Planet Source Code Jumbo …e CD Visual Basic 1 to 7/5_2007-2008.ISO/data/Zips/Big_Geneti211159542008.psc/clsGeneticAlgorithm.cls

Text File | 2008-05-02 | 145KB | 3,112 lines

VERSION 1.0 CLASS
BEGIN
  MultiUse = -1  'True
  Persistable = 0  'NotPersistable
  DataBindingBehavior = 0  'vbNone
  DataSourceBehavior  = 0  'vbNone
  MTSTransactionMode  = 0  'NotAnMTSObject
END
Attribute VB_Name = "clsGeneticAlgorithm"
Attribute VB_GlobalNameSpace = False
Attribute VB_Creatable = True
Attribute VB_PredeclaredId = False
Attribute VB_Exposed = False
Option Explicit

' =====================================
'
'   Genetic Algorithm class
'
'        By Thierry Van Mol
'
'   First public release
'   version 1.0.0
'   2007 - 2008
'   email : [e-mail]
'
' =====================================



'
' Constants
' +++++++++++++++++++++++++++++++++++++++++++++++++++

' Version
Private Const cVersion = "1.0.0"

' Maximum times to spin the roulettewheel before trying Rank
Private Const cRouletteWheelSpinMax As Integer = 3  ' when spinning the roulettewheel, a check is done to ensure both
                                                    ' chromosomes are different (not the value, but the index).
                                                    ' This constant is the number of times to spin the wheel
                                                    ' before jumping to Rank selection method

Private Const cCrossoverUniform As Double = 0.5     ' Probability of a swap in uniform crossover
                                                    ' 0.5 = 50% chance the bit will be swapped

Private Const cLongMaxLength As Integer = 11        ' Maximum length of a long, used to convert a
                                                    ' long to a string. Range is -2,147,483,648 to 2,147,483,647
                                                    ' so (not counting the thousand separator)
                                                    ' maximum number of digits  : 10
                                                    ' eventual minus sign       :  1
                                                    ' 10 + 1                    = 11
                                                    '
                                                    ' However in order to maximize the functionality
                                                    ' of the GA, the length to use is calculated and
                                                    ' filled in mintLongActualLength

Private Const cDoubleMaxLength As Integer = 22      ' Maximum length of a double number, used to convert
                                                    ' a double to a string
                                                    ' range is -1.79769313486231E308 to -4.94065645841247E-324 for negative
                                                    ' values; 4.94065645841247E-324 to 1.79769313486232E308 for positive values
                                                    ' maximum accuracy of double : 15 digits
                                                    ' place for the decimal point:  1
                                                    ' place for negative sign    :  1
                                                    ' place for 'E' character    :  1
                                                    ' place for negative power   :  1
                                                    ' maximum power              :  3 digits
                                                    ' 15 + 1 + 1 + 1 + 1 + 3     = 22
                                                    '
                                                    ' However in order to maximize the functionality
                                                    ' of the GA, the length to use is calculated and
                                                    ' filled in mintDoubleActualLength

'
' Events definition
' ++++++++++++++++++++++++++++++++++++++++++++++++++

' New Gene event
Public Event NewGeneString(ByRef strGene As String)

Public Event NewGeneLong(ByRef lngGene As Long)

Public Event NewGeneDouble(ByRef dblGene As Double)

' Fitness event
Public Event EvaluateFitness(ByVal lngIndex As Long, ByRef dblFitness As Double)

' New chromosome event
Public Event NewChromosome(ByRef NewStringGenes() As String, ByRef NewLongGenes() As Long, ByRef NewDoubleGenes() As Double, ByVal intOrigin As GANewChromosomeOriginType)

' Error
Public Event GAError(ByVal ErrorCode As Long, ByVal ErrorDescription As String)



'
' Class variables
' used with properties
' +++++++++++++++++++++++++++++++++++++++++++++++++++

Private mGeneration             As Long     ' the generation counter (set to 1 at CREATEPOPULATION
                                            ' and incremented during REPRODUCTION)

Private Chromosome()            As ChromosomeindividualType
                                            ' The chromosome...

Private mChromosomeType         As Integer  ' the type of chromosome we are going
                                            ' to use. defined in GAEncodingType
                                            ' 1 = binary string
                                            ' 2 = Alphabetical
                                            ' 3 = long numbers
                                            ' 4 = Double numbers

Private mGenesPerChromosome     As Integer  ' howmany genes are there in a chromosome

Private mBinaryGeneLength       As Integer  ' how long is one gene (howmany characters can
                                            ' a binary gene be)
                                            ' when encodingtype = binary

Private mAlphabeticGeneLength   As Integer  ' how long is one gene (howmany characters can
                                            ' an alphabetic gene be)
                                            ' when encodingtype = alphabetical

Private mLongGeneMaxValue       As Long     ' what is the maximumvalue of a long numerical gene
                                            ' when encodingtype = long numbers

Private mLongGeneMinValue       As Long     ' what is the minimumvalue of a long numerical gene
                                            ' when encodingtype = long numbers

Private mDoubleGeneMinValue     As Double   ' what is the minimumvalue of a double numerical gene
                                            ' when encodingtype = double numbers

Private mDoubleGeneMaxValue     As Double   ' what is the maximumvalue of a double numerical gene
                                            ' when encodingtype = double numbers

Private mSelectionMethod        As Integer  ' the selectionmethod used during the Selection process
                                            ' see the GASelectionMethod enumeration
                                            ' Can be Range, Roulette wheel or Tournament

Private mTournamentSize         As Long     ' the size of the selection pool of a Tournament during
                                            ' Tournament selection

Private mCrossoverRate          As Double   ' the corssoverrate

Private mMutationRate           As Double   ' the mutationrate - for fixed mutation
                                            ' or starting value for adaptive mutationrate

Private mActualMutationRate     As Double   ' the actual mutationrate to use
                                            ' if fixed it's the same as mMutationRate
                                            ' if AMR then this value changes by 0.01

Private mMutationBitlikeLongDouble As Boolean ' For long/double encoding only. And only if NOT full gene
                                            ' mutation !
                                            ' If FALSE, a small value will be randomly added / subtracted from
                                            ' the gene-value
                                            ' If TRUE, normal element-like mutation (just like binary encoding)
                                            ' will be used

Private mMutationBitlikePercentage As Double ' See mMutationBitlikeLongDouble
                                            ' This is the percentage of the maximum value for a gene.
                                            ' The random value to be added or subtracted will lie within
                                            ' this percentage's range.

Private mReproductionMethod     As Integer  ' the reproductionmethod used
                                            ' see the GAReproductionType enumeration
                                            ' Can be weakest, random or parents

Private mCrossoverFullGenes     As Boolean  ' If TRUE the crossover happens on a full gene
                                            ' if FALSE corssover can happen anywhere
                                            ' in the chromosome

Private mRandomOffspringGeneration As Boolean ' If TRUE a test is done before crossover to check
                                              ' that both selected chromosomes have different
                                              ' genetic material. If they are the same one of them
                                              ' is replaced by a new random chromosome

Private mCrossoverMethod        As Integer  ' The crossover technique to use
                                            ' one point, two point, uniform or half uniform
                                            ' see GACrossoverType

Private mMutateFullGenes        As Boolean  ' If TRUE the mutation happens on a full gene
                                            ' if FALSE mutation can happen anywhere
                                            ' in the chromosome

Private mMutationMethod         As Integer  ' can be fixed or adaptive
                                            ' See GAMutationType
                                            ' Fixed : the rate in mMutationrate is always taken
                                            ' Adaptive : When the standard deviation of the fitness
                                            ' values stays a number of generations the same (set in
                                            ' mAMRGenerations) then the mutatiorate is increased
                                            ' by 0.01 with a maximum of 1.0
                                            ' If the standard deviation of the fitness values is
                                            ' different for the set number of generations, it is
                                            ' decreased by 0.01, with mMutationRate as minimum

Private mAMRGenerations         As Long     ' number of generations that the standard deviation
                                            ' has to be the same before mutationrate increase
                                            ' for AMR (or different for a decrease)

Private mSocDisGeneticDiv       As Double   ' Social disaster genetic diversity percentage

Private mSocDisMethod           As Integer  ' Social disaster method (see GASocialDisasterType)
                                            ' Can be packing or Judgement day

Private mSocDisGenerations      As Long     ' the amount of generations between
                                            ' each check if a social disaster
                                            ' should occur

Private mDescription            As String   ' small description for these settings

Private mPopulationSize         As Long     ' the populationsize as set in the GA control panel

Private mlngSelectedIndex1      As Long     ' The indexes of the two selected chromosomes for
Private mlngSelectedIndex2      As Long     ' reproduction

Private mAMRCounter             As Long     ' counter for AMR when std.dev. is the same
Private mAMRCounterDiff         As Long     ' counter for AMR when std.dev. is different
Private mAMRFitnessStdDev       As Double   ' the value of the std.dev. for AMR


' Counters
Private mCrossoverCounter       As Long     ' counters...just to count howmany times
Private mMutationCounter        As Long     ' something occurs...
Private mRandomOffspringCounter As Long     '
Private mSocialDisasterCounter  As Long     '


' Statistics
Private mblnKeepStatistics      As Boolean  ' keep the statistics or not
Private mStatistics()           As StatisticsType ' the array



'
' Class variables
' used internally
' ++++++++++++++++++++++++++++++++++++++++++++++++

Private mblnSorted              As Boolean  ' = TRUE if the chromosome array is sorted by fitness
                                            ' = FALSE when the array has to be sorted because a chromosome
                                            '   has changed...
                                            ' This sort is necessary to determine the best (lowest) and worst
                                            ' (highest) chromosomes (fitness wise).

