Allocation of Transportation Resources. Presented by: Anteneh Yohannes
|
|
- Dana Lilian Grant
- 5 years ago
- Views:
Transcription
1 Allocation of Transportation Resources Presented by: Anteneh Yohannes
2 Problem State DOTs must allocate a budget to given projects Budget is often limited Social Welfare Benefits Different Viewpoints (Two Players) Planners Road Users
3 Purpose of Project Produce a method of prioritizing projects Consider Total System Travel Time (TSTT) performance measure Allocate the budget to priority links Provide State DOTs with a decision making tool
4 Methodology Bi-Level Optimization Planners Upper Level Problem (ULP) Minimize Total System Travel Time (TSTT) Users Lower Level Problem (LLP) Traffic Assignment (UE)
5 Data Required Number of Links in the network Capacity Length Free Flow Travel Time Alpha and Beta parameters Connecting Nodes O/D Matrix Budget
6 Formulation Upper Level problem (ULP) Objective Function : Minimize TSTT = a x a t a (x a, y a ) Subject to: a g a (y a ) B y a 0: a A Where: TSTT : Total System Travel Time x a : Flow for link a y a : Capacity expansion for link a (nonnegative real value) t a : Travel time for link a t a (x a, y a ) : Travel cost on link a as a function of flow and capacity expansion g a y a : improvement cost function for link a B : Budget (nonnegative real value)
7 Formulation Lower Level problem (LLP) Minimize TT = a A x a t a (x a, y a )dx 0 (11) Subject to: x a = f k ij q ij = k k ij f k ij (i,j) IJ k K ij (i, j) IJ ij δ ak f ij k, a A (12) (13) 0, k k ij, (i, j) IJ, (14) q ij 0, (i, j) IJ (15)
8 Notations C a : The capacity for link a r f ij : Flow on path r, connecting each Origin-Destination (O-D) pair (i-j) q ij : Demand between each Origin-Destination (O-D) pair (i-j) t a : Travel time for link a t a (x a, y a ) : Travel cost on link a as a function of flow and capacity expansion x a : Flow for link a α a : Constant, varying by facility type (BPR function) β a : Constant, varying by facility type (BPR function) r δ a,ij : binary variable 0,1 {1,if link a A is on path k k^ij:0,otherwise} t o : Free flow time on link a y a : Capacity expansion for link a (nonnegative real value)
9 Flow Chart Initial Traffic Assignment Base traffic flow X Network planner s problem Minimize TSTT = (x a t a (x a, y a )) a A Design constraints No Microsoft Solver Foundation Generalized Reduced Gradient (GRG2) algorithm Did users stop responding to improvements? Y Yes X' User equilibrium problem Minimize TT x a = t a (x a, y a )dx a A 0 Frank Wolfe Algorithm (FW) Definitional constraint Demand conservation constraint Non-negativity constraint Stop
10 LLP Frank Wolfe Algorithm (FW) SOURCE: YOSEF SHEFFI, Massachusetts Institute of Technology Step 0: Initialization Perform all-or-nothing assignment based on ta =ta (0) a. A new flow vector {xa} will be generated. Set counter n = 1. Step 1: Update Set ta=ta (xa) a Step 2: Finding Direction Perform all-or-nothing assignment based on {ta}. A new auxiliary flow vector {x a} will be generated. Step 3: Line search Find αn (0 α 1) that solves equation : x a + (x n a x n a ) 0 min z x = t a w dw Step 4: Move x a n+1 = x a n + n x a n x a n, a Step 5: Convergence test a a x a n+1 x a n 2 a x a n k
11 Test Network 1 t a x a, y a = A a + B a x a C a + y a 4 TSTT y = (t a x a, y a. x a + 1.5d a y2 a a Arc a A a B a C a d a
12 Comparison of Results Hooke- Jeeves (H-J) EDO GA Current Study Case MINOS 1 Demand =100 y y y y y Z Demand =150 y y y y y Z Demand =200 y y y y y Z Demand =300 y y y y y Z GA H-J EDO MINOS Names of heuristics Genetic Algorithm Hooke-Jeeves algorithm Equilibrium Decomposed Optimization (Bolzano search) Modular In-core Non linear System Sources Mathew (2009) Abdulaal and LeBlanc (1979) Suwansirikul et al. (1987) Suwansirikul et al. (1987)
13 Test Network 2 O/D t a x a, y a = A a + B a x a C a + y a 4 Source: Chiou et al (2005) TSTT y = (t a x a, y a. x a + θy a a Link a Aa Ba Ca θa
14 Comparison of Results Case SAB GP CG QNEW PT Current Study y y y y y Zy GP CG QNEW PT SAB Gradient Projection method Conjugate Gradient projection method Quasi-NEWton projection method PARTAN version of gradient projection method Sensitivity Analysis Based Source: Chiou et al (2005)
15 Comparison of Results Comparison of results on 9-node grid network with scaling factors Scalar SAB GP CG QNEW PT Current Study GP CG QNEW PT SAB Gradient Projection method Conjugate Gradient projection method Quasi-NEWton projection method PARTAN version of gradient projection method Sensitivity Analysis Based
