Download or read book Constrained Shortest Paths and Related Problems written by Mark Ziegelmann and published by VDM Publishing. This book was released on 2007-12-01 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: The shortest path problem arises in various applied settings where some material (e.g., computer data packet, telephone calls, vehicles) is sent between two specified points in a network as quickly, cheaply or reliably as possible. In practice we want to optimize a combination of those criteria (i.e., we have a bi- or multicriteria shortest path problem). This book proposes a 2-step method for the constrained shortest path problem. A relaxation is solved to get upper and lower bounds and then the gap is closed with clever path ranking to obtain the exact solution. Different old and new methods are compared both theoretically and experimentally. The proposed 2-step method also works for a more general class of constrained network optimization problems. In addition the generic approach is illustrated with several examples and a newly developed Constrained Network Optimization Software Package (CNOP) is introduced that provides this generic 2-step approach as well as all state of the art algorithms for constrained shortest paths. This book is a valuable resource for researchers, students as well as practitioners working on the constrained shortest path problem and related problems.
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 Column Generation written by Guy Desaulniers and published by Springer Science & Business Media. This book was released on 2006-03-20 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with "A Primer in Column Generation" which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on "Shortest Path Problems with Resource Constraints," "Vehicle Routing Problem with Time Window," "Branch-and-Price Heuristics," "Cutting Stock Problems," each dealing with methodological aspects of the field. Three chapters deal with transportation applications: "Large-scale Models in the Airline Industry," "Robust Inventory Ship Routing by Column Generation," and "Ship Scheduling with Recurring Visits and Visit Separation Requirements." Production is the focus of another three chapters: "Combining Column Generation and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for Job Shop Scheduling," and "Applying Column Generation to Machine Scheduling." The final chapter by François Vanderbeck, "Implementing Mixed Integer Column Generation," reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies).
Download or read book Algorithms ESA 2000 written by Michael S. Paterson and published by Springer Science & Business Media. This book was released on 2000-08-25 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th Annual European Symposium on Algorithms, ESA 2000, held in Saarbrcken, Germany in September 2000. The 39 revised full papers presented together with two invited papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are parallelism, distributed systems, approximation, combinatorial optimization, computational biology, computational geometry, external-memory algorithms, graph algorithms, network algorithms, online algorithms, data compression, symbolic computation, pattern matching, and randomized algorithms.
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 Resource Constrained Shortest Paths and Extensions written by Renan Garcia and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we use integer programming techniques to solve the resource constrained shortest path problem (RCSPP) which seeks a minimum cost path between two nodes in a directed graph subject to a finite set of resource constraints. Although NP-hard, the RCSPP is extremely useful in practice and often appears as a subproblem in many decomposition schemes for difficult optimization problems.
Download or read book Shortest Path Solvers From Software to Wetware written by Andrew Adamatzky and published by Springer. This book was released on 2018-04-26 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers advanced parallel and distributed algorithms and experimental laboratory prototypes of unconventional shortest path solvers. In addition, it presents novel and unique algorithms of solving shortest problems in massively parallel cellular automaton machines. The shortest path problem is a fundamental and classical problem in graph theory and computer science and is frequently applied in the contexts of transport and logistics, telecommunication networks, virtual reality and gaming, geometry, and social networks analysis. Software implementations include distance-vector algorithms for distributed path computation in dynamics networks, parallel solutions of the constrained shortest path problem, and application of the shortest path solutions in gathering robotic swarms. Massively parallel algorithms utilise cellular automata, where a shortest path is computed either via matrix multiplication in automaton arrays, or via the representation of data graphs in automaton lattices and using the propagation of wave-like patterns. Unconventional shortest path solvers are presented in computer models of foraging behaviour and protoplasmic network optimisation by the slime mould Physarum polycephalum and fluidic devices, while experimental laboratory prototypes of path solvers using chemical media, flows and droplets, and electrical current are also highlighted. The book will be a pleasure to explore for readers from all walks of life, from undergraduate students to university professors, from mathematicians, computers scientists and engineers to chemists and biologists.
Download or read book Optimization Over Integers written by Dimitris Bertsimas and published by . This book was released on 2005 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Principles and Practice of Constraint Programming CP 2011 written by Jimmy Lee and published by Springer. This book was released on 2011-09-01 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th International Conference on Principles and Practice of Constraint Programming, CP 2011, held in Perugia, Italy, September 12-16, 2011. The 51 revised full papers and 7 short papers presented together with three invited talks were carefully reviewed and selected from 159 submissions. The papers are organized in topical sections on algorithms, environments, languages, models and systems, applications such as decision making, resource allocation and agreement technologies.
