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Sensitivity-based Uncertainty Analysis of a Combined Travel Demand Model

Procedia - Social and Behavioral Sciences 2013年 80卷 395-415页

作者： Chao Yang Anthony Chen Xiangdong Xu S.C. Wong Key Laboratory of Road and Traffic Engineering Tongji University Shanghai 201804 China Department of Civil and Environmental Engineering Utah State University Logan UT 84322-4110 USA Department of Civil Engineering The University of Hong Kong Pokfulam Road<remove-image> Hong Kong China

Travel demand forecasting is subject to great uncertainties. A systematic uncertainty analysis can provide insights into the level of confidence on the model outputs, and also identify critical sources of uncertainty for enhancing the robustness of the travel demand model. In this paper, we develop a systematic framework for quantitative uncertainty analysis of a combined travel demand model (CTDM) using the analytical sensitivity- based method. The CTDM overcomes limitations of the sequential four-step procedure since it is based on a single unifying rationale. The analytical sensitivity-based method requires less computational effort than the sampling-based method. Meanwhile, the uncertainties stemming from inputs and parameters can be treated separately so that the individual and collective effects of uncertainty on the outputs can be clearly assessed and quantified. Numerical examples are finally used to demonstrate the proposed sensitivity-based uncertainty analysis method for the CTDM.

关键词： Uncertainty analysis sensitivity analysis nonlinear program combined travel demand model

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Estimation of Measures in M/M/1 Queue

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2011年第18期40卷 3327-3336页

作者： Srinivas, V. Rao, S. Subba Kale, B. K. Bangalore Univ Dept Stat Bangalore 560056 Karnataka India Univ Toledo Dept Management Toledo OH USA Univ Pune Dept Stat Pune Maharashtra India

Maximum likelihood and uniform minimum variance unbiased estimators of steady-state probability distribution of system size, probability of at least l customers in the system in steady state, and certain steady-state measures of effectiveness in the M/M/1 queue are obtained/derived based on observations on X, the number of customer arrivals during a service time. The estimators are compared using Asympotic Expected Deficiency (AED) criterion leading to recommendation of uniform minimum variance unbiased estimators over maximum likelihood estimators for some measures.

关键词： Asymptotic expected deficiency Maximum likelihood estimator nonlinear program Queues Uniform minimum variance unbiased estimator

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A dimension-reduced method of sensitivity analysis for stochastic user equilibrium assignment model

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APPLIED MATHEMATICAL MODELLING 2010年第2期34卷 325-333页

作者： Liu, Jianmei Ma, Shoufeng Huang, Chongchao Ma, Shuaiqi Tianjin Univ Sch Management Inst Syst Engn Tianjin 300072 Peoples R China Wuhan Univ Sch Math & Stat Wuhan 430072 Peoples R China Jining Univ Sch Math Jining Peoples R China

This paper gives a new dimension-reduced method of sensitivity analysis for perturbed stochastic user equilibrium assignment (SUEA) model based on the relation between its Lagrange function and logarithmic barrier function combined with a Courant quadratic penalty term. The advantage of this method is of smaller dimension than general sensitivity analysis and reducing complexity. Firstly, it presents the dimension-reduced sensitivity results of the general nonlinear programming perturbation problem and the improved results when the objective or constraint functions are not twice continuously differentiable. Then it proves the corresponding conclusion of SUEA with smooth or non-smooth cost functions by the method of converting constraint conditions and decision variables. Finally, two corresponding examples (smooth and non-smooth) are given to illustrate the feasibility of this method. (c) 2009 Elsevier Inc. All rights reserved.

