Constrained Functions of N Variables: NonGradient Based Methods


 Caitlin Glenn
 1 years ago
 Views:
Transcription
1 onstrained Functions of N Variables: NonGradient Based Methods Gerhard Venter Stellenbosch University
2 Outline Outline onstrained Optimization Nongradient based methods Genetic Algorithms (GA) Particle Swarm Optimization (PSO) Parallelization 2
3 ourse Outline Until now hapter 1: Basic concepts hapter 2: Functions of one variable hapter 3: Unconstrained functions of N variables hapter 4: Linear programming hapter 5: Sequential unconstrained minimization techniques Today: onstrained functions of N variables hapter 6: Nongradient based optimization 3
4 onstrained Optimization Standard Form Find the set of design variables that will: Minimize: F(X) Subject To: g j (X) 0 j=1,m h k (X)=0 k=1,l Xi L X i Xi U i=1,n 4
5 Kuhn Tucker onditions KuhnTucker conditions provides necessary conditions for a (local) optimum X isfeasible λ j g j (X )=0 m F(X )+ λ j g j (X )+ j=1 λ j 0 j=1,m λ m+k unrestrictedinsign l λ m+k h k (X )=0 k=1 5
6 NonGradient Based Methods Simplest is a random search Easy to implement Very robust Very inefficient Improve random search by adding some logic Example DOE search with movelimits Referred to as a structured random search We will consider two structured random searches in this class 6
7 NonGradient Based Methods Nongradient based optimization algorithms have gained a lot of attention recently Easy to program Global properties Require no gradient information High computational cost Tuned for each problem Typically based on some physical phenomena Genetic algorithms Simulated annealing Particle swarm optimization 7
8 NonGradient Based Methods an be classified as a structured random search Does not move from one design point to the next  makes use of a population of design points Numerically robust Increased changes of finding global or near global optimum designs Provides a number of good designs instead of a single optimum 8
9 Genetic Algorithms Derived from biology and making use of Darwin s principal of survival of the fittest First developed in 1975 by Holland Population adapts to its underlying environment through evolution haracteristics stored in chromosomal strings Structured but random exchange of genetic information Better designs have increased changes of reproducing 9
10 Genetic Operators Start with initial population Reproduce by using Selection rossover Occasional mutation Elitist strategy Design variables are encoded in bitstrings that are equivalent to chromosomal strings 10
11 Design Variable Encoding Traditionally binary numbers were used Example F(X) X={X 1,X 2,X 3,X 4 } 0 X 1,X X X 3 3 [ 0110 }{{} X 1 =6 101 }{{} X 2 =5 11 }{{} X 3 = }{{} X 4 =11 ] 11
12 Binary Encoding Mainly used for historical reasons Number of bits required  m 2 m Xu X l X incr +1 Use to represent integer and real numbers Smallest possible alphabet Added complexity that is not needed an use actual values (integer or real) in our bit string 12
13 Real Number Encoding Laminate stacking sequence optimization Layers can only be stacked using 0,45, 45,90 Bit string for 16ply laminate [±45 /0 4/90 2] s 13
14 Real Number Encoding Full string 4 16 = combinations [ ] Use symmetry 4 8 =65,536 combinations [ ] Balanced with stack variables combinations [2113] 3 4 =81 14
15 Typical Genetic Algorithm Start reate Initial Swarm Perform analyses onverged No Selection rossover Mutation Yes End Elitist Strategy 15
16 Initial Population Initial population Fixed size population Fixed chromosome length No fixed rule for determining population size Randomly distributed throughout the design space 16
17 Selection and Fitness Selection and fitness Selection gives more fit designs higher chance of passing their genes to the next generation Fitness based on the objective function Use SUMT approach for constrained problems Selection Using roulette wheel approach r i = F i ns j=1 F j 17
18 Selection Roulette wheel based on objective values All objective function values must be positive Little differentiation between design at end of optimization Use roulette wheel based on rank an take positive and negative objective function values Better differentiation between designs r i = 2(n s i+1) (n s +1)n s 18
19 Apply Selection reate roulette wheel with n s segments reate random number between 0 and 1 Determine segment on roulette wheel that contains the random number Segment ID corresponds to design ID Repeat to obtain two parents for reproduction through crossover 19
20 rossover over Select two parents for reproduction Apply probability of crossover, pc Pc is typically close to 1 Mix parent genes using crossover to obtain one (or two) children One point crossover Parent Parent hild
21 rossover over Two point crossover Parent Parent hild Uniform crossover Parent Parent Random hild
22 rossover over One point averaging crossover Especially useful for realnumbers Generate random number between 1 and the length of the string Say we generate 3.2 Elements 1 and 2 from Parent 1, elements 4 and 5 from parent 2, element 3 from 3 =0.2P P3 2 Parent Parent hild
23 Mutation Prevent premature loss of genetic information by introducing randomness in the population Important to create information not contained in initial population Apply probability of performing mutation, p m p m is typically small Randomly select gene to mutate Randomly modify gene 23
