Annexes. EC.1. Cycle-base move illustration. EC.2. Problem Instances

Size: px
Start display at page:

Download "Annexes. EC.1. Cycle-base move illustration. EC.2. Problem Instances"

Transcription

1 ec Annexes Ths Annex frst llustrates a cycle-based move n the dynamc-block generaton tabu search. It then dsplays the characterstcs of the nstance sets, followed by detaled results of the parametercalbraton experments, and of the study of the mpact of varous algorthmc components on the performance of the proposed algorthm. EC.. Cycle-base move llustraton An llustraton of the neghborhood move s gven below Fgure EC. shows a very smple AP(β) soluton on the car-layer projecton. demands ndcated by ther O-D pars must be satsfed. The nformaton on each lnk/block s explaned as (fxed cost, surrogate unt flow cost, current flow, flow capacty). t = n OUT n IN d d (500, 5, 0, 40) b b (600, 0, 5, 80) Fgure EC. m OUT (, 0, 0, 50) (, 0, 5, 50) m IN o o An AP(β) Soluton on Car-Layer Projecton Resdual values are collected n a resdual value set, n ths example, Γ = {0, 5}. For each resdual value γ Γ, a γ-resdual network s constructed. The lowest-cost cycles from each γ-resdual network are compared, and the one wth mnmal cost s shown n Fgure EC.. The mnmum-cost cycle has resdual value γ = 0, and wth total cost -380 (savng). Followng the mnmum-cost cycle, the car flow on block b s cleared by beng moved to block b. The procedure reaches a neghbor block desgn where block b s closed as shown n Fgure EC.3. EC.. Problem Instances Tables EC. and EC. dsplay the characterstcs of the nstance sets S and L, respectvely. Columns to 4 dsplay the numbers of blocks, servces, yards, and track sectons of the nstance. Column Tme gves the number of tme perods, and the last column dsplays the number of commodtes,.e., orgn-destnaton demands. Instances used for calbraton are dsplayed n Table EC.3.

2 ec t = n OUT n IN Fgure EC. ( 800) m OUT ( 00) 5 (00) m IN (0) 3 4 A Lowest-Cost Cycle n Resdual Network (400) t = n OUT n IN d d b b (600, 0, 45, 80) Fgure EC.3 m OUT (,, 0, ) (, 0, 45, 50) m IN o o New AP(β) Soluton on Neghbor Block Desgn Inst Block Servce Yard Track Tme Demand p p p p p p p p p p p p p p p Table EC. Instance Characterstcs, Set S Table EC.4 dsplay the characterstcs of the large nstances. The last three columns dsplay the number of blocks generated ntally and n total, and the value of the fnal soluton of the Dynamc SS procedure.

3 ec3 Inst Block Servce Yard Track Tme Demand p p p p p p p p p p p p p p p Table EC. Instance Characterstcs, Set L Inst Block Servce Yard Track Tme Demand c c c c c c c c c Table EC.3 Instance Characterstcs, Set C Inst Servce Yard Track Tme Demand Block (n) Block (fnal) DSS x x x x x x x x x Table EC.4 Instance Characterstcs and Results, Set XL EC.3. Calbraton Table EC.5 dsplays the relatve performance of the parameter combnatons used to calbrate the long-term memory-based perturbaton phase. Experments were run on nstance set C. Parameter combnatons were weghted accordng to the soluton qualty, frst place weghtng 0 ponts, second 9, and so on untl the last place weghted pont. Scores are then summed up over the problem

4 ec4 nstances and appear n Column 4. The frst three columns present the correspondng parameter values. I nonmprove max (Imax dver, Imax nten ) ω + Score 8 (, ) (, ) 49 8 (3, 3) (3, 3) 46 0 (, ) (, ) 67 0 (3, 3) (3, 3) 49 5 (, ) (, ) 6 5 (3, 3) (3, 3) 59 Table EC.5 Perturbaton Parameter Calbraton Fgures EC.4 and EC.5 llustrate the relatve behavor of the shortest augmentng-path heurstc and the Smplex method when addressng the mult-commodty network flow formulaton correspondng to the approxmaton problem generated by slope scalng. The fgures dsplay the evoluton of the soluton values R-ISSND and ISSND, respectvely, n gray for the heurstc and n black for Smplex. The fgures dsplay results for nstance c06 wth parameter settng I nonmprove max = 8, (I dver max, I nten max ) = (, ) and ω + = ). The horzontal axs gves the computng tme, and the vertcal axs gves the soluton value. Table EC.6 dsplays the performance results of the parameter settngs, three for each of the two strateges, for the ellpsodal search. The same scorng system as above s used. s, λ = 5% s, λ = 5% s, λ = 50% s, ϕ = s, ϕ = 5 s, ϕ = Table EC.6 Ellpsodal Search Parameter Calbraton EC.4. Performance of algorthmc components Ths secton of the Annex s dedcated to a bref study of the mpact of the algorthmc components on the performance of the proposed matheurstc. The study was performed on an ntal mplementaton of the Basc SS procedure. In the followng tables the soluton values for all procedures were rounded to ntegers for the sake of dsplay. The column headers SS+LMP, Basc SS, and CPLEX stand for the basc slope scalng mechansm of the Basc SS procedure, the complete basc slope scalng wth ellpsod search, and the MIP solver of CPLEX, respectvely.

