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Algorithmic Advancements in Discrete Optimization

Algorithmic Advancements in Discrete Optimization PDF Author: Jean A. Pauphilet
Publisher:
ISBN:
Category :
Languages : en
Pages : 253

Book Description
In the next ten years, hospitals will operate like air-traffic control centers whose role is to coordinate care across multiple facilities. Consequently, the future of hospital operations will have three salient characteristics. First, data. The ability to process, analyze and exploit data effectively will become a vital skill for practitioners. Second, a holistic approach, since orchestrating care requires the concurrent optimization of multiple resources, services, and time scales. Third, real-time personalized decisions, to respond to the increasingly closer monitoring of patients. To support this transition and transform our healthcare system towards better outcomes at lower costs, research in operations and analytics should address two concurrent goals: First, develop new methods and algorithms for decision-making in a data-rich environment, which answer key concerns from practitioners and regulators, such as reliability, interpretability, and fairness. Second, put its models and algorithms to the test of practice, to ensure a path towards implementation and impact. Accordingly, this thesis is comprised of two parts. The first three chapters present methodological contributions to the discrete optimization literature, with particular emphasis on problems emerging from machine learning under sparsity. Indeed, the most important operational decision-making problems are by nature discrete and their sizes have increased with the widespread adoption of connected devices and sensors. In particular, in machine learning, the gigantic amount of data now available contrasts with our limited cognitive abilities. Hence, sparse models, i.e., which only involve a small number of variables, are needed to ensure human understanding. The last two chapters present applications and implementation of machine learning and discrete optimization methods to improve operations at a major academic hospital. From raw electronic health records of patients, we build predictive models to predict patient flows and prescriptive models to optimize patient-bed assignment in real-time. More importantly, we implement our models in a 600-bed institution. Our impact is two-fold: methodological and operational. Integrating advanced analytics in their daily operations and building a data-first culture constitutes a major paradigm shift.

Algorithmic Advancements in Discrete Optimization

Algorithmic Advancements in Discrete Optimization PDF Author: Jean A. Pauphilet
Publisher:
ISBN:
Category :
Languages : en
Pages : 253

Book Description
In the next ten years, hospitals will operate like air-traffic control centers whose role is to coordinate care across multiple facilities. Consequently, the future of hospital operations will have three salient characteristics. First, data. The ability to process, analyze and exploit data effectively will become a vital skill for practitioners. Second, a holistic approach, since orchestrating care requires the concurrent optimization of multiple resources, services, and time scales. Third, real-time personalized decisions, to respond to the increasingly closer monitoring of patients. To support this transition and transform our healthcare system towards better outcomes at lower costs, research in operations and analytics should address two concurrent goals: First, develop new methods and algorithms for decision-making in a data-rich environment, which answer key concerns from practitioners and regulators, such as reliability, interpretability, and fairness. Second, put its models and algorithms to the test of practice, to ensure a path towards implementation and impact. Accordingly, this thesis is comprised of two parts. The first three chapters present methodological contributions to the discrete optimization literature, with particular emphasis on problems emerging from machine learning under sparsity. Indeed, the most important operational decision-making problems are by nature discrete and their sizes have increased with the widespread adoption of connected devices and sensors. In particular, in machine learning, the gigantic amount of data now available contrasts with our limited cognitive abilities. Hence, sparse models, i.e., which only involve a small number of variables, are needed to ensure human understanding. The last two chapters present applications and implementation of machine learning and discrete optimization methods to improve operations at a major academic hospital. From raw electronic health records of patients, we build predictive models to predict patient flows and prescriptive models to optimize patient-bed assignment in real-time. More importantly, we implement our models in a 600-bed institution. Our impact is two-fold: methodological and operational. Integrating advanced analytics in their daily operations and building a data-first culture constitutes a major paradigm shift.

Decision Diagrams for Optimization

Decision Diagrams for Optimization PDF Author: David Bergman
Publisher: Springer
ISBN: 3319428497
Category : Computers
Languages : en
Pages : 262

Book Description
This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors present chapters on the use of decision diagrams for combinatorial optimization and constraint programming, with attention to general-purpose solution methods as well as problem-specific techniques. The book will be useful for researchers and practitioners in discrete optimization and constraint programming. "Decision Diagrams for Optimization is one of the most exciting developments emerging from constraint programming in recent years. This book is a compelling summary of existing results in this space and a must-read for optimizers around the world." [Pascal Van Hentenryck]

Theory of Evolutionary Computation

Theory of Evolutionary Computation PDF Author: Benjamin Doerr
Publisher: Springer Nature
ISBN: 3030294145
Category : Computers
Languages : en
Pages : 506

Book Description
This edited book reports on recent developments in the theory of evolutionary computation, or more generally the domain of randomized search heuristics. It starts with two chapters on mathematical methods that are often used in the analysis of randomized search heuristics, followed by three chapters on how to measure the complexity of a search heuristic: black-box complexity, a counterpart of classical complexity theory in black-box optimization; parameterized complexity, aimed at a more fine-grained view of the difficulty of problems; and the fixed-budget perspective, which answers the question of how good a solution will be after investing a certain computational budget. The book then describes theoretical results on three important questions in evolutionary computation: how to profit from changing the parameters during the run of an algorithm; how evolutionary algorithms cope with dynamically changing or stochastic environments; and how population diversity influences performance. Finally, the book looks at three algorithm classes that have only recently become the focus of theoretical work: estimation-of-distribution algorithms; artificial immune systems; and genetic programming. Throughout the book the contributing authors try to develop an understanding for how these methods work, and why they are so successful in many applications. The book will be useful for students and researchers in theoretical computer science and evolutionary computing.