24 ost/reliability Algorithm is very costly ost is determined by Problem size number of design variables and number of combinations onstraint definitions Reliability can be improved by Performing more generations Increase the population size Repeat the optimization run 24
25 Typical Applications Analysis is cheap to perform Problems that contain many local minima Not that common in engineering applications Problems that has no gradient information Selecting different crosssections for a truss structure ombinatorial type problems omposite laminate design find optimum thickness and ply orientation Doptimal design of experiments 25
26 Particle Swarm Optimization Particle Swarm Optimization (PSO) is a fairly recent addition to the family of nongradient based optimization algorithms PSO is based on a simplified social model that is closely tied to swarming theory Example is a swarm of bees searching for a food source Use knowledge of individual particles and swarm as a whole Basic Assumption: A population of individuals adapts by returning to promising regions found previously 26
27 Algorithm Overview A 2 Initial Swarm A 1 A 2 A 1 P 1 A 1 P 2 A 2 Final Swarm A 1 Particle P i properties: Position: (A 1j,A 2j ) Velocity Vector Objective: W(A 1j,A 2j ) onstraints: S(A 1j,A 2j,P 1,P 2 ) 27
28 How is PSO Implemented Position Update: Velocity Vector: x i k+1=x i k+v i k+1 t v i k+1=wv i k+c 1 r 1 p i x i k t +c 2 r 2 p g k xi k t Inertia Trust in self Trust in swarm 28
29 Enhancements onvergence criterion Monitor the maximum change in the objective function for a specified number of consecutive design iterations Integer/Discrete problems Unlike genetic algorithms, PSO is inherently a continuous algorithm Round the new position to closest value before performing function evaluations raziness Similar to mutation operator in Genetic Algorithms Prevent premature convergence 29
30 onstrained Problems onstrained problems ombine constraints with objective: exterior penalty function: F(X,r p )=F(X)+r p P(X) Deal with violated design points (including points outside bounds) based on usable, feasible directions idea reate new velocity vector to point back to the feasible design space by resetting the velocity vector: v i k+1=c 1 r 1 p i x i k t +c 2 r 2 p g k xi k t 30
31 Simplified Flowchart Start reate Initial Swarm Perform analyses onverged No Adjust Parameters New Velocity Vector Update Position Yes End Apply raziness 31
32 Example Problem 1 Global optimum: Point = (0,0) Obj = 0 Local optima: Point = (1.75, 0.87) Obj = 0.3 Point = (1.75, 0.87) Obj =
33 Example Problem 2 Global optimum: Point = (0,0) Obj = 1000 Many local optima 33
34 Example Problem Multidisciplinary design optimization of a transport aircraft wing structure System level optimization PSO Algorithm Structural suboptimization GENESIS Aerodynamic analysis Simplified analysis 34
35 System Level Optimization Unconstrained problem Maximize: Range Design Variables: Aspect ratio Depthtochord ratio Number of internal spars Number of internal ribs Wing cover construction ontinuous Variables Discrete Variables 35
36 Structural SubOptimization Structural analysis using a simplified FE model of the wing box Objective is to minimize the weight of the wing Both stress and local buckling constraints are applied 80 Design Variables 206 Design Variables 36
37 Aerodynamic Analysis Assumed pressure distribution is converted to nodal loads for the structural suboptimization Simplified drag analysis: Drag of the current wing is calculated based on the total drag of the reference wing Range is calculated from the Breguet formula onstant TakeOff Gross Weight Structural weight saving is converted to fuel weight Wing is build to a jig shape to compensate for the aerodynamicstructure interaction 37
38 System Level Analysis Update FE Model System Level Analysis Apply Pressure Distribution Structural SubOptimization alculate Aerodynamic Drag alculate Range 38
39 Results Repeated optimization ten times, each with different initial swarm 39
40 Results... Reference Wing Range = n. mi. A = h/c = 0.12 Optimum Wing (Sandwich) Range = 5375 n. mi. A = h/c =
41 omputation ost What about using a gradientbased optimizer to solve this problem? Look at all possible combinations for the three truly discrete variables For each combination solve a two design variable continuous optimization problem Results in 32 optimization problems Total of 526 analyses (1500 for the PSO) Parallel implementation implications 41
42 GradientBased Results Parameter Reference Wing DOT Optimum PSO Optimum Aspect Ratio Depthtohord Ratio Num. Internal Spars Num. Internal Ribs onstruction Sandwich Sandwich Range(n. mi.) Number of Analyses
43 Numerical Noise Don t forget about NUMERIAL NOISE Severe numerical noise due to the structural suboptimization Noise due to different levels of convergence Iterative process 43
44 Remarks PSO algorithm was able to produce consistent results in the presence of truly discrete design variables and severe numerical noise PSO computational cost is high, but using a gradient based optimizer is not a feasible alternative Numerical noise Implementation issues Larger number of discrete combinations PSO has significant potential for massively parallel processing 44
45 Simplified Flowchart Start reate Initial Swarm Perform analyses Run in Parallel onverged No Adjust Parameters New Velocity Vector Update Position Yes End Apply raziness 45
