LARRY SNYDER DEPT. OF INDUSTRIAL AND SYSTEMS ENGINEERING CENTER FOR VALUE CHAIN RESEARCH LEHIGH UNIVERSITY

Size: px
Start display at page:

Download "LARRY SNYDER DEPT. OF INDUSTRIAL AND SYSTEMS ENGINEERING CENTER FOR VALUE CHAIN RESEARCH LEHIGH UNIVERSITY"

Transcription

1 Faclty Locaton Models: An Overvew 1 LARRY SNYDER DEPT. OF INDUSTRIAL AND SYSTEMS ENGINEERING CENTER FOR VALUE CHAIN RESEARCH LEHIGH UNIVERSITY EWO SEMINAR SERIES APRIL 21, 2010

2 Outlne Introducton Taxonomy of locaton models IP formulatons for some classcal models Algorthms Extensons Faclty locaton / network desgn software 2

3 Introducton 3

4 Overvew Decde where to locate facltes (factores / warehouses / DCs / retal outlets / etc.) To serve customers In order to acheve some balance between Cost Servce 4

5 Decsons Usually 2 decsons to make: Where to locate? Whch customers are assgned/allocated to whch facltes? Sometmes referred to as locaton allocaton models 5

6 Applcatons of Faclty Locaton Models Wdely appled n publc and prvate sectors: Emergency medcal servces (EMS) / fre statons Arlne hubs Blood banks Hazardous waste dsposal stes Fast-food restaurants Publc swmmng pools Schools Vehcle nspecton statons Bus stops etc. 6

7 Uses for Faclty Locaton Models Also appled to vrtual facltes : Wldlfe reserves Satellte orbts Apparel szes Flexble manufacturng system tool selecton Locaton of bank accounts Poltcal l party platforms Product postonng etc. Sometmes arse as subproblems for other OR problems Vehcle routng 7

8 Taxonomy of Locaton Models 8

9 Topology 9 Contnuous Dscrete Network Locate anywhere on plane Contnuous, non-lnear optmzaton Weber problem Locate at pre-defned ponts Integer programmng We ll consder dscrete problems (Network problems are a specal case) Locate anywhere on network Travel along arcs Integer programmng Hakm property: Optmal to locate at nodes Holds for some (not all) problems

10 Dstance Metrc 2 2 Eucldean: ( x y 10 1 x2) + ( y1 2) Rectlnear / Manhattan: x1 x2 + y1 y2 (travel along streets) Great crcle: accounts for Earth s curvature Hghway / network: shortest path wthn network (e.g., U.S. hghway network) Matrx: dstance between each par gven explctly For sake of generalty, we ll assume matrx dstances Also, dstance = transportaton cost

11 Dstance Obectve Total dstance: total dstance between customers and ther assgned facltes (dstance s usually demand-weghted) 11 dstance to assgned faclty customers Maxmum dstance: maxmum dstance between a customer and ts assgned faclty (dstance s usually unweghted) max customers {dstance to assgned faclty} Coverage: cust. s covered f dstance specfed radus Can appear n obectve functon or constrants

12 Preventng Too Many Facltes Fxed cost: fxed (annual) cost to open/operate p faclty 12 Represents constructon / leasng cost + overhead (lghts, heat, securty, etc.) Independent of volume of demand served by faclty Restrcton on # facltes: requre # of facltes P Restrcton on # facltes: requre # of facltes P n constrants

13 Classcal Models P-medan problem: mnmze demand-weghted dstance s.t. locate P facltes Uncapactated fxed-charge locaton problem (UFLP): 13 mnmze fxed cost + DWD P-center problem: mnmze maxmum dstance s.t. locate P facltes Set coverng locaton problem (SCLP): mnmze # of facltes s.t. cover all customers Maxmum coverng locaton problem (MCLP): maxmze covered demands s.t. locate P facltes

14 Capacty Most models also have a capactated verson Facltes have fxed throughput capacty Capacty s usually an nput But sometmes a decson varable 14 Dscrete choces (50,000 sq ft / 100,000 sq ft / 200,000 sq ft) Contnuous varable (cost s a functon of capacty)

15 IP Formulatons for Some Classcal Models 15

16 Sets I = {customers} J = {potental faclty stes} Parameters Notaton h = annual demand of customer I c = cost to transport one unt from J to I f = fxed (annual) cost to open a faclty at ste J Decson varables x = 1 f faclty J s opened, 0 otherwse y = 1 f faclty J serves customer I, 0 otherwse 16

17 P-Medan Formulaton 17 mn I s.t. J J J y h c y = 1 y x, x = P x {0,1} y {0,1}, Mn demand-weghted dstance (transportaton cost) Satsfy all demands Don t assgn cust to closed faclty Locate P facltes Integralty

18 UFLP Formulaton 18 mn s.t. J J y y x f x = 1 x + {0,1} I J, y { {0,1}, h c y Mn fxed + transportaton cost Satsfy all demands Don t assgn cust to closed faclty Integralty

19 Maxmal Coverng Formulaton 19 max s.t. I J x h z z x = P V x z {0,1} Maxmze covered demand Locate P facltes { 0,1} Integralty Defnton of coverage where V = set of facltes that can cover customer z = 1 f customer s covered, 0 otherwse