5 ec5 Fgure EC.4 Comparson of R-SNDP evolutons Fgure EC.5 Comparson of ISSND evolutons Tables EC.7 and EC.8 dsplay the computatonal results on nstance sets S and L, respectvely, for CPLEX (0 hours CPU tme) and the basc slope scalng mechansm after 000 teratons and 0 hours CPU tme. Soluton tmes are dsplayed n CPU seconds. Characters and t ndcate no feasble soluton found and tme lmt reached, respectvely. Columns OptGap dsplay the optmalty gap of CPLEX, whle columns CplGap dsplay the relatve gap of the proposed algorthm to the best soluton of CPLEX, when avalable, or to ts lower bound, otherwse.

6 ec6 Inst CPLEX Tme OptGap SS+LMP CplGap Tme TmeGap SS+LMP CplGap sec. 000 ter. sec. 0h p % % % % p % 748.5% % % p % % % % p % % % % p % % % % p t.78% % % % p t 35.9% % % % p t 36.07% % % % p t 6.76% % % % p t 36.3% % % % p 4070 t 0.69% % % % p t 7.6% % t 0.00% % p t p t p t Table EC.7 Basc Slope Scalng Results on Instance Set S The frst observaton s that, except for a few small nstances, CPLEX s unable to fnd the optmal soluton wthn the 0-hour tme lmt. Moreover, the effcency decreases dramatcally wth nstance sze, resultng n consderable optmal gaps for medum-szed nstances and the mpossblty to even fnd a feasble soluton for larger nstances (e.g., p3 wth 0 yards and 60 tracks). The second s that even the smple slope scalng mechansm s very close to the optmum for small nstances wth an average optmalty gap of.4% for p0 to p06 and an average of 50% reducton n computng tme. On larger nstances, the basc slope scalng mechansm performs mpressvely, outperformng CPLEX n both soluton qualty and tme. Thus, for example, the mean mprovement for nstances p07 - p s 8.7% wthn 6.70% of the CPLEX computng tme. Improvements of over 30% are observed for several nstances and slope scalng s able to address larger nstances than CPLEX. These mprovements are obtaned after 000 teratons and are enhanced when longer computng tmes are allowed. A better soluton was thus obtaned for 6 out of 4 nstances after 0 hours of computng. Then, compared to CPLEX solutons obtaned wth the same computatonal effort, slope scalng acheved an average gap of 0.88% on nstances wth 5 yards (p0-p06, p6-p), and an average mprovement of.58% on all the other, larger, nstances. Results of the complete Basc SS matheurstc, ntegratng slope scalng and ellpsodal search, for 0 hours of computng tme, are dsplayed n Tables EC.9 and EC.0. The last two columns dsplay the relatve gap of the complete method to SS+LMP and CPLEX, respectvely. These results underscore the mportant role of the ellpsodal-search phase n the soluton procedure. In almost all cases (9 nstances out of 30), ncludng the ellpsodal-search yelded better solutons

7 ec7 Inst CPLEX Tme OptGap SS+LMP CplGap Tme TmeGap SS+LMP CplGap sec. 000 ter. sec. 0h p t.76% % % % p t.54% % % % p t 0.6% % % % p % % % % p % 373.5% % % p 0380 t 3.60% % % % p 7485 t 49.59% % % % p t 36.5% % % % p p t 3.00% % 36-9.% % p p t 34.47% % % % p t p t p t Table EC.8 Basc Slope Scalng Results on Instance Set L than slope scalng wthn the same soluton tme. The average mprovement s.55% and.0% for the two nstance sets, wth a maxmum mprovement of over 6% for nstance p4. Table EC.9 Inst Basc SS SS+LMP Gap CplGap p % 0.00% p % 0.% p % 0.3% p % 0.00% p % 0.00% p % -0.08% p % -8.46% p % -6.86% p % -0.30% p % % p % -5.38% p % -0.93% p % - p % - p % - Avg -.55% Basc SS wth Ellpsodal Search Performance on Instance Set S

8 ec8 Inst Basc SS SS+LMP Gap CplGap p % -0.% p % -0.5% p % 0.00% p % 0.00% p % 0.00% p % -.48% p % % p % -7.58% p % - p % -4.0% p % - p % -6.75% p % - p % - p % - Avg -.0% Table EC.0 Basc SS wth Ellpsodal Search Results on Instance Set L

Problem Set 9 Solutions

Problem Set 9 Solutions Desgn and Analyss of Algorthms May 4, 2015 Massachusetts Insttute of Technology 6.046J/18.410J Profs. Erk Demane, Srn Devadas, and Nancy Lynch Problem Set 9 Solutons Problem Set 9 Solutons Ths problem

More information

College of Computer & Information Science Fall 2009 Northeastern University 20 October 2009

College of Computer & Information Science Fall 2009 Northeastern University 20 October 2009 College of Computer & Informaton Scence Fall 2009 Northeastern Unversty 20 October 2009 CS7880: Algorthmc Power Tools Scrbe: Jan Wen and Laura Poplawsk Lecture Outlne: Prmal-dual schema Network Desgn:

More information

Lecture Notes on Linear Regression

Lecture Notes on Linear Regression Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume

More information

The Minimum Universal Cost Flow in an Infeasible Flow Network

The Minimum Universal Cost Flow in an Infeasible Flow Network Journal of Scences, Islamc Republc of Iran 17(2): 175-180 (2006) Unversty of Tehran, ISSN 1016-1104 http://jscencesutacr The Mnmum Unversal Cost Flow n an Infeasble Flow Network H Saleh Fathabad * M Bagheran

