Solving two-person zero-sum game by Matlab
|
|
- Shanon Lester
- 6 years ago
- Views:
Transcription
1 Appled Mechancs and Materals Onlne: ISSN: , Vols , pp do: / Trans Tech Publcatons, Swtzerland Solvng two-person zero-sum game by Matlab Yanme Yang 1, a, Yan Guo 2, b, Lchao Feng 1,c, and Janyong D 3,d 1 College of Scence, Hebe Polytechnc Unversty, Tangshan, , Chna; 2 Department of Mathematcs & Physcs, North Chna Electrc Power Unversty, Baodng, , Chna 3 College of lght ndustry, Hebe Polytechnc Unversty, Tangshan, , Chna ; a yym04@163.com, b guoyan12@126.com, c flch @yahoo.cn, d danyong60@126.com Keywords: game theory; two-person zero-sum games; lnear programmng; Matlab; Abstract: In ths artcle we present an overvew on two-person zero-sum games, whch play a central role n the development of the theory of games. Two-person zero-sum games s a specal class of game theory n whch one player wns what the other player loses wth only two players. It s dffcult to solve 2-person matrx game wth the order m n(m 3,n 3). The am of the artcle s to determne the method on how to solve a 2-person matrx game by lnear programmng functon lnprog() n matlab. Wth lnear programmng technques n the Matlab software, we present effectve method for solvng large zero-sum games problems. Introducton Game theory s a branch of appled mathematcs that s used n the socal scences, most notably n economcs [1]. Two-person zero-sum games refer to games of pure conflct, whch s the smplest case of game theory. In zero-sum games the total beneft to all players n the game, for every combnaton of strateges, always adds to zero, the payoff of one player s the negatve of the payoff of the other player [2]. Two-person zero-sum games play a central role n the development of the theory of games, but t s dffcult to solve 2-person matrx game wth the order m n (m 3,n 3). The connecton wth lnear programmng was dscovered by von Neumann n Mxed strateges must exst for two-player zero-sum games had been proven by John von Neumann and Oskar Morgenstern. The Mnmax Theorem s a smple consequence of the Dualty Theorem of lnear programmng [2,3]. So usng lnear programmng technques can solve two-person zero-sum games. In ths paper we dscuss how to convert a two-person zero-sum game nto a lnear programmng problem Lnprog command n Matlab Lnear programmng s one of the most wdespread methods used to solve management and economc problems. The command lnprog from the optmzaton toolbox mplements the smplex algorthm to solve a lnear programmng problem. Matlab uses the followng format for lnear programs: All rghts reserved. No part of contents of ths paper may be reproduced or transmtted n any form or by any means wthout the wrtten permsson of Trans Tech Publcatons, (ID: , Pennsylvana State Unversty, Unversty Park, USA-09/05/16,18:08:00)
2 Appled Mechancs and Materals Vols mn z= T f x A x b s. t. Aeq x= beq lb x ub Where f, x, b, beq, lb, and ub are vectors, and A and Aeq are matrces. x = lnprog(f, A, b, Aeq, beq, lb, ub) solves the above lnear programmng mn T f x such that A x b. Whle addtonally satsfyng the equalty constrants Aeq x= beq, set A = [] and b = [] f no nequaltes exst. Defnes a set of lower and upper bounds on the desgn varables, x, so that the soluton s always n the range lb x ub, set Aeq = [] and beq = [] f no equaltes exst [4]. For example, our orgnal problem s translated nto the format: mn Z = 4x + 3x x1+ x2 5 6 x1 0 1 x Solve the problem by Matlab, frst we set up the vectors and matrces: c=[4,3]; a=[1,1]; b=[5]; lb=[-6;-1]; ub=[10;4]; Fnally, nput the command x=lnprog(c,a,b,[],[],lb,ub). Applyng wth the command lnprog n optmzaton toolbox can be solved the above problem. Solvng two-person zero-sum game by Matlab It s stll dffcult to solve the matrx game for hgh order, although there are many solvng ways. The Mnmax Theorem s the fundamental theorem n the theory of two-person zero-sum game. The Mnmax Theorem as follow: For every two-person, zero-sum game wth fnte strateges, there exsts a value V and a mxed strategy for each player, such that (a) Gven player 2's strategy, the best payoff possble for player 1 s V, and (b) Gven player 1's strategy, the best payoff possble for player 2 s V. It can be proved by technques from lnear programmng [5-7]. Seeng the relatonshp of the Mnmax Theorem and Dualty Theorem, lnear programmng can be used to solve two-person zero-sum game. We have an m n payoff matrx A=(a ) m n, The entry a represents the payoff to the row player when she pcks the th strategy and column player pcks hs th strategy. The two-person zero-sum game can be solved by solvng thus two lnear programmng:
3 264 Intellgent Structure and Vbraton Control mn Z = x a x 1 ( = 1,2,, n) x 0 ( = 1, 2,, m) max w= y a y ( = 1, 2,, m) y 0 ( = 1,2,, n) Suppose we want to solve the two-person zero-sum game, whch payoff matrx as follow, Step 1 Reduce the payoff matrx by domnance. The above payoff matrx s a smplest form. Step 2 Convert to a payoff matrx wth no negatve entres by addng a sutable fxed number to all the entres. Addng 3 to every element of the above payoff matrx, then the new matrx s Step 3 Solve the assocated standard lnear programmng problem. Solvng thus two lnear programmng: mn x + x + x max y + y + y 6x1 + 2x2+ 5x3 x 1 + 7x2 + 5x3 1 4x1+ 5x2+ 6x3 x Step 4 Calculate the optmal strateges by Matlab mn x + x + x 2y1+ 7y2+ 5y3 5y1+ 5y2+ 6y3 y mn x + x + x 6x1 + 2x2+ 5x3 6x1 2x2 5x3 1 Translated LP x 1 + 7x2 + 5x3 1 nto the format x 1 7x 2 5x 3 1 4x1+ 5x2+ 6x3 4x1 5x2 6x3 1 x x set up the vectors and matrces:: c=[1,1,1]; a=[-6,-2,-5;-1,-7,-5;-4,-5,-6]; b=[-1,-1,-1]; lb=[0;0;0]; To fnd the optmal soluton, the optmzaton toolbox has the command lnprog: x=lnprog(c,a,b,[],[],lb)
4 Appled Mechancs and Materals Vols max y + y + y Translated LP 2y1+ 7y2+ 5y3 5y1+ 5y2+ 6y3 y Solved command n Matlab s nto the format mn y y y 2y1+ 7y2+ 5y3 5y1+ 5y2+ 6y3 y clear c=[-1,-1,-1]; a=[6,1,4;2,7,5;5,5,6]; b=[1,1,1]; lb=[0;0;0]; y=lnprog(c,a,b,[],[],lb) The soluton of above two LP s x = 0,0,, y =,,0, v = The fnal result of the two-person zero-sum game s * * 4 1 x = ( 0,0,1 ), y =,,0, v= 5 3= Step by step, we show how to use ths lnear programmng method solve the two- person zero-sum game n Matlab. The help of computer tools, we can greatly reduce the solvng work tme. Concluson Matlab s a hgh-level techncal computng language. In optmzaton toolbox of Matlab, lnear programmng problem can be solved smply by the command lnprog. Many algorthms have been proposed for solvng two-player zero-sum games, but t s not easy to solve for large matrx game. Usng lnear programmng s effcent method. Especally, t uses the lnear programmng functon lnprog() n Matlab, calculates the two-person zero-sum game. Ths method s effcent and effectve for large matrx game. References [1] Fernandez, L F.; Berman, H S., Game theory wth economc applcatons, Addson-Wesley, (1998) [2] Dutta. Prat K, Strateges and games: theory and practce, MIT Press, (1999) [3] Osborne, Martn J. (2004), An ntroducton to game theory, Oxford Unversty Press [4] B.R. Hunt, R.L. Lpsman, and J.M. Rosenberg. A Gude to MATLAB, for begnners and experenced users. Cambrdge Unversty Press, 2001 [5] Phlp D.Straffn. Game theory and strategy, Mathematcal assocaton of Amerca, [6] Andrey Garnaev, Search games and other applcatons of game theory, Lecture notes n economcs and mathematcal systems 485, Sprnger, [7] Mehrotra, S., On the Implementaton of a Prmal-Dual Interor Pont Method, SIAM Journal on Optmzaton, Vol. 2, pp , 1992.
5 Intellgent Structure and Vbraton Control / Solvng Two-Person Zero-Sum Game by Matlab / DOI References [7] Mehrotra, S., On the Implementaton of a Prmal-Dual Interor Pont Method, SIAM Journal on Optmzaton, Vol. 2, pp , /
LECTURE NOTES Duality Theory, Sensitivity Analysis, and Parametric Programming
CEE 60 Davd Rosenberg p. LECTURE NOTES Dualty Theory, Senstvty Analyss, and Parametrc Programmng Learnng Objectves. Revew the prmal LP model formulaton 2. Formulate the Dual Problem of an LP problem (TUES)
More informationNUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS
ARPN Journal of Engneerng and Appled Scences 006-017 Asan Research Publshng Network (ARPN). All rghts reserved. NUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS Igor Grgoryev, Svetlana
More informationSum of Linear and Fractional Multiobjective Programming Problem under Fuzzy Rules Constraints
Australan Journal of Basc and Appled Scences, 2(4): 1204-1208, 2008 ISSN 1991-8178 Sum of Lnear and Fractonal Multobjectve Programmng Problem under Fuzzy Rules Constrants 1 2 Sanjay Jan and Kalash Lachhwan
More informationGSLM Operations Research II Fall 13/14
GSLM 58 Operatons Research II Fall /4 6. Separable Programmng Consder a general NLP mn f(x) s.t. g j (x) b j j =. m. Defnton 6.. The NLP s a separable program f ts objectve functon and all constrants are
More informationAn Optimal Algorithm for Prufer Codes *
