# Constrained Functions of N Variables: Non-Gradient Based Methods

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 onstrained Functions of N Variables: Non-Gradient Based Methods Gerhard Venter Stellenbosch University

2 Outline Outline onstrained Optimization Non-gradient 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: Non-gradient 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 Kuhn-Tucker 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 Non-Gradient 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 move-limits Referred to as a structured random search We will consider two structured random searches in this class 6

7 Non-Gradient Based Methods Non-gradient 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 Non-Gradient 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 ross-over Occasional mutation Elitist strategy Design variables are encoded in bit-strings 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 16-ply 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 ross-over 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 cross-over 19

20 ross-over over Select two parents for reproduction Apply probability of cross-over, pc Pc is typically close to 1 Mix parent genes using cross-over to obtain one (or two) children One point cross-over Parent Parent hild

21 ross-over over Two point cross-over Parent Parent hild Uniform cross-over Parent Parent Random hild

22 ross-over over One point averaging cross-over Especially useful for real-numbers 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 cross-sections for a truss structure ombinatorial type problems omposite laminate design find optimum thickness and ply orientation D-optimal design of experiments 25

26 Particle Swarm Optimization Particle Swarm Optimization (PSO) is a fairly recent addition to the family of non-gradient 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 re-setting 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 sub-optimization GENESIS Aerodynamic analysis Simplified analysis 34

35 System Level Optimization Unconstrained problem Maximize: Range Design Variables: Aspect ratio Depth-to-chord ratio Number of internal spars Number of internal ribs Wing cover construction ontinuous Variables Discrete Variables 35

36 Structural Sub-Optimization 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 sub-optimization 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 Take-Off Gross Weight Structural weight saving is converted to fuel weight Wing is build to a jig shape to compensate for the aerodynamic-structure interaction 37

38 System Level Analysis Update FE Model System Level Analysis Apply Pressure Distribution Structural Sub-Optimization 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 gradient-based 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 Gradient-Based Results Parameter Reference Wing DOT Optimum PSO Optimum Aspect Ratio Depth-to-hord 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 sub-optimization 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 part-time! 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 master-slave 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 Non-gradient 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

### An 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/

### Introduction 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

### Introduction 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

### GENETIC ALGORITHM with Hands-On exercise

GENETIC ALGORITHM with Hands-On exercise Adopted From Lecture by Michael Negnevitsky, Electrical Engineering & Computer Science University of Tasmania 1 Objective To understand the processes ie. GAs Basic

### Introduction to Design Optimization: Search Methods

Introduction to Design Optimization: Search Methods 1-D 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

### Genetic 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

### Generation 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.

### CS5401 FS2015 Exam 1 Key

CS5401 FS2015 Exam 1 Key This is a closed-book, closed-notes 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

### Evolutionary 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

### A 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

### Automated 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

### THE 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

### Genetic 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

### 1 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

### 4/22/2014. 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

### Automata 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,

### Lecture 4. Convexity Robust cost functions Optimizing non-convex functions. 3B1B Optimization Michaelmas 2017 A. Zisserman

Lecture 4 3B1B Optimization Michaelmas 2017 A. Zisserman Convexity Robust cost functions Optimizing non-convex functions grid search branch and bound simulated annealing evolutionary optimization The Optimization

### GENETIC ALGORITHM VERSUS PARTICLE SWARM OPTIMIZATION IN N-QUEEN PROBLEM

Journal of Al-Nahrain University Vol.10(2), December, 2007, pp.172-177 Science GENETIC ALGORITHM VERSUS PARTICLE SWARM OPTIMIZATION IN N-QUEEN PROBLEM * Azhar W. Hammad, ** Dr. Ban N. Thannoon Al-Nahrain

### Available 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 (INTER-ENG 2013) Steel truss optimization

### Artificial Intelligence Application (Genetic Algorithm)

Babylon University College of Information Technology Software Department Artificial Intelligence Application (Genetic Algorithm) By Dr. Asaad Sabah Hadi 2014-2015 EVOLUTIONARY ALGORITHM The main idea about

### A 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

### Evolutionary 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

### Genetic 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

### Path 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

### Optimization of Laminar Wings for Pro-Green Aircrafts

Optimization of Laminar Wings for Pro-Green Aircrafts André Rafael Ferreira Matos Abstract This work falls within the scope of aerodynamic design of pro-green aircraft, where the use of wings with higher