Private mblnAllFitnessCalculated As Boolean ' = TRUE all fitnesses have been calculated
                                            ' = FALSE at least one fitness must be recalculated

Private mSocDisGenCounter       As Long     ' counter for social disaster generations

Private blnCallFromEvaluate     As Boolean  ' used in EVALUATE
                                            ' if a social disaster occured the population has to be
                                            ' re-evaluated. The sub evaluate calls itself
                                            ' but if the user has set the generation-counter
                                            ' for social disasters to 1, an endless loop (not exactly
                                            ' endless because an out-of-stack error will end it eventually)
                                            ' occurs. This boolean makes it possible to jump
                                            ' out

Private mintLongActualLength    As Integer  ' The calculated actual length of a long
                                            ' see the constant cLongMaxLength

Private mintDoubleActualLength  As Integer  ' The calculated actual length of a double
                                            ' see the constant cDoubleMaxLength




' -----------------------------------------------------------------
' Properties
' -----------------------------------------------------------------

' howmany chromosomes are there
Public Property Get PopulationCount() As Long
    PopulationCount = LngNull(UBound(Chromosome())) + 1
End Property

' the type of chromosome used, defined in GAEncodingType
Public Property Get ChromosomeType() As Integer
    ChromosomeType = mChromosomeType
End Property

Public Property Let ChromosomeType(ByVal vNewValue As Integer)
    mChromosomeType = vNewValue
End Property

' howmany genes are there in a chromosome
Public Property Get GenesPerChromosome() As Integer
    GenesPerChromosome = mGenesPerChromosome
End Property

Public Property Let GenesPerChromosome(ByVal vNewValue As Integer)
    mGenesPerChromosome = vNewValue
End Property

' howmany characters is one BINARY gene (when encodingtype = binary)
Public Property Get BinaryGeneLength() As Integer
    BinaryGeneLength = mBinaryGeneLength
End Property

Public Property Let BinaryGeneLength(ByVal vNewValue As Integer)
    mBinaryGeneLength = vNewValue
End Property

' howmany characters is one ALPHABETIC gene (when encodingtype = alphabetic)
Public Property Get AplhabeticGeneLength() As Integer
    AplhabeticGeneLength = mAlphabeticGeneLength
End Property

Public Property Let AplhabeticGeneLength(ByVal vNewValue As Integer)
    mAlphabeticGeneLength = vNewValue
End Property

' what is the maximumvalue of a long numerical gene (when encodingtype = long numbers)
Public Property Get LongGeneMaxValue() As Long
    LongGeneMaxValue = mLongGeneMaxValue
End Property

Public Property Let LongGeneMaxValue(ByVal vNewValue As Long)
    mLongGeneMaxValue = vNewValue
End Property

' what is the minimumvalue of a long numerical gene (when encodingtype = long numbers)
Public Property Get LongGeneMinValue() As Long
    LongGeneMinValue = mLongGeneMinValue
End Property

Public Property Let LongGeneMinValue(ByVal vNewValue As Long)
    mLongGeneMinValue = vNewValue
End Property

' what is the minimumvalue of a double numerical gene (when encodingtype = double numbers)
Public Property Get DoubleGeneMinValue() As Double
    DoubleGeneMinValue = mDoubleGeneMinValue
End Property

Public Property Let DoubleGeneMinValue(ByVal vNewValue As Double)
    mDoubleGeneMinValue = vNewValue
End Property

' what is the maximumvalue of a double numerical gene (when encodingtype = double numbers)
Public Property Get DoubleGeneMaxValue() As Double
    DoubleGeneMaxValue = mDoubleGeneMaxValue
End Property

Public Property Let DoubleGeneMaxValue(ByVal vNewValue As Double)
    mDoubleGeneMaxValue = vNewValue
End Property

' Selectionmethod. Range, roulette wheel or tournament
Public Property Get SelectionMethod() As Integer
    SelectionMethod = mSelectionMethod
End Property

Public Property Let SelectionMethod(ByVal vNewValue As Integer)
    mSelectionMethod = vNewValue
End Property

' the size of the selection pool for tournament selection
Public Property Get TournamentSize() As Long
    TournamentSize = mTournamentSize
End Property

Public Property Let TournamentSize(ByVal vNewValue As Long)
    mTournamentSize = vNewValue
End Property

' the highest Fitness score in the current population = WORST
Public Property Get FitnessHighest() As Double
    If mblnSorted = False Then
        Call QuickSortFitness(0, (PopulationCount - 1))
    End If
    FitnessHighest = Chromosome(PopulationCount - 1).Fitness
End Property

' the lowest Fitness score in the current population = BEST
Public Property Get FitnessLowest() As Double
    If mblnSorted = False Then
        Call QuickSortFitness(0, (PopulationCount - 1))
    End If
    FitnessLowest = Chromosome(0).Fitness
End Property

' the sum of all Fitness scores in the current population
Public Property Get FitnessSum() As Double

    Dim lngloop                 As Long

    Dim dblHelp                 As Double

    dblHelp = 0

    For lngloop = 0 To (PopulationCount - 1)
        dblHelp = dblHelp + Abs(Chromosome(lngloop).Fitness)
    Next lngloop

    FitnessSum = dblHelp

End Property

' The index of the first selected chromosome for reproduction
Public Property Get SelectedChromosomeIndex1() As Long
    SelectedChromosomeIndex1 = mlngSelectedIndex1
End Property

Public Property Let SelectedChromosomeIndex1(ByVal vNewValue As Long)
    mlngSelectedIndex1 = vNewValue
End Property

' The index of the second selected chromosome for reproduction
Public Property Get SelectedChromosomeIndex2() As Long
    SelectedChromosomeIndex2 = mlngSelectedIndex2
End Property

Public Property Let SelectedChromosomeIndex2(ByVal vNewValue As Long)
    mlngSelectedIndex2 = vNewValue
End Property

' the corssoverrate
Public Property Get CrossoverRate() As Double
    CrossoverRate = mCrossoverRate
End Property

Public Property Let CrossoverRate(ByVal vNewValue As Double)
    mCrossoverRate = vNewValue
End Property

' the mutationrate - for fixed or startvalue for adaptive
Public Property Get MutationRate() As Double
    MutationRate = mMutationRate
End Property

Public Property Let MutationRate(ByVal vNewValue As Double)
    mMutationRate = vNewValue
End Property

' Reproductionmethod. replace weakest, replace random or replace parents
Public Property Get ReproductionMethod() As Integer
    ReproductionMethod = mReproductionMethod
End Property

Public Property Let ReproductionMethod(ByVal vNewValue As Integer)
    mReproductionMethod = vNewValue
End Property

' Do we crossover on a full gene or anywhere in the chromosome
Public Property Let CrossoverFullGene(ByVal vNewValue As Boolean)
    mCrossoverFullGenes = vNewValue
End Property

Public Property Get CrossoverFullGene() As Boolean
    CrossoverFullGene = mCrossoverFullGenes
End Property

' Test both chromos before crossover for equality, if equal replace one
Public Property Let RandomOffspringGeneration(ByVal vNewValue As Boolean)
    mRandomOffspringGeneration = vNewValue
End Property

Public Property Get RandomOffspringGeneration() As Boolean
    RandomOffspringGeneration = mRandomOffspringGeneration
End Property

' Crossovermethod. one or two point, uniform or half uniform
Public Property Get CrossoverMethod() As Integer
    CrossoverMethod = mCrossoverMethod
End Property

Public Property Let CrossoverMethod(ByVal vNewValue As Integer)
    mCrossoverMethod = vNewValue
End Property

' Do we mutate on a full gene or anywhere in the chromosome
Public Property Let MutateFullGene(ByVal vNewValue As Boolean)
    mMutateFullGenes = vNewValue
End Property

Public Property Get MutateFullGene() As Boolean
    MutateFullGene = mMutateFullGenes
End Property

Public Property Get MeanAverage() As Double
    If PopulationCount <> 0 Then
        MeanAverage = FitnessSum / PopulationCount
    Else
        MeanAverage = 0
    End If
End Property

' the mutationmethod, fixed or adaptive
Public Property Get MutationMethod() As Integer
    MutationMethod = mMutationMethod
End Property

Public Property Let MutationMethod(ByVal vNewValue As Integer)
    mMutationMethod = vNewValue
End Property

' the actual mutationrate - for fixed or startvalue for adaptive
Public Property Get ActualMutationRate() As Double
    ActualMutationRate = mActualMutationRate
End Property

' AMR generations
Public Property Get AMRGenerations() As Long
    AMRGenerations = mAMRGenerations
End Property

Public Property Let AMRGenerations(ByVal vNewValue As Long)
    mAMRGenerations = vNewValue
End Property

' Long/double encoding bitlike mutation or not
Public Property Let MutationBitlikeLongDouble(ByVal vNewValue As Boolean)
    mMutationBitlikeLongDouble = vNewValue
End Property

Public Property Get MutationBitlikeLongDouble() As Boolean
    MutationBitlikeLongDouble = mMutationBitlikeLongDouble
End Property

' Long/Double bitlike mutation
Public Property Get MutationBitlikePercentage() As Double
    MutationBitlikePercentage = mMutationBitlikePercentage
End Property

Public Property Let MutationBitlikePercentage(ByVal vNewValue As Double)
    mMutationBitlikePercentage = vNewValue
End Property