20 Algorthms 20

21 Algorthms Most faclty locaton problems are NP-hard But many classcal problems are easy computatonally LP relaxatons are often extremely tght Sometmes nteger solutons for free V t ll t f l th f d t Vrtually every type of algorthm for dscrete optmzaton has been appled to faclty locaton 21

22 Heurstcs: Greedy add/drop Swap Neghborhood search Metaheurstcs Algorthms Genetc algorthms, tabu search, varable neghborhood search, smulated annealng, ant algorthms, bee algorthms, Exact Algorthms: Branch and bound Cuttng gplanes Benders decomposton Column generaton / Dantzg-Wolfe decomposton Lagrangan a g a relaxaton ea ato 22

23 Lagrangan Relaxaton for P-Medan 23 I J y h c mn x y y J, 1 s.t. = RELAX P x y J, = y x, {0,1} {0,1}

24 Lagrangan Subproblem 24 + I J I J y y c h λ 1 mn x y, s.t. + = I I J y c h λ λ ) ( P x y J, = y x, {0,1} {0,1}

25 Faclty- Subproblem Subproblem s separable by Suppose we open ; need to solve Easy solve by nspecton: Would set y = 1 ff h c λ < 0 Beneft of openng s Open P facltes wth smallest β β = I 25 mn{ 0,h c λ } Ths gves lower bound Obtan upper bound from heurstc Update λ and repeat mn I y ( h c st s.t. y {0,1} λ ) y

26 Extensons 26

27 Obnoxous facltes Other Flavors 27 Obnoxous locaton: Maxmze dstance from facltes to customers Dsperson: Maxmze dstance among facltes Compettve locaton Multple players try to capture demand by locatng facltes Mult-obectve models Account for multple stakeholders obectves Hub locaton Flows from facltes to customers but also among facltes Quadratc obectve Dynamc locaton Facltes are located over tme, or move over tme

28 Types of randomness: Uncertanty Demand-sde: Randomness n demands, costs, etc. Supply-sde: Randomness n supply (e.g., dsruptons) 28 Approaches to uncertanty: Stochastc programmng: mn expected cost Robust optmzaton: mnmax cost, mnmax regret, CVaR, etc. Modelng approaches: Scenaro formulatons Interval uncertanty

29 Integrated Models Incorporate tactcal / operatonal costs nto strategc (faclty locaton) decsons Inventory Routng Integrated locaton-nventory model Daskn, Coullard, and Shen (Ann OR, 2002) Obectve functon ncludes two concave terms: Inventory economes of scale (EOQ) Rsk poolng (safety stock) Constrants are same as UFLP Solve va Lagrangan relaxaton Subproblem solved n O( I log I ) tme for each (UFLP: O( I ) tme for each ) 29

30 Network Desgn Mult-echelon faclty locaton models Make open/close decsons for multple ters 30 Geoffron and Graves (MS, 1974) Generalzaton: network desgn problems Usually locate arcs n the network But locatng nodes s equvalent Rch lterature on network desgn e.g., g, Magnant and Wong g( (TS, 1984)

31 Faclty Locaton / Network Desgn Software 31

32 LogcNet / LogcNet Plus Orgnally LogcTools Software Packages 32 Now ILOG Supply Chan Applcatons, part of IBM Consultng SAILS INSIGHT SAP, Oracle modules

33 Key decsons: Capabltes Faclty locatons, capactes, capabltes, volumes Dstrbuton lanes (yes/no, volumes) Make vs. buy Key features: Data mport Output report export GUI, GIS Optmzaton solver Ratng engne What-f scenaros 33

34 New features: Green Rsk management Taxes Seasonalty Cost vs. servce level tradeoffs Recent Developments Thngs most current software can t do (very well): Non-lneartes (e.g., quantty dscounts) Open/close decsons on arcs for larger models Close ntegraton wth nventory modelng Uncertanty Optmzaton under multple scenaros Rsk-averse obectves 34

35 Further Readng Textbooks on faclty locaton Daskn (1995) Drezner (1995) Drezner and Hamacher (2001) Revew artcles / book chapters 35 Dscrete locaton: Current, Daskn, and Schllng (D&H book, 2001) Contnuous locaton: Drezner, et al. (D&H book, 2001) Stochastc locaton: Snyder (IIE Trans, 2006) Locaton wth dsruptons: Snyder, et al. (INFORMS Tutoral, 2006) Locaton-nventory nventory models: Shen (JIMO, 2007)

36 Questons? 36 LARRY. EDU

MILP. LP: max cx ' MILP: some integer. ILP: x integer BLP: x 0,1. x 1. x 2 2 2, c ,

MILP. 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 information

Kent State University CS 4/ Design and Analysis of Algorithms. Dept. of Math & Computer Science LECT-16. Dynamic Programming

Kent 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 information

The Greedy Method. Outline and Reading. Change Money Problem. Greedy Algorithms. Applications of the Greedy Strategy. The Greedy Method Technique

The 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 information

GSLM Operations Research II Fall 13/14

GSLM 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 information

A mathematical programming approach to the analysis, design and scheduling of offshore oilfields