Discrete Optimization Algorithms

Discrete Optimization Algorithms PDF Author: Maciej M. Sys?o
Publisher: Courier Corporation
ISBN: 0486453537
Category : Computers
Languages : en
Pages : 564

Book Description
Rich in publications, the well-established field of discrete optimization nevertheless features relatively few books with ready-to-use computer programs. This book, geared toward upper-level undergraduates and graduate students, addresses that need. In addition, it offers a look at the programs' derivation and performance characteristics. Subjects include linear and integer programming, packing and covering, optimization on networks, and coloring and scheduling. A familiarity with design, analysis, and use of computer algorithms is assumed, along with knowledge of programming in Pascal. The book can be used as a supporting text in discrete optimization courses or as a software handbook, with twenty-six programs that execute the most common algorithms in each topic area. Each chapter is self-contained, allowing readers to browse at will.

Handbooks in Operations Research and Management Science

Handbooks in Operations Research and Management Science PDF Author: K. Aardal
Publisher: Elsevier
ISBN: 0080459218
Category : Business & Economics
Languages : en
Pages : 621

Book Description
The chapters of this Handbook volume cover nine main topics that are representative of recent theoretical and algorithmic developments in the field. In addition to the nine papers that present the state of the art, there is an article on the early history of the field. The handbook will be a useful reference to experts in the field as well as students and others who want to learn about discrete optimization.

Nonlinear Discrete Optimization

Nonlinear Discrete Optimization PDF Author: Shmuel Onn
Publisher: European Mathematical Society
ISBN: 9783037190937
Category : Combinatorial optimization
Languages : en
Pages : 0

Book Description
This monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup, which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a variety of application areas within operations research and statistics, including vector partitioning, matroid optimization, experimental design, multicommodity flows, multi-index transportation and privacy in statistical databases. This monograph is intended for graduate students and researchers. It is accessible to anyone with standard undergraduate knowledge and mathematical maturity.

Discrete Optimization

Discrete Optimization PDF Author: E. Boros
Publisher: Elsevier
ISBN: 008093028X
Category : Mathematics
Languages : en
Pages : 587

Book Description
One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world.This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc.Key features:• state of the art surveys• comprehensiveness• prominent authors• theoretical, computational and applied aspects.This book is a reprint of Discrete Applied Mathematics Volume 23, Numbers 1-3

Discrete Optimization

Discrete Optimization PDF Author: R. Gary Parker
Publisher: Elsevier
ISBN: 1483294803
Category : Mathematics
Languages : en
Pages : 485

Book Description
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas of linear programming, graph theory, and combinatorics--prerequisites for readers of the text. Numerous exercises are included at the end of each chapter.

Novel Approaches to Hard Discrete Optimization

Novel Approaches to Hard Discrete Optimization PDF Author: Panos M. Pardalos
Publisher: American Mathematical Soc.
ISBN: 0821832484
Category : Mathematics
Languages : en
Pages : 194

Book Description
During the last decade, many novel approaches have been considered for dealing with computationally difficult discrete optimization problems. Such approaches include interior point methods, semidefinite programming techniques, and global optimization. More efficient computational algorithms have been developed and larger problem instances of hard discrete problems have been solved. This progress is due in part to these novel approaches, but also to new computing facilities and massive parallelism. This volume contains the papers presented at the workshop on ``Novel Approaches to Hard Discrete Optimization''. The articles cover a spectrum of issues regarding computationally hard discrete problems.

An Introduction to Optimization

An Introduction to Optimization PDF Author: Edwin K. P. Chong
Publisher: John Wiley & Sons
ISBN: 0471654000
Category : Mathematics
Languages : en
Pages : 497

Book Description
A modern, up-to-date introduction to optimization theory and methods This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Second Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked examples to illustrate both theory and algorithms, this book also provides: * A review of the required mathematical background material * A mathematical discussion at a level accessible to MBA and business students * A treatment of both linear and nonlinear programming * An introduction to recent developments, including neural networks, genetic algorithms, and interior-point methods * A chapter on the use of descent algorithms for the training of feedforward neural networks * Exercise problems after every chapter, many new to this edition * MATLAB(r) exercises and examples * Accompanying Instructor's Solutions Manual available on request An Introduction to Optimization, Second Edition helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.