关键词： nonlinear program Dimension-reduced sensitivity analysis SUEA Penalty function Non-smoothness

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A NEW RELAXATION SCHEME FOR MATHEMATICAL programS WITH EQUILIBRIUM CONSTRAINTS

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SIAM JOURNAL ON OPTIMIZATION 2010年第5期20卷 2504-2539页

作者： Steffensen, Sonja Ulbrich, Michael Rhein Westfal TH Aachen Fak Math Informat Naturwissensch Fachgrp Math Lehr & Forschungseinheit Kontinuierl D-52056 Aachen Germany Tech Univ Munich Chair Math Optimizat Fak Math D-85747 Munich Germany

We present a new relaxation scheme for mathematical programs with equilibrium constraints (MPEC), where the complementarity constraints are replaced by a reformulation that is exact for the complementarity conditions corresponding to sufficiently nondegenerate complementarity components and relaxes only the remaining complementarity conditions. A positive parameter determines to what extent the complementarity conditions are relaxed. The relaxation scheme is such that a strongly stationary solution of the MPEC is also a solution of the relaxed problem if the relaxation parameter is chosen sufficiently small. We discuss the properties of the resulting parameterized nonlinear programs and compare stationary points and solutions. We further prove that a limit point of a sequence of stationary points of a sequence of relaxed problems is Clarke-stationary if it satisfies a so-called MPEC-constant rank constraint qualification, and it is Mordukhovich-stationary if it satisfies the MPEC-linear independence constraint qualification and the stationary points satisfy a second order sufficient condition. From this relaxation scheme, a numerical approach is derived that is applied to a comprehensive test set. The numerical results show that the approach combines good efficiency with high robustness.

关键词： mathematical program with equilibrium constraints (MPEC) relaxation complementarity constraint Clarke-stationarity Mordukhovich-stationarity strong stationarity constraint qualification nonlinear program

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Multiplier convergence in trust-region methods with application to convergence of decomposition methods for MPECs

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MATHEMATICAL programMING 2008年第2期112卷 335-369页

作者： Giallombardo, Giovanni Ralph, Daniel Univ Calabria Dipartimento Elettr Informat & Sistemist I-87036 Arcavacata Di Rende Italy Univ Cambridge Judge Business Sch Cambridge CB2 1AG England

We study piecewise decomposition methods for mathematical programs with equilibrium constraints (MPECs) for which all constraint functions are linear. At each iteration of a decomposition method, one step of a nonlinear programming scheme is applied to one piece of the MPEC to obtain the next iterate. Our goal is to understand global convergence to B-stationary points of these methods when the embedded nonlinear programming solver is a trust-region scheme, and the selection of pieces is determined using multipliers generated by solving the trust-region subproblem. To this end we study global convergence of a linear trust-region scheme for linearly-constrained NLPs that we call a trust-search method. The trust-search has two features that are critical to global convergence of decomposition methods for MPECs: a robustness property with respect to switching pieces, and a multiplier convergence result that appears to be quite new for trust-region methods. These combine to clarify and strengthen global convergence of decomposition methods without resorting either to additional conditions such as eventual inactivity of the trust-region constraint, or more complex methods that require a separate subproblem for multiplier estimation.

关键词： mathematical program with equilibrium constraints MPEC complementarity constraints MPCC B-stationary M-stationary linear constraints nonlinear program

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Allocating work in process in a multiple-product CONWIP system with lost sales

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2005年第2期43卷 223-246页

作者： Ryan, SM Vorasayan, J Iowa State Univ Dept Ind & Mfg Syst Engn Ames IA 50011 USA

To operate a multiple-product manufacturing system under a CONWIP control policy, one must decide how to assign kanbans to products. With a fixed total number of kanbans in a competitive environment, the goal is to determine their allocation to product types in order to minimize lost sales equitably. In particular, we consider systems in which the products may make multiple visits to the same station with a different processing time distribution on each repeat visit. With a fixed number of kanbans dedicated to each product, the system is modeled as a multiple-chain multiple-class closed queuing network. A nonlinear program simultaneously provides an approximate performance evaluation and optimizes the allocation of kanbans to product types. In numerical examples, the allocations identified are similar to those obtained by exhaustive enumeration with simulation, but frequently differ significantly from a naive allocation according to demand rates. A variant of the model that minimizes the total work-in-process to achieve specified throughput targets yields results similar to a previous heuristic method.