A 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 information

TWO STAGE FACILITY LOCATION PROBLEM: LAGRANGIAN BASED HEURISTICS

TWO STAGE FACILITY LOCATION PROBLEM: LAGRANGIAN BASED HEURISTICS TWO STAGE FACILITY LOCATION PROBLEM: LAGRANGIAN BASED HEURISTICS Igor Ltvnchev Nuevo Leon State Unversty Monterrey, Méxco gor@yalma.fme.uanl.mx Mguel Mata Pérez Nuevo Leon State Unversty Monterrey, Méxco

More information

11. APPROXIMATION ALGORITHMS

11. 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 information

Smoothing Spline ANOVA for variable screening

Smoothing 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 information

UC Berkeley Working Papers

UC Berkeley Working Papers UC Berkeley Workng Papers Ttle Dscretzaton and Valdaton of the Contnuum Approxmaton Scheme for Termnal System Desgn Permalnk https://escholarshp.org/uc/tem/9dm7v0cn Authors Ouyang, Yanfeng Daganzo, Carlos

More information

Cost-efficient deployment of distributed software services

Cost-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 information

LECTURE : MANIFOLD LEARNING

LECTURE : MANIFOLD LEARNING LECTURE : MANIFOLD LEARNING Rta Osadchy Some sldes are due to L.Saul, V. C. Raykar, N. Verma Topcs PCA MDS IsoMap LLE EgenMaps Done! Dmensonalty Reducton Data representaton Inputs are real-valued vectors

More information

An Iterative Solution Approach to Process Plant Layout using Mixed Integer Optimisation

An 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 information

5 The Primal-Dual Method

5 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 information

General Share-A-Ride Problem

General Share-A-Ride Problem General Share-A-Rde Problem Sesya Sr Purwant Department of Industral Engneerng, Insttut Tenolog Bandung, Bandung, Indonesa Department of Industral Management, Natonal Tawan Unversty of Scence and Technology,

More information

Machine Learning. Support Vector Machines. (contains material adapted from talks by Constantin F. Aliferis & Ioannis Tsamardinos, and Martin Law)

Machine Learning. Support Vector Machines. (contains material adapted from talks by Constantin F. Aliferis & Ioannis Tsamardinos, and Martin Law) Machne Learnng Support Vector Machnes (contans materal adapted from talks by Constantn F. Alfers & Ioanns Tsamardnos, and Martn Law) Bryan Pardo, Machne Learnng: EECS 349 Fall 2014 Support Vector Machnes

More information

Support Vector Machines

Support 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 information

Introduction to linear programming

Introduction to linear programming Introducton to lnear programmng Overvew Lnear programmng Mathematcal and lnear programs Lnear programmng and resoluton methods; Modelng n (nteger) lnear programmng; Schedulng problems; Optmzaton problems

More information

6.854 Advanced Algorithms Petar Maymounkov Problem Set 11 (November 23, 2005) With: Benjamin Rossman, Oren Weimann, and Pouya Kheradpour

6.854 Advanced Algorithms Petar Maymounkov Problem Set 11 (November 23, 2005) With: Benjamin Rossman, Oren Weimann, and Pouya Kheradpour 6.854 Advanced Algorthms Petar Maymounkov Problem Set 11 (November 23, 2005) Wth: Benjamn Rossman, Oren Wemann, and Pouya Kheradpour Problem 1. We reduce vertex cover to MAX-SAT wth weghts, such that the

More information

LP Rounding for k-centers with Non-uniform Hard Capacities

LP Rounding for k-centers with Non-uniform Hard Capacities LP Roundng for k-centers wth Non-unform Hard Capactes (Extended Abstract) Marek Cygan, MohammadTagh Hajaghay, Samr Khuller IDSIA, Unversty of Lugano, Swtzerland. Emal: marek@dsa.ch Department of Computer

More information

Course Introduction. Algorithm 8/31/2017. COSC 320 Advanced Data Structures and Algorithms. COSC 320 Advanced Data Structures and Algorithms

Course 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 information

Meta-heuristics for Multidimensional Knapsack Problems

Meta-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 information

Programming in Fortran 90 : 2017/2018

Programming 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 information

Uncertain Supply Chain Management

Uncertain Supply Chain Management Uncertan Supply Chan Management 5 (2017) 337 358 Contents lsts avalable at GrowngScence Uncertan Supply Chan Management homepage: www.growngscence.com/uscm Developng a locaton-nventory-routng model usng

More information

Greedy Technique - Definition

Greedy Technique - Definition Greedy Technque Greedy Technque - Defnton The greedy method s a general algorthm desgn paradgm, bult on the follong elements: confguratons: dfferent choces, collectons, or values to fnd objectve functon:

More information

Solving two-person zero-sum game by Matlab

Solving two-person zero-sum game by Matlab Appled Mechancs and Materals Onlne: 2011-02-02 ISSN: 1662-7482, Vols. 50-51, pp 262-265 do:10.4028/www.scentfc.net/amm.50-51.262 2011 Trans Tech Publcatons, Swtzerland Solvng two-person zero-sum game by

More information

Ecient Computation of the Most Probable Motion from Fuzzy. Moshe Ben-Ezra Shmuel Peleg Michael Werman. The Hebrew University of Jerusalem