16 Test Network 3 O/D
17 Comparison of Results Case 1 Demand (1,6)=5.0 Demand (6,1)=10.0 Names of heuristics Sources y 1 y 2 MINOS H-J EDO IOA Current Study y y 4 y 5 y y 7 y 8 y 9 IOA H-J EDO Iterative Optimization- Assignment algorithm Hooke-Jeeves algorithm Equilibrium Decomposed Optimization (Bolzano search) Allsop (1974) Abdulaal and LeBlanc (1979) Suwansirikul et al. (1987) y 10 y 11 y 12 MINOS Modular In-core Non linear System Suwansirikul et al. (1987) y 13 y 14 y y Z
18 Test Network 4 candidate links are marked by red arrow Sioux Falls Network
19 Comparison of Results Comparison of Results for Sioux Falls Network Case H-J H-J EDO SA SAB GP CG QNew PT GA Current Study y y y y y y y y y y Zy GP CG QNEW PT Gradient Projection method Conjugate Gradient projection method Quasi-NEWton projection method PARTAN version of gradient projection method
20 Comparison of Results Comparison of Results for Sioux Falls Network for different demand level Scalar SAB GP CG QNew PT EDO IOA GA Current Study FW Itr FW Itr FW Itr FW Itr FW Itr GA GP CG QNEW PT Genetic Algorithm Gradient Projection method Conjugate Gradient projection method Quasi-NEWton projection method PARTAN version of gradient projection method
21 Test Network 5 O/D t a x a, y a = A a + B a x a C a + y a TSTT y = (t a x a, y a. x a + θ y a a Linka Aa Ba Ka θa Linka Aa Ba Ka θa
22 Comparison of Results Comparison of results on 25-node grid network with scaling factors Scalar SAB GP CG QNEW PT Current Study GP CG QNEW PT Gradient Projection method Conjugate Gradient projection method Quasi-NEWton projection method PARTAN version of gradient projection method
23 Questions
Transportation Investment Decision Making for Medium to Large Transportation Networks
Title Page Click here to download Title Page TitlePage.pdf Transportation Investment Decision Making for Medium to Large Transportation Networks Sabyasachee Mishra a,c*, Amit Kumar b, Mihalis Golias a,c,
More informationFinal Report Building Our Way Out Of Congestion
Final Report 2002-01 Building Our Way Out Of Congestion 1. Report No. 2. 3. Recipients Accession No. MN/RC 2002-01 4. Title and Subtitle 5. Report Date BUILDING OUR WAY OUT OF CONGESTION? HIGHWAY CAPACITY
More informationOutline. 3. Implementation. 1. Introduction. 2. Algorithm
Outline 1. Introduction 2. Algorithm 3. Implementation What s Dynamic Traffic Assignment? Dynamic traffic assignment is aimed at allocating traffic flow to every path and making their travel time minimized
More informationNumerical Methods. V. Leclère May 15, x R n
Numerical Methods V. Leclère May 15, 2018 1 Some optimization algorithms Consider the unconstrained optimization problem min f(x). (1) x R n A descent direction algorithm is an algorithm that construct
More informationNetwork Equilibrium Models: Varied and Ambitious
Network Equilibrium Models: Varied and Ambitious Michael Florian Center for Research on Transportation University of Montreal INFORMS, November 2005 1 The applications of network equilibrium models are
More informationConservation laws and some applications to traffic flows
Conservation laws and some applications to traffic flows Khai T. Nguyen Department of Mathematics, Penn State University ktn2@psu.edu 46th Annual John H. Barrett Memorial Lectures May 16 18, 2016 Khai
More informationNetwork Flows. 6. Lagrangian Relaxation. Programming. Fall 2010 Instructor: Dr. Masoud Yaghini
In the name of God Network Flows 6. Lagrangian Relaxation 6.3 Lagrangian Relaxation and Integer Programming Fall 2010 Instructor: Dr. Masoud Yaghini Integer Programming Outline Branch-and-Bound Technique
More informatione-companion ONLY AVAILABLE IN ELECTRONIC FORM
OPERATIONS RESEARCH doi 10.1287/opre.1080.0658ec e-companion ONLY AVAILABLE IN ELECTRONIC FORM informs 2009 INFORMS Electronic Companion Test Instances for the Multicommodity Flow Problem: An Erratum by
More informationRouting. Topics: 6.976/ESD.937 1
Routing Topics: Definition Architecture for routing data plane algorithm Current routing algorithm control plane algorithm Optimal routing algorithm known algorithms and implementation issues new solution
More informationtransportation research in policy making for addressing mobility problems, infrastructure and functionality issues in urban areas. This study explored