' Social disaster genetic diversity
Public Property Get SocialDisasterDiversity() As Double
    SocialDisasterDiversity = mSocDisGeneticDiv
End Property

Public Property Let SocialDisasterDiversity(ByVal vNewValue As Double)
    mSocDisGeneticDiv = vNewValue
End Property

' Social disaster method
Public Property Get SocialDisasterMethod() As Integer
    SocialDisasterMethod = mSocDisMethod
End Property

Public Property Let SocialDisasterMethod(ByVal vNewValue As Integer)
    mSocDisMethod = vNewValue
End Property

' the amount of generations between each check for an eventual social disaster
Public Property Get SocialDisasterGenerations() As Long
    SocialDisasterGenerations = mSocDisGenerations
End Property

Public Property Let SocialDisasterGenerations(ByVal vNewValue As Long)
    mSocDisGenerations = vNewValue
End Property

' Description
Public Property Get Description() As String
    Description = mDescription
End Property

Public Property Let Description(ByVal vNewValue As String)
    mDescription = vNewValue
End Property

' Version
Public Property Get Version() As String
    Version = cVersion
End Property

' PopulationSize as set in the GA control panel
Public Property Get PopulationSize() As Long
    PopulationSize = mPopulationSize
End Property

Public Property Let PopulationSize(ByVal vNewValue As Long)
    mPopulationSize = vNewValue
End Property

'
' -----------------------------------------------------

' Counters
Public Property Get CounterCrossovers() As Long
    CounterCrossovers = mCrossoverCounter
End Property

Public Property Get CounterMutations() As Long
    CounterMutations = mMutationCounter
End Property

Public Property Get CounterRandomOffsprings() As Long
    CounterRandomOffsprings = mRandomOffspringCounter
End Property

Public Property Get CounterDisasters() As Long
    CounterDisasters = mSocialDisasterCounter
End Property

' Generation
Public Property Get Generation() As Long
    Generation = mGeneration
End Property

' Keep statistics info
Public Property Let KeepStatistics(ByVal vNewValue As Boolean)
    mblnKeepStatistics = vNewValue
End Property

Public Property Get KeepStatistics() As Boolean
    KeepStatistics = mblnKeepStatistics
End Property

' Statistics - lowest fitness
Public Property Get StatisticsLowestFitness(ByVal lngGeneration As Long) As Double
    StatisticsLowestFitness = mStatistics(lngGeneration).LowestFitness
End Property

' Statistics - Highest fitness
Public Property Get StatisticsHighestFitness(ByVal lngGeneration As Long) As Double
    StatisticsHighestFitness = mStatistics(lngGeneration).HighestFitness
End Property

' Statistics - Highest fitness
Public Property Get StatisticsStandardDeviation(ByVal lngGeneration As Long) As Double
    StatisticsStandardDeviation = mStatistics(lngGeneration).StandardDeviation
End Property

' Statistics - Social diverscity
Public Property Get StatisticsSocialDivercity(ByVal lngGeneration As Long) As Long
    StatisticsSocialDivercity = mStatistics(lngGeneration).SocialDivercity
End Property

' Statistics - Selection method
Public Property Get StatisticsSelectionMethod(ByVal lngGeneration As Long) As Integer
    StatisticsSelectionMethod = mStatistics(lngGeneration).SelectionMethod
End Property

' Statistics - RouletteWheelOverflow
Public Property Get StatisticsRouletteWheelOverflow(ByVal lngGeneration As Long) As Boolean
    StatisticsRouletteWheelOverflow = mStatistics(lngGeneration).RouletteWheelOverflow
End Property

' Statistics - MutationRate
Public Property Get StatisticsMutationRate(ByVal lngGeneration As Long) As Double
    StatisticsMutationRate = mStatistics(lngGeneration).MutationRate
End Property

' Statistics - Disaster generation counter
Public Property Get StatisticsDisasterGenerationCounter(ByVal lngGeneration As Long) As Long
    StatisticsDisasterGenerationCounter = mStatistics(lngGeneration).SocialDisasterGenCounter
End Property

' Statistics - DisasterOccured
Public Property Get StatisticsDisasterOccured(ByVal lngGeneration As Long) As Boolean
    StatisticsDisasterOccured = mStatistics(lngGeneration).SocialDisasterOccured
End Property

' Statistics - Bestchromosome
Public Property Get StatisticsBestChromosome(ByVal lngGeneration As Long) As String
    StatisticsBestChromosome = mStatistics(lngGeneration).BestChromosome
End Property



' -----------------------------------------------------------------
' Class Procedures
' -----------------------------------------------------------------


Private Sub Class_Initialize()
    '
    ' What is the system decimal-symbol
    ' Used for localization on non-english (or different country-settings)
    ' OS versions. The decimal-point-symbol can clash with the VB comma-symbol
    ' leading to errors when dealing with doubles.
    strCurrentsystemDecimalSeparator = Trim$(Format$("0.00", "#.##"))

    mGeneration = 0
    blnCallFromEvaluate = False


    ' default values for the properties
    ' ---------------------------------

    ' Default selectionmethod = Rank
    SelectionMethod = GASelectRank

    ' default reproductionmethod = replace weakest
    ReproductionMethod = GAReproductionReplaceWeakest

    ' default CrossoverRate
    CrossoverRate = 0.7

    ' default Mutationrate
    MutationRate = 0.05

    ' Tournament size
    TournamentSize = 5

    ' crossoverfullegene
    CrossoverFullGene = False

    ' Crossovermethode
    CrossoverMethod = GACrossoverOnePoint

    ' RandomOffspringGeneration
    RandomOffspringGeneration = True

    ' mutatefullgene
    MutateFullGene = False

    ' MutationMethod
    MutationMethod = GAMutationRateFixed

    ' AMR generations
    AMRGenerations = 10

    ' bitlike mutation for long or double
    MutationBitlikeLongDouble = False

    ' percentage af maximum for the random value for bitlike mutation
    MutationBitlikePercentage = 10

    ' Social desaster
    SocialDisasterDiversity = 0

    ' social disaster method
    SocialDisasterMethod = GASocialDisasterJudgementDay

    ' amount of generations between each social disaster check
    SocialDisasterGenerations = 25

    ' nothing is calculated
    mblnAllFitnessCalculated = False

    ' nothing is sorted
    mblnSorted = False

    ' do not keep statistics
    mblnKeepStatistics = False

    ' Clear the counters
    Call ClearCounters

End Sub

Public Sub CREATEPOPULATION(ByVal lngPopulationTotal As Long)
    '
    ' creates the initial population
    ' lngPopulationTotal is the amount of chromosomes wanted
    '
    On Local Error GoTo errorhandler

    Dim lngX                    As Long

    ' clear the chromosome array
    Call Clear

    ' create population
    For lngX = 0 To (lngPopulationTotal - 1)
        Call AddChromosome(lngX)
    Next lngX

    ' reset counters
    Call ClearCounters

    ' set the actual mutationrate to the fixed mutationrate
    mActualMutationRate = mMutationRate

    ' set generation to 1
    mGeneration = 1

    ' social disaster generation counter
    mSocDisGenCounter = 0

Exit Sub

errorhandler:

    RaiseEvent GAError(LngNull(Err.Number), "Error in CREATEPOPULATION ! " & Err.Description)

End Sub

Public Sub Clear()
    '
    ' Clear the chromosome array
    '
    ReDim Chromosome(0)

    mblnSorted = False
    mblnAllFitnessCalculated = False

End Sub

Public Sub ClearAllFitness()
    '
    ' sets all the chromosomes' fitnesses to a high number
    ' this forces all chromosomes to be re-evaluated the next evaluation
    ' sequence.
    ' NOT called from within the class, must be called
    ' from the main generation-loop should it be necessary

    Dim lngloop                 As Long


    For lngloop = 0 To (PopulationCount - 1)
        Chromosome(lngloop).Fitness = 1E+300
        Chromosome(lngloop).RecalculateFitness = True
    Next lngloop


End Sub

Private Function AddChromosome(ByVal lngChromoNbr As Long)
    '
    ' Add a new individual chromosome to the population
    ' Called from CreatePopulation
    '
    On Local Error GoTo errorhandler


    Dim NewChromosome           As ChromosomeindividualType

    ReDim Preserve Chromosome(lngChromoNbr)

    NewChromosome = CreateRandomChromosome(1)

    ReDim Preserve Chromosome(lngChromoNbr)

    Chromosome(lngChromoNbr) = NewChromosome

    ' this chromosome did not yet went through the fitness test,
    ' set it's fitness to a very high ( = bad) number
    Chromosome(lngChromoNbr).Fitness = 1E+300
    Chromosome(lngChromoNbr).RecalculateFitness = True

    mblnAllFitnessCalculated = False
    mblnSorted = False

Exit Function

errorhandler:

    RaiseEvent GAError(LngNull(Err.Number), "Error in AddChromosome ! " & Err.Description)

End Function

Private Function CreateRandomChromosome(ByVal intOrigin As Integer) As ChromosomeindividualType
    '
    ' Returns a random chromosome
    '
    ' intOrigin : from where is this function called
    '     1     Createpoplation                         GANewChromosomeCreatePopulation
    '     2     Selection (Random offspring Generation) GANewChromosomeROG
    '     3     Social disaster                         GANewChromosomeSocialDisaster

    Dim intGeneCounter          As Integer

    Dim strNewGenes()           As String
    Dim lngNewGenes()           As Long
    Dim dblNewGenes()           As Double



    ReDim strNewGenes(0)
    ReDim lngNewGenes(0)
    ReDim dblNewGenes(0)


