Modified Line Search Method for Global Optimization


 Corey Hopkins
 2 years ago
 Views:
Transcription
1 Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, Abstract This paper itroduces a modified versio of the well kow global optimizatio techique amed lie search method. The modificatios refer to the way i which the directio ad the steps are determied. The modified lie search techique (MLS) is applied for some global optimizatio problems. Fuctios havig a high umber of dimesios are cosidered (50 i this case). Results obtaied by the proposed method o a set of well kow bechmarks are compared to the results obtaied by the stadard lie search method, geetic algorithms ad differetial evolutio. Numerical results show the effectiveess of the proposed approach while compared to the other techiques.. Itroductio Global optimizatio is still a challegig domai ad still a huge amout of work is published every year. The stadard mathematical techiques have bee improved, modified ad hybridized so that their performace is improved. I this paper, we propose a modificatio for oe of the stadard mathematical techiques for global optimizatio: lie search. This techique is very simple ad it has several variats. We propose here a ew way of choosig the values of its parameters, amely the directio ad step. Istead of usig some sophisticated ad time cosumig techiques to set the values of these parameters, we applied a radom method. We also cosider more tha o iitial (startig) poit. A detailed descriptio of the origial lie search techique ad the proposed modificatio is preseted i Sectio 2. I order to illustrate the performace of the modified approach we perform some umerical experimets by cosiderig several fuctios havig 50 dimesios. Some comparisos with some well kow techiques for optimizatio (such as geetic algorithms ad differetial evolutio which are shortly described i Sectio 3) are performed i Sectio 4. Coclusios are provided towards the ed. 2. Modified Lie Search (MLS) The origial lie search geeral method ca be described as follows: a search directio p ad a step s are determied at each iteratio k so that the followig coditios are fulfilled:  the directio p k (directio p at iteratio k) is a descet directio, i.e. p, g 0 if g 0 k k where g deotes the gradiet; k  the step s k is calculated so that f(x k + p k s k ) < f(x k ) There are several ways to calculate adequate values for s k (like backtrackig, etc). Readers are advised to cosult [3] for more details. Fidig the right value for s k ca be sometimes difficult. Figure illustrates few situatios cosiderig differet values for p k ad s k for optimizig the fuctio f(x) = x 2 for 0 iteratios. It is observed that for smaller values of s k the fuctio coverges very slowly while for greater values it ca eve miss the optimum. Takig ito accout of this problem, we propose a very simple modificatio of the stadard lie search method as give below: (i) Istead of computig (usig differet other methods) adequate values for s k ad p k we are simply geeratig at radom the values of these parameters at each iteratio. The values of these variables vary betwee the rage [, ]. Also, the value of p k is modified at each iteratio by p k = p k () k+. (ii) Istead of cosiderig a sigle startig poit, a set of several radomly geerated poits are cosidered over the search space. The lie search procedure is applied from each of these poits. Proceedigs of the First Asia Iteratioal Coferece o Modellig & Simulatio (AMS'07)
2 Figure. Example of lie search method for the fuctio f(x)=x 2 cosiderig: (a) p k =() k+ ad s k =2+3/2 k+ ; (b) p k = ad s k =/2 k+ ; (c) p k = ad s k =3/2 k+ ; (d) p k = ad s k =5/2 k+ We preferred this way of fidig a adequate value for s k due to the fact that at each iteratio the purpose is to improve the value of the fuctio by optimizig the ewly obtaied poit. Sice sometimes it ca be time cosumig to fid the right value for s k, we applied the radom procedure to geerate aother step util the value of the fuctio i the ewly obtaied poit is improved. This way, we esure that we are movig i a better positio which ca help i fidig the global optimum poit. The modified lie search method (pseudo code) is described below: Begi Geerate N poits i, i=,, N over the search space. k:=; Repeat For i= to N do repeat p k :=radom; if odd(i) the p k :=() p k ; s k :=radom; util f( i + p k s k )<f( i ); k:=k+; for all i i := i + p k s k Util coditio Prit the best solutio. Ed The MLS may be ru for a specified umber of iteratios or whe the best solutio is foud. The algorithm may be also termiated if the solutios foud are close to the optimal value with the kow optimal value. I Figure 2, we illustrate how the MLS works for 0 iteratios. 3. Techiques Used for Comparisos The results obtaied by MLS are compared with the results obtaied by lie search ad Geetic Algorithms for all the cosidered test fuctios. The obtaied results are also compared with Differetial Evolutio but oly for two of the cosidered test fuctios [5]. Proceedigs of the First Asia Iteratioal Coferece o Modellig & Simulatio (AMS'07)