J. Software Engneerng & Applcatons, 2009, 2: 111-115 do:10.4236/jsea.2009.22016 Publshed Onlne July 2009 (www.scrp.org/journal/jsea) An Optmal Algorthm for Prufer Codes * Xaodong Wang 1, 2, Le Wang 3,
More informationAn Application of the Dulmage-Mendelsohn Decomposition to Sparse Null Space Bases of Full Row Rank Matrices
Internatonal Mathematcal Forum, Vol 7, 2012, no 52, 2549-2554 An Applcaton of the Dulmage-Mendelsohn Decomposton to Sparse Null Space Bases of Full Row Rank Matrces Mostafa Khorramzadeh Department of Mathematcal
More informationVirtual Machine Migration based on Trust Measurement of Computer Node
Appled Mechancs and Materals Onlne: 2014-04-04 ISSN: 1662-7482, Vols. 536-537, pp 678-682 do:10.4028/www.scentfc.net/amm.536-537.678 2014 Trans Tech Publcatons, Swtzerland Vrtual Machne Mgraton based on
More informationKent State University CS 4/ Design and Analysis of Algorithms. Dept. of Math & Computer Science LECT-16. Dynamic Programming
CS 4/560 Desgn and Analyss of Algorthms Kent State Unversty Dept. of Math & Computer Scence LECT-6 Dynamc Programmng 2 Dynamc Programmng Dynamc Programmng, lke the dvde-and-conquer method, solves problems
More informationParallelism for Nested Loops with Non-uniform and Flow Dependences
Parallelsm for Nested Loops wth Non-unform and Flow Dependences Sam-Jn Jeong Dept. of Informaton & Communcaton Engneerng, Cheonan Unversty, 5, Anseo-dong, Cheonan, Chungnam, 330-80, Korea. seong@cheonan.ac.kr
More informationSmoothing Spline ANOVA for variable screening
Smoothng Splne ANOVA for varable screenng a useful tool for metamodels tranng and mult-objectve optmzaton L. Rcco, E. Rgon, A. Turco Outlne RSM Introducton Possble couplng Test case MOO MOO wth Game Theory
More informationSENSITIVITY ANALYSIS IN LINEAR PROGRAMMING USING A CALCULATOR
SENSITIVITY ANALYSIS IN LINEAR PROGRAMMING USING A CALCULATOR Judth Aronow Rchard Jarvnen Independent Consultant Dept of Math/Stat 559 Frost Wnona State Unversty Beaumont, TX 7776 Wnona, MN 55987 aronowju@hal.lamar.edu
More informationFace Recognition University at Buffalo CSE666 Lecture Slides Resources:
Face Recognton Unversty at Buffalo CSE666 Lecture Sldes Resources: http://www.face-rec.org/algorthms/ Overvew of face recognton algorthms Correlaton - Pxel based correspondence between two face mages Structural
More informationOptimization Methods: Integer Programming Integer Linear Programming 1. Module 7 Lecture Notes 1. Integer Linear Programming
Optzaton Methods: Integer Prograng Integer Lnear Prograng Module Lecture Notes Integer Lnear Prograng Introducton In all the prevous lectures n lnear prograng dscussed so far, the desgn varables consdered
More informationToday Using Fourier-Motzkin elimination for code generation Using Fourier-Motzkin elimination for determining schedule constraints
Fourer Motzkn Elmnaton Logstcs HW10 due Frday Aprl 27 th Today Usng Fourer-Motzkn elmnaton for code generaton Usng Fourer-Motzkn elmnaton for determnng schedule constrants Unversty Fourer-Motzkn Elmnaton
More informationAssembler. Shimon Schocken. Spring Elements of Computing Systems 1 Assembler (Ch. 6) Compiler. abstract interface.
IDC Herzlya Shmon Schocken Assembler Shmon Schocken Sprng 2005 Elements of Computng Systems 1 Assembler (Ch. 6) Where we are at: Human Thought Abstract desgn Chapters 9, 12 abstract nterface H.L. Language
More information5 The Primal-Dual Method
5 The Prmal-Dual Method Orgnally desgned as a method for solvng lnear programs, where t reduces weghted optmzaton problems to smpler combnatoral ones, the prmal-dual method (PDM) has receved much attenton
More informationLoop Transformations, Dependences, and Parallelization
Loop Transformatons, Dependences, and Parallelzaton Announcements Mdterm s Frday from 3-4:15 n ths room Today Semester long project Data dependence recap Parallelsm and storage tradeoff Scalar expanson
More informationOn Some Entertaining Applications of the Concept of Set in Computer Science Course
On Some Entertanng Applcatons of the Concept of Set n Computer Scence Course Krasmr Yordzhev *, Hrstna Kostadnova ** * Assocate Professor Krasmr Yordzhev, Ph.D., Faculty of Mathematcs and Natural Scences,
More informationCluster Analysis of Electrical Behavior
Journal of Computer and Communcatons, 205, 3, 88-93 Publshed Onlne May 205 n ScRes. http://www.scrp.org/ournal/cc http://dx.do.org/0.4236/cc.205.350 Cluster Analyss of Electrcal Behavor Ln Lu Ln Lu, School