46 Parallel PSO: Synchronized Wait for all analyses to complete before starting next design iteration What has been done so far Straight forward to implement Overall logic of the algorithm is not changed produce same results Poor parallel speedup Some processors remain idle parttime! 46
47 Parallel PSO: Asynchronized Goal is to make all processors work all of the time Do not wait for the current design iteration to complete before starting the next Update all point information as soon as it becomes available Update iteration information as soon as a design iteration is completed Overall logic of algorithm is changed may produce different results Very good parallel speedup 47
48 Parallel Environment Implemented both synchronous and asynchronous algorithms Made use of a masterslave implementation System X from the Virginia Tech Terrascale omputing Facility 1100 dual processor 2.3 GHz compute nodes 4GB of RAM and 40 GB hard disk per node Used up to 32 processors Each run was repeated 10 times to account for variability in the results 48
49 Parallel Results: Accuracy All results averaged over 10 runs 49
50 Parallel Results: Efficiency Speedup = Time Time 1Proc nproc Time Speedup = Time 1Proc nproc Efficiency =100* Speedup nproc 50
51 Remarks PSO algorithm was able to produce consistent results in the presence of discrete design variables and severe numerical noise PSO has significant potential for parallel processing Implementation is important Hardware is important Asynchronous implementation provides almost perfect speedup 95% Efficiency with 32 processors Average time reduced from 150min (2.5 Hours) to 5 min 51
52 oncluding Remarks Nongradient based algorithms have a valuable place in design optimization These algorithms are often misused and should be applied with great care Rule of thumb is to only apply these algorithms if there is no alternative High computational cost can be alleviated by using parallel computing 52
Module 1 Lecture Notes 2. Optimization Problem and Model Formulation
Optimization Methods: Introduction and Basic concepts 1 Module 1 Lecture Notes 2 Optimization Problem and Model Formulation Introduction In the previous lecture we studied the evolution of optimization
More informationAn Introduction to Evolutionary Algorithms
An Introduction to Evolutionary Algorithms Karthik Sindhya, PhD Postdoctoral Researcher Industrial Optimization Group Department of Mathematical Information Technology Karthik.sindhya@jyu.fi http://users.jyu.fi/~kasindhy/
More informationIntroduction to Genetic Algorithms
Advanced Topics in Image Analysis and Machine Learning Introduction to Genetic Algorithms Week 3 Faculty of Information Science and Engineering Ritsumeikan University Today s class outline Genetic Algorithms
More informationIntroduction to Genetic Algorithms. Based on Chapter 10 of Marsland Chapter 9 of Mitchell
Introduction to Genetic Algorithms Based on Chapter 10 of Marsland Chapter 9 of Mitchell Genetic Algorithms  History Pioneered by John Holland in the 1970s Became popular in the late 1980s Based on ideas
More informationGENETIC ALGORITHM with HandsOn exercise
GENETIC ALGORITHM with HandsOn exercise Adopted From Lecture by Michael Negnevitsky, Electrical Engineering & Computer Science University of Tasmania 1 Objective To understand the processes ie. GAs Basic
More informationIntroduction to Design Optimization: Search Methods
Introduction to Design Optimization: Search Methods 1D Optimization The Search We don t know the curve. Given α, we can calculate f(α). By inspecting some points, we try to find the approximated shape
More informationGenetic Algorithms for Vision and Pattern Recognition
Genetic Algorithms for Vision and Pattern Recognition Faiz Ul Wahab 11/8/2014 1 Objective To solve for optimization of computer vision problems using genetic algorithms 11/8/2014 2 Timeline Problem: Computer
More informationGeneration of Ultra Side lobe levels in Circular Array Antennas using Evolutionary Algorithms
Generation of Ultra Side lobe levels in Circular Array Antennas using Evolutionary Algorithms D. Prabhakar Associate Professor, Dept of ECE DVR & Dr. HS MIC College of Technology Kanchikacherla, AP, India.
More informationCS5401 FS2015 Exam 1 Key
CS5401 FS2015 Exam 1 Key This is a closedbook, closednotes exam. The only items you are allowed to use are writing implements. Mark each sheet of paper you use with your name and the string cs5401fs2015
More informationEvolutionary Algorithms. CS Evolutionary Algorithms 1
Evolutionary Algorithms CS 478  Evolutionary Algorithms 1 Evolutionary Computation/Algorithms Genetic Algorithms l Simulate natural evolution of structures via selection and reproduction, based on performance
More informationA Genetic Algorithm for Graph Matching using Graph Node Characteristics 1 2
Chapter 5 A Genetic Algorithm for Graph Matching using Graph Node Characteristics 1 2 Graph Matching has attracted the exploration of applying new computing paradigms because of the large number of applications
More informationAutomated Test Data Generation and Optimization Scheme Using Genetic Algorithm
2011 International Conference on Software and Computer Applications IPCSIT vol.9 (2011) (2011) IACSIT Press, Singapore Automated Test Data Generation and Optimization Scheme Using Genetic Algorithm Roshni
