GEATbx:
Main page
Tutorial
Algorithms
M-functions
Parameter/Options
Example functions
www.geatbx.com
Table of Contents of GEATbx Documentation
GEATbx Tutorial
1 Introduction
2 Quick Start
2.1 First demonstration
2.2 Second demonstration
2.3 Your first optimization of an own objective function
2.4 Further Steps
3 Writing Objective Functions
3.1 Parametric optimization functions
3.2 Defining default values of the objective function
3.3 Optimization of dynamic systems
3.4 Remark
4 Variable Representation
4.1 Conversion between Variable Representations
4.2 Examples of Variable Representation
4.2.1 Real --- Real
4.2.2 Real (phenotype) --- Binary (genotype)
4.2.3 Integer (phenotype) --- Integer (genotype) or Binary (genotype)
4.2.4 Binary --- Binary
4.3 Simultaneous Use of Multiple Representations
4.3.1 Integer and Binary (phenotype) --- Integer (genotype)
4.3.2 Real and Integer and Binary (phenotype) --- Integer (genotype)
5 Overview of GEA Toolbox Structure
5.1 Naming Convention
5.2 Calling Tree
5.3 Demo / Startup function
5.4 Toolbox functions (Predefined algorithms)
5.5 Evolutionary Algorithm - Main function
5.5.1 Initialization
5.5.2 Generational loop of the EA
5.5.3 Fitness assignment by ranking
5.5.4 Selection
5.5.5 Recombination/Crossover
5.5.6 Mutation
5.5.7 Evaluation
5.5.8 Reinsertion
5.5.9 Migration
5.5.10 Competition
5.5.11 Visualization
5.6 Utility functions
6 Multi-objective Optimization in the GEATbx
6.1 Switch on multi-objective ranking
6.2 Visualization of multi-objective solutions
6.3 Definition of goals in objective functions
6.4 Archive - collect and reinsert good solutions
7 Constraint Optimization in the GEATbx
7.1 Constraining the variables
7.2 Functional constraints
7.2.1 Functional constraints using additional objectives and goals
7.2.2 Implementation of functional constraints (larger than, >=)
7.2.3 Implementation of functional constraints (smaller than, <=)
7.2.4 Implementation of functional constraints (equal to, ==)
8 Data Structures of the GEATbx
8.1 Chromosomes (genotype / individuals)
8.2 Phenotypes (decision variables / individuals)
8.3 Objective function values
8.4 Fitness values
8.5 Multiple subpopulations
9 How to Approach new Optimization Problems
9.1 Classifying the Problem and Defining the Objective Function
9.2 Investigating the System Behavior
One and Two-dimensional Slices (Variational Diagrams)
Multi-dimensional Visualization
Decreasing the System Size/Dimension
9.3 Selecting the Optimization Method
9.4 Executing and Evaluating Optimizations
Index
GEATbx: Options
Parameter Options
1 Introduction
1.1 Predefined Evolutionary Algorithms
1.2 Option handling with geaoptset.m
Default Options
Define and/or Add Options
Merge Option Structures
Check Validity of Option Structures
1.3 Examples of option settings
1.4 Status and result output during optimization
1.5 Description of Options
2 General options
NumberSubpopulation
NumberIndividuals
VariableFormat
3 Selection options
Selection.Name
Selection.Pressure
Selection.GenerationGap
Selection.ReinsertionRate
Selection.RankingMethod
Selection.RankingMultiobj
Selection.ReinsertionMethod
Selection.LocalDimension
Selection.LocalTopology
Selection.LocalDistance
4 Recombination options
Recombination.Name
Recombination.Rate
5 Mutation options
Mutation.Name
Mutation.Rate
Mutation.Range
Mutation.Precision
6 Migration options
Migration.Do
Migration.Interval
Migration.Rate
Migration.Topology
Migration.Selection
7 Competition options
Competition.Do
Competition.Interval
Competition.Rate
Competition.SubpopMinimum
8 Termination options
Termination.Method
Termination.MaxGenerations
Termination.MaxTime
Termination.Diff2Optimum
Termination.RunningMean
Termination.StdObjV
Termination.GoodWorstObjV
Termination.Phi
Termination.Kappa
Termination.Cluster
9 Output and Visualization options
Output.TextInterval
Output.GrafikInterval
Output.GrafikMethod
Output.GrafikStyle
Output.SaveTextInterval
Output.SaveTextFileName
Output.SaveBinDataInterval
Output.SaveBinDataFileName
Output.StatePlotInterval
Output.StatePlotFunction
Output.TextExclude* and Output.SaveTextExclude*
10 Result and run time options
Run.BestObjectiveValue
Run.CountObjFun
Run.Generation
Run.DoTerminate
11 Objective function options
System.ObjFunFilename
System.ObjFunVarBounds
System.ObjFunAddPara
System.ObjFunVarBoundOut
System.ObjFunGoals
System.ObjFunMinimum
System.ObjFunDescription
12 Special initialization options
Special.InitPresetKeep
Special.InitUniformCreate
Special.InitPresetRand
Special.InitDo
Special.InitFunction
Special.CollectBest.Interval
Special.CollectBest.Rate
Special.CollectBest.Compare
Special.CollectBest.WriteFile
Special.CollectBest.FileName
13 Comparison of Options (1.9x / 2.x / 3.x)
Index
GEATbx: Introduction