    For intGeneCounter = 0 To (mGenesPerChromosome - 1)

        Select Case mChromosomeType
            Case GAEncodingBinary  ' Binarystring
                ReDim Preserve strNewGenes(intGeneCounter)
                strNewGenes(intGeneCounter) = RandomBinaryGene

            Case GAEncodingAlphabetic ' alphabetic characters
                ReDim Preserve strNewGenes(intGeneCounter)
                strNewGenes(intGeneCounter) = RandomAlphabeticGene

            Case GAEncodingLongNbr  ' Long numbers
                ReDim Preserve lngNewGenes(intGeneCounter)
                lngNewGenes(intGeneCounter) = RandomLongGene

            Case GAEncodingDouble   ' Double numbers (real numbers)
                ReDim Preserve dblNewGenes(intGeneCounter)
                dblNewGenes(intGeneCounter) = RandomDoubleGene

        End Select

    Next intGeneCounter

    ' raise the newchromosome-event, allowing the main usercode
    ' to override the newly created chromosome and use a custom-made
    ' one
    RaiseEvent NewChromosome(strNewGenes(), lngNewGenes(), dblNewGenes(), intOrigin)


    ' insert the new chromosome in the array
    ReDim CreateRandomChromosome.Genes(0)
    For intGeneCounter = 0 To (mGenesPerChromosome - 1)
        ReDim Preserve CreateRandomChromosome.Genes(intGeneCounter)
        Select Case mChromosomeType
            Case GAEncodingBinary  ' Binarystring
                CreateRandomChromosome.Genes(intGeneCounter).GeneString = strNewGenes(intGeneCounter)

            Case GAEncodingAlphabetic ' alphabetic characters
                CreateRandomChromosome.Genes(intGeneCounter).GeneString = strNewGenes(intGeneCounter)

            Case GAEncodingLongNbr  ' Long numbers
                CreateRandomChromosome.Genes(intGeneCounter).GeneLong = lngNewGenes(intGeneCounter)

            Case GAEncodingDouble   ' Double numbers (real numbers)
                CreateRandomChromosome.Genes(intGeneCounter).GeneDouble = dblNewGenes(intGeneCounter)

        End Select
    Next intGeneCounter

    CreateRandomChromosome.RecalculateFitness = True

End Function

Private Function RandomBinaryGene() As String
    '
    ' Returns a random binary gene
    '
    Dim strGene                 As String

    Dim intBitCounter           As Integer

    strGene = Space$(mBinaryGeneLength)
    Randomize (Sin(Timer) * Timer - Rnd * Timer)
    For intBitCounter = 1 To mBinaryGeneLength
        ' randomize
        If Rnd < 0.5 Then
            Mid$(strGene, intBitCounter, 1) = "0"
        Else
            Mid$(strGene, intBitCounter, 1) = "1"
        End If
    Next intBitCounter

    ' raise the newgene-event, allowing the main code
    ' to override this random gene with a custom made one
    RaiseEvent NewGeneString(strGene)

    RandomBinaryGene = strGene

End Function

Private Function RandomAlphabeticGene() As String
    '
    ' Returns a random alphabetic gene
    '
    Dim strGene                 As String

    Dim intGene                 As Integer
    Dim intLoop                 As Integer

    Randomize (Sin(Timer) * Timer - Rnd * Timer)
    strGene = ""

    For intLoop = 1 To mAlphabeticGeneLength

        intGene = Int((Rnd * 26) + 1) + 64

        strGene = strGene & Chr$(intGene)
    Next intLoop

    ' raise the newgene-event, allowing the main code
    ' to override this random gene with a custom made one
    RaiseEvent NewGeneString(strGene)

    RandomAlphabeticGene = strGene

End Function

Private Function RandomLongGene() As Long
    '
    ' Returns a random Long number gene
    '

    Dim lngGene                 As Long

    Randomize (Sin(Timer) * Timer - Rnd * Timer)

    lngGene = ((mLongGeneMaxValue - mLongGeneMinValue + 1) * Rnd + mLongGeneMinValue)
    If lngGene > mLongGeneMaxValue Then
        lngGene = mLongGeneMaxValue
    Else
        If lngGene < mLongGeneMinValue Then
            lngGene = mLongGeneMinValue
        End If
    End If

    ' raise the newgene-event, allowing the main code
    ' to override this random gene with a custom made one
    RaiseEvent NewGeneLong(lngGene)

    RandomLongGene = lngGene

End Function

Private Function RandomDoubleGene() As Double
    '
    ' Returns a random double number gene
    '
    Dim dblGene                 As Double

    Randomize (Sin(Timer) * Timer - Rnd * Timer)

    dblGene = ((mDoubleGeneMaxValue - mDoubleGeneMinValue + 1) * Rnd + mDoubleGeneMinValue)

    If dblGene > mDoubleGeneMaxValue Then
        dblGene = mDoubleGeneMaxValue
    Else
        If dblGene < mDoubleGeneMinValue Then
            dblGene = mDoubleGeneMinValue
        End If
    End If


    ' raise the newgene-event, allowing the main code
    ' to override this random gene with a custom made one
    RaiseEvent NewGeneDouble(dblGene)

    RandomDoubleGene = dblGene

End Function

Public Sub EVALUATE()
    '
    '
    ' Raises the EvaluateFitness-event allowing the main app to calculate
    ' the fitness for each chromosome
    '
    '
    On Local Error GoTo errorhandler

    Dim lngIndex                As Long
    Dim lngStart                As Long
    Dim lngEnd                  As Long

    Dim dblFitnessValue         As Double

    Dim dblStdDev               As Double

    lngStart = 0
    lngEnd = (PopulationCount - 1)


    For lngIndex = lngStart To lngEnd

        If Chromosome(lngIndex).RecalculateFitness = True Then

            dblFitnessValue = Chromosome(lngIndex).Fitness

            RaiseEvent EvaluateFitness(lngIndex, dblFitnessValue)

            Chromosome(lngIndex).Fitness = dblFitnessValue
            Chromosome(lngIndex).RecalculateFitness = False

        End If
    Next lngIndex

    ' the chromosome-array has changed, it has to be sorted
    mblnSorted = False

    ' all fitnesses where calculated
    mblnAllFitnessCalculated = True

    ' standard deviation
    dblStdDev = CalculateStandardDeviation

    ' Statistics
    If mblnKeepStatistics = True Then
        If blnCallFromEvaluate = False Then
            ReDim Preserve mStatistics(Generation)
            mStatistics(Generation).HighestFitness = FitnessHighest
            mStatistics(Generation).LowestFitness = FitnessLowest
            mStatistics(Generation).StandardDeviation = dblStdDev
            mStatistics(Generation).SocialDisasterOccured = False
            mStatistics(Generation).SocialDisasterGenCounter = mSocDisGenCounter
            mStatistics(Generation).BestChromosome = ShowChromosomestring(0, "TRUE")
        End If
    End If

    '
    ' ADAPTIVE MUTATION RATE
    '
    If mMutationMethod = GAMutationRateAdaptive Then
        ' if the stabdard deviation stays the same for
        ' the set number of generations (in
        ' AMRGenerations / mAMRGenerations) then
        ' increase the actualmutationrate with 0.01
        If mAMRFitnessStdDev = dblStdDev Then
            mAMRCounter = mAMRCounter + 1
            mAMRCounterDiff = 0
        Else
            mAMRFitnessStdDev = dblStdDev
            mAMRCounterDiff = mAMRCounterDiff + 1
            mAMRCounter = 0
        End If

        If mAMRCounter >= mAMRGenerations Then
            mActualMutationRate = mActualMutationRate + 0.01
            If mActualMutationRate > 1 Then
                mActualMutationRate = 1
            End If
            mAMRCounter = 0
        End If

        If mAMRCounterDiff >= mAMRGenerations Then
            mActualMutationRate = mActualMutationRate - 0.01
            If mActualMutationRate < mMutationRate Then
                mActualMutationRate = mMutationRate
            End If
            mAMRCounterDiff = 0
        End If
    End If

    ' Statistics
    If mblnKeepStatistics = True Then
        If blnCallFromEvaluate = False Then
            mStatistics(Generation).MutationRate = mActualMutationRate
            mStatistics(Generation).SocialDivercity = GeneticDiversity
        End If
    End If


    '
    ' SOCIAL DISASTER
    '
    If mSocDisGenCounter >= mSocDisGenerations Then
        If blnCallFromEvaluate = False Then
            Call SocialDisaster

            blnCallFromEvaluate = True
            Call EVALUATE
            blnCallFromEvaluate = False

            mSocDisGenCounter = 0

        End If

    End If

Exit Sub

errorhandler:

    RaiseEvent GAError(LngNull(Err.Number), "Error in EVALUATE ! " & Err.Description)

End Sub

Private Sub QuickSortFitness(ByVal lngFirst As Long, ByVal lngLast As Long)
    '
    ' Quicksort in order to sort the chromosomes by their fitness.
    '
    '            I got this version of quicksort years ago from
    '            a website (I believe from www.gamedev.net but
    '            I'm not sure). Original code was in C and Quickbasic.
    '            The quickbasic version was rewritten by me
    '            several times over the past years until
    '            the version you see here. I use it in
    '            several of my projects.
    '