Ecient Computation of the Most Probable Motion from Fuzzy. Moshe Ben-Ezra Shmuel Peleg Michael Werman. The Hebrew University of Jerusalem Ecent Computaton of the Most Probable Moton from Fuzzy Correspondences Moshe Ben-Ezra Shmuel Peleg Mchael Werman Insttute of Computer Scence The Hebrew Unversty of Jerusalem 91904 Jerusalem, Israel Emal:

More information

Support Vector Machines

Support 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 information

Hermite Splines in Lie Groups as Products of Geodesics

Hermite 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 information

CS 534: Computer Vision Model Fitting

CS 534: Computer Vision Model Fitting CS 534: Computer Vson Model Fttng Sprng 004 Ahmed Elgammal Dept of Computer Scence CS 534 Model Fttng - 1 Outlnes Model fttng s mportant Least-squares fttng Maxmum lkelhood estmaton MAP estmaton Robust

More information

Control strategies for network efficiency and resilience with route choice

Control strategies for network efficiency and resilience with route choice Control strateges for networ effcency and reslence wth route choce Andy Chow Ru Sha Centre for Transport Studes Unversty College London, UK Centralsed strateges UK 1 Centralsed strateges Some effectve

More information

UNCAPACITATED FACILITY LOCATION PROBLEMS: CONTRIBUTIONS

UNCAPACITATED FACILITY LOCATION PROBLEMS: CONTRIBUTIONS versão mpressa ISSN 0101-7438 / versão onlne ISSN 1678-5142 UNCAPACITATED FACILITY LOCATION PROBLEMS: CONTRIBUTIONS Roberto Déguez Galvão Programa de Engenhara de Produção / COPPE Unversdade Federal do

More information

LECTURE NOTES Duality Theory, Sensitivity Analysis, and Parametric Programming

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 information

A Fuzzy Goal Programming Approach for a Single Machine Scheduling Problem

A Fuzzy Goal Programming Approach for a Single Machine Scheduling Problem Proceedngs of e 9 WSEAS Internatonal Conference on Appled Maematcs, Istanbul, Turkey, May 7-9, 006 (pp40-45 A Fuzzy Goal Programmng Approach for a Sngle Machne Schedulng Problem REZA TAVAKKOLI-MOGHADDAM,

More information

Needed Information to do Allocation

Needed Information to do Allocation Complexty n the Database Allocaton Desgn Must tae relatonshp between fragments nto account Cost of ntegrty enforcements Constrants on response-tme, storage, and processng capablty Needed Informaton to

More information

People have been thinking about network problems for a long time Koenigsberg Bridge problem (Euler, 1736)

People have been thinking about network problems for a long time Koenigsberg Bridge problem (Euler, 1736) Networks People have been thnkng about network problems for a long tme Koengsberg Brdge problem (Euler, 1736) Can you cross all 7 brdges exactly once on a walk? Lesson 8-1, p. 1 Types of Network Flow Problems

More information

Efficient Load-Balanced IP Routing Scheme Based on Shortest Paths in Hose Model. Eiji Oki May 28, 2009 The University of Electro-Communications

Efficient 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 information

Review of approximation techniques

Review of approximation techniques CHAPTER 2 Revew of appromaton technques 2. Introducton Optmzaton problems n engneerng desgn are characterzed by the followng assocated features: the objectve functon and constrants are mplct functons evaluated

More information

TPL-Aware Displacement-driven Detailed Placement Refinement with Coloring Constraints

TPL-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 information

Support Vector Machines. CS534 - Machine Learning

Support 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 information

Classification / Regression Support Vector Machines

Classification / 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 information

NGPM -- A NSGA-II Program in Matlab

NGPM -- A NSGA-II Program in Matlab Verson 1.4 LIN Song Aerospace Structural Dynamcs Research Laboratory College of Astronautcs, Northwestern Polytechncal Unversty, Chna Emal: lsssswc@163.com 2011-07-26 Contents Contents... 1. Introducton...

More information

All-Pairs Shortest Paths. Approximate All-Pairs shortest paths Approximate distance oracles Spanners and Emulators. Uri Zwick Tel Aviv University

All-Pairs Shortest Paths. Approximate All-Pairs shortest paths Approximate distance oracles Spanners and Emulators. Uri Zwick Tel Aviv University Approxmate All-Pars shortest paths Approxmate dstance oracles Spanners and Emulators Ur Zwck Tel Avv Unversty Summer School on Shortest Paths (PATH05 DIKU, Unversty of Copenhagen All-Pars Shortest Paths

More information

INTRODUCTION INTRODUCTION. Moisès Graells Semi-continuous processes

INTRODUCTION INTRODUCTION. Moisès Graells Semi-continuous processes INTRODUCTION Mosès Graells (moses.graells@upc.edu) Barcelona / Catalona / Span Unverstat Poltècnca de Catalunya CEPIMA, PSE research group Emertus Prof. Lus Puganer IECR Specal Issue INTRODUCTION Sem-contnuous

More information

Compiler Design. Spring Register Allocation. Sample Exercises and Solutions. Prof. Pedro C. Diniz

Compiler 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 information

Range images. Range image registration. Examples of sampling patterns. Range images and range surfaces

Range 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 information

An Application of Network Simplex Method for Minimum Cost Flow Problems

An 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 information

Problem Definitions and Evaluation Criteria for Computational Expensive Optimization