ABSTRACT: Demand supply system are the three core clusters of transportation research in policy making for addressing mobility problems, infrastructure and functionality issues in urban areas. This study
More informationPareto-Improving Congestion Pricing on General Transportation Networks
Transportation Seminar at University of South Florida, 02/06/2009 Pareto-Improving Congestion Pricing on General Transportation Netorks Yafeng Yin Transportation Research Center Department of Civil and
More informationNetwork Analysis with ArcGIS Online. Deelesh Mandloi Dmitry Kudinov
Deelesh Mandloi Dmitry Kudinov Introductions Who are we? - Network Analyst Product Engineers Who are you? - Network Analyst users? - ArcGIS Online users? - Trying to figure out what is ArcGIS Online? Slides
More informationLagrangian road pricing
Lagrangian road pricing Vianney Boeuf 1, Sébastien Blandin 2 1 École polytechnique Paristech, France 2 IBM Research Collaboratory, Singapore vianney.boeuf@polytechnique.edu, sblandin@sg.ibm.com Keywords:
More informationSupplementary Technical Details and Results
Supplementary Technical Details and Results April 6, 2016 1 Introduction This document provides additional details to augment the paper Efficient Calibration Techniques for Large-scale Traffic Simulators.
More informationA three-level MILP model for generation and transmission expansion planning
A three-level MILP model for generation and transmission expansion planning David Pozo Cámara (UCLM) Enzo E. Sauma Santís (PUC) Javier Contreras Sanz (UCLM) Contents 1. Introduction 2. Aims and contributions
More informationThe discrete-time second-best day-to-day dynamic pricing scheme
The discrete-time second-best day-to-day dynamic pricing scheme Linghui Han, David Z.W. Wang & Chengjuan Zhu 25-07-2017 School of Civil & Environmental Engineering Nanyang Technological University, Singapore
More informationLecture 8 Network Optimization Algorithms
Advanced Algorithms Floriano Zini Free University of Bozen-Bolzano Faculty of Computer Science Academic Year 2013-2014 Lecture 8 Network Optimization Algorithms 1 21/01/14 Introduction Network models have
More informationArcGIS Online Routing and Network Analysis. Deelesh Mandloi Matt Crowder
ArcGIS Online Routing and Network Analysis Deelesh Mandloi Matt Crowder Introductions Who are we? - Members of the Network Analyst development team Who are you? - Network Analyst users? - ArcGIS Online
More informationAnalysis and Design of Urban Transportation Network for Pyi Gyi Ta Gon Township PHOO PWINT ZAN 1, DR. NILAR AYE 2
www.semargroup.org, www.ijsetr.com ISSN 2319-8885 Vol.03,Issue.10 May-2014, Pages:2058-2063 Analysis and Design of Urban Transportation Network for Pyi Gyi Ta Gon Township PHOO PWINT ZAN 1, DR. NILAR AYE
More informationComputing risk averse equilibrium in incomplete market. Henri Gerard Andy Philpott, Vincent Leclère
Computing risk averse equilibrium in incomplete market Henri Gerard Andy Philpott, Vincent Leclère YEQT XI: Winterschool on Energy Systems Netherlands, December, 2017 CERMICS - EPOC 1/43 Uncertainty on
More informationNONLINEAR. (Hillier & Lieberman Introduction to Operations Research, 8 th edition)
NONLINEAR PROGRAMMING (Hillier & Lieberman Introduction to Operations Research, 8 th edition) Nonlinear Programming g Linear programming has a fundamental role in OR. In linear programming all its functions
More informationECE580 Exam 2 November 01, Name: Score: / (20 points) You are given a two data sets
ECE580 Exam 2 November 01, 2011 1 Name: Score: /100 You must show ALL of your work for full credit. This exam is closed-book. Calculators may NOT be used. Please leave fractions as fractions, etc. I do
More informationA new genetic approach for transport network design and optimization
BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES, Vol. 59, No. 3, 2011 DOI: 10.2478/v10175-011-0032-z A new genetic approach for transport network design and optimization S. DINU and G. BORDEA
More informationSustainable Transportation Network Design Incorporating Environment Disruption under Strategic User Equilibrium
Sustainable Transportation Network Design Incorporating Environment Disruption under Strategic User Equilibrium Xiang Zhang (Corresponding Author) School of Civil and Environmental Engineering, University
More informationAPPENDIX Should the Private Sector Provide Public Capital?