3 Ed Step 3.. Evaluate idividuals from P(t); Step 3.2. Selectio o P(t). Let P (t) be the set of selected idividuals. Step 3.3. Crossover o P (t); Step 3.4. Mutatio o P (t); Step 3.5. Survival o P (t); Step 3.6. t=t+; P(t)=P (t) Util t=number_of_geeratios 3.2 Differetial Evolutio Figure 2. Example of the LMS behaviour after 0 iteratios with radom p k ad s k. 3. Geetic Algorithms Geetic algorithms (GA) cosider a populatio of chromosomes (idividuals) ecodig potetial solutios to a give problem [2]. Each chromosome represets a poit i the search space. The idividuals i the populatio the go through a process of simulated evolutio. The search progress is obtaied by modificatio of the chromosome populatio. The most importat search operator is traditioally cosidered to be recombiatio (crossover). Radom mutatio of ewly geerated offsprig iduces variability i the populatio prevetig the premature covergece. A fitess fuctio is used to measure the quality of each idividual. The selectio for crossover is based o the fitess value. A probabilistic selectio operator esures the 'fittest' idividuals the highest probability to produce offsprig. Oe iteratio of the algorithm is referred to as a geeratio. The basic GA is very geeric ad there are may aspects that ca be implemeted differetly accordig to the problem (example, represetatio of solutio (chromosomes), type of ecodig, selectio strategy, type of crossover ad mutatio operators, etc.). I practice, GA's are implemeted by havig arrays of bits or characters to represet the chromosomes The basic geetic algorithm is described below: DE is a populatio based, stochastic fuctio miimizer. A populatio of solutio vectors is successively updated by the additio, subtractio, ad compoet swappig, util the populatio coverges to the optimum. V i = x r +F(x r2  x r3 ). The algorithm starts with NP radomly chose solutio vectors. For each i (,,NP) a mutat vector is formed: Where r, r2, ad r3 are three mutually distict radomly draw idices from (, NP), ad also distict from i, ad 0<F<=2 Mutatio ad recombiatio are the operators used to improve the quality of solutios. 3. Experimet Setup ad Results We performed several experimets by cosiderig well kow test fuctios. I order to illustrate the performace of the algorithms used, we cosider a high umber of dimesios (50 i our case) because all these algorithms were tested for a small umber of dimesios ad the coclusio is that they all work pretty well. 3.. Test fuctios used There are several test fuctios for global optimizatio available i the literature. We used four test fuctios which is foud i [] [6] ad [7]. Although the objective fuctios are build i a way that the optimal solutios are kow, the optimizatio problems caot be trivially solved by search procedures that do ot exploit the special structure associated with each fuctio [4]. begi Step. Set t= 0; Step 2. Radomly iitialize the populatio P(t); Step 3. Repeat Proceedigs of the First Asia Iteratioal Coferece o Modellig & Simulatio (AMS'07)
4 Figure 3. Covergece toward the optimum solutios of the algorithms MLS, GA ad LS: (a) Sphere test fuctio; (b) Dixo ad Price test fuctio; (c) Ackley test fuctio; (d) Griewak test fuctio. The followig test fuctios were cosidered: Sphere fuctio (f ) 2 x i f(x)= i= Number of dimesios: ; Rage of iitial poits:  0 xi 0 for i=...; Global miimum: x* = (0, 0,...,0), f(x*) = 0 Dixo ad Price fuctio (f 2 ) f(x)= 2 2 i( 2xi xi ) + ( x + i= Number of dimesios: ; Rage of iitial poits:  ) 0 xi 0 for i=...; Global miimum: z=2 i, f(x*) = 0 2 x i z z = 2, Proceedigs of the First Asia Iteratioal Coferece o Modellig & Simulatio (AMS'07)
5 Fuctio Algorithm No of dimesios No of iitial poits (for MLS) ad populatio size for GA No of iteratios Optimum foud Actual optimum MLS , f f 2 f 3 f 4 GA , DE , LS , MLS , GA , DE LS , MLS , GA , DE , LS , MLS , GA , DE LS , Table. Parameters used ad results obtaied by the cosidered techiques for all the four test fuctios. Ackley fuctio (f 3 ) x i e i = i = f(x)=20 + e 20  Number of dimesios: ; Rage of iitial poits: xi 5.2 for i=...; Global miimum: x* = (0, 0,...,0), f(x*) = 0 Griewak fuctio (f 4 ) f(x)= 2 xi 4000 i= i= e xi cos + i cos(2π ) Number of dimesios: ; Rage of iitial poits:  0 xi 0 for i=...; Global miimum: x* = (0, 0,...,0), f(x*) = 0 x i 3.. Results ad discussios Table depicts the values of the parameters used for each techique ad the results obtaied for the four test fuctios. I Figure 3, the covergece of the test fuctios towards the optimum poit is depicted. Comparisos betwee MLS, GA ad LS are performed. As evidet from Table ad from Figure 3, MLS obtaied the best results for all the test fuctios (except for Dixo ad Price fuctio where the stadard LS performed well). Also, there is a big differece betwee results obtaied by MLS ad the results obtaied by the other techiques used (example: GA ad DE). Proceedigs of the First Asia Iteratioal Coferece o Modellig & Simulatio (AMS'07)