### Witold Pedrycz. University of Alberta Edmonton, Alberta, Canada

2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC) Banff Center, Banff, Canada, October 5-8, 2017 Analysis of Optimization Algorithms in Automated Test Pattern Generation for Sequential

### CHAPTER 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

OPTIMIZATION METHODS modefrontier is a registered product of ESTECO srl Copyright ESTECO srl 1999-2007 For more information visit: www.esteco.com or send an e-mail to: modefrontier@esteco.com NEOS Optimization

### Operations 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

### Frequency 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

### Particle 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)

### Automatic differentiation based for particle swarm optimization steepest descent direction

International Journal of Advances in Intelligent Informatics ISSN: 2442-6571 Vol 1, No 2, July 2015, pp. 90-97 90 Automatic differentiation based for particle swarm optimization steepest descent direction

### Optimization 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

### Genetic Algorithm Performance with Different Selection Methods in Solving Multi-Objective Network Design Problem

etic Algorithm Performance with Different Selection Methods in Solving Multi-Objective Network Design Problem R. O. Oladele Department of Computer Science University of Ilorin P.M.B. 1515, Ilorin, NIGERIA

### CT79 SOFT COMPUTING ALCCS-FEB 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

### What 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

### Introduction (7.1) Genetic Algorithms (GA) (7.2) Simulated Annealing (SA) (7.3) Random Search (7.4) Downhill Simplex Search (DSS) (7.

Chapter 7: Derivative-Free Optimization Introduction (7.1) Genetic Algorithms (GA) (7.2) Simulated Annealing (SA) (7.3) Random Search (7.4) Downhill Simplex Search (DSS) (7.5) Jyh-Shing Roger Jang et al.,

### Genetic 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

### AIRFOIL 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

### Genetic.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 Self-taught, passion for development. Java, Cassandra, Spark, JPPF. @jsebrien, julien.sebrien@genetic.io Distribution of IT solutions (SaaS,

### Optimization 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

### An Application of Genetic Algorithm for Auto-body Panel Die-design Case Library Based on Grid

An Application of Genetic Algorithm for Auto-body Panel Die-design 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

### Binary 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, population-based optimization approach. The

### Bayesian 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

### Optimizing 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

### APPLICATION OF VARIABLE-FIDELITY MODELS TO AERODYNAMIC OPTIMIZATION

Applied Mathematics and Mechanics (English Edition), 2006, 27(8):1089 1095 c Editorial Committee of Appl. Math. Mech., ISSN 0253-4827 APPLICATION OF VARIABLE-FIDELITY MODELS TO AERODYNAMIC OPTIMIZATION

### A 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

### An 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,

### Introduction 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

### Outline. Best-first search. Greedy best-first search A* search Heuristics Local search algorithms

Outline Best-first search Greedy best-first search A* search Heuristics Local search algorithms Hill-climbing search Beam search Simulated annealing search Genetic algorithms Constraint Satisfaction Problems

### Reducing 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,

### Genetic Algorithms For Vertex. Splitting in DAGs 1

Genetic Algorithms For Vertex Splitting in DAGs 1 Matthias Mayer 2 and Fikret Ercal 3 CSC-93-02 Fri Jan 29 1993 Department of Computer Science University of Missouri-Rolla Rolla, MO 65401, U.S.A. (314)

### Genetic 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.soft-sys.matlab support@mathworks.com suggest@mathworks.com bugs@mathworks.com

### Towards 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

### Discussion of Various Techniques for Solving Economic Load Dispatch

International Journal of Enhanced Research in Science, Technology & Engineering ISSN: 2319-7463, Vol. 4 Issue 7, July-2015 Discussion of Various Techniques for Solving Economic Load Dispatch Veerpal Kaur

### A 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,

### GENERATIONAL MODEL GENETIC ALGORITHM FOR REAL WORLD SET PARTITIONING PROBLEMS

International Journal of Electronic Commerce Studies Vol.4, No.1, pp. 33-46, 2013 doi: 10.7903/ijecs.1138 GENERATIONAL MODEL GENETIC ALGORITHM FOR REAL WORLD SET PARTITIONING PROBLEMS Chi-san Althon Lin

