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A New and Faster Representation for Counting Integer Points in Parametric Polyhedra

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arXiv 2023年

作者： Gribanov, Dmitry V. Malyshev, Dmitry S. Pardalos, Panos M. Zolotykh, Nikolai Yu. Laboratory of Discrete and Combinatorial Optimization Moscow Institute of Physics and Technology Institutsky Lane 9 Moscow Region Dolgoprudny141700 Russia Laboratory of Algorithms and Technologies for Network Analysis HSE University 136 Rodionova Ulitsa Nizhny Novgorod603093 Russia Department of Industrial and Systems Engineering University of Florida 401 Weil Hall GainesvilleFL116595 United States Lobachevsky State University of Nizhny Novgorod 23 Gagarina Avenue Nizhny Novgorod603950 Russia

In this paper, we consider the counting function EP(y) = | Py ∩ Znx | for a parametric polyhedron Py = {x ∈ Rnx : Ax ≤ b + By}, where y ∈ Rny. We give a new representation of EP(y), called a piece-wise step-polynomial with periodic coefficients, which is a generalization of piece-wise step-polynomials and integer/rational Ehrhart’s quasi-polynomials. It gives the fastest way to calculate EP(y) in certain scenarios. The most important cases are the following: 1) We show that, for the parametric polyhedron Py defined by a standard-form system Ax = y, x ≥ 0 with a fixed number of equalities, the function EP(y) can be represented by a polynomial-time computable function. In turn, such a representation of EP(y) can be constructed by an poly(n, A∞)-time algorithm;2) Assuming again that the number of equalities is fixed, we show that integer/rational Ehrhart’s quasi-polynomials of a polytope can be computed by FPT-algorithms, parameterized by sub-determinants of A or its elements;3) Our representation of EP is more efficient than other known approaches, if A has bounded elements, especially if it is sparse in addition;Additionally, we provide a discussion about possible applications in the area of compiler optimization. In some "natural" assumptions on a program code, our approach has the fastest complexity bounds. Copyright © 2023, The Authors. All rights reserved.

关键词： Polynomial approximation

PUTTING AN OIL-SPILL CLEANUP COMPUTER-MODEL TO WORK FOR THE NAVY

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NAVAL ENGINEERS JOURNAL 1983年第3期95卷 165-172页

作者： NYHART, JD PSARAFTIS, HN YAROSCHAK, PJ Mr. J. D. Nyhart:is professor of management at the Sloan School of Management and the Department of Ocean Engineering at the Massachusetts Institute of Technology. His current research and writing focus on the use of scientific and technical material in formal judicial and administrative proceedings as well as the development of economic and regulatory models appropriate for deep ocean mining and oil-spill control. Harilaos N. Psaraftis:is Assistant Professor of Marine Systems at the Department of Ocean Engineering at the Operations Research Center at M.I.T. Professor Psaraftis received two M.Sc. degrees in 1977 (in Naval Architecture and Marine Engineering and in Shipping and Shipbuilding Management) and a Ph.D. in 1979 (in Ocean Systems Operations Research) all from M.I.T. Professor Psaraftis has been conducting research in problem areas such as the probabilistic modeling of underwater detection and optimal sensor allocation (project sponsored by ONR) the optimization of oil spill cleanup operations (project sponsored by a consortium of government and industry organizations) the development of routing and scheduling algorithms in transportation problems (project sponsored by DOT) and the analysis and solution algorithms of sealift routing and scheduling problems (project sponsored by ONR and the Military Sealift Command). Professor Psaraftis has published in various journals and is currently the Chairman of the Ocean Systems Management Program at M.I.T. Mr. Paul J. Yaroschak:received his Bachelors Degree in Civil Engineering from Villanova University and his Masters Degree in Environmental Engineering from Northeastern University. He has served in the Civil Engineer Corps U.S. Navy in Public Works and Construction Management and as a Project Engineer for Navy-wide Water and Wastewater Treatment Projects for the Naval Facilities Engineering Command. He is currently Head of the Environmental Engineering Branch of the Naval Facilities Engineering Command. Mr. Yaroschak is a Registered Professional Engineer i