6 4. Coclusios I this paper, we proposed a modified versio of a well kow mathematical techique used for global optimizatio: lie search. The modified versio uses radom geerated values for directio ad step. Some umerical experimets were performed usig popular optimizatio fuctios ivolvig 50 dimesios. Comparisos with stadard lie search, geetic algorithms ad differetial evolutio were performed. Empirical results illustrate that the modified lie search algorithm performs better tha the other cosidered techiques ad better that the stadard lie search for three of the four test fuctios cosidered. The proposed approach ca be exteded for other classes of optimizatio problems ad for high dimesio problems. Refereces [] Floudas, C.A., Pardalos, P.M. A collectio of test problems for costrait global optimizatio algorithms, SprigerVerlag, Berli Heidelberg, 990. [2] Goldberg DE (989), Geetic algorithms i search, optimizatio ad machie learig. Addiso Wesley, Readig, MA. [3] Gould, N., A itroductio to algorithms for cotiuous optimizatio, Oxford Uiversity Computig Laboratory Notes, [4] Lagua, M., Marti, R. Experimetal testig of advaced scatter search desigs for global optimizatio of multimodal fuctios, Joural of Global Optimizatio, 33, pp , 2005 [5] Stor, R, O the usage of differetial evolutio for fuctio optimizatio. I: Bieial coferece of the North America fuzzy iformatio processig society, pp , 996. [6] (accessed o Ja 24, 2007) [7] problems.html (accessed o Ja 24, 2007) Proceedigs of the First Asia Iteratioal Coferece o Modellig & Simulatio (AMS'07)
A Combined Continuous/Binary Genetic Algorithm for Microstrip Antenna Design
A Combied Cotiuous/Biary Geetic Algorithm for Microstrip Atea Desig Rady L. Haupt The Pesylvaia State Uiversity Applied Research Laboratory P. O. Box 30 State College, PA 168040030 haupt@ieee.org Abstract:
More informationIn nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008
I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces
More informationCOMPARISON OF THE EFFICIENCY OF SCONTROL CHART AND EWMAS 2 CONTROL CHART FOR THE CHANGES IN A PROCESS
COMPARISON OF THE EFFICIENCY OF SCONTROL CHART AND EWMAS CONTROL CHART FOR THE CHANGES IN A PROCESS Supraee Lisawadi Departmet of Mathematics ad Statistics, Faculty of Sciece ad Techoology, Thammasat
More informationHeterogeneous Vehicle Routing Problem with profits Dynamic solving by Clustering Genetic Algorithm
IJCSI Iteratioal Joural of Computer Sciece Issues, Vol. 10, Issue 4, No 1, July 2013 ISSN (Prit): 16940814 ISSN (Olie): 16940784 www.ijcsi.org 247 Heterogeeous Vehicle Routig Problem with profits Dyamic
More informationVladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT
Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee
More informationThe analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection
The aalysis of the Courot oligopoly model cosiderig the subjective motive i the strategy selectio Shigehito Furuyama Teruhisa Nakai Departmet of Systems Maagemet Egieerig Faculty of Egieerig Kasai Uiversity
More informationResearch Article Allocating Freight Empty Cars in Railway Networks with Dynamic Demands
Discrete Dyamics i Nature ad Society, Article ID 349341, 12 pages http://dx.doi.org/10.1155/2014/349341 Research Article Allocatig Freight Empty Cars i Railway Networks with Dyamic Demads Ce Zhao, Lixig
More informationHypergeometric Distributions
7.4 Hypergeometric Distributios Whe choosig the startig lieup for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you
More informationResearch Article Sign Data Derivative Recovery
Iteratioal Scholarly Research Network ISRN Applied Mathematics Volume 0, Article ID 63070, 7 pages doi:0.540/0/63070 Research Article Sig Data Derivative Recovery L. M. Housto, G. A. Glass, ad A. D. Dymikov
More informationEvaluation of Different Fitness Functions for the Evolutionary Testing of an Autonomous Parking System
Evaluatio of Differet Fitess Fuctios for the Evolutioary Testig of a Autoomous Parkig System Joachim Wegeer 1, Oliver Bühler 2 1 DaimlerChrysler AG, Research ad Techology, AltMoabit 96 a, D1559 Berli,
More informationI. Chisquared Distributions
1 M 358K Supplemet to Chapter 23: CHISQUARED DISTRIBUTIONS, TDISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad tdistributios, we first eed to look at aother family of distributios, the chisquared distributios.
