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A REGRESSION FORMULATION OF THE MATRIX ESTIMATION PROBLEM

TRANSPORTATION SCIENCE 1985年第3期19卷 278-292页

作者： MCNEIL, S HENDRICKSON, C PRINCETON UNIV PRINCETONNJ 08544 CARNEGIE MELLON UNIV PITTSBURGHPA 15213

Matrices are widely used in transportation planning to represent the distribution of characteristics or as origin-destination matrices. Developing such matrices by means of surveys is expensive and time consuming, and once the survey data are collected and compiled the matrices are rapidly outdated. Other methods which are commonly used are unable to include all available data or to provide a measure of the uncertainty of the estimates. This paper formulates a quadratic programming method to estimate matrix entry estimates as an equivalent constrained generalized least squares estimation problem. As well as being able to include any available information in the form of constraints, the variance-covariance matrix of the entry estimates may be found and confidence intervals calculated for matrix entry estimates with some added distributional assumptions. The problem of updating the proportions of nationwide automobile trips by purpose and trip length from 1970 to 1977 is included as a simple example to illustrate the method.

关键词： Covariance matrices Estimation methods Traffic estimation Least squares Quadratic programming Distribution functions objective functions Trip length Coefficients

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OPTIMIZING SINGLE VEHICLE MANY-TO-MANY OPERATIONS WITH DESIRED DELIVERY TIMES .1. SCHEDULING

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TRANSPORTATION SCIENCE 1985年第4期19卷 378-410页

作者： SEXTON, TR BODIN, LD SUNY STONY BROOK STONY BROOK NY 11794 USA UNIV MARYLAND COLLEGE PK MD 20742 USA

A set of n customers is given. Each customer has a desired point of pickup, a desired point of delivery and a desired time of delivery. The problem is to determine the order of pickup and delivery and the times of pickup and delivery of these n customers by a single vehicle in order to minimize total customer inconvenience. Here, a mathematical programming formulating of this problem is subjected to Benders' decomposition procedure. The result is a heuristic routing and scheduling algorithm which is shown to produce high quality solutions in reasonable computation time by testing on moderately sized real data bases from both Gaithers-burg, Maryland, and Baltimore, Maryland. This study is divided into two parts, the first detailing the scheduling analysis and the second focusing on the routing component.

关键词： Scheduling Vehicles Algorithms Vehicle operation Unit costs Travel time Supply Heuristics objective functions

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Assessment of rainfall-runoff models based upon wavelet analysis

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HYDROLOGICAL PROCESSES 2007年第5期21卷 586-607页

作者： Lane, Stuart N. Univ Durham Dept Geog Sci Labs Durham DH1 3LE England

A basic hypothesis is proposed: given that wavelet-based analysis has been used to interpret runoff time-series, it may be extended to evaluation of rainfall-runoff model results. Conventional objective functions make certain assumptions about the data series to which they are applied (e.g. uncorrelated error, homoscedasticity). The difficulty that objective functions have in distinguishing between different realizations of the same model, or different models of the same system, is that they may have contributed in part to the occurrence of model equifinality. Of particular concern is the fact that the error present in a rainfall-runoff model may be time dependent, requiring some form of time localization in both identification of error and derivation of global objective functions. We explore the use of a complex Gaussian (order 2) wavelet to describe: (1) a measured hydrograph;(2) the same hydrograph with different simulated errors introduced;and (3) model predictions of the same hydrograph based upon a modified form of TOPMODEL. The analysis of results was based upon: (a) differences in wavelet power (the wavelet power error) between the measured hydrograph and both the simulated error and modelled hydrographs;and (b) the wavelet phase. Power difference and wavelet phase were used to develop two objective functions, RMSE(power) and RMS(phase), which were shown to distinguish between simulated errors and model predictions with similar values of the commonly adopted Nash-Sutcliffe efficiency index. These objective functions suffer because they do not retain time, frequency or time-frequency localization. Consideration of wavelet power spectra and time- and frequency-integrated power spectra shows that the impacts of different types of simulated error can be seen through retention of some localization, especially in relation to when and the scale over which error was manifest. Theoretical objections to the use of wavelet analysis for this type of application are note