More informationTHE DEVELOPMENT OF THE POTENTIAL AND ACADMIC PROGRAMMES OF WROCLAW UNIVERISTY OF TECHNOLOGY METAHEURISTICS
METAHEURISTICS 1. Objectives The goals of the laboratory workshop are as follows: to learn basic properties of evolutionary computation techniques and other metaheuristics for solving various global optimization
More informationGenetic Algorithms. Kang Zheng Karl Schober
Genetic Algorithms Kang Zheng Karl Schober Genetic algorithm What is Genetic algorithm? A genetic algorithm (or GA) is a search technique used in computing to find true or approximate solutions to optimization
More information1 Lab + Hwk 5: Particle Swarm Optimization
1 Lab + Hwk 5: Particle Swarm Optimization This laboratory requires the following equipment: C programming tools (gcc, make). Webots simulation software. Webots User Guide Webots Reference Manual. The
More information4/22/2014. Genetic Algorithms. Diwakar Yagyasen Department of Computer Science BBDNITM. Introduction
4/22/24 s Diwakar Yagyasen Department of Computer Science BBDNITM Visit dylycknow.weebly.com for detail 2 The basic purpose of a genetic algorithm () is to mimic Nature s evolutionary approach The algorithm
More informationAutomata Construct with Genetic Algorithm
Automata Construct with Genetic Algorithm Vít Fábera Department of Informatics and Telecommunication, Faculty of Transportation Sciences, Czech Technical University, Konviktská 2, Praha, Czech Republic,
More informationLecture 4. Convexity Robust cost functions Optimizing nonconvex functions. 3B1B Optimization Michaelmas 2017 A. Zisserman
Lecture 4 3B1B Optimization Michaelmas 2017 A. Zisserman Convexity Robust cost functions Optimizing nonconvex functions grid search branch and bound simulated annealing evolutionary optimization The Optimization
More informationGENETIC ALGORITHM VERSUS PARTICLE SWARM OPTIMIZATION IN NQUEEN PROBLEM
Journal of AlNahrain University Vol.10(2), December, 2007, pp.172177 Science GENETIC ALGORITHM VERSUS PARTICLE SWARM OPTIMIZATION IN NQUEEN PROBLEM * Azhar W. Hammad, ** Dr. Ban N. Thannoon AlNahrain
More informationAvailable online at ScienceDirect. Razvan Cazacu*, Lucian Grama
Available online at www.sciencedirect.com ScienceDirect Procedia Technology 12 ( 2014 ) 339 346 The 7 th International Conference Interdisciplinarity in Engineering (INTERENG 2013) Steel truss optimization
More informationArtificial Intelligence Application (Genetic Algorithm)
Babylon University College of Information Technology Software Department Artificial Intelligence Application (Genetic Algorithm) By Dr. Asaad Sabah Hadi 20142015 EVOLUTIONARY ALGORITHM The main idea about
More informationA Genetic Algorithm Framework
Fast, good, cheap. Pick any two. The Project Triangle 3 A Genetic Algorithm Framework In this chapter, we develop a genetic algorithm based framework to address the problem of designing optimal networks
More informationEvolutionary Computation Algorithms for Cryptanalysis: A Study
Evolutionary Computation Algorithms for Cryptanalysis: A Study Poonam Garg Information Technology and Management Dept. Institute of Management Technology Ghaziabad, India pgarg@imt.edu Abstract The cryptanalysis
More informationGenetic Algorithms: Setting Parmeters and Incorporating Constraints OUTLINE OF TOPICS: 1. Setting GA parameters. 2. Constraint Handling (two methods)
Genetic Algorithms: Setting Parmeters and Incorporating Constraints OUTLINE OF TOPICS: 1. Setting GA parameters general guidelines for binary coded GA (some can be extended to real valued GA) estimating
More informationPath Planning Optimization Using Genetic Algorithm A Literature Review
International Journal of Computational Engineering Research Vol, 03 Issue, 4 Path Planning Optimization Using Genetic Algorithm A Literature Review 1, Er. Waghoo Parvez, 2, Er. Sonal Dhar 1, (Department
More informationOptimization of Laminar Wings for ProGreen Aircrafts
Optimization of Laminar Wings for ProGreen Aircrafts André Rafael Ferreira Matos Abstract This work falls within the scope of aerodynamic design of progreen aircraft, where the use of wings with higher
More informationWitold Pedrycz. University of Alberta Edmonton, Alberta, Canada
2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC) Banff Center, Banff, Canada, October 58, 2017 Analysis of Optimization Algorithms in Automated Test Pattern Generation for Sequential
More informationCHAPTER 4 GENETIC ALGORITHM
69 CHAPTER 4 GENETIC ALGORITHM 4.1 INTRODUCTION Genetic Algorithms (GAs) were first proposed by John Holland (Holland 1975) whose ideas were applied and expanded on by Goldberg (Goldberg 1989). GAs is
More informationOPTIMIZATION METHODS. For more information visit: or send an to:
OPTIMIZATION METHODS modefrontier is a registered product of ESTECO srl Copyright ESTECO srl 19992007 For more information visit: www.esteco.com or send an email to: modefrontier@esteco.com NEOS Optimization
More informationOperations Research and Optimization: A Primer
Operations Research and Optimization: A Primer Ron Rardin, PhD NSF Program Director, Operations Research and Service Enterprise Engineering also Professor of Industrial Engineering, Purdue University Introduction
More informationFrequency Response Optimization of Saw Filter using Canonical Genetic Algorithm
Frequency Response Optimization of Saw Filter using Canonical Genetic Algorithm Prachi Chaudhary & Tech., Murthal, Haryana Priyanka & Tech., Murthal, Haryana Manoj Duhan & Tech., Murthal, Haryana, ABSTRACT