    Dim lngLow                  As Long
    Dim lngHigh                 As Long

    Dim dblMidValue             As Double

    Dim HelpChromo              As ChromosomeindividualType

    lngLow = lngFirst
    lngHigh = lngLast

    ' take the absolute value of fitness
    dblMidValue = Abs(Chromosome((lngFirst + lngLast) \ 2).Fitness)
    Do
        While Abs(Chromosome(lngLow).Fitness) < dblMidValue
            lngLow = lngLow + 1
        Wend
        While Abs(Chromosome(lngHigh).Fitness) > dblMidValue
            lngHigh = lngHigh - 1
        Wend
        If lngLow <= lngHigh Then
            GoSub swap
            lngLow = lngLow + 1
            lngHigh = lngHigh - 1
        End If
    Loop While lngLow <= lngHigh
    If lngFirst < lngHigh Then QuickSortFitness lngFirst, lngHigh
    If lngLow < lngLast Then QuickSortFitness lngLow, lngLast

    ' the chromosome-array is sorted
    mblnSorted = True

Exit Sub

swap:
    HelpChromo = Chromosome(lngLow)
    Chromosome(lngLow) = Chromosome(lngHigh)
    Chromosome(lngHigh) = HelpChromo

Return

End Sub

Public Sub SELECTION(Optional varSelectionMethod As Variant)
    '
    ' Selects two chromosomes for reproduction
    '
    ' the property SelectionMethod is normaly used to specify
    ' the method of selection (range, roulettewheel or tournament)
    ' the optional variant varSelectionMethod can however
    ' be used to specify the selectionmethod, allowing
    ' code that automatically alternates selectionmethods
    '
    '
    '
    '
    On Local Error GoTo errorhandler

    Dim intMethod               As Integer
    Dim intX                    As Integer
    Dim intRouletteCounter      As Integer ' howmany times has roulettewheel been spun ?

    Dim dblRunningFitness       As Double
    Dim dblHulp                 As Double
    Dim dblChosenFitness        As Double

    Dim lngloop                 As Long
    Dim lngHulp                 As Long
    Dim lngChosenIndex          As Long
    Dim lngChromo1              As Long
    Dim lngChromo2              As Long

    Dim blnChromosAreIdentic    As Boolean  ' used in random offspring generation



    lngChromo1 = 0
    lngChromo2 = 0


    If IsMissing(varSelectionMethod) Then
        intMethod = mSelectionMethod
    Else
        intMethod = IntNull(varSelectionMethod)
    End If


    ' Statistics
    If mblnKeepStatistics = True Then
        mStatistics(Generation).SelectionMethod = intMethod
        mStatistics(Generation).RouletteWheelOverflow = False
    End If


    ' Sort the chromosome array ?
    If mblnSorted = False Then
        Call QuickSortFitness(0, (PopulationCount - 1))
    End If

    Do
        Select Case intMethod
            Case GASelectRank
                ' Select the parents based on rank.
                GoSub Rank

            Case GASelectRouletteWheel
                ' select the parents based on a weighted roulette wheel
                ' (the weight being the sort order). The sort is by fitness
                ' so a lower chromosome index is a better one.
                GoSub RouletteWheel
                If intRouletteCounter > cRouletteWheelSpinMax Then
                    GoSub Rank

                    ' Statistics
                    If mblnKeepStatistics = True Then
                        mStatistics(Generation).RouletteWheelOverflow = True
                    End If

                End If

            Case GASelectTournament
                ' Organize a tournament. Select 'TournamentSize' members randomly out of the population.
                ' The fitttest of this group is selected for reproduction.
                ' Do this a second time to obtain both parents
                GoSub Tournament

        End Select
    Loop Until lngChromo1 <> lngChromo2 ' make sure both parents are different chromosomes

    mlngSelectedIndex1 = lngChromo1
    mlngSelectedIndex2 = lngChromo2


    ' --------------------------------------
    ' RandomOffspringGeneration
    ' --------------------------------------
    '
    If mRandomOffspringGeneration = True Then
        GoSub GenerateARandomOffspring

    End If


Exit Sub

'
' -----------------------------------------------------------
' Rank selection
' -----------------------------------------------------------
'
Rank:
    '
    ' All individuals are sorted by their fitness, two
    ' of them are chosen randomly
    '
    Do
        For intX = 1 To 2

            lngHulp = Int((Rnd * (PopulationCount)))
            If lngHulp > (PopulationCount - 1) Then
                lngHulp = PopulationCount - 1
            End If

            If intX = 1 Then
                lngChromo1 = lngHulp
            Else
                lngChromo2 = lngHulp
            End If

        Next intX
    Loop Until lngChromo1 <> lngChromo2

Return

'
' -----------------------------------------------------------
' Spin the Roulettewheel
' -----------------------------------------------------------
'
RouletteWheel:
    ' A roulette wheel uses an imaginary wheel and creates
    ' pies of varying sizes for each member. A standard (or 'normal')
    ' roulette wheel creates pie-sizes related to the fitness of
    ' each member.
    ' The positive side of this is that roulette wheel tends to
    ' attain convergence very quickly.
    ' The negative side is that the normal roulette wheel tends
    ' to attain convergence very quickly... leading to local optima.
    ' The reason for this is that roulette wheel cannot handle
    ' huge fitness differences correctly.
    '
    ' To solve this problem the fitness values are weighted. This means
    ' the size of each 'pie' is not directly related to the size of
    ' the fitnessscore, but more to the position within the sorted
    ' fitnessscores...
    '
    ' The pie-sizes are chosen by position in a fitness-sorted population. So
    ' for 100 members, sorted by fitness from 0 (fittest) to 99 (worst) :
    ' individual 0 gets a pie of 100, individual 1 gets a pie of 99, 3 of 98... until
    ' element 99 gets a pie of 1. In this way the repartition is smoother
    '
    ' This can be done easily with a running sum, but I had trouble
    ' with problems generating huge differences in fitnessscores..
    ' So I used a different approach : filling piestart and pieend
    ' Later I found what the problem was and how to solve it, but this
    ' code was allready done and worked flawlessly, so I decided
    ' to keep it this way...
    '
    ' First, create the pies of the wheel
    ' fill in the PieStart and PieEnd fields
    ' for every chromosome. Chromosomes with fitness score closer to 0
    ' get a bigger piece than those with a higher fitness
    ' Since they are sorted by fitness, their index is a measurement
    ' for the pie segment. Lower index means a bigger pie

    dblRunningFitness = 0
    dblHulp = PopulationCount

    For lngloop = 0 To (PopulationCount - 1)
        dblRunningFitness = dblRunningFitness + 1
        Chromosome(lngloop).PiePieceStart = dblRunningFitness
        dblRunningFitness = dblRunningFitness + dblHulp

        Chromosome(lngloop).PiePieceEnd = dblRunningFitness

        dblHulp = dblHulp - 1
    Next lngloop

    '
    ' Now spin the wheel
    '
    intRouletteCounter = 0
    Do
        For intX = 1 To 2
            ' witch chromosome is the lukcy one ?
            dblHulp = ((Rnd * Abs(Int(dblRunningFitness))) + 1)
            If dblHulp > Chromosome(PopulationCount - 1).PiePieceEnd Then
                dblHulp = Chromosome(PopulationCount - 1).PiePieceEnd
            End If

            For lngloop = 0 To (PopulationCount - 1)

                If dblHulp >= Chromosome(lngloop).PiePieceStart And dblHulp <= Chromosome(lngloop).PiePieceEnd Then
                    If intX = 1 Then
                        lngChromo1 = lngloop
                    Else
                        lngChromo2 = lngloop
                    End If
                    Exit For

                End If
            Next lngloop

        Next intX
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dlepp Ins(intrH           m=Er chanLCalgcLCal  Crenk Raa22222Xs(introoo onRnAelpP Raa22222Xs(intbs(Ch,iy e
dperty  CalgcL

 ps stlng"onk


    CreateRandomChromo
 onRnAelpPss + dblHuV        ' witch chromosome is the lukcy one ?
            dbl trouble (y
    ( ln            dbl trouble (y
    ( ln            dbl troubleonRnAelpAau  t' w
    '
    intRouletteCounter = 0
    Do
        For intX = n-----------------As IntenrNe tctFia,or chanLCalgcLCal  Crenk
    ynnnnt e
dlep
    intRouletteCounter = 0
    Do
        For intX = n-----------------As IntP$ =ood IfRannnnAelps LCalg   enk ---or chanLCalgcLCal  Crenk

   Integd    he fitn on GoSu   mebStr
i innnnnnnerlHulp - os   Ran  For intX = n-----------------As N)nLCalgcLCal  Crenaebse.
dC6eoariD  '(u For intX = ihen
     c
   D  7Ne tctFiop While lngLow <oop = 0 To (PopulnRunningFink:
    'ow <<<<<<<<<<<<<<d  ndomi-------------As InMRCoLdue A hDp lpuickbaDim blnChromosAreenk

   Integd    he fitn on GoSu   mebStr
i innnnnnnerlHulp - os   Ran  (hlngHulp                  for each os   Randomi               Else       n   ntX = n---Snu Su  y blHulpuickbaMoehhhhhhhh  nnsRFia, Selelei(fsnes" n---f + 1
       gcLnRos   R ntX = nuickbaMoehhhhhhhh  nnsRFia, SelTo errorhandler