More informationQuality Improvement Algorithm for Tetrahedral Mesh Based on Optimal Delaunay Triangulation
Intellgent Informaton Management, 013, 5, 191-195 Publshed Onlne November 013 (http://www.scrp.org/journal/m) http://dx.do.org/10.36/m.013.5601 Qualty Improvement Algorthm for Tetrahedral Mesh Based on
More informationHarvard University CS 101 Fall 2005, Shimon Schocken. Assembler. Elements of Computing Systems 1 Assembler (Ch. 6)
Harvard Unversty CS 101 Fall 2005, Shmon Schocken Assembler Elements of Computng Systems 1 Assembler (Ch. 6) Why care about assemblers? Because Assemblers employ some nfty trcks Assemblers are the frst
More informationThe Greedy Method. Outline and Reading. Change Money Problem. Greedy Algorithms. Applications of the Greedy Strategy. The Greedy Method Technique
//00 :0 AM Outlne and Readng The Greedy Method The Greedy Method Technque (secton.) Fractonal Knapsack Problem (secton..) Task Schedulng (secton..) Mnmum Spannng Trees (secton.) Change Money Problem Greedy
More informationRange images. Range image registration. Examples of sampling patterns. Range images and range surfaces
Range mages For many structured lght scanners, the range data forms a hghly regular pattern known as a range mage. he samplng pattern s determned by the specfc scanner. Range mage regstraton 1 Examples
More informationCourse Introduction. Algorithm 8/31/2017. COSC 320 Advanced Data Structures and Algorithms. COSC 320 Advanced Data Structures and Algorithms
Course Introducton Course Topcs Exams, abs, Proects A quc loo at a few algorthms 1 Advanced Data Structures and Algorthms Descrpton: We are gong to dscuss algorthm complexty analyss, algorthm desgn technques
More informationSupport Vector Machines. CS534 - Machine Learning
Support Vector Machnes CS534 - Machne Learnng Perceptron Revsted: Lnear Separators Bnar classfcaton can be veed as the task of separatng classes n feature space: b > 0 b 0 b < 0 f() sgn( b) Lnear Separators
More informationCompiler Design. Spring Register Allocation. Sample Exercises and Solutions. Prof. Pedro C. Diniz
Compler Desgn Sprng 2014 Regster Allocaton Sample Exercses and Solutons Prof. Pedro C. Dnz USC / Informaton Scences Insttute 4676 Admralty Way, Sute 1001 Marna del Rey, Calforna 90292 pedro@s.edu Regster
More informationA Facet Generation Procedure. for solving 0/1 integer programs
A Facet Generaton Procedure for solvng 0/ nteger programs by Gyana R. Parja IBM Corporaton, Poughkeepse, NY 260 Radu Gaddov Emery Worldwde Arlnes, Vandala, Oho 45377 and Wlbert E. Wlhelm Teas A&M Unversty,
More informationON SOME ENTERTAINING APPLICATIONS OF THE CONCEPT OF SET IN COMPUTER SCIENCE COURSE
Yordzhev K., Kostadnova H. Інформаційні технології в освіті ON SOME ENTERTAINING APPLICATIONS OF THE CONCEPT OF SET IN COMPUTER SCIENCE COURSE Yordzhev K., Kostadnova H. Some aspects of programmng educaton
More informationProblem Set 3 Solutions
Introducton to Algorthms October 4, 2002 Massachusetts Insttute of Technology 6046J/18410J Professors Erk Demane and Shaf Goldwasser Handout 14 Problem Set 3 Solutons (Exercses were not to be turned n,
More informationMeta-heuristics for Multidimensional Knapsack Problems
2012 4th Internatonal Conference on Computer Research and Development IPCSIT vol.39 (2012) (2012) IACSIT Press, Sngapore Meta-heurstcs for Multdmensonal Knapsack Problems Zhbao Man + Computer Scence Department,
More informationDesign of Structure Optimization with APDL
Desgn of Structure Optmzaton wth APDL Yanyun School of Cvl Engneerng and Archtecture, East Chna Jaotong Unversty Nanchang 330013 Chna Abstract In ths paper, the desgn process of structure optmzaton wth
More informationSupport Vector Machines
/9/207 MIST.6060 Busness Intellgence and Data Mnng What are Support Vector Machnes? Support Vector Machnes Support Vector Machnes (SVMs) are supervsed learnng technques that analyze data and recognze patterns.
More informationFinite Element Analysis of Rubber Sealing Ring Resilience Behavior Qu Jia 1,a, Chen Geng 1,b and Yang Yuwei 2,c
Advanced Materals Research Onlne: 03-06-3 ISSN: 66-8985, Vol. 705, pp 40-44 do:0.408/www.scentfc.net/amr.705.40 03 Trans Tech Publcatons, Swtzerland Fnte Element Analyss of Rubber Sealng Rng Reslence Behavor
More informationDetermining the Optimal Bandwidth Based on Multi-criterion Fusion
Proceedngs of 01 4th Internatonal Conference on Machne Learnng and Computng IPCSIT vol. 5 (01) (01) IACSIT Press, Sngapore Determnng the Optmal Bandwdth Based on Mult-crteron Fuson Ha-L Lang 1+, Xan-Mn