More informationReliable Job Scheduler using RFOH in Grid Computing
VOL, NO, JULY 200 ISSN 20798407 2009200 CIS Joural All rights reserved http://wwwcisjouralorg Reliable Job Scheduler usig RFOH i Grid Computig Leyli Mohammad Khali Dept of Computer Sciece, Tabriz Uiversity
More informationChapter 6: Variance, the law of large numbers and the MonteCarlo method
Chapter 6: Variace, the law of large umbers ad the MoteCarlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value
More informationMeasures of Spread and Boxplots Discrete Math, Section 9.4
Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,
More informationApplication of the Global Optimization Approaches to Planar NearField Antenna Phaseless Measurements
RADIOENGINEERING, VOL. 8, NO., APRIL 009 9 Applicatio of the Global Optimizatio Approaches to Plaar NearField Atea Phaseless Measuremets Ja PUSKELY, Zdeěk NOVÁČEK Dept. of Radio Electroics, Bro Uiversity
More informationNEW HIGH PERFORMANCE COMPUTATIONAL METHODS FOR MORTGAGES AND ANNUITIES. Yuri Shestopaloff,
NEW HIGH PERFORMNCE COMPUTTIONL METHODS FOR MORTGGES ND NNUITIES Yuri Shestopaloff, Geerally, mortgage ad auity equatios do ot have aalytical solutios for ukow iterest rate, which has to be foud usig umerical
More informationConfidence Intervals for One Mean
Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a
More informationLecture 2: Karger s Min Cut Algorithm
priceto uiv. F 3 cos 5: Advaced Algorithm Desig Lecture : Karger s Mi Cut Algorithm Lecturer: Sajeev Arora Scribe:Sajeev Today s topic is simple but gorgeous: Karger s mi cut algorithm ad its extesio.
More informationThe Impact of Feature Selection on Web Spam Detection
I.J. Itelliget Systems ad Applicatios, 2012, 9, 6167 Published Olie August 2012 i MECS (http://www.mecspress.org/) DOI: 10.5815/ijisa.2012.09.08 The Impact of Feature Selectio o Web Spam Detectio Jaber
More informationPattern Synthesis Using Real Coded Genetic Algorithm and Accelerated Particle Swarm Optimization
Iteratioal Joural of Applied Egieerig Research ISSN 09734562 Volume 11, Number 6 (2016) pp 37533760 Research Idia Publicatios. http://www.ripublicatio.com Patter Sythesis Usig Real Coded Geetic Algorithm
More informationResearch Article Crude Oil Price Prediction Based on a Dynamic Correcting Support Vector Regression Machine
Abstract ad Applied Aalysis Volume 2013, Article ID 528678, 7 pages http://dx.doi.org/10.1155/2013/528678 Research Article Crude Oil Price Predictio Based o a Dyamic Correctig Support Vector Regressio
More informationAnalyzing Longitudinal Data from Complex Surveys Using SUDAAN
Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical
More informationSoving Recurrence Relations
Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree
More informationCHAPTER 3 THE TIME VALUE OF MONEY
CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all
More informationTaking DCOP to the Real World: Efficient Complete Solutions for Distributed MultiEvent Scheduling
Taig DCOP to the Real World: Efficiet Complete Solutios for Distributed MultiEvet Schedulig Rajiv T. Maheswara, Milid Tambe, Emma Bowrig, Joatha P. Pearce, ad Pradeep araatham Uiversity of Souther Califoria
More informationDomain 1: Designing a SQL Server Instance and a Database Solution
Maual SQL Server 2008 Desig, Optimize ad Maitai (70450) 18004186789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a
More informationDESIGN OPTIMIZATION OF 3D STEEL FRAME STRUCTURES
I DESIGN OPTIMIZATION OF 3D STEEL FRAME STRUCTURES 9.1 Objectives Two objectives are associated with this chapter. First is to ascertai the advatages, metioed i Chapter 8, of the developed algorithm cosiderig
More informationSequences and Series
CHAPTER 9 Sequeces ad Series 9.. Covergece: Defiitio ad Examples Sequeces The purpose of this chapter is to itroduce a particular way of geeratig algorithms for fidig the values of fuctios defied by their
More informationSequences, Series and Convergence with the TI 92. Roger G. Brown Monash University
Sequeces, Series ad Covergece with the TI 92. Roger G. Brow Moash Uiversity email: rgbrow@deaki.edu.au Itroductio. Studets erollig i calculus at Moash Uiversity, like may other calculus courses, are itroduced
More informationOutput Analysis (2, Chapters 10 &11 Law)
B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should
More informationChapter 7 Methods of Finding Estimators
Chapter 7 for BST 695: Special Topics i Statistical Theory. Kui Zhag, 011 Chapter 7 Methods of Fidig Estimators Sectio 7.1 Itroductio Defiitio 7.1.1 A poit estimator is ay fuctio W( X) W( X1, X,, X ) of
More informationGCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.
GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea  add up all
More informationCase Study. Normal and t Distributions. Density Plot. Normal Distributions
Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca
More informationSystems Design Project: Indoor Location of Wireless Devices
Systems Desig Project: Idoor Locatio of Wireless Devices Prepared By: Bria Murphy Seior Systems Sciece ad Egieerig Washigto Uiversity i St. Louis Phoe: (805) 6985295 Email: bcm1@cec.wustl.edu Supervised
More informationEscola Federal de Engenharia de Itajubá
Escola Federal de Egeharia de Itajubá Departameto de Egeharia Mecâica PósGraduação em Egeharia Mecâica MPF04 ANÁLISE DE SINAIS E AQUISÇÃO DE DADOS SINAIS E SISTEMAS Trabalho 02 (MATLAB) Prof. Dr. José
More information5 Boolean Decision Trees (February 11)
5 Boolea Decisio Trees (February 11) 5.1 Graph Coectivity Suppose we are give a udirected graph G, represeted as a boolea adjacecy matrix = (a ij ), where a ij = 1 if ad oly if vertices i ad j are coected
More informationDepartment of Computer Science, University of Otago
Departmet of Computer Sciece, Uiversity of Otago Techical Report OUCS200609 Permutatios Cotaiig May Patters Authors: M.H. Albert Departmet of Computer Sciece, Uiversity of Otago Micah Colema, Rya Fly
More informationHypothesis testing. Null and alternative hypotheses
Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate
More information1 Computing the Standard Deviation of Sample Means
Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.
More informationDivide and Conquer. Maximum/minimum. Integer Multiplication. CS125 Lecture 4 Fall 2015
CS125 Lecture 4 Fall 2015 Divide ad Coquer We have see oe geeral paradigm for fidig algorithms: the greedy approach. We ow cosider aother geeral paradigm, kow as divide ad coquer. We have already see a
More informationMatrix Model of Trust Management in P2P Networks
Matrix Model of Trust Maagemet i P2P Networks Miroslav Novotý, Filip Zavoral Faculty of Mathematics ad Physics Charles Uiversity Prague, Czech Republic miroslav.ovoty@mff.cui.cz Abstract The trust maagemet
More informationBASIC STATISTICS. Discrete. Mass Probability Function: P(X=x i ) Only one finite set of values is considered {x 1, x 2,...} Prob. t = 1.
BASIC STATISTICS 1.) Basic Cocepts: Statistics: is a sciece that aalyzes iformatio variables (for istace, populatio age, height of a basketball team, the temperatures of summer moths, etc.) ad attempts
More informationReliability Analysis in HPC clusters
Reliability Aalysis i HPC clusters Narasimha Raju, Gottumukkala, Yuda Liu, Chokchai Box Leagsuksu 1, Raja Nassar, Stephe Scott 2 College of Egieerig & Sciece, Louisiaa ech Uiversity Oak Ridge Natioal Lab
More informationYour organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows:
Subettig Subettig is used to subdivide a sigle class of etwork i to multiple smaller etworks. Example: Your orgaizatio has a Class B IP address of 166.144.0.0 Before you implemet subettig, the Network
More information(VCP310) 18004186789
Maual VMware Lesso 1: Uderstadig the VMware Product Lie I this lesso, you will first lear what virtualizatio is. Next, you ll explore the products offered by VMware that provide virtualizatio services.
More informationLocating Performance Monitoring Mobile Agents in Scalable Active Networks
Locatig Performace Moitorig Mobile Agets i Scalable Active Networks Amir Hossei Hadad, Mehdi Dehgha, ad Hossei Pedram Amirkabir Uiversity, Computer Sciece Faculty, Tehra, Ira a_haddad@itrc.ac.ir, {dehgha,
More informationUniversity of California, Los Angeles Department of Statistics. Distributions related to the normal distribution
Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chisquare (χ ) distributio.