APPENIX Should the Private Sector Provide Public Capital? Santanu Chatterjee epartment of Economics Terry College of Business University of eorgia Appendix A The appendix describes the optimization problem
More informationTRANSPORTATION MODELING
TRANSPORTATION MODELING Modeling Concept Model Tools and media to reflect and simple a measured reality. Types of Model Physical Model Map and Chart Model Statistics and mathematical Models MODEL? Physical
More informationThe N k Problem using AC Power Flows
The N k Problem using AC Power Flows Sean Harnett 5-19-2011 Outline Introduction AC power flow model The optimization problem Some results Goal: find a small set of lines whose removal will cause the power
More informationMicroeconomic Algorithms for Flow Control in Virtual Circuit Networks (Subset in Infocom 1989)
Microeconomic Algorithms for Flow Control in Virtual Circuit Networks (Subset in Infocom 1989) September 13th, 1995 Donald Ferguson*,** Christos Nikolaou* Yechiam Yemini** *IBM T.J. Watson Research Center
More informationUser Equilibrium CE 392C. September 1, User Equilibrium
CE 392C September 1, 2016 REVIEW 1 Network definitions 2 How to calculate path travel times from path flows? 3 Principle of user equilibrium 4 Pigou-Knight Downs paradox 5 Smith paradox Review OUTLINE
More informationBeyond Normality: A Distributionally Robust Stochastic User Equilibrium Model
Beyond Normality: A Distributionally Robust Stochastic User Equilibrium Model Selin Damla Ahipasaoglu Rudabeh Meskarian Thomas L. Magnanti Karthik Natarajan June 15, 2014 Abstract The Stochastic User Equilibrium
More informationTravel Time Calculation With GIS in Rail Station Location Optimization
Travel Time Calculation With GIS in Rail Station Location Optimization Topic Scope: Transit II: Bus and Rail Stop Information and Analysis Paper: # UC8 by Sutapa Samanta Doctoral Student Department of
More informationTwo hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Thursday 17th May 2018 Time: 09:45-11:45. Please answer all Questions.
COMP 34120 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE AI and Games Date: Thursday 17th May 2018 Time: 09:45-11:45 Please answer all Questions. Use a SEPARATE answerbook for each SECTION
More informationRANDOM SIMULATIONS OF BRAESS S PARADOX
RANDOM SIMULATIONS OF BRAESS S PARADOX PETER CHOTRAS APPROVED: Dr. Dieter Armbruster, Director........................................................ Dr. Nicolas Lanchier, Second Committee Member......................................
More informationLecture 3 Cost Structure
Lecture 3 Dr. Anna Nagurney John F. Smith Memorial Professor Isenberg School of Management University of Massachusetts Amherst, Massachusetts 01003 c 2009 Cost is a disutility - Cost is a function of travel
More informationChapter 1. Trip Distribution. 1.1 Overview. 1.2 Definitions and notations Trip matrix
Chapter 1 Trip Distribution 1.1 Overview The decision to travel for a given purpose is called trip generation. These generated trips from each zone is then distributed to all other zones based on the choice
More informationIndex Terms: Demand, Effective Travel Time, Perception Error.