More informationParticle Swarm Optimization
Dario Schor, M.Sc., EIT schor@ieee.org Space Systems Department Magellan Aerospace Winnipeg Winnipeg, Manitoba 1 of 34 Optimization Techniques Motivation Optimization: Where, min x F(x), subject to g(x)
More informationAutomatic differentiation based for particle swarm optimization steepest descent direction
International Journal of Advances in Intelligent Informatics ISSN: 24426571 Vol 1, No 2, July 2015, pp. 9097 90 Automatic differentiation based for particle swarm optimization steepest descent direction
More informationOptimization of Benchmark Functions Using Genetic Algorithm
Optimization of Benchmark s Using Genetic Algorithm Vinod Goyal GJUS&T, Hisar Sakshi Dhingra GJUS&T, Hisar Jyoti Goyat GJUS&T, Hisar Dr Sanjay Singla IET Bhaddal Technical Campus, Ropar, Punjab Abstrat
More informationGenetic Algorithm Performance with Different Selection Methods in Solving MultiObjective Network Design Problem
etic Algorithm Performance with Different Selection Methods in Solving MultiObjective Network Design Problem R. O. Oladele Department of Computer Science University of Ilorin P.M.B. 1515, Ilorin, NIGERIA
More informationCT79 SOFT COMPUTING ALCCSFEB 2014
Q.1 a. Define Union, Intersection and complement operations of Fuzzy sets. For fuzzy sets A and B Figure Fuzzy sets A & B The union of two fuzzy sets A and B is a fuzzy set C, written as C=AUB or C=A OR
More informationWhat is GOSET? GOSET stands for Genetic Optimization System Engineering Tool
Lecture 5: GOSET 1 What is GOSET? GOSET stands for Genetic Optimization System Engineering Tool GOSET is a MATLAB based genetic algorithm toolbox for solving optimization problems 2 GOSET Features Wide
More informationIntroduction (7.1) Genetic Algorithms (GA) (7.2) Simulated Annealing (SA) (7.3) Random Search (7.4) Downhill Simplex Search (DSS) (7.
Chapter 7: DerivativeFree Optimization Introduction (7.1) Genetic Algorithms (GA) (7.2) Simulated Annealing (SA) (7.3) Random Search (7.4) Downhill Simplex Search (DSS) (7.5) JyhShing Roger Jang et al.,
More informationGenetic algorithm based on number of children and height task for multiprocessor task Scheduling
Genetic algorithm based on number of children and height task for multiprocessor task Scheduling Marjan Abdeyazdan 1,Vahid Arjmand 2,Amir masoud Rahmani 3, Hamid Raeis ghanavati 4 1 Department of Computer
More informationAIRFOIL SHAPE OPTIMIZATION USING IMPROVED SIMPLE GENETIC ALGORITHM (ISGA)
HEFAT007 5 th International onference on Heat Transfer, Fluid Mechanics and Thermodynamics Sun ity, South Africa MK1 AIRFOIL SHAPE OPTIMIZATION USING IMPROVED SIMPLE GENETI ALGORITHM (ISGA) Karim Mazaheri
More informationGenetic.io. Genetic Algorithms in all their shapes and forms! Genetic.io Make something of your big data
Genetic Algorithms in all their shapes and forms! Julien Sebrien Selftaught, passion for development. Java, Cassandra, Spark, JPPF. @jsebrien, julien.sebrien@genetic.io Distribution of IT solutions (SaaS,
More informationOptimization of Constrained Function Using Genetic Algorithm
Optimization of Constrained Function Using Genetic Algorithm Afaq Alam Khan 1* Roohie Naaz Mir 2 1. Department of Information Technology, Central University of Kashmir 2. Department of Computer Science
More informationAn Application of Genetic Algorithm for Autobody Panel Diedesign Case Library Based on Grid
An Application of Genetic Algorithm for Autobody Panel Diedesign Case Library Based on Grid Demin Wang 2, Hong Zhu 1, and Xin Liu 2 1 College of Computer Science and Technology, Jilin University, Changchun
More informationBinary Differential Evolution Strategies
Binary Differential Evolution Strategies A.P. Engelbrecht, Member, IEEE G. Pampará Abstract Differential evolution has shown to be a very powerful, yet simple, populationbased optimization approach. The
More informationBayesian Methods in Vision: MAP Estimation, MRFs, Optimization
Bayesian Methods in Vision: MAP Estimation, MRFs, Optimization CS 650: Computer Vision Bryan S. Morse Optimization Approaches to Vision / Image Processing Recurring theme: Cast vision problem as an optimization
More informationOptimizing Flow Shop Sequencing Through Simulation Optimization Using Evolutionary Methods
Optimizing Flow Shop Sequencing Through Simulation Optimization Using Evolutionary Methods Sucharith Vanguri 1, Travis W. Hill 2, Allen G. Greenwood 1 1 Department of Industrial Engineering 260 McCain
More informationAPPLICATION OF VARIABLEFIDELITY MODELS TO AERODYNAMIC OPTIMIZATION
Applied Mathematics and Mechanics (English Edition), 2006, 27(8):1089 1095 c Editorial Committee of Appl. Math. Mech., ISSN 02534827 APPLICATION OF VARIABLEFIDELITY MODELS TO AERODYNAMIC OPTIMIZATION
More informationA Modified Genetic Algorithm for Process Scheduling in Distributed System
A Modified Genetic Algorithm for Process Scheduling in Distributed System Vinay Harsora B.V.M. Engineering College Charatar Vidya Mandal Vallabh Vidyanagar, India Dr.Apurva Shah G.H.Patel College of Engineering
More informationAn Evolutionary Algorithm for Minimizing Multimodal Functions
An Evolutionary Algorithm for Minimizing Multimodal Functions D.G. Sotiropoulos, V.P. Plagianakos and M.N. Vrahatis University of Patras, Department of Mamatics, Division of Computational Mamatics & Informatics,
More informationIntroduction to ANSYS DesignXplorer