A research group at the Massachusetts Institute of Technology has completed the first phase of the development of a computer assisted model for analyzing complex decisions and policies regarding oil spill cleanup. The model is the product of an ongoing MIT Sea Grant project, sponsored by a consortium of government and industry organizations, including the National Oceanic and Atmospheric Administration, the U.S. C oast G uard , the U.S. N avy , the Commonwealth of Massachusetts, the Spill Control Association of America, JFB Scientific Corporation, the Doherty Foundation, Petro-Canada and Texaco. The model can be used, among other things, in strategic planning for the long-term oil spill response needs of a region, in assisting On Scene Coordinators in responding to a specific spill (tactical/operational setting), in evaluating the environmental and economic damages of a spill versus the cost of cleanup, in simulation and training, and in the analysis of various policy and regulatory issues such as the effects of delays, the use of dispersants and the investigation of liability and compensation issues. The paper describes the model in detail, focuses on its potential uses and presents experience with its application in conjunction with pollution control efforts of the U.S. Navy. Specifically, we outline the application of the model in the Port of Charleston, South Carolina, an ongoing project sponsored by the Naval Facilities Engineering Command. The difficulty of gathering data for such an application is discussed.

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ECONOMICS OF DECLINING WATER-SUPPLIES IN THE OGALLALA AQUIFER

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GROUND WATER 1982年第1期20卷 73-79页

作者： WARREN, J MAPP, H RAY, D KLETKE, D WANG, C Assistant Professor Professors and Research Associate Department of Agricultural Economics Agricultural Hall Room 555 Stillwater Oklahoma 74074. Harry P. Mapp Jr. received a Ph.D. in Agricultural Economics from Oklahoma State University in 1972 and has been a member of the faculty at Cornell University and Oklahoma State University. He has been involved in several research projects and has a number of publications on the economics of irrigation from ground-water sources. Daryll E. Ray received his Ph.D. in Economics from Iowa State University in 1971. He has been with Oklahoma State University since October 1971. He is the developer of the National Agricultural Policy Simulator (POLYSIM) and is the author of numerous journal articles and professional publications in the public policy and production economics areas. Darrel D. Kletke received the B.S. degree in Agriculture Education and M.S. and Ph.D. degrees in Agricultural Economics from Oklahoma State University. Research emphasis is farm level optimization algorithms irrigation cost estimation and decision model design and development. He has numerous publications in these areas.

A large portion of northwest Oklahoma is situated over the Ogallala Aquifer. Economic growth in the region has been tied closely to irrigated agriculture which depends on declining ground-water resources in the Ogallala formation. As part of an integrated six-State study, Oklahoma researchers developed a computer model of the agricultural sector of northwestern Oklahoma and estimated irrigated and dryland cropping patterns, farm output and farm income over a 40-year planning horizon. Projections were made for a “baseline” situation, and the sensitivity of these results to alternative assumptions on energy costs, commodity prices and technological development was also analyzed. Preliminary results of the baseline analysis suggest a favorable outlook for irrigated agriculture in the area through the near to mid-term, with increases in irrigated acreage, production, and returns to land and management. However, the baseline case is dependent on several relatively optimistic assumptions regarding future fuel prices, yields, and agricultural commodity prices. Even fairly large changes in fuel prices and yields are not particularly critical for model results, but if agricultural commodity prices are substantially lower than projected, the outlook for irrigated agriculture in the area is not favorable.

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The SCIP optimization suite 8.0