More information

Winter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan

Winter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan Wnter 2008 CS567 Stochastc Lnear/Integer Programmng Guest Lecturer: Xu, Huan Class 2: More Modelng Examples 1 Capacty Expanson Capacty expanson models optmal choces of the tmng and levels of nvestments

More information

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons

More information

VQ widely used in coding speech, image, and video

VQ widely used in coding speech, image, and video at Scalar quantzers are specal cases of vector quantzers (VQ): they are constraned to look at one sample at a tme (memoryless) VQ does not have such constrant better RD perfomance expected Source codng

More information

Chapter Newton s Method

Chapter Newton s Method Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve

More information

Appendix B: Resampling Algorithms

Appendix B: Resampling Algorithms 407 Appendx B: Resamplng Algorthms A common problem of all partcle flters s the degeneracy of weghts, whch conssts of the unbounded ncrease of the varance of the mportance weghts ω [ ] of the partcles

More information

Resource Allocation with a Budget Constraint for Computing Independent Tasks in the Cloud

Resource Allocation with a Budget Constraint for Computing Independent Tasks in the Cloud Resource Allocaton wth a Budget Constrant for Computng Independent Tasks n the Cloud Wemng Sh and Bo Hong School of Electrcal and Computer Engneerng Georga Insttute of Technology, USA 2nd IEEE Internatonal

More information

4DVAR, according to the name, is a four-dimensional variational method.

4DVAR, according to the name, is a four-dimensional variational method. 4D-Varatonal Data Assmlaton (4D-Var) 4DVAR, accordng to the name, s a four-dmensonal varatonal method. 4D-Var s actually a drect generalzaton of 3D-Var to handle observatons that are dstrbuted n tme. The

More information

On the Multicriteria Integer Network Flow Problem

On the Multicriteria Integer Network Flow Problem BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 5, No 2 Sofa 2005 On the Multcrtera Integer Network Flow Problem Vassl Vasslev, Marana Nkolova, Maryana Vassleva Insttute of

More information

Simultaneous Optimization of Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problems in Container Terminals

Simultaneous Optimization of Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problems in Container Terminals Smultaneous Optmzaton of Berth Allocaton, Quay Crane Assgnment and Quay Crane Schedulng Problems n Contaner Termnals Necat Aras, Yavuz Türkoğulları, Z. Caner Taşkın, Kuban Altınel Abstract In ths work,

More information

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:

More information

Module 9. Lecture 6. Duality in Assignment Problems

Module 9. Lecture 6. Duality in Assignment Problems Module 9 1 Lecture 6 Dualty n Assgnment Problems In ths lecture we attempt to answer few other mportant questons posed n earler lecture for (AP) and see how some of them can be explaned through the concept

More information

3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X

3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number

More information

APPENDIX 2 FITTING A STRAIGHT LINE TO OBSERVATIONS

APPENDIX 2 FITTING A STRAIGHT LINE TO OBSERVATIONS Unversty of Oulu Student Laboratory n Physcs Laboratory Exercses n Physcs 1 1 APPEDIX FITTIG A STRAIGHT LIE TO OBSERVATIOS In the physcal measurements we often make a seres of measurements of the dependent

More information

An Admission Control Algorithm in Cloud Computing Systems

An Admission Control Algorithm in Cloud Computing Systems An Admsson Control Algorthm n Cloud Computng Systems Authors: Frank Yeong-Sung Ln Department of Informaton Management Natonal Tawan Unversty Tape, Tawan, R.O.C. ysln@m.ntu.edu.tw Yngje Lan Management Scence

More information

An Optimization Model for Routing in Low Earth Orbit Satellite Constellations

An Optimization Model for Routing in Low Earth Orbit Satellite Constellations An Optmzaton Model for Routng n Low Earth Orbt Satellte Constellatons A. Ferrera J. Galter P. Mahey Inra Inra Inra Afonso.Ferrera@sopha.nra.fr Jerome.Galter@nra.fr Phlppe.Mahey@sma.fr G. Mateus A. Olvera

More information

CHAPTER 7 STOCHASTIC ECONOMIC EMISSION DISPATCH-MODELED USING WEIGHTING METHOD

CHAPTER 7 STOCHASTIC ECONOMIC EMISSION DISPATCH-MODELED USING WEIGHTING METHOD 90 CHAPTER 7 STOCHASTIC ECOOMIC EMISSIO DISPATCH-MODELED USIG WEIGHTIG METHOD 7.1 ITRODUCTIO early 70% of electrc power produced n the world s by means of thermal plants. Thermal power statons are the

More information

Min Cut, Fast Cut, Polynomial Identities

Min Cut, Fast Cut, Polynomial Identities Randomzed Algorthms, Summer 016 Mn Cut, Fast Cut, Polynomal Identtes Instructor: Thomas Kesselhem and Kurt Mehlhorn 1 Mn Cuts n Graphs Lecture (5 pages) Throughout ths secton, G = (V, E) s a mult-graph.