Problem Definitions and Evaluation Criteria for Computational Expensive Optimization Problem efntons and Evaluaton Crtera for Computatonal Expensve Optmzaton B. Lu 1, Q. Chen and Q. Zhang 3, J. J. Lang 4, P. N. Suganthan, B. Y. Qu 6 1 epartment of Computng, Glyndwr Unversty, UK Faclty

More information

Concurrent Apriori Data Mining Algorithms

Concurrent Apriori Data Mining Algorithms Concurrent Apror Data Mnng Algorthms Vassl Halatchev Department of Electrcal Engneerng and Computer Scence York Unversty, Toronto October 8, 2015 Outlne Why t s mportant Introducton to Assocaton Rule Mnng

More information

A Facet Generation Procedure. for solving 0/1 integer programs

A 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 information

INTEGER PROGRAMMING MODELING FOR THE CHINESE POSTMAN PROBLEMS

INTEGER 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 information

Efficient Distributed File System (EDFS)

Efficient Distributed File System (EDFS) Effcent Dstrbuted Fle System (EDFS) (Sem-Centralzed) Debessay(Debsh) Fesehaye, Rahul Malk & Klara Naherstedt Unversty of Illnos-Urbana Champagn Contents Problem Statement, Related Work, EDFS Desgn Rate

More information

Air Transport Demand. Ta-Hui Yang Associate Professor Department of Logistics Management National Kaohsiung First Univ. of Sci. & Tech.

Air Transport Demand. Ta-Hui Yang Associate Professor Department of Logistics Management National Kaohsiung First Univ. of Sci. & Tech. Ar Transport Demand Ta-Hu Yang Assocate Professor Department of Logstcs Management Natonal Kaohsung Frst Unv. of Sc. & Tech. 1 Ar Transport Demand Demand for ar transport between two ctes or two regons

More information

Innovation Typology. Collaborative Authoritativeness. Focused Web Mining. Text and Data Mining In Innovation. Generational Models

Innovation Typology. Collaborative Authoritativeness. Focused Web Mining. Text and Data Mining In Innovation. Generational Models Text and Data Mnng In Innovaton Joseph Engler Innovaton Typology Generatonal Models 1. Lnear or Push (Baroque) 2. Pull (Romantc) 3. Cyclc (Classcal) 4. Strategc (New Age) 5. Collaboratve (Polyphonc) Collaboratve

More information

Clustering on antimatroids and convex geometries

Clustering 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 information

COMPLEX METHODOLOGY FOR STUDY OF INTERCITY RAIL TRANSPORT

COMPLEX METHODOLOGY FOR STUDY OF INTERCITY RAIL TRANSPORT ENGINEERING FOR RURA DEVEOPMENT Jelgava 5.-7.05.06. COMPEX METHODOOGY FOR STUDY OF INTERCITY RAI TRANSPORT Svetla Stolova Radna Nkolova Techncal Unversty-Sofa Bulgara stolova@tu-sofa.bg r.nkolova@tu-sofa.bg

More information

A Min-Cost Flow Based Detailed Router for FPGAs

A Min-Cost Flow Based Detailed Router for FPGAs A Mn-Cost Flow Based Detaled Router for FPGAs eokn Lee Dept. of ECE The Unversty of Texas at Austn Austn, TX 78712 Yongseok Cheon Dept. of Computer cences The Unversty of Texas at Austn Austn, TX 78712

More information

Outline. Discriminative classifiers for image recognition. Where in the World? A nearest neighbor recognition example 4/14/2011. CS 376 Lecture 22 1

Outline. Discriminative classifiers for image recognition. Where in the World? A nearest neighbor recognition example 4/14/2011. CS 376 Lecture 22 1 4/14/011 Outlne Dscrmnatve classfers for mage recognton Wednesday, Aprl 13 Krsten Grauman UT-Austn Last tme: wndow-based generc obect detecton basc ppelne face detecton wth boostng as case study Today:

More information

A Novel Fuzzy Multi-Objective Method for Supplier Selection and Order Allocation Problem Using NSGA II

A Novel Fuzzy Multi-Objective Method for Supplier Selection and Order Allocation Problem Using NSGA II A Novel Fuzzy Mult-Objectve Method for Suppler Selecton and Order Allocaton Problem Usng NSGA II Mohammad Al Sobhanolah a, Ahmad Mahmoodzadeh *, Bahman Nader b Department of Industral Engneerng, Faculty

More information

XLVII SIMPÓSIO BRASILEIRO DE PESQUISA OPERACIONAL

XLVII SIMPÓSIO BRASILEIRO DE PESQUISA OPERACIONAL LP-BASED HEURISTIC FOR PACKING CIRCULAR-LIKE OBJECTS IN A RECTANGULAR CONTAINER Igor Ltvnchev Computng Center of Russan,Academy of Scences Moscow 119991, Vavlov 40, Russa gorltvnchev@gmal.com Lus Alfonso

More information

Sum of Linear and Fractional Multiobjective Programming Problem under Fuzzy Rules Constraints

Sum 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 information

Overview. Basic Setup [9] Motivation and Tasks. Modularization 2008/2/20 IMPROVED COVERAGE CONTROL USING ONLY LOCAL INFORMATION