关键词： rainfall-runoff models hydrological modelling model validation objective functions wavelet analysis

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PRIMAL GEOMETRIC PROGRAMS TREATED BY LINEAR-PROGRAMMING

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SIAM JOURNAL ON APPLIED MATHEMATICS 1976年第3期30卷 538-556页

作者： BENTAL, A BENISRAEL, A UNIV TEXAS CTR CYBERNETIC STUDIESAUSTINTX 78712 TEL AVIV UNIV DEPT STATISTICSTEL AVIVISRAEL NORTHWESTERN UNIV DEPT IND ENGN & MANAGEMENT SCIEVANSTONIL 60201 TECHNION ISRAEL INST TECHNOL DEPT APPL MATHHAIFAISRAEL

Necessary and sufficient optimality conditions, requiring no constraint qualifications, are given in terms of associated linear programs which also serve in the characterization of, and the reduction to, canonical programs. An iterative method for solving superconsistent geometric programs, based on the above conditions, is described.

关键词： Mathematical theorems Optimal solutions Linear programming Iterative methods Geometric programming Zero Necessary conditions for optimality objective functions

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ALTERNATIVE MODEL FORMULATIONS IN NONLINEAR-PROGRAMMING - SOME DISASTROUS RESULTS

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OPERATIONS RESEARCH 1985年第1期33卷 218-222页

作者： DRUD, A WORLD BANK WASHINGTONDC 20433 USA

This paper describes some experiments with two alternative formulations of a nonlinear programming model. One apparently suitable formulation proves to be numerically disastrous for several algorithms. The paper discusses the reasons for this behavior and argues that solution systems need to be strengthened so that they can cope with alternative model formulations. As argued in the paper, it would be desirable to improve the numerical algorithms themselves, or to develop computerized modeling systems that can reformulate models into the form most suitable for a particular existing algorithm. [ABSTRACT FROM AUTHOR]

关键词： Algorithms World Bank objective functions Algebra

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NEW PRODUCT EVALUATION USING A BAYESIAN DYNAMIC PROGRAM

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1981年第3期32卷 223-232页

作者： ROM, WO WINTER, FW UNIV ILLINOIS URBANAIL 61801

A method of scheduling new product evaluation steps is proposed. The method presented offers promise in reducing the costs of this evaluation. The value of each evaluation is based on Bayesian methods.

关键词： objective functions Capital costs Expected values Scheduling Fixed costs Experimentation Cost estimates Dynamic programming Recursion Unit costs

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STATISTICAL-ANALYSIS OF EMPIRICAL-MODELS FITTED BY OPTIMIZATION

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BIOMETRIKA 1983年第1期70卷 67-88页

作者： JONES, DA Institutes of HydrologyWallingford Oxfordshire

Practical procedures for statistical inference about the parameters of empirical models are presented. These avoid the necessity of formulating an explicit statistical model and can allow for general statistical dependency within the data used for model fitting. The theory is an asymptotic one, and one which allows the construction of significance tests and confidence regions for subsets of the model parameters. Other results concern the comparison of structurally different models, and of different objective functions for parameter fitting.