### Evolving 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

### A Parallel Genetic Algorithm for Maximum Flow Problem

A Parallel Genetic Algorithm for Maximum Flow Problem Ola M. Surakhi Computer Science Department University of Jordan Amman-Jordan Mohammad Qatawneh Computer Science Department University of Jordan Amman-Jordan

### Theoretical 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

### A Steady-State Genetic Algorithm for Traveling Salesman Problem with Pickup and Delivery

A Steady-State 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,

### Machine Learning for Software Engineering

Machine Learning for Software Engineering Single-State Meta-Heuristics Prof. Dr.-Ing. Norbert Siegmund Intelligent Software Systems 1 2 Recap: Goal is to Find the Optimum Challenges of general optimization

### OPTIMAL 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, E1-08-21, Engineering

### Another 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

### MATLAB Based Optimization Techniques and Parallel Computing

MATLAB Based Optimization Techniques and Parallel Computing Bratislava June 4, 2009 2009 The MathWorks, Inc. Jörg-M. Sautter Application Engineer The MathWorks Agenda Introduction Local and Smooth Optimization

### Thresholds 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

### CHAPTER 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

### The exam is closed book, closed notes except your one-page (two-sided) 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 one-page (two-sided) cheat sheet. No calculators or

### THE 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.

### Derivative-Free Optimization

Derivative-Free 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

### Particle 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

### Derating 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

### A 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 equality-constrained optimization/lagrange

### ANTICIPATORY 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

### Multi-Disciplinary Optimization with Minamo

EXCELLENCE IN SIMULATION TECHNOLOGIES Multi-Disciplinary Optimization with Minamo Ingrid Lepot Numerical Methods and Optimization Group, Cenaero CESAR Training Workshop, Mar 18, 2009 Surrogate Based Optimization

### Differential Evolution

Chapter 13 Differential Evolution Differential evolution (DE) is a stochastic, population-based search strategy developed by Storn and Price [696, 813] in 1995. While DE shares similarities with other

### Abstract. 1 Introduction

Shape optimal design using GA and BEM Eisuke Kita & Hisashi Tanie Department of Mechano-Informatics and Systems, Nagoya University, Nagoya 464-01, Japan Abstract This paper describes a shape optimization

### Design 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

### Design of Large-Scale Optical Networks Λ

Design of Large-Scale Optical Networks Λ Yufeng Xin, George N. Rouskas, Harry G. Perros Department of Computer Science, North Carolina State University, Raleigh NC 27695 E-mail: fyxin,rouskas,hpg@eos.ncsu.edu

### Outline. 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

### Introduction 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

### GA 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,

### Three-Dimensional Off-Line Path Planning for Unmanned Aerial Vehicle Using Modified Particle Swarm Optimization

Three-Dimensional Off-Line 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

### Optimization 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

### Surrogate-assisted Self-accelerated Particle Swarm Optimization

Surrogate-assisted Self-accelerated Particle Swarm Optimization Kambiz Haji Hajikolaei 1, Amir Safari, G. Gary Wang ±, Hirpa G. Lemu, ± School of Mechatronic Systems Engineering, Simon Fraser University,

### AN EVOLUTIONARY APPROACH TO DISTANCE VECTOR ROUTING

International Journal of Latest Research in Science and Technology Volume 3, Issue 3: Page No. 201-205, May-June 2014 http://www.mnkjournals.com/ijlrst.htm ISSN (Online):2278-5299 AN EVOLUTIONARY APPROACH

### Genetic 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.soft-sys.matlab Newsgroup

### CONCEPT 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 E-MAIL: Koza@Sunburn.Stanford.Edu

### PACKING 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

### Lecture

Lecture.. 7 Constrained problems & optimization Brief introduction differential evolution Brief eample of hybridization of EAs Multiobjective problems & optimization Pareto optimization This slides mainly

### Engineering optimization. Chapter 7: Constrained direct search

Engineering optimization. Chapter 7: Constrained direct search Huy-Dung Han, Fabio E. Lapiccirella Department of Electrical and Computer Engineering University of California, Davis Davis, CA 95616, U.S.A.

### Network 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

### SIZE 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

### Simulated 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

### Analyzing 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

### Machine 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

### Journal 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