Overview. Basic Setup [9] Motivation and Tasks. Modularization 2008/2/20 IMPROVED COVERAGE CONTROL USING ONLY LOCAL INFORMATION Overvew 2 IMPROVED COVERAGE CONTROL USING ONLY LOCAL INFORMATION Introducton Mult- Smulator MASIM Theoretcal Work and Smulaton Results Concluson Jay Wagenpfel, Adran Trachte Motvaton and Tasks Basc Setup

More information

Topology Design using LS-TaSC Version 2 and LS-DYNA

Topology Design using LS-TaSC Version 2 and LS-DYNA Topology Desgn usng LS-TaSC Verson 2 and LS-DYNA Wllem Roux Lvermore Software Technology Corporaton, Lvermore, CA, USA Abstract Ths paper gves an overvew of LS-TaSC verson 2, a topology optmzaton tool

More information

COMPARISON OF NON-SPLIT AND SPLIT DELIVERY STRATEGIES FOR THE HETEROGENEOUS VEHICLE ROUTING PROBLEM

COMPARISON OF NON-SPLIT AND SPLIT DELIVERY STRATEGIES FOR THE HETEROGENEOUS VEHICLE ROUTING PROBLEM Endüstr Mühendslð Dergs Clt: 18 Sayý: 4 Sayfa: (2-13) Mana Mühendsler Odasý COMPARISON OF NON-SPLIT AND SPLIT DELIVERY STRATEGIES FOR THE HETEROGENEOUS VEHICLE ROUTING PROBLEM Pınar MIZRAK ÖZFIRAT* 1,

More information

Outline. Self-Organizing Maps (SOM) US Hebbian Learning, Cntd. The learning rule is Hebbian like:

Outline. Self-Organizing Maps (SOM) US Hebbian Learning, Cntd. The learning rule is Hebbian like: Self-Organzng Maps (SOM) Turgay İBRİKÇİ, PhD. Outlne Introducton Structures of SOM SOM Archtecture Neghborhoods SOM Algorthm Examples Summary 1 2 Unsupervsed Hebban Learnng US Hebban Learnng, Cntd 3 A

More information

Session 5.3. Switching/Routing and Transmission planning

Session 5.3. Switching/Routing and Transmission planning ITU Regonal Semnar Belgrade Serba and Montenegro 20-24 24 June 2005 Sesson 5.3 Swtchng/Routng and Transmsson plannng volvng nfrastructures to NGN and related Plannng Strateges and Tools I.S. Sesson 5.3-1

More information

Hierarchical clustering for gene expression data analysis

Hierarchical clustering for gene expression data analysis Herarchcal clusterng for gene expresson data analyss Gorgo Valentn e-mal: valentn@ds.unm.t Clusterng of Mcroarray Data. Clusterng of gene expresson profles (rows) => dscovery of co-regulated and functonally

More information

Optimization Methods: Integer Programming Integer Linear Programming 1. Module 7 Lecture Notes 1. Integer Linear Programming

Optimization 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 information

U.C. Berkeley CS294: Beyond Worst-Case Analysis Handout 5 Luca Trevisan September 7, 2017

U.C. Berkeley CS294: Beyond Worst-Case Analysis Handout 5 Luca Trevisan September 7, 2017 U.C. Bereley CS294: Beyond Worst-Case Analyss Handout 5 Luca Trevsan September 7, 207 Scrbed by Haars Khan Last modfed 0/3/207 Lecture 5 In whch we study the SDP relaxaton of Max Cut n random graphs. Quc

More information

A HEURISTIC METHOD FOR RELIABILITY REDUNDANCY OPTIMIZATION OF FLOW NETWORKS

A HEURISTIC METHOD FOR RELIABILITY REDUNDANCY OPTIMIZATION OF FLOW NETWORKS Kumar Pardeep and Chaturved D.K., Pahua G.L. - A HEURISTIC METHOD FOR RELIABILITY REDUNDANCY OPTIMIZATION OF FLOW NETWORKS A HEURISTIC METHOD FOR RELIABILITY REDUNDANCY OPTIMIZATION OF FLOW NETWORKS Kumar

More information

A New Approach For the Ranking of Fuzzy Sets With Different Heights

A 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 information

MOBILE Cloud Computing (MCC) extends the capabilities

MOBILE Cloud Computing (MCC) extends the capabilities 1 Resource Sharng of a Computng Access Pont for Mult-user Moble Cloud Offloadng wth Delay Constrants Meng-Hs Chen, Student Member, IEEE, Mn Dong, Senor Member, IEEE, Ben Lang, Fellow, IEEE arxv:1712.00030v2

More information

Steps for Computing the Dissimilarity, Entropy, Herfindahl-Hirschman and. Accessibility (Gravity with Competition) Indices

Steps for Computing the Dissimilarity, Entropy, Herfindahl-Hirschman and. Accessibility (Gravity with Competition) Indices Steps for Computng the Dssmlarty, Entropy, Herfndahl-Hrschman and Accessblty (Gravty wth Competton) Indces I. Dssmlarty Index Measurement: The followng formula can be used to measure the evenness between

More information

Polyhedral Compilation Foundations

Polyhedral 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 information

1 Introducton Effcent and speedy recovery of electrc power networks followng a major outage, caused by a dsaster such as extreme weather or equpment f