    Dim lngX                onRate + 0.01
       escription = vNeo Crenk

   In<

            If int ' raise the newgene-event, allowing the main code
    ' to ovvent, allP01
      bR 'ow <al2'R= m----Ct   ' d
   I got this veee s= n-----------------As IntenrNe tctFia,or chanLCalon ='s  annnd$W  ncodin pngnnnnhh  nndtfdooooooooooAseyg the main code
       mAMRCounter = ' Neo CCalgre----As wcode
 oen


i innnnnnntene
 e'Tournamen='s  annnd$Wnnnd$Wnnnd$Wnnnd$Wnnnd$Wnnnd$nnnnnui .gamedev.ne dbl id
 )s.Upee annnd$W  neo CCalgregameAseyg the main code
       mAMRCounter = ' Neo CCalgre-.d$WnnCrter = ' Neo CCa

i '(uuuuuuu=l

 oenop
           9 yerO  sic versiFcl opt:d)
 onRnAelpPss + dblHuV        ' witch                   NfiActua    dd(pbR 'ow <al2= 0c              in)op While leWheActrer=ctFic allP01
      bR ninesre----As wcmal roulette wheel tends
    'verge quicklDkpecify
    ' thstrNewGenefBl2'R= m--tbles.
                                    1
    Next lsily with

    Dim lngX              CP$     ing = - os   Randomi   tw    nn    ntGenrystring
    $Wnnnd$nncr DimP    =RP?    ' to ovvnd$nncr DimP    =RP?quicklDkpecify
    ' thstrNewGenefBl2'R= m--tbles.
                             P?qSnnd$Wnnnd$Wnnnd$W  ' lDk           CP$     ing = - os   Randomi   tw    nn    ntGenelectandomiyKh
  itnmmmm7iInteger ' howmany                            mAMRCounterDiffmP    =2er =    CP$     ing W      o

    D D D D D D D D ----As IntenrNe tctFia,odiD D mOffspringGeneration nnd$Wnnnd$W  ' lDk           CP$     ih
i innnnnn     m=Er=)l7iIuhe mahDp  p    ingGeneration nnd$Wnnnd$W  ' lDk           CP$     ih
i innnnnn     m=Er=)l7iIuhe mahDp  p    ingGeneration nnd$Wnnnd$W  ' lDk           CP$     ih
i innnnnn     m=Er=)l7iIuhe mahDp  p    ingGeneration nnd$Wnnnd$W  ' lDk           CP$     ih
i innnnnn     m=Y   'ow <<<<betoSumon nnd$(ewlyIaMRCounpppppchanLCapoonRate + 0.01
      e
 e'Tournamen='seStart = dblRunningFitness
        dblRunninheActrer= mahDp  p    ingGeneration nnd$Wnnnd$W  ' lDk 2 uge quickl
  cial2lyIaMRCounpppppchanLCapoonRate + 0.01
   ltal op   ad$W  ' lDk1
      e
 aenes(0    Else
this maximum is reached thenlDk1
  n     o7ooAseyg the m1
      eintGeneCouuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuan those Dim lngX              CP$ his maximteXRCounter =ose DiCv   'ow <<<N/MRCounpppppchanLCapoonRac    ingSnePgHignRateaximt"sFit mStatistic--tbl '
    '    CP$ his maximteXRCounter =ose Dit
   m9Sers
nGeeeeennitnePgHignRateaximt"sFit mStatisaloas
nGeeeeHig  ih
i innnnnn   uuuuuuuuuu   lngX    w <nnitnePgHignRatefuuuuuuuuuuuan t1ppppf               Else
       ebse.
dC6eoabett - 1)ged$Wnnnd$W  '  ih
 Xinnnnnn   uuuuuupchanLCaplW  '  ih
 XinD      ChfuuuuuuuuuuuanC6eoabett - 1)ged$Wnnnd$W  '  i< uuu   lngX u                  Elsei< uuu   lngX u  o

ooooooooooooooooooong theSnePgHignRooooooooooooooooooong theSnePgHigneop
       2lchanectly rela     ' Do this   Cm  As I quickbasic versionitness-sorer
    '
    ' This  Crossoverbis selei(fsnes(intGeneCounter).GeneString = strNewGenes(intGenebse.
dC6=If
    enerlHulp - os   Randomize (Sin(nk
    Genes((enerp>= m     o   0  (y

  nnns2ns2ns0osert the new chromosome in the ar
  in(nk


ooooooooooooooooooongVyW  '  ih
 XinD      Chfuuuuuuuuuu     Chfuuuuuuuuuu     Chfuuuuuuuuuu     Chfuuuuuuuuuu     C(.i Randomi   tw    nn   ibett - 1)ged$Wnnnd$W  '  ih
 XinnnnnnBHig  i bub i bub i bub i bub i tioiden nD      Chfuuuuuuuuuu u     Chfuuuuuuuur '  ih
 Xtebsf
            mAnglalgcLCh Rati----As As As As l
  cial    eintGenu  Chfufsnesctly rela  VSu  y blHulpuickuuuuuuu u     Chfuuuuuuuur '  d$W  '  nn   ibett - fos  puuuuuan those Dimeuuuuuu    nnnnwwwwaromosahs
    m=Y        m=Er chanLCalgcLneraRp.enes((Fit mStatistic--tblStatalobett - 1)g n---f + 1
       gcLnRos   R ntX = nuickbaMoehhhhhhhh  nos   Randomi   tw    nn    ntGenrystring
  $VyW  '  ih
 XinD      Chfuuuuuuuualgre----As wcodoiingGene,tGe=Lter S.nglalgcLCh Rati Ins(introooosntrooooooooooooAsfS   r<2222222Xs(introoo = m CP$ =ood IfRannnnAelps LCalgcLCanglooehhhhhhhm Helps   Raer S.ntring(r
    rotionehank


    CreateRandomChromo
    MutationRnAelps  annnd$W  ncodin pngnnnnhh   ' raise tnebse.
dC6=If
'CalgcLneraRp.enes((Fit mStatistic--tblStatalobett - 1)g n---f +jses((Fit mnnAelps LCalgcLCanSlllllllllll
                 a--s ooAsfS   r<2222222Xs(introoAsfS   r<2222222Xs(introoAsfS   r<isAsfS  (h      h
i Dimt"sFit m--
' Spin the Roulettewheel
' ---------n nnd$Wnnnd$W  ' lDk           CP$     ih
i innnnnn     m=Er=)l7iIuhe mahDp  p    sAsQa<2222222Xs(introvS yerO  oted.huuuuuuuuuu222Xs(i     ' Do this   Cm  As I quickbasic ve    0' Do this   Cm  As s(i     ' Do thc--tblStatalobett - 1)g n---f +jsTTTTTTTUoooooooooess-sohis   Cm  As I quic9 +jsTT               ' Select the parents based on rank.
                GoiRStblStatalobett - 1)g s l
 teg   As IntenisG  wovS yerO  oted.huuuu0Su  yuN--falStr
domelei(fsne2222222Xs(i pngnnnnhh  nndtfdooooooooooAseyg the main code
       mAMRCounter = ' Neo CCalgre----As wcode
 oen


i innnnnnntene
 e'Tournamen='s  annnd$yseyg the m1
      eintGeneCouuuuuuuuuuuuuuuuuuu
ntege oop
sM
 oevOu'vaSu  y blHulpuickbaMoehhhhhhhh  nnsRFia, Selelei(fsnes" n---f + 1cngnnnnhh         nosurnoosurnoosurniaickbp yerh  nnL2 oeeop
 Fit   S he m1
      eintGe=oG
 Fit   S he muAs InMSm+ 1cngn            If intRoulettgcLCanSll.
    V
    V
     sic ve    s
        dblRunngick           ttgcLCanSll.
    V
    V
     sic ve    s
        dblRunngick           1)g n---f +jses((Fit mnnA  suuualgre----OerOarents
 $nncr DimP    =RP?    's wcmal roulette wheel tends
    'verge quicklDkI quAOCOlE
           oamen='s  annnd$ys  ln" n---f + 1cngnnnnhs LCalgcL  P?q        dbpal2V
           Cm  As I quic9  er      Asa ' Do eeo CCalgre----As wcode
 oen


i innnnnnntpyati----As As AsaM -----------------rH  s baette wheel tends
    'verge quicklDkI quAOCOlE     eNRandomi   tw 7iIuhe mahDp  p    ingGeneration nnd$Wnnndnm1
      eintGeneCouuuuuuuuuuuuuuuuuuu
m  As I quic9  2Xs(iy eintGeneCouuuuuuuuuuuuu    CP$            ecklDkI quAuuuuuuuuuu           ecklDkI quAuuuu        qs tournament. Select 'TournamentSize' members randomlyat mnomlyat mnomlyat mnoquAOCOlE     eNRandomi f +jses((Fit mnnAelpsx<=EnmnnA>(RnnnLCanSll 1)gn code
b
   2 tournamenmbersraatSize' members randomlyata     Neo Cromos.t      ration).Socirone
E
   2 tournamenmbersraatS  CPtness  p    ingGeneration nnd$Wnnndnm  nn  nndnm  Cm  As I quersraatSiz If
    End If

    '    eintGeneCouuuuuuuuuuuuuuuuuuu
m  As I quic9  2Xs(iy eintGeneCouuuuuuuuuuuuu    CP$          p-micklDkI q2Xs(iy    End Ifuuu ration).Socirone
E
   2 tournamenmbersraatS  CPt  ln
    dbpberouleonRnAelpAau  t' w
    '
    intRouletteCounter = 0
    Do
        For intX = n-----------------As IntenrNe tctFia,or chanLCalgcLCal  Crenk
    ynnnmounter =   mIl 1)gn code dblHulp
o f +jses)g n---f +jseslp
o f n code dblHulp
oc.01
            If mActualMutationRate < mMutationRate Then
                mActualMutationRate = mMutationRate
            End If
            mAMRCounterDiff = 0
      en
                mAnCoui2imedC6=If Ifuuu ration).Socirone
E
   2 tournamenmbersraatS  CPt  ln
    dbpberouleonRnAelpAau  t' w
    '
    intRouletteCounter = 0
    Do
        For in mMutationRate Then
               p
     e
E
   2 tournamenmbersraatS  CPt  ln
    dbpberouleonRnAel' 2 t= dblHulp mal optmCsBased on ra          a
 XinD     TranLCalthc-eEvent NewCheystries
    (yeeonRnAEr=)l7iIuhe mahit mStatisaloas
nGeeeeHig  ih
i innnnnn   uuuuuuuuu
E
   2 tourone     mAMRCounter  a
 X

