de recherche sur les transports (C.R.T.) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Hybrid Metaheuristics For Generalized Network Design Problems
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Author : Bin Hu
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2012
Hybrid Metaheuristics For Generalized Network Design Problems written by Bin Hu and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
In this book, we consider several generalized network design problems which belong to the family of NP-hard combinatorial optimization problems. In contrast to their classical counterparts, the generalized versions are defined on graphs whose node sets are partitioned into clusters. The goal is to find a subgraph which spans exactly one node from each cluster and also meets further constraints respectively. Applicable methodologies for solving combinatorial optimization problems can roughly be divided into two mainstreams. The first class consists of algorithms which aim to solve these problems to proven optimality - provided that they are given enough run-time and memory. The second class are metaheuristics which compute approximate solutions but usually require significantly less run-time. By combining these two classes, we are able to form collaboration algorithms that benefit from advantages of both sides. Such approaches are considered for solving the generalized network design problems in this book.
Design And Implementation Of Data Structures For Generalized Networks
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Author : Agha Iqbal Ali
language : en
Publisher:
Release Date : 1984
Design And Implementation Of Data Structures For Generalized Networks written by Agha Iqbal Ali and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Algorithms categories.
The specialization of the simplex algorithm for the solution of generalized network flow problems rests on the fact that a basis for the problem may be represented graphically as a spanning forest in which each component is either a one-tree or a rooted tree. The design of a specialized algorithm for efficient solution of generalized network problems necessarily depends on data structures chosen to represent the basis. This paper presents the design and detailed algorithmic specification of the primal simplex algorithm for such problems. Computational testing to determine the overhead required by generalized network data structures over pure network data structures indicates that generalized network algorithms are on the order of 2.5 to 3.5 times slower than pure network algorithms. Computational testing with generalized network problems with up to 1000 nodes and 7000 arcs establishes the suitability of the data-structures for efficient implementation of primal simplex calculations. Keywords: Linear programming. (Author).
Network Optimization Problems Algorithms Applications And Complexity
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Author : Ding-zhu Du
language : en
Publisher: World Scientific
Release Date : 1993-04-27
Network Optimization Problems Algorithms Applications And Complexity written by Ding-zhu Du and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-27 with categories.
In the past few decades, there has been a large amount of work on algorithms for linear network flow problems, special classes of network problems such as assignment problems (linear and quadratic), Steiner tree problem, topology network design and nonconvex cost network flow problems.Network optimization problems find numerous applications in transportation, in communication network design, in production and inventory planning, in facilities location and allocation, and in VLSI design.The purpose of this book is to cover a spectrum of recent developments in network optimization problems, from linear networks to general nonconvex network flow problems./a
Network Flows And Network Design In Theory And Practice
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Author : Jannik Matuschke
language : en
Publisher: Jannik Matuschke
Release Date : 2014
Network Flows And Network Design In Theory And Practice written by Jannik Matuschke and has been published by Jannik Matuschke this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Network flow and network design problems arise in various application areas of combinatorial optimization, e.g., in transportation, production, or telecommunication. This thesis contributes new results to four different problem classes from this area, providing models and algorithms with immediate practical impact as well as theoretical insights into complexity and combinatorial structure of network optimization problems: (i) We introduce a new model for tactical transportation planning that employs a cyclic network expansion to integrate routing and inventory decisions into a unified capacitated network design formulation. We also devise several algorithmic approaches to solve the resulting optimization problem and demonstrate the applicability of our approach on a set of real-world logistic networks. (ii) We present approximation algorithms for combined location and network design problems, including the first constant factor approximation for capacitated location routing. (iii) We derive a max-flow/min-cut theorem for abstract flows over time, a generalization of the well-known work of Ford and Fulkerson that restricts to a minimal set of structural requirements. (iv) We devise algorithms for finding orientations of embedded graphs with degree constraints on vertices and faces, answering an open question by Frank.
Solving Network Design Problems Via Decomposition Aggregation And Approximation
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Author : Andreas Bärmann
language : en
Publisher: Springer
Release Date : 2016-06-02
Solving Network Design Problems Via Decomposition Aggregation And Approximation written by Andreas Bärmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-02 with Mathematics categories.
Andreas Bärmann develops novel approaches for the solution of network design problems as they arise in various contexts of applied optimization. At the example of an optimal expansion of the German railway network until 2030, the author derives a tailor-made decomposition technique for multi-period network design problems. Next, he develops a general framework for the solution of network design problems via aggregation of the underlying graph structure. This approach is shown to save much computation time as compared to standard techniques. Finally, the author devises a modelling framework for the approximation of the robust counterpart under ellipsoidal uncertainty, an often-studied case in the literature. Each of these three approaches opens up a fascinating branch of research which promises a better theoretical understanding of the problem and an increasing range of solvable application settings at the same time.