Modeling Impacts of Travel Time in Route Choice Decisions under Rainy Conditions J.P.Singh 1, Prabhat Shrivastava 2 1. Associate Professor (Applied Mechanics Dept. S.A.K.E.C, Chembur Mumbai-88, INDIA,
More informationTraffic Demand Forecast
Chapter 5 Traffic Demand Forecast One of the important objectives of traffic demand forecast in a transportation master plan study is to examine the concepts and policies in proposed plans by numerically
More informationGame Theory: introduction and applications to computer networks
Game Theory: introduction and applications to computer networks Introduction Giovanni Neglia INRIA EPI Maestro 27 January 2014 Part of the slides are based on a previous course with D. Figueiredo (UFRJ)
More informationChanges in the Spatial Distribution of Mobile Source Emissions due to the Interactions between Land-use and Regional Transportation Systems
Changes in the Spatial Distribution of Mobile Source Emissions due to the Interactions between Land-use and Regional Transportation Systems A Framework for Analysis Urban Transportation Center University
More informationMath 5490 Network Flows
Math 90 Network Flows Lecture 8: Flow Decomposition Algorithm Stephen Billups University of Colorado at Denver Math 90Network Flows p./6 Flow Decomposition Algorithms Two approaches to modeling network
More informationAccessibility as an Instrument in Planning Practice. Derek Halden DHC 2 Dean Path, Edinburgh EH4 3BA
Accessibility as an Instrument in Planning Practice Derek Halden DHC 2 Dean Path, Edinburgh EH4 3BA derek.halden@dhc1.co.uk www.dhc1.co.uk Theory to practice a starting point Shared goals for access to
More informationA Framework for Dynamic O-D Matrices for Multimodal transportation: an Agent-Based Model approach
A Framework for Dynamic O-D Matrices for Multimodal transportation: an Agent-Based Model approach Nuno Monteiro - FEP, Portugal - 120414020@fep.up.pt Rosaldo Rossetti - FEUP, Portugal - rossetti@fe.up.pt
More informationCyber-Physical Cooperative Freight Routing System
1 Cyber-Physical Cooperative Freight Routing System Ioannis Kordonis Member, IEEE, Maged M. Dessouky, Petros Ioannou Fellow IEEE Abstract The efficient use of the road network for freight transport has
More informationHow to Estimate, Take Into Account, and Improve Travel Time Reliability in Transportation Networks
University of Texas at El Paso DigitalCommons@UTEP Departmental Technical Reports (CS) Department of Computer Science 11-1-2007 How to Estimate, Take Into Account, and Improve Travel Time Reliability in
More informationReturns to Scale in Networks. Marvin Kraus * June Keywords: Networks, congestion, returns to scale, congestion pricing
Returns to Scale in Networks by Marvin Kraus * June 2006 Keywords: Networks, congestion, returns to scale, congestion pricing * Department of Economics, Boston College, Chestnut Hill, MA 02467, USA. E-mail:
More informationAlternative network robustness measure using system-wide transportation capacity for identifying critical links in road networks
Special Issue Article Alternative network robustness measure using system-wide transportation capacity for identifying critical links in road networks Advances in Mechanical Engineering 2017, Vol. 9(4)
More informationUtility Maximizing Routing to Data Centers
0-0 Utility Maximizing Routing to Data Centers M. Sarwat, J. Shin and S. Kapoor (Presented by J. Shin) Sep 26, 2011 Sep 26, 2011 1 Outline 1. Problem Definition - Data Center Allocation 2. How to construct
More informationA LAGRANGIAN RELAXATION FOR CAPACITATED SINGLE ALLOCATION P-HUB MEDIAN PROBLEM WITH MULTIPLE CAPACITY LEVELS
A LAGRANGIAN RELAXATION FOR CAPACITATED SINGLE ALLOCATION P-HUB MEDIAN PROBLEM WITH MULTIPLE CAPACITY LEVELS Ching-Jung Ting Department of Industrial Engineering and Management, Yuan Ze University Kuo-Rui
More informationFriday, September 21, Flows
Flows Building evacuation plan people to evacuate from the offices corridors and stairways capacity 10 10 5 50 15 15 15 60 60 50 15 10 60 10 60 15 15 50 For each person determine the path to follow to
More informationDecision Mathematics D1 Advanced/Advanced Subsidiary. Wednesday 23 January 2013 Morning Time: 1 hour 30 minutes
Paper Reference(s) 6689/01 Edexcel GCE Decision Mathematics D1 Advanced/Advanced Subsidiary Wednesday 23 January 2013 Morning Time: 1 hour 30 minutes Materials required for examination Nil Items included
More information0-1 Reformulations of the Network Loading Problem
0-1 Reformulations of the Network Loading Problem Antonio Frangioni 1 frangio@di.unipi.it Bernard Gendron 2 bernard@crt.umontreal.ca 1 Dipartimento di Informatica Università di Pisa Via Buonarroti, 2 56127
More informationCity monitoring with travel demand momentum vector fields: theoretical and empirical findings
City monitoring with travel demand momentum vector fields: theoretical and empirical findings Xintao Liu 1, Joseph Y.J. Chow 2 1 Department of Civil Engineering, Ryerson University, Canada 2 Tandon School
More informationMarginal Cost Pricing for System Optimal Traffic Assignment with Recourse under Supply-Side Uncertainty
Marginal Cost Pricing for System Optimal Traffic Assignment with Recourse under Supply-Side Uncertainty Tarun Rambha, Stephen D. Boyles, Avinash Unnikrishnan, Peter Stone Abstract Transportation networks
More informationA Capacity Scaling Procedure for the Multi-Commodity Capacitated Network Design Problem. Ryutsu Keizai University Naoto KATAYAMA
A Capacity Scaling Procedure for the Multi-Commodity Capacitated Network Design Problem Ryutsu Keizai University Naoto KATAYAMA Problems 2006 1 Multi-Commodity Network Design Problem The basic model for
More informationTrip Distribution Modeling Milos N. Mladenovic Assistant Professor Department of Built Environment
Trip Distribution Modeling Milos N. Mladenovic Assistant Professor Department of Built Environment 25.04.2017 Course Outline Forecasting overview and data management Trip generation modeling Trip distribution
More informationCo-optimization of topology design and parameterized control in a traffic network
Delft University of Technology Delft Center for Systems and Control Technical report 14-003 Co-optimization of topology design and parameterized control in a traffic network Z. Cong, B. De Schutter, and
More informationCapacitor Placement for Economical Electrical Systems using Ant Colony Search Algorithm
Capacitor Placement for Economical Electrical Systems using Ant Colony Search Algorithm Bharat Solanki Abstract The optimal capacitor placement problem involves determination of the location, number, type
More informationCS360 Homework 12 Solution
CS360 Homework 12 Solution Constraint Satisfaction 1) Consider the following constraint satisfaction problem with variables x, y and z, each with domain {1, 2, 3}, and constraints C 1 and C 2, defined
More informationTHEODORE VORONOV DIFFERENTIABLE MANIFOLDS. Fall Last updated: November 26, (Under construction.)