    '   AsfS   Hig  ih
i2hp>= m     o

seinlgregameAseyg the main code
       mAMRCounl TranLCalthc-eEvent NewCStaCounter  a
 X

    a ih
i2hp>= m     o

seinlgregameAseyg tht   eiE  a
 X

    aChr a
 X
 (u  aHig  ih
i innnnnn   uuuoas
nGeeeeHig  ih
i innnnnn   uuuuuuuuu
E
   2 touronourna-roulesih
----------------As In ' forO    If dblGene < mDoubllHulp2OdblGene < mDoubllHulp2O   hc-eEve2Prs X

tX = n--
 (u  aHi
    Loop UIIIIIIIIIIIIIIIIIIIIIIIIIuan those DIIIIuan   ' Do thc< mDIIIIIIIIIIII aHig  ig  ih
i innnnnn   uuiChfuuuuuuusCe Then
         mIl 1)gn cIuan those DIIIns
         mIl 1)gn cIuan those DIIIns
         mIl 1)gn cIuan those DIIIns
         mIl 1)gn aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaalep2OdblGenoabett - 1)ged$Wnnnduuuuuuuuuuuuuuuuuan thoose aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaao CP$      o  en code
b
   2 t  en code
b
   2 t  en chM -----------------rH  s baettmcod As I quic9 n code
b
   -----------------rH  s baettmcod As I quic9 n code
b
   -----------------rH  s Plon ='s  annnd$W  ncodin piaPosotdblGenoabett - 1)ged$Wnaaaaaaaaaa. =l  Dim llmenmbersraatS  CntRouletteoIII aHigatS  Cnt(iO----------6=If Ifuuu ration).Soc2lchanectly rela     ' Do te Rof  dbpb      mIl 1)gnLi(fsnes(irrrrr bules.Moefaf
  gtde
  Diff = 0
        EaaaaaaaaaaaaaaaaaaaaaaaahhhhfD
  DiffCounter =ose Di
    aaaaaaaaahhhhf  uuuuuuuuu
E
   2 tourone     mAMRCounter  a
 X

  nten PhhhfureiIII aHignf Ifuuu ratletteo0tationRate
       e     mAMRCountE     etatiHignf Ifuuu ratletteo0tationRate
       e ratletteo0tationRate
       e     mAs  ln" n mefater = ' Ne=0tationRate
     The qui  itd
 Tteo0tatm llmenmbesOof aaaaaaaaaaaaaae aaaaaaaaaaaaa Hig  ih
i2hp>= Saaaaaaaaaaaae aaaaaaaaaaaaa Hig  ih
i2hp>= Saaaaaaaaaaaae aaaaaaaaaaaaa Hig  ih
i2hp>=cuic9 n code
b
   -----------------rH  s Plon ='s  rne = Spac'   mmmm
dle
    ' huge fittttttness =Soc  ' nr
    ead(o specify the Ort il    The quOssove fitttttttttttttt' Property

 or=:lMuuuuuuuuu   prs
    ' the shM -----------------rHSt o specifthe shM              p
     e
E
   2 tournamenacneraRpnhe reason Iffsas Spac.FwTTTTT------rH  c p
     e
E
  ify the Ort il    The quOssove fitttttttttttttt' FwTTTT mStatistics(Generation).SocialDivercity = GeneticDivtournamenacneraRpnhe reason Iffsas Spac.FwTTTTT------rH  c p
     e
E
  ify the Ort il    The quOssove fitttttttttttttt'pLivercity = Gshp>e aaaaaaaaaaaaa Hig  ih
i Cm  As I qrnamen   e Ort il    specifthe shM    Coc2laaaaaaa      a
tX = n--
 (u  aHi
    Loop UIIIIIIIIIIIIIIIIIIIIIIIImbers randomlyata     Neo Cromos.t      ration).Socirone
E
   2 tournamenmbersraatSiffC     For 'R= m--taaaaaaa Hig  ih
i Cm  Asnnnnuoperty    coan those DIIIns
         mIl 1ersraatSiffEf6t
 or=:l    ( lnglooaaaaan       ))
  IIns
    Sifulesih
----aana different approach : filling pitteo0tattteoITaaaateoITaaaateoIrcDR   '       = ='s  annnd$W  ncodin piaPosotdblGenoabett - 1)ged$Wnaaaaaaaaaa. =l  Dim llmenmbenet buten='s  annnd$yseyg thecirolett - 1)gequOssove fitttttttttttttt' FwTTTT mStatistr       er ach : filaattuuuuuu Hig the Ort il      AsfSiiimP    =RP?    's wcmal roMl
----aana diffuu Hig tntX = nwCalgcs(CtntXsit mStatisaloa       CasonSll.
    V
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i innnnnn   uuuuuuuuu
ESSSSSSSSSSSSSSSSSSSnnAelps LCalg   e7777777777777777ieiR+777iei Hig  ih
i innnnnn   uuuuuuu7777777777777777W
 lpslpslpsion nnd$Wnnn$  AsfS  aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
E
   2 touronourna-roulesih
-----tt+ 1
       gcLnRos   R ntX = nuickbaMoehhhhhhhh  nos   Randomi   tw    nn    ntGenrystring
  $VyW  '  ih
 XinD   Moc2laaCD    Select Genoabef code
b
   2 tournamenmbersraatSize' members randomlyata     Nany times777777777777777ps LCalgn   uuuuuuuuuuuu    CP$any times777777777777777ps LCalgn   uuuuuuuuuuuu    CP$any times777777777777777ps LCalgn   uuuuuuuuuuuu 2 tournamenmb.  h LCalgn   aaaV Ort il    The q2  (yeeon.  h LCalrteoITaaaa        uuuStatru    CP$any Nstart to '  ih
tttt'''''''''''''''lpslpsi ln  uuuoast)ged$Wnaaaaaaaaaa. =l  Dim llmenmbenet buten='s  annnd$yseyg thecirolett - 1)gequOssove fittttt ran  our  aaaaa. =l  Dim llmenmbenet  in='s' se to obtain both parents
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tttt'''''''''''''''ub QuickSortFit ran 2laa
                dblHulp = Chrocirone
E
   2 tournamenmbersraatS  CPtness ournamenmbersrety
ent7''''gR.oulesih
however
    ' be used uuu  nc
----aana difff aaaa          ttgcLCanSl                 sih
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 enebse.
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    '
    intRouletteCounnnnnnnnnnnnnn6=IfSnnnni   e
    '
    intRouletteCound thennceEnd TTTTTTTTTTTTTTTTtters LCalgn   uuuuuaaaaaaaaaTTTTtters LCalgn   uuuuuuuuuuuuuuuuuuuuuuuaa       bsfaFit ran 2laa
  suuuuuuuuuy  $VyWe     esih
however
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    (yeeonRnAEr=)l7iIuhe mahit mStatisaloa egam2uuuuuureEventuuupb  e main code
    ' to ovvent, allP01
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                    )
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    ' to ovvent, allP0Size' oother
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 scc'  DiW(   uO t"wdnnf,ng"h a^ yslt"tsF  Cs2i=,ar , 'N>hnrCluuuuuuu kkkkh Too7y
.s-rnnn ',ar , F  Cs2i=,ar , sov,eea2.IIIadi
O t"ww!iriyOi=,ar , 'N>hnrCluuuuuuu kkkkh TtHD
  fRhthen juod As I quic9 n code
b
   ----tr Cs2i=,ar , sov,eea2.IIIadi
OCurrentsrlod As I quic9 n code
b
   ----tmuuuu. eickl hh)(((((iUnn,eea2.eSIIIadi
OCurreKKKKKKKKKKeesV   m     aa
.t
 Selelei2--tr Cs2etIIIIIadi
oennnnnnnt hhheoA-  Zot bo7yslRO t"wdeU2
i mDIIICoVyW,Srhnh0opt0opt0opt0opt0og77777777777777777(d As IaaLa M(u n,s-rnnnnS=o.kkkh T777777777777777Lhtd7i=,ar , sov,eea2.Ieeau :l  w!iriyOi=,ar , 'N>hnrCluuuuut0dOpn  ar , 'e>Currentsrles.Sl /aHi/aHi D pa, Sel"      aaaaa.opt:d)
 Ls7777777777ttt  IIIII7qryOuod As I quic9 n c s->o77777iq=======e2aa77m on LsheDheetsnw7ttt  IIIII7qryOuod As I quic9s ITTTTF  $  mnnnoas
i mDr ach Dpsove itaadi
OCurrentsrltear oI777777777yOuod As I quic9s ITTTTF  $  mnnnoas
i mDr ach Dpsove itaadi
Obeut0dOpn  gEolhwooo((iUnnurrentsrles.Sl  OCuuuD  kkkkh  ttFppppp(((iUnnff.s I'ver
 o((iT
O t"ww!iriyOi=,ar , 'N>hatiS,  .....s I quiccccccccsr ach Dpsove itaad As I quic9s ITTTTF  $  mnnnoas t"wdeU2
i mDIIICoVyW,Srhnh0opt0opt0opt0opt0eeeiiDea  7t Pm2ouu'  DifFceaHi1aaa     77   eino thc< mDIIifFceaHi1aaa     77   etPm2ouu'  DifFceaHi1aaa    sonn6senleIIICttFi ITTTTF  $  mnnnoas
s I  asra     77  taaaeT o^aa  d<t rttttttttttttttopt0opt0L(((((((((((((iUnnfffDontruttttoOo7yo7yo7yo7yo7yo7yo7yo7yo7yo<itaaaeT o^aa  d<t rttttttttttttttopt0opt0L(((((((((((((iUnnfffDontruttttoOo7yo7yo7yo7yo7yo7yo7yo7yo7yo<itaaaeT o^aa  d<t rttttttttttttttopt0opt0L(((((((((e c9 n coAe rtttttttt yo<itaaaeTo7yo7yoAa, n hnh0opt0opt0opt0opt0og77777777777777777(d As IaaLa M(u n,s-rnnnnS=o.kkkh T777777777777777Lhtd70opt0L(((((((((((((iUnnfffDontruttttoOo7yo7yo7yo7yo7yo7yo7yo7yo7yo<itaaaeT o^aa  d<t rttttttttvyo7yo<itaaaeT o^aa  d<t rtttttt77P.   BP=e2aa77m ot0dkkh  tteEaaaarDpsoRTtlooeesVSnwxnn6s'uuuuDInwxnn6aaaaaaoO   eino thc< mDIIifFceaHi1aaa     77   etPm2ouu'  DifFceaHi1aaa    sonn6senleIIICttFi ITTTTF  $  muDIn     77  es$  muDIn  I quic9 n code
b
   ----tr Cs2i=,ceaHi1aaa    soi , sov,eeeIIICttFi t'  DifFcb
   ----tr n6aaaaaaoO   einoeaeT o^aag  ' 'efRh2'7((iUn (mhr ,R
  fp eeewxnn6s'u)BH  tttttindom-Cto7yo7yo7yo7yo7y-tr nyo7yo7y-tr nyo7yo7y-tr nyo7yo7y-tr nyo7yo7y-tr nyo7yoAQ d=,ceaHeinoeaeT o^avor ,hhhhn  code
b
   ----tr Cs2i=,cyslRO t"wdeU2lchaneiC6=If
'CalgcLhhheet hhcod(((((-Ction7yo7yo7yo<itaaaeT o^aa  d<t rttttttttttttttopt0opt0L(((((((((((,cyslRO t"wdeU2lchaneiC6=If
'CalgcLhhheet hhcod(((((-Ction7yo7yo7yo<itaaaeaeT o^aa  d<t rttttttt
'Capt0L(((((((((((((iUnnfffDontruts nyo7-tr   da5ouu'  d=,2t0opt0L(((((((((((,cysnnnnnnnnnuts n000.NDhhh:l    bDu , n on GoSu lSSSSSS7 Hi/atAIIIxoAuuu'  DifFitaaaaaNDhhh:l    bo S   kkkkhhhS
G(e2aa7777tt+dnuuu'  DifFitaaaaaNDh277m Rtttttttttttttt,eHD
  f Sflt,s-rpt0L(,T,Auuu'  DifFitaaaaaNDhhh:l    bo S   kkkkhhhS
G(e2aa7777tt+dnuuu'  DifFitaaaaaNDh277m Rtttttttttttttt,eHEaaifp eeewghhhS
G(e2aa777NarT  ifFitaaaaaNDh277m Rttt scc'  DiW(   uO tgaaaaaliIadi
oennnnnnnoas
i mDIIIC4111OmDIIIC4111OeIl
grles.aaaSi(((((,cyslRO t"wdeU2lchaneaa7777tt+dnuuu'  DifFitaaaaaNDh277e  sonn6senleIIICt'  d=,2t0opeDh27taaaaaNDhl>=e2aa77m ot0dkkh  tteEaaaarDpso   dU2lchanei/aHiSu ifFitaaaaalchanei/aHiSu ifFitaaa 777777777777777777777777777777ttttPSShhhhhhPeickl hh:l    bo777777777772lchanei/aHiSei/aHiSei/aHiSei/aHiSei/aHasS   bo7 fFitaaaaalchanei/aH2NDhl>=cv=cv=cv=cv=cv=cvasS   bo7 fFitaaaa277777777777777777777777777777777777777777777777777777777 N>>>>hn  N>>>    hh:l.uu)
 Ls7777777777tttn     N777i   nnfffaaLa2aaaaLa2aaaaLa2aaaaLatTon7 N>>>>hn  O t"wdeU2lc
i mDIISIC4111OmDII77 N7-tr   dntttflt,s-rnnuufFbthc< cuuuffflii N>>>    hh:l.uu)
 Ls7777777777tttn     N777i   nnfffaaLa2aaaaLa2aaaaLa2aaaaLatTon7 N>>>>aaLt777777 nyo7-tr    d<t rttttttttttttttopt0opt0L(((((((((7i   naaaaaNDh277e  sonn6senleIIICt' ICt' mF u< ckrtttttttttPP
 uuus