关键词： objective functions Mathematical independent variables Empirical modeling Covariance matrices Statistical models Estimation theory Conceptual frameworks Maximum likelihood estimation Standard error

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Comparison of interpolation polynomials with divided differences, interpolation polynomials with finite differences, and quadratic functions obtained by the least squares method in modeling of chromatographic responses

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JOURNAL OF CHEMOMETRICS 2013年第12期27卷 466-474页

作者： Rakic, Tijana Stanimirovic, Zorica Denic, Aleksandar Maric, Miroslav Jancic-Stojanovic, Biljana Medenica, Mirjana Univ Belgrade Fac Pharm Dept Drug Anal Belgrade 11000 Serbia Univ Belgrade Fac Math Dept Numer Math & Optimizat Belgrade 11000 Serbia Univ Belgrade Fac Math Dept Informat & Comp Sci Belgrade 11000 Serbia Univ Belgrade Fac Pharm Dept Phys Chem & Instrumental Methods Belgrade 11000 Serbia

A novel approach to mathematical modeling of chromatographic responses based on interpolation polynomials with divided differences and with finite differences is discussed. These interpolational techniques as well as traditionally applied second-order polynomial models obtained by least squares are compared. Interpolation techniques can be useful in situations where commonly used linear or quadratic models are not applicable: when the nature of dependence is complex or the investigated factor intervals are broad. The three analyzed modeling techniques are incorporated in a design of experiments methodology for systematic development and optimization of liquid chromatographic methods. The direct modeling of retention factors is carried out first, while the objective function for final quality measurement is calculated last. An interpolation polynomial with divided differences resulted in a high quality fit compared with the results obtained by the other two modeling approaches and succeeded in locating the desired optimum. It is shown that this modeling technique can be a useful alternative for modeling of chromatographic responses. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： interpolation polynomial with divided differences interpolation polynomial with finite differences chromatographic response modeling optimization objective functions liquid chromatography

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PVM-based intelligent predictive control of HVAC systems

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IFAC-PapersOnLine 2016年第5期49卷 371-376页

作者： Ruano, A. Pesteh, S. Silva, S. Duarte, H. Mestre, G. Ferreira, P.M. Khosravani, H. Horta, R. Faculty of Science and Technology University of Algarve Faro Portugal and IDMEC Instituto Superior Técnico Universidade de Lisboa Lisboa Portugal Faculty of Science and Technology University of Algarve Faro Portugal Easy Sensing - Intelligent Systems Centro Empresarial de Gambelas University of Algarve Faro8005-139 Portugal LaSIGE Faculdade de Ciências Universidade de Lisboa Portugal Rolear SA Faro8001-906 Portugal

This paper describes the application of a complete MBPC solution for existing HVAC systems, with a focus on the implementation of the objective function employed. Real-time results obtained with this solution, in term... 详细信息

关键词： Wireless sensor networks Genetic algorithms Model predictive control Neural networks Thermal comfort Hvac models HVAC system Intelligent predictive control Multi objective genetic algorithm objective functions Predicted mean vote Real time Weather stations

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SURROGATE CONSTRAINT DUALITY IN MATHEMATICAL PROGRAMMING

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OPERATIONS RESEARCH 1975年第3期23卷 434-451页

作者： GLOVER, F UNIV COLORADO BOULDERCO 80302

This paper presents a unified development of a surrogate duality theory that is applicable to problems in which Lagrangean duality gaps limit the usefulness of standard duality approaches. A surrogate dual is created by generating a single constraint to replace the original problem constraints, rather than by absorbing these constraints into the objective function as in the Lagrangean. We give necessary and sufficient conditions for optimality both with and without the imposition of complementary slackness, and also consider a related “overestimating” surrogate that may be used in a strategy to bracket the optimal value of the primal. The optimality conditions invite direct comparison with those for Lagrangean duality, demonstrating not only that the surrogate approach yields smaller duality gaps than the Lagrangean (as first observed by Greenberg and Pierskalla), but also giving a precise characterization of the manner and extent to which this occurs. Concepts of parametric and relative subgradients, paralleling (and generalizing) the concept of the subgradient of ordinary duality theory, lead to easily stated results that encompass both surrogate and Lagrangean duality, as well as their composite, in a single framework.

关键词： Mathematical duality objective functions Optimal solutions Convexity Sufficient conditions Sufficient conditions for optimality Mathematical concepts Mathematical functions Mathematical theorems Integer programming

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