4 Vector fields Last updated: November 26, 2009. (Under construction.) 4.1 Tangent vectors as derivations After we have introduced topological notions, we can come back to analysis on manifolds. Let M
More informationmin 4x 1 5x 2 + 3x 3 s.t. x 1 + 2x 2 + x 3 = 10 x 1 x 2 6 x 1 + 3x 2 + x 3 14
The exam is three hours long and consists of 4 exercises. The exam is graded on a scale 0-25 points, and the points assigned to each question are indicated in parenthesis within the text. If necessary,
More informationThe conjugate gradient method
The conjugate gradient method Michael S. Floater November 1, 2011 These notes try to provide motivation and an explanation of the CG method. 1 The method of conjugate directions We want to solve the linear
More informationECE Optimization for wireless networks Final. minimize f o (x) s.t. Ax = b,
ECE 788 - Optimization for wireless networks Final Please provide clear and complete answers. PART I: Questions - Q.. Discuss an iterative algorithm that converges to the solution of the problem minimize
More informationCSE 150. Assignment 6 Summer Maximum likelihood estimation. Out: Thu Jul 14 Due: Tue Jul 19
SE 150. Assignment 6 Summer 2016 Out: Thu Jul 14 ue: Tue Jul 19 6.1 Maximum likelihood estimation A (a) omplete data onsider a complete data set of i.i.d. examples {a t, b t, c t, d t } T t=1 drawn from
More informationTravelling Salesman Problem
Travelling Salesman Problem Fabio Furini November 10th, 2014 Travelling Salesman Problem 1 Outline 1 Traveling Salesman Problem Separation Travelling Salesman Problem 2 (Asymmetric) Traveling Salesman
More informationUnconstrained optimization
Chapter 4 Unconstrained optimization An unconstrained optimization problem takes the form min x Rnf(x) (4.1) for a target functional (also called objective function) f : R n R. In this chapter and throughout
More informationM.A. Botchev. September 5, 2014
Rome-Moscow school of Matrix Methods and Applied Linear Algebra 2014 A short introduction to Krylov subspaces for linear systems, matrix functions and inexact Newton methods. Plan and exercises. M.A. Botchev
More informationDeparture time choice equilibrium problem with partial implementation of congestion pricing
Departure time choice equilibrium problem with partial implementation of congestion pricing Tokyo Institute of Technology Postdoctoral researcher Katsuya Sakai 1 Contents 1. Introduction 2. Method/Tool
More informationLecture 19: Common property resources
Lecture 19: Common property resources Economics 336 Economics 336 (Toronto) Lecture 19: Common property resources 1 / 19 Introduction Common property resource: A resource for which no agent has full property
More informationLecture XI. Approximating the Invariant Distribution
Lecture XI Approximating the Invariant Distribution Gianluca Violante New York University Quantitative Macroeconomics G. Violante, Invariant Distribution p. 1 /24 SS Equilibrium in the Aiyagari model G.