1 Introducton Effcent and speedy recovery of electrc power networks followng a major outage, caused by a dsaster such as extreme weather or equpment f Effcent Recovery from Power Outage (Extended Summary) Sudpto Guha Λ Anna Moss y Joseph (Seff) Naor z Baruch Scheber x Abstract We study problems that are motvated by the real-lfe problem of effcent recovery

More information

Attila Pém* and Levente Mályusz Arrangement of material depots for line segment modeled structures using continuous conditions

Attila Pém* and Levente Mályusz Arrangement of material depots for line segment modeled structures using continuous conditions Organzaton, Technology and Management n Constructon 206; 8: 0 Research rtcle Open ccess ttla Pém* and Levente Mályusz rrangement of materal depots for lne segment modeled structures usng contnuous condtons

More information

Array transposition in CUDA shared memory

Array transposition in CUDA shared memory Array transposton n CUDA shared memory Mke Gles February 19, 2014 Abstract Ths short note s nspred by some code wrtten by Jeremy Appleyard for the transposton of data through shared memory. I had some

More information

Design of Structure Optimization with APDL

Design 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 information

Dijkstra s Single Source Algorithm. All-Pairs Shortest Paths. Dynamic Programming Solution. Performance. Decision Sequence.

Dijkstra s Single Source Algorithm. All-Pairs Shortest Paths. Dynamic Programming Solution. Performance. Decision Sequence. All-Pars Shortest Paths Gven an n-vertex drected weghted graph, fnd a shortest path from vertex to vertex for each of the n vertex pars (,). Dstra s Sngle Source Algorthm Use Dstra s algorthm n tmes, once

More information

Multicriteria Decision Making

Multicriteria 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 information

Decision Support for the Dynamic Reconfiguration of Machine Layout and Part Routing in Cellular Manufacturing

Decision Support for the Dynamic Reconfiguration of Machine Layout and Part Routing in Cellular Manufacturing Decson Support for the Dynamc Reconfguraton of Machne Layout and Part Routng n Cellular Manufacturng Hao W. Ln and Tomohro Murata Abstract A mathematcal based approach s presented to evaluate the dynamc

More information

EVALUATION OF THE PERFORMANCES OF ARTIFICIAL BEE COLONY AND INVASIVE WEED OPTIMIZATION ALGORITHMS ON THE MODIFIED BENCHMARK FUNCTIONS

EVALUATION OF THE PERFORMANCES OF ARTIFICIAL BEE COLONY AND INVASIVE WEED OPTIMIZATION ALGORITHMS ON THE MODIFIED BENCHMARK FUNCTIONS Academc Research Internatonal ISS-L: 3-9553, ISS: 3-9944 Vol., o. 3, May 0 EVALUATIO OF THE PERFORMACES OF ARTIFICIAL BEE COLOY AD IVASIVE WEED OPTIMIZATIO ALGORITHMS O THE MODIFIED BECHMARK FUCTIOS Dlay

More information

Shape Optimization of Shear-type Hysteretic Steel Damper for Building Frames using FEM-Analysis and Heuristic Approach

Shape Optimization of Shear-type Hysteretic Steel Damper for Building Frames using FEM-Analysis and Heuristic Approach The Seventh Chna-Japan-Korea Jont Symposum on Optmzaton of Structural and Mechancal Systems Huangshan, June, 18-21, 2012, Chna Shape Optmzaton of Shear-type Hysteretc Steel Damper for Buldng Frames usng

More information

Solving Mixed Integer Formulation of the KS Maximization Problem Dual Based Methods and Results from Large Practical Problems

Solving Mixed Integer Formulation of the KS Maximization Problem Dual Based Methods and Results from Large Practical Problems Solvng Mxed Integer Formulaton of the KS Maxmzaton Problem Dual ased Methods and Results from Large Practcal Problems Debashsh Sarkar Management Scences roup CIT, New Jersey, USA (August 24, 2005) 1 Abstract

More information

3. CR parameters and Multi-Objective Fitness Function

3. CR parameters and Multi-Objective Fitness Function 3 CR parameters and Mult-objectve Ftness Functon 41 3. CR parameters and Mult-Objectve Ftness Functon 3.1. Introducton Cogntve rados dynamcally confgure the wreless communcaton system, whch takes beneft

More information

CS246: Mining Massive Datasets Jure Leskovec, Stanford University

CS246: Mining Massive Datasets Jure Leskovec, Stanford University CS46: Mnng Massve Datasets Jure Leskovec, Stanford Unversty http://cs46.stanford.edu /19/013 Jure Leskovec, Stanford CS46: Mnng Massve Datasets, http://cs46.stanford.edu Perceptron: y = sgn( x Ho to fnd

More information

Feedback Min-Max Model Predictive Control Based on a Quadratic Cost Function

Feedback 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 information

Machine Learning. Topic 6: Clustering

Machine Learning. Topic 6: Clustering Machne Learnng Topc 6: lusterng lusterng Groupng data nto (hopefully useful) sets. Thngs on the left Thngs on the rght Applcatons of lusterng Hypothess Generaton lusters mght suggest natural groups. Hypothess