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arXiv 2021年

作者： Bestuzheva, Ksenia Besançon, Mathieu Chen, Wei-Kun Chmiela, Antonia Donkiewicz, Tim Van Doornmalen, Jasper Eifler, Leon Gaul, Oliver Gamrath, Gerald Gleixner, Ambros Gottwald, Leona Graczyk, Christoph Halbig, Katrin Hoen, Alexander Hojny, Christopher Van Der Hulst, Rolf Koch, Thorsten Lübbecke, Marco Maher, Stephen J. Matter, Frederic Mühmer, Erik Müller, Benjamin Pfetsch, Marc E. Rehfeldt, Daniel Schlein, Steffan Schlösser, Franziska Serrano, Felipe Shinano, Yuji Sofranac, Boro Turner, Mark Vigerske, Stefan Wegscheider, Fabian Wellner, Philipp Weninger, Dieter Witzig, Jakob Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China RWTH Aachen University Lehrstuhl für Operations Research Kackertstr. 7 Aachen52072 Germany Technische Universiteit Eindhoven Department of Mathematics and Computer Science P.O. Box 513 Eindhoven5600 MB Netherlands I2DAMO GmbH Englerallee 19 Berlin14195 Germany Friedrich-Alexander Universität Erlangen-Nürnberg Department of Data Science Cauerstr. 11 Erlangen91058 Germany University of Twente Department of Discrete Mathematics and Mathematical Programming P.O. Box 217 Enschede7500 AE Netherlands Technische Universität Berlin Software and Algorithms for Discrete Optimization Straße des 17. Juni 135 Berlin10623 Germany Zuse Institute Berlin Department A2IM Takustr. 7 Berlin14195 Germany University of Exeter College of Engineering Mathematics and Physical Sciences Exeter United Kingdom Technische Universität Darmstadt Fachbereich Mathematik Dolivostr. 15 Darmstadt64293 Germany Technische Universität Berlin Straße des 17. Juni 135 Berlin10623 Germany Software and Algorithms for Discrete Optimization Institute of Mathematics Technische Universität Berlin Straße des 17. Juni 135 Berlin10623 Germany GAMS Software GmbH C/o Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany

The SCIP optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in *** Codes 90C05, 90C10, 90C11, 90C30, 90C90, 65Y05 Copyright © 2021, The Authors. All rights reserved.

关键词： Integer programming

Enabling Research through the SCIP optimization Suite 8.0

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arXiv 2023年

作者： Bestuzheva, Ksenia Besançon, Mathieu Chen, Wei-Kun Chmiela, Antonia Donkiewicz, Tim van Doornmalen, Jasper Eifler, Leon Gaul, Oliver Gamrath, Gerald Gleixner, Ambros Gottwald, Leona Graczyk, Christoph Halbig, Katrin Hoen, Alexander Hojny, Christopher van der Hulst, Rolf Koch, Thorsten Lübbecke, Marco Maher, Stephen J. Matter, Frederic Mühmer, Erik Müller, Benjamin Pfetsch, Marc E. Rehfeldt, Daniel Schlein, Steffan Schlösser, Franziska Serrano, Felipe Shinano, Yuji Sofranac, Boro Turner, Mark Vigerske, Stefan Wegscheider, Fabian Wellner, Philipp Weninger, Dieter Witzig, Jakob Zuse Institute Berlin Department AIS2T Takustr. 7 Berlin14195 Germany ZIB-AIS2T Germany School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China RWTH Aachen University Lehrstuhl für Operations Research Kackertstr. 7 Aachen52072 Germany Eindhoven University of Technology Department of Mathematics and Computer Science Netherlands ZIB-AIS2T I2DAMO GmbH Englerallee 19 Berlin14195 Germany ZIB-AIS2T HTW Berlin Germany Friedrich-Alexander Universität Erlangen-Nürnberg Department of Data Science Cauerstr. 11 Erlangen91058 Germany University of Twente Department of Discrete Mathematics and Mathematical Programming P.O. Box 217 Enschede7500 AE Netherlands Technische Universität Berlin Software and Algorithms for Discrete Optimization Straße des 17. Juni 135 Berlin10623 Germany ZIB Department A2IM Takustr. 7 Berlin14195 Germany RWTH Aachen-Lehrstuhl für OR Germany University of Exeter College of Engineering Mathematics and Physical Sciences Exeter United Kingdom Technische Universität Darmstadt Fachbereich Mathematik Dolivostr. 15 Darmstadt64293 Germany TU Darmstadt Fachbereich Mathematik Germany ZIB-A2IM Germany TU Berlin Germany ZIB-A2IM Software and Algorithms for Discrete Optimization Institute of Mathematics TU Berlin Germany GAMS Software GmbH c/o ZIB-AIS2T Germany

The SCIP optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this paper is on the role of the SCIP optimization Suite in supporting research. SCIP's main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP's application as a research tool and as a platform for further developments. Further, the paper gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon *** Codes 90C05, 90C10, 90C11, 90C30, 90C90, 65Y05 Copyright © 2023, The Authors. All rights reserved.