More information1.225 Transportation Flow Systems Quiz (December 17, 2001; Duration: 3 hours)
1.225 Transportation Flow Systems Quiz (December 17, 2001; Duration: 3 hours) Student Name: Alias: Instructions: 1. This exam is open-book 2. No cooperation is permitted 3. Please write down your name
More informationAteneo de Manila, Philippines
Ideal Flow Based on Random Walk on Directed Graph Ateneo de Manila, Philippines Background Problem: how the traffic flow in a network should ideally be distributed? Current technique: use Wardrop s Principle:
More informationInvestigating uncertainty in BPR formula parameters
Young Researchers Seminar 2013 Young Researchers Seminar 2011 Lyon, France, June 5-7 2013 DTU, Denmark, June 8-10, 2011 Investigating uncertainty in BPR formula parameters The Næstved model case study
More informationA Model of Traffic Congestion, Housing Prices and Compensating Wage Differentials
A Model of Traffic Congestion, Housing Prices and Compensating Wage Differentials Thomas F. Rutherford Institute on Computational Economics (ICE05) University of Chicago / Argonne National Laboratory Meeting
More informationOn the Smoothed Price of Anarchy of the Traffic Assignment Problem
On the Smoothed Price of Anarchy of the Traffic Assignment Problem Luciana Buriol 1, Marcus Ritt 1, Félix Rodrigues 1, and Guido Schäfer 2 1 Universidade Federal do Rio Grande do Sul, Informatics Institute,
More information8 Numerical methods for unconstrained problems
8 Numerical methods for unconstrained problems Optimization is one of the important fields in numerical computation, beside solving differential equations and linear systems. We can see that these fields
More informationPublication List PAPERS IN REFEREED JOURNALS. Submitted for publication
Publication List YU (MARCO) NIE SEPTEMBER 2010 Department of Civil and Environmental Engineering Phone: (847) 467-0502 2145 Sheridan Road, A328 Technological Institute Fax: (847) 491-4011 Northwestern
More informationDynamic Pricing, Managed Lanes and Integrated Corridor Management: Challenges for Advanced Network Modeling Methodologies
Dynamic Pricing Managed Lanes and Integrated Corridor Management: Challenges for Advanced Network Modeling Methodologies Hani S. Mahmassani Transportation Center Northwestern University November 16 2007
More informationOIM 413 Logistics and Transportation Lecture 6: Equilibration Algorithms for a General Network
OIM 413 Logistics and Transportation Lecture 6: Equilibration Algorithms for a General Network Professor Anna Nagurney John F. Smith Memorial Professor and Director Virtual Center for Supernetworks Department
More informationA Comprehensive Modeling Framework for Hazmat Network Design, Hazmat Response Team Location, and Equity of Risk
A Comprehensive Modeling Framework for Hazmat Network Design, Hazmat Response Team Location, and Equity of Risk Masoumeh Taslimi a, Rajan Batta b, and Changhyun Kwon c a CSX Transportation, Jacksonville,
More informationLecture 12 The Spatial Price Equilibrium Problem
Lecture 12 The Spatial Price Equilibrium Problem Dr. Anna Nagurney John F. Smith Memorial Professor Isenberg School of Management University of Massachusetts Amherst, Massachusetts 01003 c 2009 Parallel
More informationCongestion Equilibrium for Differentiated Service Classes Richard T. B. Ma
Congestion Equilibrium for Differentiated Service Classes Richard T. B. Ma School of Computing National University of Singapore Allerton Conference 2011 Outline Characterize Congestion Equilibrium Modeling
More informationExtended breadth-first search algorithm in practice
Proceedings of the 9 th International Conference on Applied Informatics Eger, Hungary, January 29 February 1, 2014. Vol. 1. pp. 59 66 doi: 10.14794/ICAI.9.2014.1.59 Extended breadth-first search algorithm
More informationTropical Optimization Framework for Analytical Hierarchy Process
Tropical Optimization Framework for Analytical Hierarchy Process Nikolai Krivulin 1 Sergeĭ Sergeev 2 1 Faculty of Mathematics and Mechanics Saint Petersburg State University, Russia 2 School of Mathematics
More informationAdvanced Linear Programming: The Exercises
Advanced Linear Programming: The Exercises The answers are sometimes not written out completely. 1.5 a) min c T x + d T y Ax + By b y = x (1) First reformulation, using z smallest number satisfying x z
More informationWhat is an integer program? Modelling with Integer Variables. Mixed Integer Program. Let us start with a linear program: max cx s.t.