Download or read book On a Routing Problem written by Richard Bellman and published by . This book was released on 1956 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: An attempt to determine an optimal route from one point to another, given a set of N cities, with every two linked by a road, and the times required to transverse these roads. The times are not directly proportional to the distances because of the varying quality of roads and quantities of traffic. The functional equation technique of dynamic programming, combined with approximation in policy space, yields an iterative algorithm which converges after a finite number if iterations bounded in advance.
Download or read book The Shortest Path Problem written by Camil Demetrescu and published by American Mathematical Soc.. This book was released on with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solution Algorithms for Resource and Route Constrained Shortest Path Problems in Time dependent Transportation Networks written by Erkut Yucaoğlu and published by . This book was released on 1973 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorial Optimization and Applications written by Ding-Zhu Du and published by Springer. This book was released on 2021-12-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2021, which took place in Tianjin, China, during December 17-19, 2021. The 55 papers presented in this volume were carefully reviewed and selected from 122 submissions. They deal with combinatorial optimization and its applications in general, focusing on algorithms design, theoretical and experimental analysis, and applied research of general algorithmic interest.
Download or read book Optimization Algorithms for Networks and Graphs written by James Evans and published by CRC Press. This book was released on 2017-10-19 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revised and expanded advanced-undergraduate/graduate text (first ed., 1978) about optimization algorithms for problems that can be formulated on graphs and networks. This edition provides many new applications and algorithms while maintaining the classic foundations on which contemporary algorithm
Download or read book Combinatorial Optimization written by Eugene Lawler and published by Courier Corporation. This book was released on 2012-10-16 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perceptive text examines shortest paths, network flows, bipartite and nonbipartite matching, matroids and the greedy algorithm, matroid intersections, and the matroid parity problems. Suitable for courses in combinatorial computing and concrete computational complexity.
Download or read book Time Constrained Shortest Paths in Stochastic and Dynamic Transportation Networks written by Deepak Kumar and published by . This book was released on 2004 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis develops methodologies for solving constrained shortest path problems in dynamic and random conditions. Due to the randomness of the network, the decisions need to account for uncertainty of the future real-time network state. Currently the randomness of the arc attributes is not taken into consideration. In this thesis, the intent is to develop methodologies for finding best paths when the arc attributes are uncertain, and change with time. Modified label correcting algorithms are developed for several new variations of the constrained stochastic dynamic shortest path problem where the objective is to minimize the expected cost subject to a specified constraint on the travel time of the path. The constraint can be placed on the expected travel time of the path, or on the cumulative probability of experiencing a maximum travel time. Unlike deterministic networks, in which a single minimum cost path can be determined between an origin and a destination, several paths may each have some positive probability of having the least cost for some realization of the network when the arc times and costs are stochastic and thus, a set of Pareto-optimal paths can be generated. Multiple variations are also examined when considering the FIFO nature of travel times in the network. The correctness of the proposed algorithms is proved. Extensive numerical experiments are conducted to access the performance of these procedures. Also some of the instances are discussed where this problem has practical significance
Download or read book Formal Language Constrained Path Problems written by and published by . This book was released on 1997 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many path finding problems arising in practice, certain patterns of edge/vertex labels in the labeled graph being traversed are allowed/preferred, while others are disallowed. Motivated by such applications as intermodal transportation planning, the authors investigate the complexity of finding feasible paths in a labeled network, where the mode choice for each traveler is specified by a formal language. The main contributions of this paper include the following: (1) the authors show that the problem of finding a shortest path between a source and destination for a traveler whose mode choice is specified as a context free language is solvable efficiently in polynomial time, when the mode choice is specified as a regular language they provide algorithms with improved space and time bounds; (2) in contrast, they show that the problem of finding simple paths between a source and a given destination is NP-hard, even when restricted to very simple regular expressions and/or very simple graphs; (3) for the class of treewidth bounded graphs, they show that (i) the problem of finding a regular language constrained simple path between source and a destination is solvable in polynomial time and (ii) the extension to finding context free language constrained simple paths is NP-complete. Several extensions of these results are presented in the context of finding shortest paths with additional constraints. These results significantly extend the results in [MW95]. As a corollary of the results, they obtain a polynomial time algorithm for the BEST k-SIMILAR PATH problem studied in [SJB97]. The previous best algorithm was given by [SJB97] and takes exponential time in the worst case.