More informationA New Approach For the Ranking of Fuzzy Sets With Different Heights
New pproach For the ankng of Fuzzy Sets Wth Dfferent Heghts Pushpnder Sngh School of Mathematcs Computer pplcatons Thapar Unversty, Patala-7 00 Inda pushpndersnl@gmalcom STCT ankng of fuzzy sets plays
More informationAn Application of Network Simplex Method for Minimum Cost Flow Problems
BALKANJM 0 (0) -0 Contents lsts avalable at BALKANJM BALKAN JOURNAL OF MATHEMATICS journal homepage: www.balkanjm.com An Applcaton of Network Smplex Method for Mnmum Cost Flow Problems Ergun EROGLU *a
More informationIntra-Parametric Analysis of a Fuzzy MOLP
Intra-Parametrc Analyss of a Fuzzy MOLP a MIAO-LING WANG a Department of Industral Engneerng and Management a Mnghsn Insttute of Technology and Hsnchu Tawan, ROC b HSIAO-FAN WANG b Insttute of Industral
More informationPolyhedral Compilation Foundations
Polyhedral Complaton Foundatons Lous-Noël Pouchet pouchet@cse.oho-state.edu Dept. of Computer Scence and Engneerng, the Oho State Unversty Feb 8, 200 888., Class # Introducton: Polyhedral Complaton Foundatons
More informationEfficient Load-Balanced IP Routing Scheme Based on Shortest Paths in Hose Model. Eiji Oki May 28, 2009 The University of Electro-Communications
Effcent Loa-Balance IP Routng Scheme Base on Shortest Paths n Hose Moel E Ok May 28, 2009 The Unversty of Electro-Communcatons Ok Lab. Semnar, May 28, 2009 1 Outlne Backgroun on IP routng IP routng strategy
More informationClassification / Regression Support Vector Machines
Classfcaton / Regresson Support Vector Machnes Jeff Howbert Introducton to Machne Learnng Wnter 04 Topcs SVM classfers for lnearly separable classes SVM classfers for non-lnearly separable classes SVM
More informationAn Iterative Solution Approach to Process Plant Layout using Mixed Integer Optimisation
17 th European Symposum on Computer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edtors) 2007 Elsever B.V. All rghts reserved. 1 An Iteratve Soluton Approach to Process Plant Layout usng Mxed
More informationThe Shortest Path of Touring Lines given in the Plane
Send Orders for Reprnts to reprnts@benthamscence.ae 262 The Open Cybernetcs & Systemcs Journal, 2015, 9, 262-267 The Shortest Path of Tourng Lnes gven n the Plane Open Access Ljuan Wang 1,2, Dandan He
More informationImproving Low Density Parity Check Codes Over the Erasure Channel. The Nelder Mead Downhill Simplex Method. Scott Stransky
Improvng Low Densty Party Check Codes Over the Erasure Channel The Nelder Mead Downhll Smplex Method Scott Stransky Programmng n conjuncton wth: Bors Cukalovc 18.413 Fnal Project Sprng 2004 Page 1 Abstract
More informationLearning the Kernel Parameters in Kernel Minimum Distance Classifier
Learnng the Kernel Parameters n Kernel Mnmum Dstance Classfer Daoqang Zhang 1,, Songcan Chen and Zh-Hua Zhou 1* 1 Natonal Laboratory for Novel Software Technology Nanjng Unversty, Nanjng 193, Chna Department
More informationSupport Vector Machines
Support Vector Machnes Decson surface s a hyperplane (lne n 2D) n feature space (smlar to the Perceptron) Arguably, the most mportant recent dscovery n machne learnng In a nutshell: map the data to a predetermned
More informationFeedback Min-Max Model Predictive Control Based on a Quadratic Cost Function
Proceedngs of the 26 Amercan Control Conference Mnneapols, Mnnesota, USA, June 14-16, 26 WeC5.5 Feedback Mn-Max Model Predctve Control Based on a Quadratc Cost Functon D. Muñoz de la Peña,T.Alamo, A. Bemporad
More informationSubspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points;
Subspace clusterng Clusterng Fundamental to all clusterng technques s the choce of dstance measure between data ponts; D q ( ) ( ) 2 x x = x x, j k = 1 k jk Squared Eucldean dstance Assumpton: All features
More information11. APPROXIMATION ALGORITHMS
Copng wth NP-completeness 11. APPROXIMATION ALGORITHMS load balancng center selecton prcng method: vertex cover LP roundng: vertex cover generalzed load balancng knapsack problem Q. Suppose I need to solve
More informationCost-efficient deployment of distributed software services
1/30 Cost-effcent deployment of dstrbuted software servces csorba@tem.ntnu.no 2/30 Short ntroducton & contents Cost-effcent deployment of dstrbuted software servces Cost functons Bo-nspred decentralzed
More informationAssignment # 2. Farrukh Jabeen Algorithms 510 Assignment #2 Due Date: June 15, 2009.