Evolutionary Algorithms: Overview, Methods and Operators
1 Introduction
2 Overview
2.1 Selection
2.2 Recombination
2.3 Mutation
2.4 Reinsertion
2.5 Population models - parallel implementation of evolutionary algorithms
2.6 Application of multiple/different strategies and competition between subpopulations
3 Selection
3.1 Rank-based fitness assignment
3.1.1 Linear ranking
3.1.2 Non-linear ranking
3.1.3 Comparison of linear and non-linear ranking
3.1.4 Analysis of linear ranking
3.2 Multi-objective Ranking
3.3 Roulette wheel selection
3.4 Stochastic universal sampling
3.5 Local selection
3.6 Truncation selection
3.6.1 Analysis of truncation selection
3.7 Tournament selection
3.7.1 Analysis of tournament selection
3.8 Comparison of selection schemes
3.8.1 Selection parameter and selection intensity
3.8.2 Loss of diversity and selection intensity
3.8.3 Selection variance and selection intensity
4 Recombination
4.1 All representations - Discrete recombination
4.2 Real valued recombination
4.2.1 Intermediate recombination
4.2.2 Line recombination
4.2.3 Extended line recombination
4.3 Binary valued recombination (crossover)
4.3.1 Single-point / double point / multi-point crossover
4.3.2 Uniform crossover
4.3.3 Shuffle crossover
4.3.4 Crossover with reduced surrogate
5 Mutation
5.1 Real valued mutation
5.2 Binary mutation
5.3 Real valued mutation with adaptation of step-sizes
6 Reinsertion
6.1 Global reinsertion
6.2 Local reinsertion
7 Multi-objective Optimization
7.1 PARETO-ranking (Multi-objective Ranking)
7.2 Goal attainment or method of inequalities
7.3 Sharing in search space or in solution space
7.4 Further information on multi-objective optimization
7.5 Weighted sum - aggregation or scalarization of multiple objectives
8 Population models - Parallel implementations
8.1 Global model - worker/farmer
8.2 Local model - Diffusion model
8.3 Regional model - Migration
9 Application of different strategies
9.1 Different strategies for each subpopulation
9.1.1 Order of Subpopulations
9.2 Competition between subpopulations
9.2.1 Division of Resources
9.2.2 Distribution of Resources
9.2.3 Resource Consumption
9.2.4 Competition Interval and Competition Rate
9.2.5 Competition Selection
9.2.6 Subpopulation Minimum
9.3 Application of Different Strategies
9.4 Application of Competing Subpopulations
9.5 Conclusion
10 Combination of Operators and Options to Produce Evolutionary Algorithms
10.1 Generally Adjustable Operators and Options
10.1.1 Operators and Options for Fitness Assignment and Selection
10.1.2 Operators and Options for Application of Different Strategies and Competition between Subpopulations
10.1.3 Operators and Options for Regional Population Model (Migration between Subpopulations)
10.1.4 Summary of generally adjustable operators and options
10.2 Globally Oriented Parameter Optimization
10.2.1 Recombination
10.2.2 Mutation
10.3 Locally Oriented Parameter Optimization
10.3.1 Recombination
10.3.2 Mutation
10.3.3 Fitness Assignment and Selection
10.4 Parameter Optimization of Binary Variables
10.4.1 Recombination
10.4.2 Mutation
10.5 Combinatorial Optimization
10.5.1 Recombination
10.5.2 Mutation
10.6 Parameter Optimization of Variables of different Representations
10.6.1 Integer and Binary Variables
10.6.2 Use of Integer Representation
10.6.3 Use of Binary Representation
10.6.4 Use of real representation
10.7 Summary
11 Reference
11.1 Evolutionary Algorithms
11.2 Population models and parallel EA
11.3 Combinatorial optimization
11.4 Visualization
11.5 Polyploidy and Evolutionary Algorithms
11.6 Biology, Genetics and Population genetics
11.7 Multiobjective optimization
GEATbx Examples
Examples of
Objective Functions
1 Introduction
1.1 Examples of Parametric Optimization
1.2 Examples of Multi-objective Optimization
2 Parametric Optimization
2.1 De Jong's function 1
2.2 Axis parallel hyper-ellipsoid function
2.3 Rotated hyper-ellipsoid function
2.4 Moved axis parallel hyper-ellipsoid function
2.5 Rosenbrock's valley (De Jong's function 2)
2.6 Rastrigin's function 6
2.7 Schwefel's function 7
2.8 Griewangk's function 8
2.9 Sum of different power function 9
2.10 Ackley's Path function 10
2.11 Langermann's function 11
2.12 Michalewicz's function 12
2.13 Branins's rcos function
2.14 Easom's function
2.15 Goldstein-Price's function
2.16 Six-hump camel back function
3 Multi-objective Optimization
3.1 Fonseca's function 1 and 2
Index
GEATbx:
Main page
Tutorial
Algorithms
M-functions
Parameter/Options
Example functions
www.geatbx.com
This document is part of
version 3.8
of the
GEATbx: Genetic and Evolutionary Algorithm Toolbox for use with Matlab -
www.geatbx.com
.
The Genetic and Evolutionary Algorithm Toolbox is
not public domain
.
© 1994-2006 Hartmut Pohlheim, All Rights Reserved, (
support@geatbx.com
).