More information

Design and Optimization of Fuzzy Controller for Inverse Pendulum System Using Genetic Algorithm

Design and Optimization of Fuzzy Controller for Inverse Pendulum System Using Genetic Algorithm Desgn and Optmzaton of Fuzzy Controller for Inverse Pendulum System Usng Genetc Algorthm H. Mehraban A. Ashoor Unversty of Tehran Unversty of Tehran h.mehraban@ece.ut.ac.r a.ashoor@ece.ut.ac.r Abstract:

More information

10-701/ Machine Learning, Fall 2005 Homework 3

10-701/ Machine Learning, Fall 2005 Homework 3 10-701/15-781 Machne Learnng, Fall 2005 Homework 3 Out: 10/20/05 Due: begnnng of the class 11/01/05 Instructons Contact questons-10701@autonlaborg for queston Problem 1 Regresson and Cross-valdaton [40

More information

Calculation of time complexity (3%)

Calculation of time complexity (3%) Problem 1. (30%) Calculaton of tme complexty (3%) Gven n ctes, usng exhaust search to see every result takes O(n!). Calculaton of tme needed to solve the problem (2%) 40 ctes:40! dfferent tours 40 add

More information

Approximate Smallest Enclosing Balls

Approximate Smallest Enclosing Balls Chapter 5 Approxmate Smallest Enclosng Balls 5. Boundng Volumes A boundng volume for a set S R d s a superset of S wth a smple shape, for example a box, a ball, or an ellpsod. Fgure 5.: Boundng boxes Q(P

More information

Large-scale packing of ellipsoids

Large-scale packing of ellipsoids Large-scale packng of ellpsods E. G. Brgn R. D. Lobato September 7, 017 Abstract The problem of packng ellpsods n the n-dmensonal space s consdered n the present work. The proposed approach combnes heurstc

More information

A SEPARABLE APPROXIMATION DYNAMIC PROGRAMMING ALGORITHM FOR ECONOMIC DISPATCH WITH TRANSMISSION LOSSES. Pierre HANSEN, Nenad MLADENOVI]

A SEPARABLE APPROXIMATION DYNAMIC PROGRAMMING ALGORITHM FOR ECONOMIC DISPATCH WITH TRANSMISSION LOSSES. Pierre HANSEN, Nenad MLADENOVI] Yugoslav Journal of Operatons Research (00) umber 57-66 A SEPARABLE APPROXIMATIO DYAMIC PROGRAMMIG ALGORITHM FOR ECOOMIC DISPATCH WITH TRASMISSIO LOSSES Perre HASE enad MLADEOVI] GERAD and Ecole des Hautes

More information

Linköping University Post Print. Solving a minimum-power covering problem with overlap constraint for cellular network design

Linköping University Post Print. Solving a minimum-power covering problem with overlap constraint for cellular network design Lnköpng Unversty Post Prnt Solvng a mnmum-power coverng problem wth overlap constrant for cellular network desgn Le Chen and D Yuan N.B.: When ctng ths work, cte the orgnal artcle. Orgnal Publcaton: Le

More information

Optimal Solution to the Problem of Balanced Academic Curriculum Problem Using Tabu Search

Optimal Solution to the Problem of Balanced Academic Curriculum Problem Using Tabu Search Optmal Soluton to the Problem of Balanced Academc Currculum Problem Usng Tabu Search Lorna V. Rosas-Téllez 1, José L. Martínez-Flores 2, and Vttoro Zanella-Palacos 1 1 Engneerng Department,Unversdad Popular

More information

An Interactive Optimisation Tool for Allocation Problems

An Interactive Optimisation Tool for Allocation Problems An Interactve Optmsaton ool for Allocaton Problems Fredr Bonäs, Joam Westerlund and apo Westerlund Process Desgn Laboratory, Faculty of echnology, Åbo Aadem Unversty, uru 20500, Fnland hs paper presents

More information

Errors for Linear Systems

Errors for Linear Systems Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch

More information

ECE559VV Project Report

ECE559VV Project Report ECE559VV Project Report (Supplementary Notes Loc Xuan Bu I. MAX SUM-RATE SCHEDULING: THE UPLINK CASE We have seen (n the presentaton that, for downlnk (broadcast channels, the strategy maxmzng the sum-rate

More information

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle

More information

Minimizing earliness and tardiness penalties on a single machine scheduling problem with distinct due windows and sequence-dependent setup times

Minimizing earliness and tardiness penalties on a single machine scheduling problem with distinct due windows and sequence-dependent setup times Mnmzng earlness and tardness penaltes on a sngle machne schedulng problem wth dstnct due wndows and sequence-dependent setup tmes Marcone J. F. Souza a, Luz S. Och b and Nelson Maculan c a Departamento

More information

Technical Note: Capacity Constraints Across Nests in Assortment Optimization Under the Nested Logit Model

Technical Note: Capacity Constraints Across Nests in Assortment Optimization Under the Nested Logit Model Techncal Note: Capacty Constrants Across Nests n Assortment Optmzaton Under the Nested Logt Model Jacob B. Feldman, Huseyn Topaloglu School of Operatons Research and Informaton Engneerng, Cornell Unversty,

More information

Computing Correlated Equilibria in Multi-Player Games

Computing Correlated Equilibria in Multi-Player Games Computng Correlated Equlbra n Mult-Player Games Chrstos H. Papadmtrou Presented by Zhanxang Huang December 7th, 2005 1 The Author Dr. Chrstos H. Papadmtrou CS professor at UC Berkley (taught at Harvard,

More information

The Study of Teaching-learning-based Optimization Algorithm

The Study of Teaching-learning-based Optimization Algorithm Advanced Scence and Technology Letters Vol. (AST 06), pp.05- http://dx.do.org/0.57/astl.06. The Study of Teachng-learnng-based Optmzaton Algorthm u Sun, Yan fu, Lele Kong, Haolang Q,, Helongang Insttute