Farrukh Jabeen Algorthms 51 Assgnment #2 Due Date: June 15, 29. Assgnment # 2 Chapter 3 Dscrete Fourer Transforms Implement the FFT for the DFT. Descrbed n sectons 3.1 and 3.2. Delverables: 1. Concse descrpton
More informationTPL-Aware Displacement-driven Detailed Placement Refinement with Coloring Constraints
TPL-ware Dsplacement-drven Detaled Placement Refnement wth Colorng Constrants Tao Ln Iowa State Unversty tln@astate.edu Chrs Chu Iowa State Unversty cnchu@astate.edu BSTRCT To mnmze the effect of process
More informationUNIT 2 : INEQUALITIES AND CONVEX SETS
UNT 2 : NEQUALTES AND CONVEX SETS ' Structure 2. ntroducton Objectves, nequaltes and ther Graphs Convex Sets and ther Geometry Noton of Convex Sets Extreme Ponts of Convex Set Hyper Planes and Half Spaces
More informationLU Decomposition Method Jamie Trahan, Autar Kaw, Kevin Martin University of South Florida United States of America
nbm_sle_sm_ludecomp.nb 1 LU Decomposton Method Jame Trahan, Autar Kaw, Kevn Martn Unverst of South Florda Unted States of Amerca aw@eng.usf.edu nbm_sle_sm_ludecomp.nb 2 Introducton When solvng multple
More informationPositive Semi-definite Programming Localization in Wireless Sensor Networks
Postve Sem-defnte Programmng Localzaton n Wreless Sensor etworks Shengdong Xe 1,, Jn Wang, Aqun Hu 1, Yunl Gu, Jang Xu, 1 School of Informaton Scence and Engneerng, Southeast Unversty, 10096, anjng Computer
More informationA NOTE ON FUZZY CLOSURE OF A FUZZY SET
(JPMNT) Journal of Process Management New Technologes, Internatonal A NOTE ON FUZZY CLOSURE OF A FUZZY SET Bhmraj Basumatary Department of Mathematcal Scences, Bodoland Unversty, Kokrajhar, Assam, Inda,
More informationA CLASS OF TRANSFORMED EFFICIENT RATIO ESTIMATORS OF FINITE POPULATION MEAN. Department of Statistics, Islamia College, Peshawar, Pakistan 2
Pa. J. Statst. 5 Vol. 3(4), 353-36 A CLASS OF TRANSFORMED EFFICIENT RATIO ESTIMATORS OF FINITE POPULATION MEAN Sajjad Ahmad Khan, Hameed Al, Sadaf Manzoor and Alamgr Department of Statstcs, Islama College,
More informationLecture 5: Multilayer Perceptrons
Lecture 5: Multlayer Perceptrons Roger Grosse 1 Introducton So far, we ve only talked about lnear models: lnear regresson and lnear bnary classfers. We noted that there are functons that can t be represented
More informationAn Efficient Algorithm for Minimum Vertex Cover Problem
An Effcent Algorthm for Mnmum Vertex Cover Problem Rong Long Wang Zheng Tang Xn Shun Xu Member Non-member Non-member Paper An effcent parallel algorthm for solvng the mnmum vertex cover problem usng bnary
More informationModule Management Tool in Software Development Organizations
Journal of Computer Scence (5): 8-, 7 ISSN 59-66 7 Scence Publcatons Management Tool n Software Development Organzatons Ahmad A. Al-Rababah and Mohammad A. Al-Rababah Faculty of IT, Al-Ahlyyah Amman Unversty,
More informationSequential search. Building Java Programs Chapter 13. Sequential search. Sequential search
Sequental search Buldng Java Programs Chapter 13 Searchng and Sortng sequental search: Locates a target value n an array/lst by examnng each element from start to fnsh. How many elements wll t need to
More informationBiostatistics 615/815
The E-M Algorthm Bostatstcs 615/815 Lecture 17 Last Lecture: The Smplex Method General method for optmzaton Makes few assumptons about functon Crawls towards mnmum Some recommendatons Multple startng ponts
More informationMIXED INTEGER-DISCRETE-CONTINUOUS OPTIMIZATION BY DIFFERENTIAL EVOLUTION Part 1: the optimization method
MIED INTEGER-DISCRETE-CONTINUOUS OPTIMIZATION BY DIFFERENTIAL EVOLUTION Part : the optmzaton method Joun Lampnen Unversty of Vaasa Department of Informaton Technology and Producton Economcs P. O. Box 700
More informationStudy of key algorithms in topology optimization
Int J Adv Manuf Technol (2007) 32: 787 796 DOI 101007/s00170-005-0387-0 ORIGINAL ARTICLE Kong-Tan Zuo L-Png Chen Yun-Qng Zhang Jngzhou Yang Study of key algorthms n topology optmzaton Receved: 30 Aprl
More informationFast Computation of Shortest Path for Visiting Segments in the Plane
Send Orders for Reprnts to reprnts@benthamscence.ae 4 The Open Cybernetcs & Systemcs Journal, 04, 8, 4-9 Open Access Fast Computaton of Shortest Path for Vstng Segments n the Plane Ljuan Wang,, Bo Jang
More informationMulticriteria Decision Making
Multcrtera Decson Makng Andrés Ramos (Andres.Ramos@comllas.edu) Pedro Sánchez (Pedro.Sanchez@comllas.edu) Sonja Wogrn (Sonja.Wogrn@comllas.edu) Contents 1. Basc concepts 2. Contnuous methods 3. Dscrete
More informationAn Application of LFP Method for Sintering Ore Ratio
An Applcaton of LFP Method for Snterng Ore Rato X Cheng, Kalng Pan, and Yunfeng Ma School of Management, Wuhan Unversty of Scence and Technology, P.R.Chna, 408 suxn49@63.com Abstract. The proper rato decson
More informationS1 Note. Basis functions.
