248 research outputs found
The Cutting Plane Method is Polynomial for Perfect Matchings
The cutting plane approach to optimal matchings has been discussed by several
authors over the past decades (e.g., Padberg and Rao '82, Grotschel and Holland
'85, Lovasz and Plummer '86, Trick '87, Fischetti and Lodi '07) and its
convergence has been an open question. We give a cutting plane algorithm that
converges in polynomial-time using only Edmonds' blossom inequalities; it
maintains half-integral intermediate LP solutions supported by a disjoint union
of odd cycles and edges. Our main insight is a method to retain only a subset
of the previously added cutting planes based on their dual values. This allows
us to quickly find violated blossom inequalities and argue convergence by
tracking the number of odd cycles in the support of intermediate solutions
System design for express airlines
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1988.Includes bibliographical references.by Michael R. Fisher, Jr.Ph.D
Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization
International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM
OPTIMIZATION OF RAILWAY TRANSPORTATION HAZMATS AND REGULAR COMMODITIES
Transportation of dangerous goods has been receiving more attention in the realm of academic and scientific research during the last few decades as countries have been increasingly becoming industrialized throughout the world, thereby making Hazmats an integral part of our life style. However, the number of scholarly articles in this field is not as many as those of other areas in SCM. Considering the low-probability-and-high-consequence (LPHC) essence of transportation of Hazmats, on the one hand, and immense volume of shipments accounting for more than hundred tons in North America and Europe, on the other, we can safely state that the number of scholarly articles and dissertations have not been proportional to the significance of the subject of interest. On this ground, we conducted our research to contribute towards further developing the domain of Hazmats transportation, and sustainable supply chain management (SSCM), in general terms.
Transportation of Hazmats, from logistical standpoint, may include all modes of transport via air, marine, road and rail, as well as intermodal transportation systems. Although road shipment is predominant in most of the literature, railway transportation of Hazmats has proven to be a potentially significant means of transporting dangerous goods with respect to both economies of scale and risk of transportation; these factors, have not just given rise to more thoroughly investigation of intermodal transportation of Hazmats using road and rail networks, but has encouraged the competition between rail and road companies which may indeed have some inherent advantages compared to the other medium due to their infrastructural and technological backgrounds. Truck shipment has ostensibly proven to be providing more flexibility; trains, per contra, provide more reliability in terms of transport risk for conveying Hazmats in bulks.
In this thesis, in consonance with the aforementioned motivation, we provide an introduction into the hazardous commodities shipment through rail network in the first chapter of the thesis. Providing relevant statistics on the volume of Hazmat goods, number of accidents, rate of incidents, and rate of fatalities and injuries due to the incidents involving Hazmats, will shed light onto the significance of the topic under study. As well, we review the most pertinent articles while putting more emphasis on the state-of-the-art papers, in chapter two. Following the discussion in chapter 3 and looking at the problem from carrier company’s perspective, a mixed integer quadratically constraint problem (MIQCP) is developed which seeks for the minimization of transportation cost under a set of constraints including those associating with Hazmats. Due to the complexity of the problem, the risk function has been piecewise linearized using a set of auxiliary variables, thereby resulting in an MIP problem. Further, considering the interests of both carrier companies and regulatory agencies, which are minimization of cost and risk, respectively, a multiobjective MINLP model is developed, which has been reduced to an MILP through piecewise linearization of the risk term in the objective function. For both single-objective and multiobjective formulations, model variants with bifurcated and nonbifurcated flows have been presented. Then, in chapter 4, we carry out experiments considering two main cases where the first case presents smaller instances of the problem and the second case focuses on a larger instance of the problem.
Eventually, in chapter five, we conclude the dissertation with a summary of the overall discussion as well as presenting some comments on avenues of future work
Operational Research: Methods and Applications
Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes
Resource optimization for fault-tolerant quantum computing
In this thesis we examine a variety of techniques for reducing the resources
required for fault-tolerant quantum computation. First, we show how to simplify
universal encoded computation by using only transversal gates and standard
error correction procedures, circumventing existing no-go theorems. We then
show how to simplify ancilla preparation, reducing the cost of error correction
by more than a factor of four. Using this optimized ancilla preparation, we
develop improved techniques for proving rigorous lower bounds on the noise
threshold.
Additional overhead can be incurred because quantum algorithms must be
translated into sequences of gates that are actually available in the quantum
computer. In particular, arbitrary single-qubit rotations must be decomposed
into a discrete set of fault-tolerant gates. We find that by using a special
class of non-deterministic circuits, the cost of decomposition can be reduced
by as much as a factor of four over state-of-the-art techniques, which
typically use deterministic circuits.
Finally, we examine global optimization of fault-tolerant quantum circuits
under physical connectivity constraints. We adapt techniques from VLSI in order
to minimize time and space usage for computations in the surface code, and we
develop a software prototype to demonstrate the potential savings.Comment: 231 pages, Ph.D. thesis, University of Waterlo
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