Deep Dual Optimal Inequalities For Generalized Capacitated Fixed Charge Network Design Problems
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Author : David Franz Koza
language : en
Publisher:
Release Date : 2020
Deep Dual Optimal Inequalities For Generalized Capacitated Fixed Charge Network Design Problems written by David Franz Koza and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Capacitated fixed-charge network design problems and generalizations, such as service network design problems, have a wide range of applications but are known to be very difficult to solve. Many exact and heuristic algorithms to solve these problems rely on column-and-row generation (CRG), which frequently suffer from primal degeneracy. We present a set of dual inequalities, equivalent to a simple primal relaxation, that speed up CRG algorithms for generalized capacitated fixed charge network design problems. We investigate the impact of the dual inequalities theoretically as well as experimentally. For practical applications, the presented technique is simple to implement, has no additional computational cost and can accelerate CRG by orders of magnitude, depending on the problem size and structure.
On Several Geometric Network Design Problems
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Author : Yang Yang
language : en
Publisher:
Release Date : 2008
On Several Geometric Network Design Problems written by Yang Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Geometric network design problems arise in many applications such as VLSI circuit design, telecommunications, road network design, medical imaging and site layout. Frequently encountered such problems include Traveling Salesman problem, spanner, geometric minimum spanning tree, and some covering problems. Generally speaking, a geometric network design problem is to determine a "minimum" subgraph (in terms of the size or some other measure) of some underlying graphs which maintains certain properties. In this dissertation, we study the generalizations of several classical geometric network design problems. Our problems either consider more complicated geometric objects or use more general measures, and thus provide a better modeling for many real world problems. The first problem we study is a variant of the Traveling Salesman problem (called segment TSP) in which a traveling salesman tour is sought to traverse a set of n [straight epsilon]-separated segments in two dimensional space. In this problem, the distance between two segment is not metric due to the shape of the segments. We present a polynomial time approximation scheme (PTAS) for the segment TSP problem. Our results are based on an interesting combinatorial result which bounds the total number of entry points in an optimal TSP tour and a generalization of Arora's technique for Euclidean TSP (of a set of points). The randomized version of our algorithm takes O (n 2 (log n) O (1/[straight epsilon]2)) time to compute a (1 + [straight epsilon])-approximation with probability - 1/2, and can be derandomized with an additional factor of O (n 2). The second problem we study is the Geometric Spanners of Segments, which can be viewed as a generalization of the classic geometric spanner. In this problem we are given a set of S of disjoint 2-D segments, find a spanning network G with minimum size so that for any pair of points in S, there exists a path in G with length no more than t times their Euclidean distance. Based on a number of interesting techniques (such as weakly dominating set, strongly dominating set, and interval cover), we present an efficient algorithm to construct the segment spanner. Our approach first identifies a set of Steiner points in S and then construct a point spanner for the set of Steiner points. Our algorithm runs in O (i Q l+ 2 log n) time, where Q is the set of Steiner points. We show that Q is an O(1)-approximation in terms of its size when S is relatively "well" separated by a constant. The third problem we study is an interesting generalization of the weighted vertex cover problem, called the Facility Terminal Cover (FTC) problem. In the FTC problem, each vertex is associated with a positive weight, each edge is associated with a positive demand, and the objective is to determine a subset of vertices and a capacity for each selected vertex so that the demand of each edge is covered by the capacity of one of its two endpoints and the total weighted capacity of all selected vertices is minimized. We present two linear time approximation algorithms for this problem: The first algorithm deterministically achieves an approximation ratio of 8 by using an interesting rounding technique and a lower-bounding technique; the second algorithm further improves the approximation ratio to 2 e with some randomization techniques, where e is the natural logarithmic base. The second algorithm can be easily derandomized in quadratic time. The fourth problem we study is a natural generalization of the classical minimum spanning tree problem called Minimum Spanning Tree with Neighborhoods (MSTN), which seeks a tree of minimum length to span a set of 2D regions called neighborhoods. Each neighborhood contributes exact one node to the tree, and the MSTN has the minimum total length among all possible trees spanning the set of nodes. When the regions considered are a set of disjoint 2D unit discs, we present the following approximation results: (1) A simple algorithm that achieves an approximation ratio of 7.4; (2) Lower bounds and two 3-approximation algorithms; (3) A PTAS for this problem. Our algorithms can be easily generalized to higher dimensions.
Solving Generalized Networks
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Author : G. G. Brown
language : en
Publisher:
Release Date : 1982
Solving Generalized Networks written by G. G. Brown and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
A complete, unified description is given of the design, implementation and use of a family of very fast and efficient large scale minimum-cost (primal simplex) network programs. The class of capacitated generalized transshipment problems solved includes the capacitated and uncapacitated generalized transportation problems and the continuous generalized assignment problem, as well as the pure network flow models which are specializations of these problems. These formulations are used for a large number of diverse applications to determine how (or at what rate) flows through the arcs of a network can minimize total shipment costs. A generalized network problem can also be viewed as a linear program with at most two non-zero entries in each column of the constraint matrix; this property is exploited in the mathematical presentation with special emphasis on data structures for basis representation, basis manipulation, and pricing mechanisms. A literature review accompanies computational testing of a promising ideas, and extensive experimentation is reported which has produced GENNET, an extremely efficient family of generalized network systems. (Author).