关键词： Integer programming

Article's Scientific Prestige: Measuring the impact of individual articles in the Web of Science

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arXiv 2022年

作者： Chen, Ying Koch, Thorsten Zakiyeva, Nazgul Liu, Kailiang Xu, Zhitong Chen, Chun-Houh Nakano, Junji Honda, Keisuke Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore117543 Singapore Risk Management Institute National University of Singapore 21 Heng Mui Keng Terrace 04-03 Singapore119613 Singapore Technische Universität Berlin Software and Algorithms for Discrete Optimization Straße des 17. Juni 135 Berlin10623 Germany Zuse Institute Berlin Applied Algorithmic Intelligence Methods Department Takustraße 7 Berlin14195 Germany Research Institute Chongqing Internet Institute Building 5B No. 16 South Huashan Road Chongqing Liang Jiang New Area Chongqing China Department of Statistics and Data Science National University of Singapore 6 Science Drive 2 Singapore117546 Singapore The Institute of Statistical Science Academia Sinica 128 Academia Road Nankang Taipei11529 Taiwan Department of Global Management Chuo University 742-1 Higashinakano Hachioji Tokyo192-0393 Japan Institute of Statistical Mathematics 10-3 Midoricho Tachikawa Tokyo190-0014 Japan

We performed a citation analysis on the Web of Science publications consisting of more than 63 million articles and 1.45 billion citations on 254 subjects from 1981 to 2020. We proposed the Article's Scientific Prestige (ASP) metric and compared this metric to number of citations (#Cit) and journal grade in measuring the scientific impact of individual articles in the large-scale hierarchical and multi-disciplined citation network. In contrast to #Cit, ASP, that is computed based on the eigenvector centrality, considers both direct and indirect citations, and provides steady-state evaluation cross different disciplines. We found that ASP and #Cit are not aligned for most articles, with a growing mismatch amongst the less cited articles. While both metrics are reliable for evaluating the prestige of articles such as Nobel Prize winning articles, ASP tends to provide more persuasive rankings than #Cit when the articles are not highly cited. The journal grade, that is eventually determined by a few highly cited articles, is unable to properly reect the scientific impact of individual articles. The number of references and coauthors are less relevant to scientiffc impact, but subjects do make a difference. Copyright © 2022, The Authors. All rights reserved.

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Modern applications of machine learning in quantum sciences

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arXiv 2022年

作者： Dawid, Anna Arnold, Julian Requena, Borja Gresch, Alexander Plodzien, Marcin Donatella, Kaelan Nicoli, Kim A. Stornati, Paolo Koch, Rouven Büttner, Miriam Okula, Robert Muñoz–Gil, Gorka Vargas–Hernández, Rodrigo A. Cervera-Lierta, Alba Carrasquilla, Juan Dunjko, Vedran Gabrié, Marylou Huembeli, Patrick van Nieuwenburg, Evert Vicentini, Filippo Wang, Lei Wetzel, Sebastian J. Carleo, Giuseppe Greplová, Eliška Krems, Roman Marquardt, Florian Tomza, Michal Lewenstein, Maciej Dauphin, Alexandre Faculty of Physics University of Warsaw Poland ICFO - Institut de Ciències Fotòniques The Barcelona Institute of Science and Technology Castelldefels Barcelona08860 Spain Center for Computational Quantum Physics Flatiron Institute New York United States Department of Physics University of Basel Switzerland Institute for Theoretical Physics Heinrich Heine University Düsseldorf Germany Institute for Quantum Inspired and Quantum Optimization Hamburg University of Technology Germany Université de Paris CNRS Laboratoire Matériaux et Phénomènes Quantiques France Machine Learning Group Technische Universität Berlin Germany BIFOLD Berlin Institute for the Foundations of Learning and Data Berlin10587 Germany Department of Applied Physics Aalto University Espoo Finland Institute of Physics Albert-Ludwig University of Freiburg Germany International Centre for Theory of Quantum Technologies University of Gdańsk Poland Department of Algorithms and System Modeling Faculty of Electronics Faculty of Electronics Telecommunications and Informatics Gdańsk University of Technology Poland Institute for Theoretical Physics University of Innsbruck Austria Department of Chemistry University of Toronto Canada Vector Institute for Artificial Intelligence MaRS Centre Toronto Canada Department of Chemistry and Chemical Biology McMaster University Hamilton Canada Barcelona Supercomputing Center Spain LIACS Leiden University Netherlands CMAP École Polytechnique France Switzerland Menten AI Inc. Palo AltoCA United States Niels Bohr Institute Copenhagen Denmark CPHT CNRS École Polytechnique Institut Polytechnique de Paris PalaiseauF-91128 France Beijing National Lab for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences Beijing China Songshan Lake Materials Laboratory Dongguan China Perimeter Institute for Theoretical Physics Waterloo Canada Kavli Institute of Nanoscience Delft University of Technology DelftNL-2600 GA Netherlands Department of