More information

Optimum Design of Steel Frames Considering Uncertainty of Parameters

Optimum Design of Steel Frames Considering Uncertainty of Parameters 9 th World Congress on Structural and Multdscplnary Optmzaton June 13-17, 211, Shzuoka, Japan Optmum Desgn of Steel Frames Consderng ncertanty of Parameters Masahko Katsura 1, Makoto Ohsak 2 1 Hroshma

More information

Optimal Scheduling Algorithms to Minimize Total Flowtime on a Two-Machine Permutation Flowshop with Limited Waiting Times and Ready Times of Jobs

Optimal Scheduling Algorithms to Minimize Total Flowtime on a Two-Machine Permutation Flowshop with Limited Waiting Times and Ready Times of Jobs Optmal Schedulng Algorthms to Mnmze Total Flowtme on a Two-Machne Permutaton Flowshop wth Lmted Watng Tmes and Ready Tmes of Jobs Seong-Woo Cho Dept. Of Busness Admnstraton, Kyongg Unversty, Suwon-s, 443-760,

More information

Queueing Networks II Network Performance

Queueing Networks II Network Performance Queueng Networks II Network Performance Davd Tpper Assocate Professor Graduate Telecommuncatons and Networkng Program Unversty of Pttsburgh Sldes 6 Networks of Queues Many communcaton systems must be modeled

More information

Suppose that there s a measured wndow of data fff k () ; :::; ff k g of a sze w, measured dscretely wth varable dscretzaton step. It s convenent to pl

Suppose that there s a measured wndow of data fff k () ; :::; ff k g of a sze w, measured dscretely wth varable dscretzaton step. It s convenent to pl RECURSIVE SPLINE INTERPOLATION METHOD FOR REAL TIME ENGINE CONTROL APPLICATIONS A. Stotsky Volvo Car Corporaton Engne Desgn and Development Dept. 97542, HA1N, SE- 405 31 Gothenburg Sweden. Emal: astotsky@volvocars.com

More information

Some modelling aspects for the Matlab implementation of MMA

Some modelling aspects for the Matlab implementation of MMA Some modellng aspects for the Matlab mplementaton of MMA Krster Svanberg krlle@math.kth.se Optmzaton and Systems Theory Department of Mathematcs KTH, SE 10044 Stockholm September 2004 1. Consdered optmzaton

More information

CS 331 DESIGN AND ANALYSIS OF ALGORITHMS DYNAMIC PROGRAMMING. Dr. Daisy Tang

CS 331 DESIGN AND ANALYSIS OF ALGORITHMS DYNAMIC PROGRAMMING. Dr. Daisy Tang CS DESIGN ND NLYSIS OF LGORITHMS DYNMIC PROGRMMING Dr. Dasy Tang Dynamc Programmng Idea: Problems can be dvded nto stages Soluton s a sequence o decsons and the decson at the current stage s based on the

More information

Lecture 4: Constant Time SVD Approximation

Lecture 4: Constant Time SVD Approximation Spectral Algorthms and Representatons eb. 17, Mar. 3 and 8, 005 Lecture 4: Constant Tme SVD Approxmaton Lecturer: Santosh Vempala Scrbe: Jangzhuo Chen Ths topc conssts of three lectures 0/17, 03/03, 03/08),

More information

Comparative Analysis of SPSO and PSO to Optimal Power Flow Solutions

Comparative Analysis of SPSO and PSO to Optimal Power Flow Solutions Internatonal Journal for Research n Appled Scence & Engneerng Technology (IJRASET) Volume 6 Issue I, January 018- Avalable at www.jraset.com Comparatve Analyss of SPSO and PSO to Optmal Power Flow Solutons

More information

More metrics on cartesian products

More metrics on cartesian products More metrcs on cartesan products If (X, d ) are metrc spaces for 1 n, then n Secton II4 of the lecture notes we defned three metrcs on X whose underlyng topologes are the product topology The purpose of

More information

Abstract. The assumptions made for rank computation are as follows. (see Figure 1)

Abstract. The assumptions made for rank computation are as follows. (see Figure 1) A Novel Metrc for Interconnect Archtecture Performance Parthasarath Dasgupta, Andrew B. Kahng, and Swamy Muddu CSE Department, UCSD, La Jolla, CA 92093-0114 ECE Department, UCSD, La Jolla, CA 92093-0407

More information

Statistics II Final Exam 26/6/18

Statistics II Final Exam 26/6/18 Statstcs II Fnal Exam 26/6/18 Academc Year 2017/18 Solutons Exam duraton: 2 h 30 mn 1. (3 ponts) A town hall s conductng a study to determne the amount of leftover food produced by the restaurants n the

More information

Hongyi Miao, College of Science, Nanjing Forestry University, Nanjing ,China. (Received 20 June 2013, accepted 11 March 2014) I)ϕ (k)

Hongyi Miao, College of Science, Nanjing Forestry University, Nanjing ,China. (Received 20 June 2013, accepted 11 March 2014) I)ϕ (k) ISSN 1749-3889 (prnt), 1749-3897 (onlne) Internatonal Journal of Nonlnear Scence Vol.17(2014) No.2,pp.188-192 Modfed Block Jacob-Davdson Method for Solvng Large Sparse Egenproblems Hongy Mao, College of

More information

Vickrey Auction VCG Combinatorial Auctions. Mechanism Design. Algorithms and Data Structures. Winter 2016

Vickrey Auction VCG Combinatorial Auctions. Mechanism Design. Algorithms and Data Structures. Winter 2016 Mechansm Desgn Algorthms and Data Structures Wnter 2016 1 / 39 Vckrey Aucton Vckrey-Clarke-Groves Mechansms Sngle-Mnded Combnatoral Auctons 2 / 39 Mechansm Desgn (wth Money) Set A of outcomes to choose

More information

COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS

COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS

More information

The equation of motion of a dynamical system is given by a set of differential equations. That is (1)

The equation of motion of a dynamical system is given by a set of differential equations. That is (1) Dynamcal Systems Many engneerng and natural systems are dynamcal systems. For example a pendulum s a dynamcal system. State l The state of the dynamcal system specfes t condtons. For a pendulum n the absence

More information

Structure and Drive Paul A. Jensen Copyright July 20, 2003

Structure and Drive Paul A. Jensen Copyright July 20, 2003 Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.