More informationConvention Paper 6764
Audio Egieerig Society Covetio Paper 6764 Preseted at the 10th Covetio 006 May 0 3 Paris, Frace This covetio paper has bee reproduced from the author's advace mauscript, without editig, correctios, or
More informationThe second difference is the sequence of differences of the first difference sequence, 2
Differece Equatios I differetial equatios, you look for a fuctio that satisfies ad equatio ivolvig derivatives. I differece equatios, istead of a fuctio of a cotiuous variable (such as time), we look for
More informationDAME  Microsoft Excel addin for solving multicriteria decision problems with scenarios Radomir Perzina 1, Jaroslav Ramik 2
Itroductio DAME  Microsoft Excel addi for solvig multicriteria decisio problems with scearios Radomir Perzia, Jaroslav Ramik 2 Abstract. The mai goal of every ecoomic aget is to make a good decisio,
More information{{1}, {2, 4}, {3}} {{1, 3, 4}, {2}} {{1}, {2}, {3, 4}} 5.4 Stirling Numbers
. Stirlig Numbers Whe coutig various types of fuctios from., we quicly discovered that eumeratig the umber of oto fuctios was a difficult problem. For a domai of five elemets ad a rage of four elemets,
More information76 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 9  NUMBER 1  YEAR 2011 ISSN: 16904524
The Fuzzy ad Compartmet System Cocept for the Commuicatio System takig accout of the Hadicapped situatio M asahiroaruga DepartmetofHuma ad Iformatio Sciece,School ofiformatio Sciecead Techology,TokaiUiversity
More information3.1 Measures of Central Tendency. Introduction 5/28/2013. Data Description. Outline. Objectives. Objectives. Traditional Statistics Average
5/8/013 C H 3A P T E R Outlie 3 1 Measures of Cetral Tedecy 3 Measures of Variatio 3 3 3 Measuresof Positio 3 4 Exploratory Data Aalysis Copyright 013 The McGraw Hill Compaies, Ic. C H 3A P T E R Objectives
More informationNPTEL STRUCTURAL RELIABILITY
NPTEL Course O STRUCTURAL RELIABILITY Module # 0 Lecture 1 Course Format: Web Istructor: Dr. Aruasis Chakraborty Departmet of Civil Egieerig Idia Istitute of Techology Guwahati 1. Lecture 01: Basic Statistics
More informationCHAPTER 7: Central Limit Theorem: CLT for Averages (Means)
CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:
More informationFinding the circle that best fits a set of points
Fidig the circle that best fits a set of poits L. MAISONOBE October 5 th 007 Cotets 1 Itroductio Solvig the problem.1 Priciples............................... Iitializatio.............................
More informationSolutions to Selected Problems In: Pattern Classification by Duda, Hart, Stork
Solutios to Selected Problems I: Patter Classificatio by Duda, Hart, Stork Joh L. Weatherwax February 4, 008 Problem Solutios Chapter Bayesia Decisio Theory Problem radomized rules Part a: Let Rx be the
More information7. Sample Covariance and Correlation
1 of 8 7/16/2009 6:06 AM Virtual Laboratories > 6. Radom Samples > 1 2 3 4 5 6 7 7. Sample Covariace ad Correlatio The Bivariate Model Suppose agai that we have a basic radom experimet, ad that X ad Y
More informationLECTURE 13: Crossvalidation
LECTURE 3: Crossvalidatio Resampli methods Cross Validatio Bootstrap Bias ad variace estimatio with the Bootstrap Threeway data partitioi Itroductio to Patter Aalysis Ricardo GutierrezOsua Texas A&M
More informationA model of Virtual Resource Scheduling in Cloud Computing and Its
A model of Virtual Resource Schedulig i Cloud Computig ad Its Solutio usig EDAs 1 Jiafeg Zhao, 2 Wehua Zeg, 3 Miu Liu, 4 Guagmig Li 1, First Author, 3 Cogitive Sciece Departmet, Xiame Uiversity, Xiame,
More informationINFINITE SERIES KEITH CONRAD
INFINITE SERIES KEITH CONRAD. Itroductio The two basic cocepts of calculus, differetiatio ad itegratio, are defied i terms of limits (Newto quotiets ad Riema sums). I additio to these is a third fudametal
More informationTheorems About Power Series
Physics 6A Witer 20 Theorems About Power Series Cosider a power series, f(x) = a x, () where the a are real coefficiets ad x is a real variable. There exists a real oegative umber R, called the radius
More informationChapter 7  Sampling Distributions. 1 Introduction. What is statistics? It consist of three major areas:
Chapter 7  Samplig Distributios 1 Itroductio What is statistics? It cosist of three major areas: Data Collectio: samplig plas ad experimetal desigs Descriptive Statistics: umerical ad graphical summaries
More informationResearch Article HeuristicBased Firefly Algorithm for Bound Constrained Nonlinear Binary Optimization
Advaces i Operatios Research, Article ID 215182, 12 pages http://dx.doi.org/10.1155/2014/215182 Research Article HeuristicBased Firefly Algorithm for Boud Costraied Noliear Biary Optimizatio M. Ferada
More information3. Covariance and Correlation
Virtual Laboratories > 3. Expected Value > 1 2 3 4 5 6 3. Covariace ad Correlatio Recall that by takig the expected value of various trasformatios of a radom variable, we ca measure may iterestig characteristics
More informationPROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUSMALUS SYSTEM
PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical ad Mathematical Scieces 2015, 1, p. 15 19 M a t h e m a t i c s AN ALTERNATIVE MODEL FOR BONUSMALUS SYSTEM A. G. GULYAN Chair of Actuarial Mathematics
More informationCS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations
CS3A Hadout 3 Witer 00 February, 00 Solvig Recurrece Relatios Itroductio A wide variety of recurrece problems occur i models. Some of these recurrece relatios ca be solved usig iteratio or some other ad
More informationChapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions
Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig
More informationLearning outcomes. Algorithms and Data Structures. Time Complexity Analysis. Time Complexity Analysis How fast is the algorithm? Prof. Dr.