Lecture 5 Goal Driven Optimization 14. 5 Release Introduction to ANSYS DesignXplorer 1 2013 ANSYS, Inc. September 27, 2013 Goal Driven Optimization (GDO) Goal Driven Optimization (GDO) is a multi objective
More informationOutline. Bestfirst search. Greedy bestfirst search A* search Heuristics Local search algorithms
Outline Bestfirst search Greedy bestfirst search A* search Heuristics Local search algorithms Hillclimbing search Beam search Simulated annealing search Genetic algorithms Constraint Satisfaction Problems
More informationReducing Graphic Conflict In Scale Reduced Maps Using A Genetic Algorithm
Reducing Graphic Conflict In Scale Reduced Maps Using A Genetic Algorithm Dr. Ian D. Wilson School of Technology, University of Glamorgan, Pontypridd CF37 1DL, UK Dr. J. Mark Ware School of Computing,
More informationGenetic Algorithms For Vertex. Splitting in DAGs 1
Genetic Algorithms For Vertex Splitting in DAGs 1 Matthias Mayer 2 and Fikret Ercal 3 CSC9302 Fri Jan 29 1993 Department of Computer Science University of MissouriRolla Rolla, MO 65401, U.S.A. (314)
More informationGenetic Algorithm and Direct Search Toolbox
Genetic Algorithm and Direct Search Toolbox For Use with MATLAB User s Guide Version 1 How to Contact The MathWorks: www.mathworks.com comp.softsys.matlab support@mathworks.com suggest@mathworks.com bugs@mathworks.com
More informationTowards Automatic Recognition of Fonts using Genetic Approach
Towards Automatic Recognition of Fonts using Genetic Approach M. SARFRAZ Department of Information and Computer Science King Fahd University of Petroleum and Minerals KFUPM # 1510, Dhahran 31261, Saudi
More informationDiscussion of Various Techniques for Solving Economic Load Dispatch
International Journal of Enhanced Research in Science, Technology & Engineering ISSN: 23197463, Vol. 4 Issue 7, July2015 Discussion of Various Techniques for Solving Economic Load Dispatch Veerpal Kaur
More informationA New Selection Operator  CSM in Genetic Algorithms for Solving the TSP
A New Selection Operator  CSM in Genetic Algorithms for Solving the TSP Wael Raef Alkhayri Fahed Al duwairi High School Aljabereyah, Kuwait Suhail Sami Owais Applied Science Private University Amman,
More informationGENERATIONAL MODEL GENETIC ALGORITHM FOR REAL WORLD SET PARTITIONING PROBLEMS
International Journal of Electronic Commerce Studies Vol.4, No.1, pp. 3346, 2013 doi: 10.7903/ijecs.1138 GENERATIONAL MODEL GENETIC ALGORITHM FOR REAL WORLD SET PARTITIONING PROBLEMS Chisan Althon Lin
More informationEvolving SQL Queries for Data Mining
Evolving SQL Queries for Data Mining Majid Salim and Xin Yao School of Computer Science, The University of Birmingham Edgbaston, Birmingham B15 2TT, UK {msc30mms,x.yao}@cs.bham.ac.uk Abstract. This paper
More informationA Parallel Genetic Algorithm for Maximum Flow Problem
A Parallel Genetic Algorithm for Maximum Flow Problem Ola M. Surakhi Computer Science Department University of Jordan AmmanJordan Mohammad Qatawneh Computer Science Department University of Jordan AmmanJordan
More informationTheoretical Concepts of Machine Learning
Theoretical Concepts of Machine Learning Part 2 Institute of Bioinformatics Johannes Kepler University, Linz, Austria Outline 1 Introduction 2 Generalization Error 3 Maximum Likelihood 4 Noise Models 5
More informationA SteadyState Genetic Algorithm for Traveling Salesman Problem with Pickup and Delivery
A SteadyState Genetic Algorithm for Traveling Salesman Problem with Pickup and Delivery Monika Sharma 1, Deepak Sharma 2 1 Research Scholar Department of Computer Science and Engineering, NNSS SGI Samalkha,
More informationMachine Learning for Software Engineering
Machine Learning for Software Engineering SingleState MetaHeuristics Prof. Dr.Ing. Norbert Siegmund Intelligent Software Systems 1 2 Recap: Goal is to Find the Optimum Challenges of general optimization
More informationOPTIMAL DOCK BLOCK ARRANGEMENT CONSIDERING SUBSEQUENT SHIPS SOLVED BY GENETIC ALGORITHM
OPTIMAL DOCK BLOCK ARRANGEMENT CONSIDERING SUBSEQUENT SHIPS SOLVED BY GENETIC ALGORITHM Chen Chen Department of Civil and Environmental Engineering, National University of Singapore, E10821, Engineering
More informationAnother Case Study: Genetic Algorithms
Chapter 4 Another Case Study: Genetic Algorithms Genetic Algorithms The section on Genetic Algorithms (GA) appears here because it is closely related to the problem of unsupervised learning. Much of what
More informationMATLAB Based Optimization Techniques and Parallel Computing
MATLAB Based Optimization Techniques and Parallel Computing Bratislava June 4, 2009 2009 The MathWorks, Inc. JörgM. Sautter Application Engineer The MathWorks Agenda Introduction Local and Smooth Optimization
More informationThresholds Determination for Probabilistic Rough Sets with Genetic Algorithms
Thresholds Determination for Probabilistic Rough Sets with Genetic Algorithms Babar Majeed, Nouman Azam, JingTao Yao Department of Computer Science University of Regina {majeed2b,azam200n,jtyao}@cs.uregina.ca
More informationCHAPTER 4 FEATURE SELECTION USING GENETIC ALGORITHM
CHAPTER 4 FEATURE SELECTION USING GENETIC ALGORITHM In this research work, Genetic Algorithm method is used for feature selection. The following section explains how Genetic Algorithm is used for feature
More informationThe exam is closed book, closed notes except your onepage (twosided) cheat sheet.