More information

Chapter 6. Supplemental Text Material

Chapter 6. Supplemental Text Material Chapter 6. Supplemental Text Materal S6-. actor Effect Estmates are Least Squares Estmates We have gven heurstc or ntutve explanatons of how the estmates of the factor effects are obtaned n the textboo.

More information

Modelling and Constraint Hardness Characterisation of the Unique-Path OSPF Weight Setting Problem

Modelling and Constraint Hardness Characterisation of the Unique-Path OSPF Weight Setting Problem Modellng and Constrant Hardness Charactersaton of the Unque-Path OSPF Weght Settng Problem Changyong Zhang and Robert Rodose IC-Parc, Imperal College London, London SW7 2AZ, Unted Kngdom {cz, r.rodose}@cparc.mperal.ac.u

More information

U.C. Berkeley CS294: Beyond Worst-Case Analysis Luca Trevisan September 5, 2017

U.C. Berkeley CS294: Beyond Worst-Case Analysis Luca Trevisan September 5, 2017 U.C. Berkeley CS94: Beyond Worst-Case Analyss Handout 4s Luca Trevsan September 5, 07 Summary of Lecture 4 In whch we ntroduce semdefnte programmng and apply t to Max Cut. Semdefnte Programmng Recall that

More information

Formulas for the Determinant

Formulas for the Determinant page 224 224 CHAPTER 3 Determnants e t te t e 2t 38 A = e t 2te t e 2t e t te t 2e 2t 39 If 123 A = 345, 456 compute the matrx product A adj(a) What can you conclude about det(a)? For Problems 40 43, use

More information

On the Interval Zoro Symmetric Single-step Procedure for Simultaneous Finding of Polynomial Zeros

On the Interval Zoro Symmetric Single-step Procedure for Simultaneous Finding of Polynomial Zeros Appled Mathematcal Scences, Vol. 5, 2011, no. 75, 3693-3706 On the Interval Zoro Symmetrc Sngle-step Procedure for Smultaneous Fndng of Polynomal Zeros S. F. M. Rusl, M. Mons, M. A. Hassan and W. J. Leong

More information

DECOUPLING THEORY HW2

DECOUPLING THEORY HW2 8.8 DECOUPLIG THEORY HW2 DOGHAO WAG DATE:OCT. 3 207 Problem We shall start by reformulatng the problem. Denote by δ S n the delta functon that s evenly dstrbuted at the n ) dmensonal unt sphere. As a temporal

More information

We propose a tabu search algorithm for the generalized assignment problem, which is one of the representative

We propose a tabu search algorithm for the generalized assignment problem, which is one of the representative INFORMS Journal on Computng Vol. 16, No. 2, Sprng 2004, pp. 133 151 ssn 0899-1499 essn 1526-5528 04 1602 0133 nforms do 10.1287/joc.1030.0036 2004 INFORMS An Ejecton Chan Approach for the Generalzed Assgnment

More information

Lecture 20: November 7

Lecture 20: November 7 0-725/36-725: Convex Optmzaton Fall 205 Lecturer: Ryan Tbshran Lecture 20: November 7 Scrbes: Varsha Chnnaobreddy, Joon Sk Km, Lngyao Zhang Note: LaTeX template courtesy of UC Berkeley EECS dept. Dsclamer:

More information

IJRSS Volume 2, Issue 2 ISSN:

IJRSS Volume 2, Issue 2 ISSN: IJRSS Volume, Issue ISSN: 49-496 An Algorthm To Fnd Optmum Cost Tme Trade Off Pars In A Fractonal Capactated Transportaton Problem Wth Restrcted Flow KAVITA GUPTA* S.R. ARORA** _ Abstract: Ths paper presents

More information

A Variable Neighbourhood Descent Algorithm for the Redundancy Allocation Problem

A Variable Neighbourhood Descent Algorithm for the Redundancy Allocation Problem EMS Vol. 4, No., pp. 94-0, June 2005. A Varable Neghbourhood Descent Algorthm for the Redundancy Allocaton Problem Yun-Cha Lang Cha-Chuan u Department of ndustral Engneerng and Management, Yuan Ze Unversty

More information

On a direct solver for linear least squares problems

On a direct solver for linear least squares problems ISSN 2066-6594 Ann. Acad. Rom. Sc. Ser. Math. Appl. Vol. 8, No. 2/2016 On a drect solver for lnear least squares problems Constantn Popa Abstract The Null Space (NS) algorthm s a drect solver for lnear

More information

EEE 241: Linear Systems

EEE 241: Linear Systems EEE : Lnear Systems Summary #: Backpropagaton BACKPROPAGATION The perceptron rule as well as the Wdrow Hoff learnng were desgned to tran sngle layer networks. They suffer from the same dsadvantage: they