Algorithms ad Data Structures Algorithm efficiecy Learig outcomes Able to carry out simple asymptotic aalysisof algorithms Prof. Dr. Qi Xi 2 Time Complexity Aalysis How fast is the algorithm? Code the
More informationUnit 20 Hypotheses Testing
Uit 2 Hypotheses Testig Objectives: To uderstad how to formulate a ull hypothesis ad a alterative hypothesis about a populatio proportio, ad how to choose a sigificace level To uderstad how to collect
More informationPlugin martingales for testing exchangeability online
Plugi martigales for testig exchageability olie Valetia Fedorova, Alex Gammerma, Ilia Nouretdiov, ad Vladimir Vovk Computer Learig Research Cetre Royal Holloway, Uiversity of Lodo, UK {valetia,ilia,alex,vovk}@cs.rhul.ac.uk
More informationChapter 7: Confidence Interval and Sample Size
Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum
More informationRecursion and Recurrences
Chapter 5 Recursio ad Recurreces 5.1 Growth Rates of Solutios to Recurreces Divide ad Coquer Algorithms Oe of the most basic ad powerful algorithmic techiques is divide ad coquer. Cosider, for example,
More informationLesson 15 ANOVA (analysis of variance)
Outlie Variability betwee group variability withi group variability total variability Fratio Computatio sums of squares (betwee/withi/total degrees of freedom (betwee/withi/total mea square (betwee/withi
More informationSECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,
More informationEngineering Data Management
BaaERP 5.0c Maufacturig Egieerig Data Maagemet Module Procedure UP128A US Documetiformatio Documet Documet code : UP128A US Documet group : User Documetatio Documet title : Egieerig Data Maagemet Applicatio/Package
More informationCHAPTER 3 DIGITAL CODING OF SIGNALS
CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity
More informationClass Meeting # 16: The Fourier Transform on R n
MATH 18.152 COUSE NOTES  CLASS MEETING # 16 18.152 Itroductio to PDEs, Fall 2011 Professor: Jared Speck Class Meetig # 16: The Fourier Trasform o 1. Itroductio to the Fourier Trasform Earlier i the course,
More informationThe Euler Totient, the Möbius and the Divisor Functions
The Euler Totiet, the Möbius ad the Divisor Fuctios Rosica Dieva July 29, 2005 Mout Holyoke College South Hadley, MA 01075 1 Ackowledgemets This work was supported by the Mout Holyoke College fellowship
More informationA probabilistic proof of a binomial identity
A probabilistic proof of a biomial idetity Joatho Peterso Abstract We give a elemetary probabilistic proof of a biomial idetity. The proof is obtaied by computig the probability of a certai evet i two
More informationKey Ideas Section 81: Overview hypothesis testing Hypothesis Hypothesis Test Section 82: Basics of Hypothesis Testing Null Hypothesis
Chapter 8 Key Ideas Hypothesis (Null ad Alterative), Hypothesis Test, Test Statistic, Pvalue Type I Error, Type II Error, Sigificace Level, Power Sectio 81: Overview Cofidece Itervals (Chapter 7) are
More informationTrigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is
0_0605.qxd /5/05 0:45 AM Page 470 470 Chapter 6 Additioal Topics i Trigoometry 6.5 Trigoometric Form of a Complex Number What you should lear Plot complex umbers i the complex plae ad fid absolute values
More informationStandard Errors and Confidence Intervals
Stadard Errors ad Cofidece Itervals Itroductio I the documet Data Descriptio, Populatios ad the Normal Distributio a sample had bee obtaied from the populatio of heights of 5yearold boys. If we assume
More informationEstimating the Mean and Variance of a Normal Distribution
Estimatig the Mea ad Variace of a Normal Distributio Learig Objectives After completig this module, the studet will be able to eplai the value of repeatig eperimets eplai the role of the law of large umbers
More informationChair for Network Architectures and Services Institute of Informatics TU München Prof. Carle. Network Security. Chapter 2 Basics
Chair for Network Architectures ad Services Istitute of Iformatics TU Müche Prof. Carle Network Security Chapter 2 Basics 2.4 Radom Number Geeratio for Cryptographic Protocols Motivatio It is crucial to