In this book, we provide a comprehensive introduction to the most recentadvances in the application of machine learning methods in quantum sciences. Wecover the use of deep learning and kernel methods in supervised, unsupervised,and reinforcement learning algorithms for phase classification, representationof many-body quantum states, quantum feedback control, and quantum circuitsoptimization. Moreover, we introduce and discuss more specialized topics suchas differentiable programming, generative models, statistical approach tomachine learning, and quantum machine learning. © 2022, CC BY.

关键词： Deep learning

ACCURACY REQUIREMENTS FOR MEASUREMENT SYSTEMS WITH UNIFORM AND NORMAL ERRORS

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NAVAL ENGINEERS JOURNAL 1993年第1期105卷 66-69页

作者： SNOW, JM STUCKMAN, BE USHER, JS Jeffrey M. Snow:received his B.S. degree in mechanical engineering from the University of Washington in 1977. He has worked at Boeing Commercial Aircraft Company and Puget Sound Naval Shipyard. Since 1985 he has been at Naval Surface Warfare Center Crane Division (NSWCC). From 1987 to 1990 he was in charge of quality assurance configuration management and reliability for Aegis (SPY-1 and Mk-99) microwave tubes. He currently is in the Radar System Branch at NSWCC. He is a member of ASQC and ASME. His areas of interest include the use of statistics in process improvement efforts and objectively rating and rewarding suppliers for better quality. Bruce E. Stuckman:holds a Ph.D. degree in systems engineering from Oakland University where he also obtained M.S. and B.S. degrees in electrical and computer engineering. In 1992 Dr. Stuckman obtained his J.D. from the University of Louisville where he graduated cum laude. He is currently an associate in the patent and computer law department of Brooks & Kushman a law firm specializing in intellectual property and technology related causes. Prior to this he was an associate professor of both electrical engineering at the University of Louisville and a member of the Research Advisory Board of the South Central Bell Telecommunications Research Center. Dr. Stuckman is the author of over 75 published works in a variety of research areas including global optimization algorithms control systems communication and telecommunication systems and instrumentation electronics. He has served as a technical consultant to such organizations as Control Data Corporation General Electric General Motors Research Laboratories Gulf & Western AT&T Bell Laboratories ARCO Research and Technical Services and the U.S. Government and has been a frequent lecturer at national and international symposia. He is a senior member of IEEE and a member of ASNE Eta Kappa Nu Tau Beta Pi Sigma Xi and Phi Kappa Phi. John S. Usher Ph.D. P.E.:is an assistant professor of industrial engineering

Accuracy requirements are usually determined as a percentage of the specification range of the measured part or process. Setting accuracy requirements in this manner results in a wide and unpredictable range of false rejection and acceptance probabilities. This causes extra costs due to either: 1) over specification of measurement systems accuracy requirements;2) time, effort, retesting, and resolution of false rejections;or 3) system degradation caused by false acceptance of out-of-specification parts. Achieving a consistent and known risk of false acceptance is only possible by considering the measured process C(pk), the process's mean in relation to the center of the specification range, and the measurement system error distribution. This paper presents a method for calculating the probabilities of false rejection and false acceptance for a normal process which is measured with, alternately, uniform and normally distributed error. It is shown that under most conditions uniform error causes 20% to 30% higher false rejection and acceptance probabilities. Thus, knowledge of measurement error distribution could provide lower total production cost.

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