More information

Lecture 12: Discrete Laplacian

Lecture 12: Discrete Laplacian Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly

More information

STAT 3008 Applied Regression Analysis

STAT 3008 Applied Regression Analysis STAT 3008 Appled Regresson Analyss Tutoral : Smple Lnear Regresson LAI Chun He Department of Statstcs, The Chnese Unversty of Hong Kong 1 Model Assumpton To quantfy the relatonshp between two factors,

More information

A HYBRID DIFFERENTIAL EVOLUTION -ITERATIVE GREEDY SEARCH ALGORITHM FOR CAPACITATED VEHICLE ROUTING PROBLEM

A HYBRID DIFFERENTIAL EVOLUTION -ITERATIVE GREEDY SEARCH ALGORITHM FOR CAPACITATED VEHICLE ROUTING PROBLEM IJCMA: Vol. 6, No. 1, January-June 2012, pp. 1-19 Global Research Publcatons A HYBRID DIFFERENTIAL EVOLUTION -ITERATIVE GREEDY SEARCH ALGORITHM FOR CAPACITATED VEHICLE ROUTING PROBLEM S. Kavtha and Nrmala

More information

A Minimum Cost Flow Formulation for Approximated MLC Segmentation

A Minimum Cost Flow Formulation for Approximated MLC Segmentation A Mnmum Cost Flow Formulaton for Approxmated MLC Segmentaton Thomas Kalnowsk Abstract Shape matrx decomposton s a subproblem n radaton therapy plannng. A gven fluence matrx A has to be wrtten as a sum

More information

Note 10. Modeling and Simulation of Dynamic Systems

Note 10. Modeling and Simulation of Dynamic Systems Lecture Notes of ME 475: Introducton to Mechatroncs Note 0 Modelng and Smulaton of Dynamc Systems Department of Mechancal Engneerng, Unversty Of Saskatchewan, 57 Campus Drve, Saskatoon, SK S7N 5A9, Canada

More information

Dynamic Programming. Lecture 13 (5/31/2017)

Dynamic Programming. Lecture 13 (5/31/2017) Dynamc Programmng Lecture 13 (5/31/2017) - A Forest Thnnng Example - Projected yeld (m3/ha) at age 20 as functon of acton taken at age 10 Age 10 Begnnng Volume Resdual Ten-year Volume volume thnned volume

More information

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng

More information

Dynamic Bid Prices in Revenue Management

Dynamic Bid Prices in Revenue Management OPERATIONS RESEARCH Vol. 55, No. 4, July August 2007, pp. 647 661 ssn 0030-364X essn 1526-5463 07 5504 0647 nforms do 10.1287/opre.1060.0368 2007 INFORMS Dynamc Bd Prces n Revenue Management Danel Adelman

More information

An Integrated OR/CP Method for Planning and Scheduling

An Integrated OR/CP Method for Planning and Scheduling An Integrated OR/CP Method for Plannng and Schedulng John Hooer Carnege Mellon Unversty IT Unversty of Copenhagen June 2005 The Problem Allocate tass to facltes. Schedule tass assgned to each faclty. Subect

More information

Negative Binomial Regression

Negative Binomial Regression STATGRAPHICS Rev. 9/16/2013 Negatve Bnomal Regresson Summary... 1 Data Input... 3 Statstcal Model... 3 Analyss Summary... 4 Analyss Optons... 7 Plot of Ftted Model... 8 Observed Versus Predcted... 10 Predctons...

More information

Math1110 (Spring 2009) Prelim 3 - Solutions

Math1110 (Spring 2009) Prelim 3 - Solutions Math 1110 (Sprng 2009) Solutons to Prelm 3 (04/21/2009) 1 Queston 1. (16 ponts) Short answer. Math1110 (Sprng 2009) Prelm 3 - Solutons x a 1 (a) (4 ponts) Please evaluate lm, where a and b are postve numbers.

More information

Chapter - 2. Distribution System Power Flow Analysis

Chapter - 2. Distribution System Power Flow Analysis Chapter - 2 Dstrbuton System Power Flow Analyss CHAPTER - 2 Radal Dstrbuton System Load Flow 2.1 Introducton Load flow s an mportant tool [66] for analyzng electrcal power system network performance. Load

More information

A PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS

A PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS HCMC Unversty of Pedagogy Thong Nguyen Huu et al. A PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS Thong Nguyen Huu and Hao Tran Van Department of mathematcs-nformaton,

More information

Kernel Methods and SVMs Extension

Kernel Methods and SVMs Extension Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general

More information

The Second Anti-Mathima on Game Theory

The Second Anti-Mathima on Game Theory The Second Ant-Mathma on Game Theory Ath. Kehagas December 1 2006 1 Introducton In ths note we wll examne the noton of game equlbrum for three types of games 1. 2-player 2-acton zero-sum games 2. 2-player

More information

Parametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010

Parametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010 Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton

More information

Embedded Systems. 4. Aperiodic and Periodic Tasks

Embedded Systems. 4. Aperiodic and Periodic Tasks Embedded Systems 4. Aperodc and Perodc Tasks Lothar Thele 4-1 Contents of Course 1. Embedded Systems Introducton 2. Software Introducton 7. System Components 10. Models 3. Real-Tme Models 4. Perodc/Aperodc

More information

GEO-SLOPE International Ltd, Calgary, Alberta, Canada Vibrating Beam

GEO-SLOPE International Ltd, Calgary, Alberta, Canada   Vibrating Beam GEO-SLOPE Internatonal Ltd, Calgary, Alberta, Canada www.geo-slope.com Introducton Vbratng Beam Ths example looks at the dynamc response of a cantlever beam n response to a cyclc force at the free end.