CS 189 Spring 2015 Introduction to Machine Learning Final You have 2 hours 50 minutes for the exam. The exam is closed book, closed notes except your onepage (twosided) cheat sheet. No calculators or
More informationTHE MAIN purpose of optimal reactive power flow (ORPF)
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 21, NO. 3, AUGUST 2006 1163 A Hybrid Genetic Algorithm Interior Point Method for Optimal Reactive Power Flow Wei Yan, Fang Liu, C. Y. Chung, Member, IEEE, and K.
More informationDerivativeFree Optimization
DerivativeFree Optimization Chapter 7 from Jang Outline Simulated Annealing (SA) Downhill simplex search Random search Genetic algorithms (GA) 2 The Big Picture Model space Adaptive networks Neural networks
More informationParticle Swarm Optimization Methods for Pattern. Recognition and Image Processing
Particle Swarm Optimization Methods for Pattern Recognition and Image Processing by Mahamed G. H. Omran Submitted in partial fulfillment of the requirements for the degree Philosophiae Doctor in the Faculty
More informationDerating NichePSO. Clive Naicker
Derating NichePSO by Clive Naicker Submitted in partial fulfillment of the requirements for the degree Magister Scientiae (Computer Science) in the Faculty of Engineering, Built Environment and Information
More informationA Short SVM (Support Vector Machine) Tutorial
A Short SVM (Support Vector Machine) Tutorial j.p.lewis CGIT Lab / IMSC U. Southern California version 0.zz dec 004 This tutorial assumes you are familiar with linear algebra and equalityconstrained optimization/lagrange
More informationANTICIPATORY VERSUS TRADITIONAL GENETIC ALGORITHM
Anticipatory Versus Traditional Genetic Algorithm ANTICIPATORY VERSUS TRADITIONAL GENETIC ALGORITHM ABSTRACT Irina Mocanu 1 Eugenia Kalisz 2 This paper evaluates the performances of a new type of genetic
More informationMultiDisciplinary Optimization with Minamo
EXCELLENCE IN SIMULATION TECHNOLOGIES MultiDisciplinary Optimization with Minamo Ingrid Lepot Numerical Methods and Optimization Group, Cenaero CESAR Training Workshop, Mar 18, 2009 Surrogate Based Optimization
More informationDifferential Evolution
Chapter 13 Differential Evolution Differential evolution (DE) is a stochastic, populationbased search strategy developed by Storn and Price [696, 813] in 1995. While DE shares similarities with other
More informationAbstract. 1 Introduction
Shape optimal design using GA and BEM Eisuke Kita & Hisashi Tanie Department of MechanoInformatics and Systems, Nagoya University, Nagoya 46401, Japan Abstract This paper describes a shape optimization
More informationDesign Optimization of Laminated Composite Structures Using. Explicit Finite Element Analysis. Krista Mika
Design Optimization of Laminated Composite Structures Using Explicit Finite Element Analysis by Krista Mika A Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science
More informationDesign of LargeScale Optical Networks Λ
Design of LargeScale Optical Networks Λ Yufeng Xin, George N. Rouskas, Harry G. Perros Department of Computer Science, North Carolina State University, Raleigh NC 27695 Email: fyxin,rouskas,hpg@eos.ncsu.edu
More informationOutline. Motivation. Introduction of GAs. Genetic Algorithm 9/7/2017. Motivation Genetic algorithms An illustrative example Hypothesis space search
Outline Genetic Algorithm Motivation Genetic algorithms An illustrative example Hypothesis space search Motivation Evolution is known to be a successful, robust method for adaptation within biological
More informationIntroduction to Machine Learning. Xiaojin Zhu
Introduction to Machine Learning Xiaojin Zhu jerryzhu@cs.wisc.edu Read Chapter 1 of this book: Xiaojin Zhu and Andrew B. Goldberg. Introduction to Semi Supervised Learning. http://www.morganclaypool.com/doi/abs/10.2200/s00196ed1v01y200906aim006
More informationGA is the most popular population based heuristic algorithm since it was developed by Holland in 1975 [1]. This algorithm runs faster and requires les
Chaotic Crossover Operator on Genetic Algorithm Hüseyin Demirci Computer Engineering, Sakarya University, Sakarya, 54187, Turkey Ahmet Turan Özcerit Computer Engineering, Sakarya University, Sakarya, 54187,
More informationThreeDimensional OffLine Path Planning for Unmanned Aerial Vehicle Using Modified Particle Swarm Optimization
ThreeDimensional OffLine Path Planning for Unmanned Aerial Vehicle Using Modified Particle Swarm Optimization Lana Dalawr Jalal Abstract This paper addresses the problem of offline path planning for
More informationOptimization Technique for Maximization Problem in Evolutionary Programming of Genetic Algorithm in Data Mining
