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
• 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 Data Structures of the GEATbx
• 6.1 Chromosomes (genotype / individuals)
• 6.2 Phenotypes (decision variables / individuals)
• 6.3 Objective function values
• 6.4 Fitness values
• 6.5 Multiple subpopulations
• 7 How to Approach new Optimization Problems
• 7.1 Classifying the Problem and Defining the Objective Function
• 7.2 Investigating the System Behavior
• One and Two-dimensional Slices (Variational Diagrams)
• Multi-dimensional Visualization
• Decreasing the System Size/Dimension
• 7.3 Selecting the Optimization Method
• 7.4 Executing and Evaluating Optimizations

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
• 3.2.1 PARETO-ranking
• 3.2.2 Goal attainment or method of inequalities
• 3.2.3 Sharing
• 3.2.4 Further information on multi-objective optimization
• 3.2.5 Weighted sum - aggregation or scalarization of multiple objectives
• 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 Population models - Parallel implementations
• 7.1 Global model - worker/farmer
• 7.2 Local model - Diffusion model
• 7.3 Regional model - Migration
• 8 Application of different strategies
• 8.1 Different strategies for each subpopulation
• 8.1.1 Order of Subpopulations
• 8.2 Competition between subpopulations
• 8.2.1 Division of Resources
• 8.2.2 Distribution of Resources
• 8.2.3 Resource Consumption
• 8.2.4 Competition Interval and Competition Rate
• 8.2.5 Competition Selection
• 8.2.6 Subpopulation Minimum
• 8.3 Application of Different Strategies
• 8.4 Application of Competing Subpopulations
• 8.5 Conclusion
• 9 Combination of Operators and Options to Produce Evolutionary Algorithms
• 9.1 Generally Adjustable Operators and Options
• 9.1.1 Operators and Options for Fitness Assignment and Selection
• 9.1.2 Operators and Options for Application of Different Strategies and Competition between Subpopulations
• 9.1.3 Operators and Options for Regional Population Model (Migration between Subpopulations)
• 9.1.4 Summary of generally adjustable operators and options
• 9.2 Globally Oriented Parameter Optimization
• 9.2.1 Recombination
• 9.2.2 Mutation
• 9.3 Locally Oriented Parameter Optimization
• 9.3.1 Recombination
• 9.3.2 Mutation
• 9.3.3 Fitness Assignment and Selection
• 9.4 Parameter Optimization of Binary Variables
• 9.4.1 Recombination
• 9.4.2 Mutation
• 9.5 Combinatorial Optimization
• 9.5.1 Recombination
• 9.5.2 Mutation
• 9.6 Parameter Optimization of Variables of different Representations
• 9.6.1 Integer and Binary Variables
• 9.6.2 Use of Integer Representation
• 9.6.3 Use of Binary Representation
• 9.6.4 Use of real representation
• 9.7 Summary
• 10 Reference
• 10.1 Evolutionary Algorithms
• 10.2 Population models and parallel EA
• 10.3 Combinatorial optimization
• 10.4 Visualization
• 10.5 Polyploidy and Evolutionary Algorithms
• 10.6 Biology, Genetics and Population genetics

GEATbx Examples
Examples of
Objective Functions

• 1 Introduction
• 1.1 Examples of Parametric 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
• Index