More information

Inexact Newton Methods for Inverse Eigenvalue Problems

Inexact Newton Methods for Inverse Eigenvalue Problems Inexact Newton Methods for Inverse Egenvalue Problems Zheng-jan Ba Abstract In ths paper, we survey some of the latest development n usng nexact Newton-lke methods for solvng nverse egenvalue problems.

More information

NP-Completeness : Proofs

NP-Completeness : Proofs NP-Completeness : Proofs Proof Methods A method to show a decson problem Π NP-complete s as follows. (1) Show Π NP. (2) Choose an NP-complete problem Π. (3) Show Π Π. A method to show an optmzaton problem

More information

THE ARIMOTO-BLAHUT ALGORITHM FOR COMPUTATION OF CHANNEL CAPACITY. William A. Pearlman. References: S. Arimoto - IEEE Trans. Inform. Thy., Jan.

THE ARIMOTO-BLAHUT ALGORITHM FOR COMPUTATION OF CHANNEL CAPACITY. William A. Pearlman. References: S. Arimoto - IEEE Trans. Inform. Thy., Jan. THE ARIMOTO-BLAHUT ALGORITHM FOR COMPUTATION OF CHANNEL CAPACITY Wllam A. Pearlman 2002 References: S. Armoto - IEEE Trans. Inform. Thy., Jan. 1972 R. Blahut - IEEE Trans. Inform. Thy., July 1972 Recall

More information

Uncertainty in measurements of power and energy on power networks

Uncertainty in measurements of power and energy on power networks Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:

More information

2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification

2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification E395 - Pattern Recognton Solutons to Introducton to Pattern Recognton, Chapter : Bayesan pattern classfcaton Preface Ths document s a soluton manual for selected exercses from Introducton to Pattern Recognton

More information

SINGLE EVENTS, TIME SERIES ANALYSIS, AND PLANETARY MOTION

SINGLE EVENTS, TIME SERIES ANALYSIS, AND PLANETARY MOTION SINGLE EVENTS, TIME SERIES ANALYSIS, AND PLANETARY MOTION John N. Harrs INTRODUCTION The advent of modern computng devces and ther applcaton to tme-seres analyses permts the nvestgaton of mathematcal and

More information

E O C NO N MIC C D I D SP S A P T A C T H C H A N A D N D UN U I N T T CO C MMITM T EN E T

E O C NO N MIC C D I D SP S A P T A C T H C H A N A D N D UN U I N T T CO C MMITM T EN E T Chapter 4 ECOOMIC DISPATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the

More information

Online Appendix: Reciprocity with Many Goods

Online Appendix: Reciprocity with Many Goods T D T A : O A Kyle Bagwell Stanford Unversty and NBER Robert W. Stager Dartmouth College and NBER March 2016 Abstract Ths onlne Appendx extends to a many-good settng the man features of recprocty emphaszed

More information

Newton s Method for One - Dimensional Optimization - Theory

Newton s Method for One - Dimensional Optimization - Theory Numercal Methods Newton s Method for One - Dmensonal Optmzaton - Theory For more detals on ths topc Go to Clck on Keyword Clck on Newton s Method for One- Dmensonal Optmzaton You are free to Share to copy,

More information

Assortment Optimization under MNL

Assortment Optimization under MNL Assortment Optmzaton under MNL Haotan Song Aprl 30, 2017 1 Introducton The assortment optmzaton problem ams to fnd the revenue-maxmzng assortment of products to offer when the prces of products are fxed.

More information

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient 58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),

More information

Computational Biology Lecture 8: Substitution matrices Saad Mneimneh

Computational Biology Lecture 8: Substitution matrices Saad Mneimneh Computatonal Bology Lecture 8: Substtuton matrces Saad Mnemneh As we have ntroduced last tme, smple scorng schemes lke + or a match, - or a msmatch and -2 or a gap are not justable bologcally, especally

More information

SIMPLE LINEAR REGRESSION

SIMPLE LINEAR REGRESSION Smple Lnear Regresson and Correlaton Introducton Prevousl, our attenton has been focused on one varable whch we desgnated b x. Frequentl, t s desrable to learn somethng about the relatonshp between two

More information

Prof. Dr. I. Nasser Phys 630, T Aug-15 One_dimensional_Ising_Model

Prof. Dr. I. Nasser Phys 630, T Aug-15 One_dimensional_Ising_Model EXACT OE-DIMESIOAL ISIG MODEL The one-dmensonal Isng model conssts of a chan of spns, each spn nteractng only wth ts two nearest neghbors. The smple Isng problem n one dmenson can be solved drectly n several

More information

Difference Equations

Difference Equations Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1

More information

Chapter 11: Simple Linear Regression and Correlation

Chapter 11: Simple Linear Regression and Correlation Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests

More information

EEL 6266 Power System Operation and Control. Chapter 3 Economic Dispatch Using Dynamic Programming

EEL 6266 Power System Operation and Control. Chapter 3 Economic Dispatch Using Dynamic Programming EEL 6266 Power System Operaton and Control Chapter 3 Economc Dspatch Usng Dynamc Programmng Pecewse Lnear Cost Functons Common practce many utltes prefer to represent ther generator cost functons as sngle-

More information