S1 Note. Bass functons. Contents Types of bass functons...1 The Fourer bass...2 B-splne bass...3 Power and type I error rates wth dfferent numbers of bass functons...4 Table S1. Smulaton results of type
More informationOutline. Type of Machine Learning. Examples of Application. Unsupervised Learning
Outlne Artfcal Intellgence and ts applcatons Lecture 8 Unsupervsed Learnng Professor Danel Yeung danyeung@eee.org Dr. Patrck Chan patrckchan@eee.org South Chna Unversty of Technology, Chna Introducton
More informationCS1100 Introduction to Programming
Factoral (n) Recursve Program fact(n) = n*fact(n-) CS00 Introducton to Programmng Recurson and Sortng Madhu Mutyam Department of Computer Scence and Engneerng Indan Insttute of Technology Madras nt fact
More informationAn Efficient Genetic Algorithm with Fuzzy c-means Clustering for Traveling Salesman Problem
An Effcent Genetc Algorthm wth Fuzzy c-means Clusterng for Travelng Salesman Problem Jong-Won Yoon and Sung-Bae Cho Dept. of Computer Scence Yonse Unversty Seoul, Korea jwyoon@sclab.yonse.ac.r, sbcho@cs.yonse.ac.r
More informationAssembler. Building a Modern Computer From First Principles.
Assembler Buldng a Modern Computer From Frst Prncples www.nand2tetrs.org Elements of Computng Systems, Nsan & Schocken, MIT Press, www.nand2tetrs.org, Chapter 6: Assembler slde Where we are at: Human Thought
More informationTsinghua University at TAC 2009: Summarizing Multi-documents by Information Distance
Tsnghua Unversty at TAC 2009: Summarzng Mult-documents by Informaton Dstance Chong Long, Mnle Huang, Xaoyan Zhu State Key Laboratory of Intellgent Technology and Systems, Tsnghua Natonal Laboratory for
More informationComparing High-Order Boolean Features
Brgham Young Unversty BYU cholarsarchve All Faculty Publcatons 2005-07-0 Comparng Hgh-Order Boolean Features Adam Drake adam_drake@yahoo.com Dan A. Ventura ventura@cs.byu.edu Follow ths and addtonal works
More informationA Fast Visual Tracking Algorithm Based on Circle Pixels Matching
A Fast Vsual Trackng Algorthm Based on Crcle Pxels Matchng Zhqang Hou hou_zhq@sohu.com Chongzhao Han czhan@mal.xjtu.edu.cn Ln Zheng Abstract: A fast vsual trackng algorthm based on crcle pxels matchng
More informationChapter 6 Programmng the fnte element method Inow turn to the man subject of ths book: The mplementaton of the fnte element algorthm n computer programs. In order to make my dscusson as straghtforward
More informationConditional Speculative Decimal Addition*
Condtonal Speculatve Decmal Addton Alvaro Vazquez and Elsardo Antelo Dep. of Electronc and Computer Engneerng Unv. of Santago de Compostela, Span Ths work was supported n part by Xunta de Galca under grant
More informationProgramming Assignment Six. Semester Calendar. 1D Excel Worksheet Arrays. Review VBA Arrays from Excel. Programming Assignment Six May 2, 2017
Programmng Assgnment Sx, 07 Programmng Assgnment Sx Larry Caretto Mechancal Engneerng 09 Computer Programmng for Mechancal Engneers Outlne Practce quz for actual quz on Thursday Revew approach dscussed
More informationProgramming in Fortran 90 : 2017/2018
Programmng n Fortran 90 : 2017/2018 Programmng n Fortran 90 : 2017/2018 Exercse 1 : Evaluaton of functon dependng on nput Wrte a program who evaluate the functon f (x,y) for any two user specfed values
More informationMathematics 256 a course in differential equations for engineering students
Mathematcs 56 a course n dfferental equatons for engneerng students Chapter 5. More effcent methods of numercal soluton Euler s method s qute neffcent. Because the error s essentally proportonal to the
More informationLecture 13: High-dimensional Images
Lec : Hgh-dmensonal Images Grayscale Images Lecture : Hgh-dmensonal Images Math 90 Prof. Todd Wttman The Ctadel A grayscale mage s an nteger-valued D matrx. An 8-bt mage takes on values between 0 and 55.
More informationThe Methods of Maximum Flow and Minimum Cost Flow Finding in Fuzzy Network
The Methods of Mamum Flow and Mnmum Cost Flow Fndng n Fuzzy Network Aleandr Bozhenyuk, Evgenya Gerasmenko, and Igor Rozenberg 2 Southern Federal Unversty, Taganrog, Russa AVB002@yande.ru, e.rogushna@gmal.com
More informationINTEGER PROGRAMMING MODELING FOR THE CHINESE POSTMAN PROBLEMS
INTEGER PROGRAMMING MODELING FOR THE CHINESE POSTMAN PROBLEMS ABSTRACT Feng Junwen School of Economcs and Management, Nanng Unversty of Scence and Technology, Nanng, 2009, Chna As far as the tradtonal
More informationSolitary and Traveling Wave Solutions to a Model. of Long Range Diffusion Involving Flux with. Stability Analysis
Internatonal Mathematcal Forum, Vol. 6,, no. 7, 8 Soltary and Travelng Wave Solutons to a Model of Long Range ffuson Involvng Flux wth Stablty Analyss Manar A. Al-Qudah Math epartment, Rabgh Faculty of
More informationA Saturation Binary Neural Network for Crossbar Switching Problem
A Saturaton Bnary Neural Network for Crossbar Swtchng Problem Cu Zhang 1, L-Qng Zhao 2, and Rong-Long Wang 2 1 Department of Autocontrol, Laonng Insttute of Scence and Technology, Benx, Chna bxlkyzhangcu@163.com
More informationAn Indian Journal FULL PAPER ABSTRACT KEYWORDS. Trade Science Inc.