关键词： CONWIP lost sales nonlinear program multiclass closed queuing network

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Using spreadsheet solvers in sample design

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2004年第3期44卷 527-546页

作者： Stokes, L Plummer, J So Methodist Univ Dept Stat Dallas TX 75275 USA Univ Texas Dept Management Sci & Informat Syst Austin TX 78712 USA

nonlinear programming (NLP) has been used for some time in planning of sample designs more complex than a single objective stratified or two-stage design. This paper discusses the new NLP solver tools that are now widely available in commercial spreadsheet products, and illustrates how to use them in these kinds of sample design problems. These tools eliminate the need for acquiring special purpose software or writing code, and have a natural interface so that setting up the problem is straightforward. However, they often require considerable tuning and experimentation to produce usable solutions. In this paper, we give practical advice on helping the solver tools find solutions in typical sample design problems. The methods are illustrated using Excel's solver on three examples of real sample design problems with complex features. (C) 2002 Published by Elsevier B.V.

关键词： nonlinear program optimization excel stratified sample

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Optimization of class-2 tensegrity towers

Optimization of class-2 tensegrity towers

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Smart Structures and Materials 2004 Conference

作者： Masic, M Skelton, RE Univ Calif San Diego Dept Mech & Aerosp Engn Struct Syst & Control Lab La Jolla CA 92093 USA

ISBN: (纸本)0819453072

This paper concerns the optimal mass-to-stiffness ratio design of class-2 tensegrity towers. For different loading scenarios, the procedure seeks the topology and geometry of the structure that yields an optimal design satisfying common constraints. The domain of feasible tenseuritv -eometries is defined by imposing tensegrity equilibrium conditions on both unloaded and loaded structure. Remainin- constraints include strength constraints for all elements of the structure and buckling constraints for bars. The symmetry of the design is imposed by restricting the domain of geometric variables and element parameters. The static response of the structure is computed by using a nonlinear large displacement model. The problem is cast in the form of a nonlinear pro-ram. The influence of material parameters on the optimal shape of the structure is investigated.

关键词： tensegrity optimal stiffness geometry design constraints nonlinear program

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Discovering the characteristics of mathematical programs via sampling

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OPTIMIZATION METHODS & SOFTWARE 2002年第2期17卷 319-352页

作者： Chinneck, JW Carleton Univ Ottawa ON K1S 5B6 Canada

It is often important to know more about the characteristics of a mathematical program than the simple information that is returned by a solver. For example, to choose an appropriate solution algorithm, one may need to know something about the convexity of the functions in a nonlinear program, or about which constraints are redundant. For the complex model forms, particularly nonlinear programs and mixed-integer programs, random sampling can discover a great deal of information. This paper describes how to discover interesting characteristics of mathematical programs via sampling, and describes solutions to several difficulties that arise in practice. Several new techniques for discovering characteristics and for improving the accuracy of the characterizations are described.

关键词： mathematical program complex model forms nonlinear program

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Convergent infeasible interior-point trust-region methods for constrained minimization

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SIAM JOURNAL ON OPTIMIZATION 2002年第2期13卷 432-469页

作者： Tseng, P Univ Washington Dept Math Seattle WA 98195 USA

We study an infeasible primal-dual interior-poin trust-region method for constrained minimization. This method uses a log-barrier function for the slack variables and updates the slack variables using second-order correction. We show that if a certain set containing the initial iterate is bounded and the origin is not in the convex hull of the nearly active constrain gradients everywhere on this set, then the iterates remain in this set, and any cluster point of the iterates is a first-order stationary point. Moreover, any subsequence of iterates converging to the cluster point has an asymptotic second-order stationarity property, which, when the constrain functions are a ne or when the active constrain gradients are linearly independent, implies that the cluster point is a second-order stationary point. Preliminary numerical experience with the method is reported. A primal method and its extension to semidefinite nonlinear programming is also discussed.

关键词： nonlinear program log-barrier function interior-point method trust-region strategy first- and second-order stationary points semidefinite programming

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