More informationEstimating Probability Distributions by Observing Betting Practices
5th Iteratioal Symposium o Imprecise Probability: Theories ad Applicatios, Prague, Czech Republic, 007 Estimatig Probability Distributios by Observig Bettig Practices Dr C Lych Natioal Uiversity of Irelad,
More informationWeek 3 Conditional probabilities, Bayes formula, WEEK 3 page 1 Expected value of a random variable
Week 3 Coditioal probabilities, Bayes formula, WEEK 3 page 1 Expected value of a radom variable We recall our discussio of 5 card poker hads. Example 13 : a) What is the probability of evet A that a 5
More informationSWARM INTELLIGENCE OPTIMIZATION OF WORM AND WORM WHEEL DESIGN
VOL. 0, NO. 3, JULY 05 ISSN 896608 00605 Asia Research Publishig Network (ARPN). All rights reserved. SWARM INTELLIGENCE OPTIMIZATION OF WORM AND WORM WHEEL DESIGN M. Chadrasekara, Padmaabha S. ad V.
More informationInstallment Joint Life Insurance Actuarial Models with the Stochastic Interest Rate
Iteratioal Coferece o Maagemet Sciece ad Maagemet Iovatio (MSMI 4) Istallmet Joit Life Isurace ctuarial Models with the Stochastic Iterest Rate NiaNia JI a,*, Yue LI, DogHui WNG College of Sciece, Harbi
More informationConfidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.
Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).
More informationRobust and Resistant Regression
Chapter 13 Robust ad Resistat Regressio Whe the errors are ormal, least squares regressio is clearly best but whe the errors are oormal, other methods may be cosidered. A particular cocer is logtailed
More informationBasic Measurement Issues. Sampling Theory and AnalogtoDigital Conversion
Theory ad AalogtoDigital Coversio Itroductio/Defiitios Aalogtodigital coversio Rate Frequecy Aalysis Basic Measuremet Issues Reliability the extet to which a measuremet procedure yields the same results
More informationStatistical Methods. Chapter 1: Overview and Descriptive Statistics
Geeral Itroductio Statistical Methods Chapter 1: Overview ad Descriptive Statistics Statistics studies data, populatio, ad samples. Descriptive Statistics vs Iferetial Statistics. Descriptive Statistics
More informationOn The Comparison of Several Goodness of Fit Tests: With Application to Wind Speed Data
Proceedigs of the 3rd WSEAS It Cof o RENEWABLE ENERGY SOURCES O The Compariso of Several Goodess of Fit Tests: With Applicatio to Wid Speed Data FAZNA ASHAHABUDDIN, KAMARULZAMAN IBRAHIM, AND ABDUL AZIZ
More informationThe following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles
The followig eample will help us uderstad The Samplig Distributio of the Mea Review: The populatio is the etire collectio of all idividuals or objects of iterest The sample is the portio of the populatio
More informationQuadrat Sampling in Population Ecology
Quadrat Samplig i Populatio Ecology Backgroud Estimatig the abudace of orgaisms. Ecology is ofte referred to as the "study of distributio ad abudace". This beig true, we would ofte like to kow how may
More information5: Introduction to Estimation
5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample
More informationCS103X: Discrete Structures Homework 4 Solutions
CS103X: Discrete Structures Homewor 4 Solutios Due February 22, 2008 Exercise 1 10 poits. Silico Valley questios: a How may possible sixfigure salaries i whole dollar amouts are there that cotai at least
More informationAn Efficient Polynomial Approximation of the Normal Distribution Function & Its Inverse Function
A Efficiet Polyomial Approximatio of the Normal Distributio Fuctio & Its Iverse Fuctio Wisto A. Richards, 1 Robi Atoie, * 1 Asho Sahai, ad 3 M. Raghuadh Acharya 1 Departmet of Mathematics & Computer Sciece;
More informationGrade 7. Strand: Number Specific Learning Outcomes It is expected that students will:
Strad: Number Specific Learig Outcomes It is expected that studets will: 7.N.1. Determie ad explai why a umber is divisible by 2, 3, 4, 5, 6, 8, 9, or 10, ad why a umber caot be divided by 0. [C, R] [C]
More information