[Type text] [Type text] [Type text] ISSN : 97-735 Volume Issue 9 BoTechnology An Indan Journal FULL PAPER BTAIJ, (9), [333-3] Matlab mult-dmensonal model-based - 3 Chnese football assocaton super league
More informationNumerical model describing optimization of fibres winding process on open and closed frame
Journal of Physcs: Conference Seres PAPER OPEN ACCESS Numercal model descrbng optmzaton of fbres wndng process on open and closed frame To cte ths artcle: M Petr et al 06 J Phys: Conf Ser 738 0094 Vew
More informationComplex Numbers. Now we also saw that if a and b were both positive then ab = a b. For a second let s forget that restriction and do the following.
Complex Numbers The last topc n ths secton s not really related to most of what we ve done n ths chapter, although t s somewhat related to the radcals secton as we wll see. We also won t need the materal
More informationModeling, Manipulating, and Visualizing Continuous Volumetric Data: A Novel Spline-based Approach
Modelng, Manpulatng, and Vsualzng Contnuous Volumetrc Data: A Novel Splne-based Approach Jng Hua Center for Vsual Computng, Department of Computer Scence SUNY at Stony Brook Talk Outlne Introducton and
More informationLOOP ANALYSIS. The second systematic technique to determine all currents and voltages in a circuit
LOOP ANALYSS The second systematic technique to determine all currents and voltages in a circuit T S DUAL TO NODE ANALYSS - T FRST DETERMNES ALL CURRENTS N A CRCUT AND THEN T USES OHM S LAW TO COMPUTE
More informationAPPLICATION OF IMPROVED K-MEANS ALGORITHM IN THE DELIVERY LOCATION
An Open Access, Onlne Internatonal Journal Avalable at http://www.cbtech.org/pms.htm 2016 Vol. 6 (2) Aprl-June, pp. 11-17/Sh Research Artcle APPLICATION OF IMPROVED K-MEANS ALGORITHM IN THE DELIVERY LOCATION
More informationHigh-Boost Mesh Filtering for 3-D Shape Enhancement
Hgh-Boost Mesh Flterng for 3-D Shape Enhancement Hrokazu Yagou Λ Alexander Belyaev y Damng We z Λ y z ; ; Shape Modelng Laboratory, Unversty of Azu, Azu-Wakamatsu 965-8580 Japan y Computer Graphcs Group,
More informationLecture #15 Lecture Notes
Lecture #15 Lecture Notes The ocean water column s very much a 3-D spatal entt and we need to represent that structure n an economcal way to deal wth t n calculatons. We wll dscuss one way to do so, emprcal
More informationClustering on antimatroids and convex geometries
Clusterng on antmatrods and convex geometres YULIA KEMPNER 1, ILYA MUCNIK 2 1 Department of Computer cence olon Academc Insttute of Technology 52 Golomb tr., P.O. Box 305, olon 58102 IRAEL 2 Department
More informationAn Accurate Evaluation of Integrals in Convex and Non convex Polygonal Domain by Twelve Node Quadrilateral Finite Element Method
Internatonal Journal of Computatonal and Appled Mathematcs. ISSN 89-4966 Volume, Number (07), pp. 33-4 Research Inda Publcatons http://www.rpublcaton.com An Accurate Evaluaton of Integrals n Convex and
More informationA mathematical programming approach to the analysis, design and scheduling of offshore oilfields
17 th European Symposum on Computer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edtors) 2007 Elsever B.V. All rghts reserved. 1 A mathematcal programmng approach to the analyss, desgn and
More informationRelated-Mode Attacks on CTR Encryption Mode
Internatonal Journal of Network Securty, Vol.4, No.3, PP.282 287, May 2007 282 Related-Mode Attacks on CTR Encrypton Mode Dayn Wang, Dongda Ln, and Wenlng Wu (Correspondng author: Dayn Wang) Key Laboratory
More informationMILP. LP: max cx ' MILP: some integer. ILP: x integer BLP: x 0,1. x 1. x 2 2 2, c ,
MILP LP: max cx ' s.t. Ax b x 0 MILP: some nteger x max 6x 8x s.t. x x x 7 x, x 0 c A 6 8, 0 b 7 ILP: x nteger BLP: x 0, x 4 x, cx * * 0 4 5 6 x 06 Branch and Bound x 4 0 max 6x 8x s.t. xx x 7 x, x 0 x,
More informationA Simple and Efficient Goal Programming Model for Computing of Fuzzy Linear Regression Parameters with Considering Outliers
62626262621 Journal of Uncertan Systems Vol.5, No.1, pp.62-71, 211 Onlne at: www.us.org.u A Smple and Effcent Goal Programmng Model for Computng of Fuzzy Lnear Regresson Parameters wth Consderng Outlers
More informationHermite Splines in Lie Groups as Products of Geodesics
Hermte Splnes n Le Groups as Products of Geodescs Ethan Eade Updated May 28, 2017 1 Introducton 1.1 Goal Ths document defnes a curve n the Le group G parametrzed by tme and by structural parameters n the
More informationA fast algorithm for color image segmentation
Unersty of Wollongong Research Onlne Faculty of Informatcs - Papers (Arche) Faculty of Engneerng and Informaton Scences 006 A fast algorthm for color mage segmentaton L. Dong Unersty of Wollongong, lju@uow.edu.au
More information