Modelling with Integer Variables jesla@mandtudk Department of Management Engineering Technical University of Denmark What is an integer program? Let us start with a linear program: st Ax b x 0 where A
More informationOD-matrix Estimation Based on a Dual Formulation of Traffic Assignment Problem
Informatica 4 (216) 393 398 393 OD-matrix Estimation Based on a Dual Formulation of Traffic Assignment Problem Alexander Yu. Krylatov, Anastasiia P. Shirokolobova and Victor V. Zakharov Saint Petersburg
More informationIMPACTS OF THE EARTHQUAKES ON EXISTING TRANSPORTATION NETWORKS IN MEMPHIS AREA
10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska IMPACTS OF THE 1811-1812 EARTHQUAKES ON EXISTING TRANSPORTATION NETWORKS
More informationVasil Khalidov & Miles Hansard. C.M. Bishop s PRML: Chapter 5; Neural Networks
C.M. Bishop s PRML: Chapter 5; Neural Networks Introduction The aim is, as before, to find useful decompositions of the target variable; t(x) = y(x, w) + ɛ(x) (3.7) t(x n ) and x n are the observations,
More informationTopic 2: Algorithms. Professor Anna Nagurney
Topic 2: Algorithms John F. Smith Memorial Professor and Director Virtual Center for Supernetworks Isenberg School of Management University of Massachusetts Amherst, Massachusetts 01003 SCH-MGMT 825 Management
More informationYu (Marco) Nie. Appointment Northwestern University Assistant Professor, Department of Civil and Environmental Engineering, Fall present.
Yu (Marco) Nie A328 Technological Institute Civil and Environmental Engineering 2145 Sheridan Road, Evanston, IL 60202-3129 Phone: (847) 467-0502 Fax: (847) 491-4011 Email: y-nie@northwestern.edu Appointment
More informationThe Equilibrium Equivalent Representation for Variational Inequalities Problems with Its Application in Mixed Traffic Flows
The 7th International Symposium on Operations Research and Its Applications (ISORA 08) Lijiang, China, October 31 Novemver 3, 2008 Copyright 2008 ORSC & APORC, pp. 119 124 The Equilibrium Equivalent Representation
More informationPublic Transport Versus Private Car: GIS-Based Estimation of Accessibility Applied to the Tel Aviv Metropolitan Area
Public Transport Versus Private Car: GIS-Based Estimation of Accessibility Applied to the Tel Aviv Metropolitan Area Itzhak Benenson 1, Karel Martens 3, Yodan Rofe 2, Ariela Kwartler 1 1 Dept of Geography
More informationTrip Distribution Model for Flood Disaster Evacuation Operation
Trip Distribution Model for Flood Disaster Evacuation Operation The devastating consequences of disasters in both developed and developing countries indicate significant lack or absence of disaster management
More informationPresentation in Convex Optimization
Dec 22, 2014 Introduction Sample size selection in optimization methods for machine learning Introduction Sample size selection in optimization methods for machine learning Main results: presents a methodology
More informationDecision Mathematics D2 Advanced/Advanced Subsidiary. Monday 1 June 2009 Morning Time: 1 hour 30 minutes
Paper Reference(s) 6690/01 Edexcel GCE Decision Mathematics D2 Advanced/Advanced Subsidiary Monday 1 June 2009 Morning Time: 1 hour 30 minutes Materials required for examination Nil Items included with
More informationCapacity Planning with uncertainty in Industrial Gas Markets
Capacity Planning with uncertainty in Industrial Gas Markets A. Kandiraju, P. Garcia Herreros, E. Arslan, P. Misra, S. Mehta & I.E. Grossmann EWO meeting September, 2015 1 Motivation Industrial gas markets
More informationImprovements to Benders' decomposition: systematic classification and performance comparison in a Transmission Expansion Planning problem
Improvements to Benders' decomposition: systematic classification and performance comparison in a Transmission Expansion Planning problem Sara Lumbreras & Andrés Ramos July 2013 Agenda Motivation improvement
More informationApproximation. Inderjit S. Dhillon Dept of Computer Science UT Austin. SAMSI Massive Datasets Opening Workshop Raleigh, North Carolina.
Using Quadratic Approximation Inderjit S. Dhillon Dept of Computer Science UT Austin SAMSI Massive Datasets Opening Workshop Raleigh, North Carolina Sept 12, 2012 Joint work with C. Hsieh, M. Sustik and
More informationELEMENTARY LINEAR ALGEBRA
ELEMENTARY LINEAR ALGEBRA K. R. MATTHEWS DEPARTMENT OF MATHEMATICS UNIVERSITY OF QUEENSLAND Second Online Version, December 1998 Comments to the author at krm@maths.uq.edu.au Contents 1 LINEAR EQUATIONS
More informationConstraint satisfaction search. Combinatorial optimization search.
CS 1571 Introduction to AI Lecture 8 Constraint satisfaction search. Combinatorial optimization search. Milos Hauskrecht milos@cs.pitt.edu 539 Sennott Square Constraint satisfaction problem (CSP) Objective:
More information