More information

Radial Basis Functions

Radial Basis Functions Radal Bass Functons Mesh Reconstructon Input: pont cloud Output: water-tght manfold mesh Explct Connectvty estmaton Implct Sgned dstance functon estmaton Image from: Reconstructon and Representaton of

More information

Dijkstra s Single Source Algorithm. All-Pairs Shortest Paths. Dynamic Programming Solution. Performance

Dijkstra s Single Source Algorithm. All-Pairs Shortest Paths. Dynamic Programming Solution. Performance All-Pars Shortest Paths Gven an n-vertex drected weghted graph, fnd a shortest path from vertex to vertex for each of the n vertex pars (,). Dkstra s Sngle Source Algorthm Use Dkstra s algorthm n tmes,

More information

Distributed Middlebox Placement Based on Potential Game

Distributed Middlebox Placement Based on Potential Game Int. J. Communcatons, Network and System Scences, 2017, 10, 264-273 http://www.scrp.org/ournal/cns ISSN Onlne: 1913-3723 ISSN Prnt: 1913-3715 Dstrbuted Mddlebox Placement Based on Potental Game Yongwen

More information

Modeling and Solving Nontraditional Optimization Problems Session 2a: Conic Constraints

Modeling and Solving Nontraditional Optimization Problems Session 2a: Conic Constraints Modelng and Solvng Nontradtonal Optmzaton Problems Sesson 2a: Conc Constrants Robert Fourer Industral Engneerng & Management Scences Northwestern Unversty AMPL Optmzaton LLC 4er@northwestern.edu 4er@ampl.com

More information

Collision Detection. Overview. Efficient Collision Detection. Collision Detection with Rays: Example. C = nm + (n choose 2)

Collision Detection. Overview. Efficient Collision Detection. Collision Detection with Rays: Example. C = nm + (n choose 2) Overvew Collson detecton wth Rays Collson detecton usng BSP trees Herarchcal Collson Detecton OBB tree, k-dop tree algorthms Multple object CD system Collson Detecton Fundamental to graphcs, VR applcatons

More information

SUMMARY... I TABLE OF CONTENTS...II INTRODUCTION...

SUMMARY... I TABLE OF CONTENTS...II INTRODUCTION... Summary A follow-the-leader robot system s mplemented usng Dscrete-Event Supervsory Control methods. The system conssts of three robots, a leader and two followers. The dea s to get the two followers to

More information

Active Contours/Snakes

Active Contours/Snakes Actve Contours/Snakes Erkut Erdem Acknowledgement: The sldes are adapted from the sldes prepared by K. Grauman of Unversty of Texas at Austn Fttng: Edges vs. boundares Edges useful sgnal to ndcate occludng

More information

An efficient iterative source routing algorithm

An efficient iterative source routing algorithm An effcent teratve source routng algorthm Gang Cheng Ye Tan Nrwan Ansar Advanced Networng Lab Department of Electrcal Computer Engneerng New Jersey Insttute of Technology Newar NJ 7 {gc yt Ansar}@ntedu

More information

CHAPTER 2 PROPOSED IMPROVED PARTICLE SWARM OPTIMIZATION

CHAPTER 2 PROPOSED IMPROVED PARTICLE SWARM OPTIMIZATION 24 CHAPTER 2 PROPOSED IMPROVED PARTICLE SWARM OPTIMIZATION The present chapter proposes an IPSO approach for multprocessor task schedulng problem wth two classfcatons, namely, statc ndependent tasks and

More information

A Mixed Linear Program for a Multi-Part Cyclic Hoist Scheduling Problem

A Mixed Linear Program for a Multi-Part Cyclic Hoist Scheduling Problem A Mxed Lnear Program for a MultPart Cyclc Host Schedulng Problem Adnen El Amraou,, MareAnge Maner, Abdellah El Moudn and Mohamed Benrejeb U.R. LARA Automatque, Ecole Natonale d Ingéneurs de Tuns, Tunse.

More information

Contour line construction for a new rectangular facility in an existing layout with rectangular departments

Contour line construction for a new rectangular facility in an existing layout with rectangular departments Contour lne constructon for a new rectangular faclty n an exstng layout wth rectangular departments by Har Kelachankuttu, Raan Batta, Rakesh Nag Department of Industral Engneerng, 438 Bell Hall Unversty

More information

SHAPE OPTIMIZATION OF STRUCTURES BY MODIFIED HARMONY SEARCH

SHAPE OPTIMIZATION OF STRUCTURES BY MODIFIED HARMONY SEARCH INTERNATIONAL JOURNAL OF OPTIMIZATION IN CIVIL ENGINEERING Int. J. Optm. Cvl Eng., 2011; 3:485-494 SHAPE OPTIMIZATION OF STRUCTURES BY MODIFIED HARMONY SEARCH S. Gholzadeh *,, A. Barzegar and Ch. Gheyratmand

More information

Constructing Minimum Connected Dominating Set: Algorithmic approach

Constructing Minimum Connected Dominating Set: Algorithmic approach Constructng Mnmum Connected Domnatng Set: Algorthmc approach G.N. Puroht and Usha Sharma Centre for Mathematcal Scences, Banasthal Unversty, Rajasthan 304022 usha.sharma94@yahoo.com Abstract: Connected

More information