Optimization Technique for Maximization Problem in Evolutionary Programming of Genetic Algorithm in Data Mining R. Karthick Assistant Professor, Dept. of MCA Karpagam Institute of Technology karthick2885@yahoo.com
More informationSurrogateassisted Selfaccelerated Particle Swarm Optimization
Surrogateassisted Selfaccelerated Particle Swarm Optimization Kambiz Haji Hajikolaei 1, Amir Safari, G. Gary Wang ±, Hirpa G. Lemu, ± School of Mechatronic Systems Engineering, Simon Fraser University,
More informationAN EVOLUTIONARY APPROACH TO DISTANCE VECTOR ROUTING
International Journal of Latest Research in Science and Technology Volume 3, Issue 3: Page No. 201205, MayJune 2014 http://www.mnkjournals.com/ijlrst.htm ISSN (Online):22785299 AN EVOLUTIONARY APPROACH
More informationGenetic Algorithm and Direct Search Toolbox For Use with MATLAB
Genetic Algorithm and Direct Search Toolbox For Use with MATLAB Computation Visualization Programming User s Guide Version 2 How to Contact The MathWorks www.mathworks.com Web comp.softsys.matlab Newsgroup
More informationCONCEPT FORMATION AND DECISION TREE INDUCTION USING THE GENETIC PROGRAMMING PARADIGM
1 CONCEPT FORMATION AND DECISION TREE INDUCTION USING THE GENETIC PROGRAMMING PARADIGM John R. Koza Computer Science Department Stanford University Stanford, California 94305 USA EMAIL: Koza@Sunburn.Stanford.Edu
More informationPACKING AND OPTIMIZING THE CENTER OF GRAVITY LOCATION USING A GENETIC ALGORITHM
PACKING AND OPTIMIZING THE CENTER OF GRAVITY LOCATION USING A GENETIC ALGORITHM John R. Wodziak, Georges M. Fadel Design Methodology Group Clemson University, Clemson SC 29634 ABSTRACT This paper presents
More informationLecture
Lecture.. 7 Constrained problems & optimization Brief introduction differential evolution Brief eample of hybridization of EAs Multiobjective problems & optimization Pareto optimization This slides mainly
More informationEngineering optimization. Chapter 7: Constrained direct search
Engineering optimization. Chapter 7: Constrained direct search HuyDung Han, Fabio E. Lapiccirella Department of Electrical and Computer Engineering University of California, Davis Davis, CA 95616, U.S.A.
More informationNetwork Reconfiguration for Loss Reduction in Electrical Distribution System Using Genetic Algorithm
Network Reconfiguration for Loss Reduction in Electrical Distribution System Using Genetic Algorithm S. A. Nagy*, I. S. Ibrahim, M. K. Ahmed*, A. S. Adail and S. Soliman Hot Labs Center, Atomic Energy
More informationSIZE AND SHAPE OPTIMIZATION OF FRAME AND TRUSS STRUCTURES THROUGH EVOLUTIONARY METHODS. A Thesis
SIZE AND SHAPE OPTIMIZATION OF FRAME AND TRUSS STRUCTURES THROUGH EVOLUTIONARY METHODS A Thesis Presented in Partial Fulfillment of the Requirements for the Degree of Master of Science with a Major in
More informationSimulated Annealing. G5BAIM: Artificial Intelligence Methods. Graham Kendall. 15 Feb 09 1
G5BAIM: Artificial Intelligence Methods Graham Kendall 15 Feb 09 1 G5BAIM Artificial Intelligence Methods Graham Kendall Simulated Annealing Simulated Annealing Motivated by the physical annealing process
More informationAnalyzing Stochastic Gradient Descent for Some Non Convex Problems
Analyzing Stochastic Gradient Descent for Some Non Convex Problems Christopher De Sa Soon at Cornell University cdesa@stanford.edu stanford.edu/~cdesa Kunle Olukotun Christopher Ré Stanford University
More informationMachine Evolution. Machine Evolution. Let s look at. Machine Evolution. Machine Evolution. Machine Evolution. Machine Evolution
Let s look at As you will see later in this course, neural networks can learn, that is, adapt to given constraints. For example, NNs can approximate a given function. In biology, such learning corresponds
More informationJournal of Computational Science and Technology
Science and Technology Vol., No. 1, 008 Optimization of Blade Stiffened Composite Panel under Buckling and Strength Constraints Akira TODOROKI and Masato SEKISHIRO Department of Mechanical Sciences and
More informationSparse Matrices Reordering using Evolutionary Algorithms: A Seeded Approach
1 Sparse Matrices Reordering using Evolutionary Algorithms: A Seeded Approach David Greiner, Gustavo Montero, Gabriel Winter Institute of Intelligent Systems and Numerical Applications in Engineering (IUSIANI)
More informationIntroduction to optimization methods and line search
Introduction to optimization methods and line search Jussi Hakanen Postdoctoral researcher jussi.hakanen@jyu.fi How to find optimal solutions? Trial and error widely used in practice, not efficient and
More information