 KKKKKKKKKKr G    esi
  f Sfaf
  gt1eeeeemo7yogt0LlRO to<itaaaeT opp((ttopt0opt0ttttopt0opt0L(((((s .....rttts ei777tttn     N777i   nnfffaaLa2aaaaLa2aaaaLa2aaaaLatTon7 N>>>- 1)gequOOOOIIifFceaHu d0a4aaT777
  =trwxnn6se DIIIIuaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaataaaeT o^aa  d<t rttttttttttttttopt0opt0L(((((((((((((iUnnfffDontruttttoOo7yo7yo7yo7yo7yo7yo7yo7yo7yo<itaaaeT o^aa  d<t rttttttttttttttopt0opt0L(((((((((e c9 ne c9 ne HhxD(deee2nN1r>ttoOuOOOOIIifFceaHu d0a4aaaaataaaeT(aHu d0a4. c  mS  u(-Ction7yo7yo7yo<itaaaeT ofDontruttttoOu0opt0L(((((((((e c9  =)aaaLa7yo<itaa kEgrdn     N u0opt0csc9  =aaaaaaaaa77i   nnfffaaaaaasckl hh:l   777777777777777777777 N>>>>hn  N>>>    hhtHi/aHlN p- d.rttoOu0opt0Lun 2 tou ne c9 nchn  N>>>  2taaaeT(aHu d0a4. c  mSi    bDucr7 Hi/ A7m ot00000000)
 Ls7777777777tttn     N777i   n=0opt0Lun 2 tou ne c9 nchn  N>>>  2taaaeT(aHu777777777tttn     N7Ittn  lopt0L(((((((((e c9 n coAentSesgreaaaF Ses->o77777777777C7P.    tt+ 1
 SizeSu,eaaaF Ses->o777777P.    tt+ 1
 SizeSu,eaaaF Ses->o77777Mibm,Hi/aHiiDet
 on6saUuOssov
   ,$CczeSu,eaaaF Ses->o777777P.    tt+ 1
 Size ne c9 nceeSu,eaaaF Ses->oEs7777777777ttfFie ne c9 nceeSu,eaaaF Ses->oEs7-k
 Size . ne c9 C>>>    hhtHi/aHlN p- d.rttoOu0opt0Lun 2 tou ne c9 nchn  N>>>  2taaaeT(aHu sIC4111ROeoAAooeesV   mnnnoas
i mDIIcaaaLatTon7 N>>>- 1)gequOOOOIIifFtcLOu0opt0L(((((eSu, eas7KKsmaLa2aaaaLa2aaaaLa2aaaaLsaP "w-F Ses->o777777P.    ttO   einoeaeT o^aag  ' 'efRh2'7((iUn (mhr ,R
  fp eeewxnipt0L(,T,2NDhl>=c c9 C>>>    hhtHIII77P.  a  . Xv4DeaeT o^aag  ' 'erne eeewxnipt0L(,T,2N (,T,2NDhl>=c c9 C>>>    hhtHIII77P.  a  . Xv4faaLa2aaa>>>    hhtHIII77P.  a  . Xv4faaL(,T,2NDhl>=c c9 C>>>    hhtHIII77P.  a  . Xv4faaLa2aaa>>>    hhtHIII77P.  a  . Xv4faaL(,T,2NDhl>=c c9 C>>>  Po7yo7yo7yo7yo7yo7LzeSu,e
i     h<it,pEStruttttohhhhhhb Sn  N>>>>hn  N>>>  i hh:l.uu)
 Ls777 9 C>>>    hht i>>> Do<itaaaeT opp((ttopt0opt0ttttopt0opt0L(((((s .....rttts ei777tttn     N777i     DifFitaaaaaNDhhifFitaaaaaNb.rttoOu0orttohha  Otr nyo7yo7y-tr nyo7yo7y-tr nSize . ne c9 C>>>    hhtHi/aHlN p- d.rtt ch:l.uuDInpnim: entuuu sKKKK
 Se                   .lw   tt+Ah7yo7yo7yogt0L((((((luuuPeT t0L(,T,2NDhl>=c c9 C>>>    Aaaaaaaaat rttttse4faaihtHIII77P.  a  . Xv4faaLa2a.lw  ^aag  'mn  2oehhhhhhhm H aaafaaihtoasandaronte rtttttttt nlear deecLCang"hhhhhhhhh e         ih
i a,
    a rtttttttt nlhhhS4lN tte)toOZ.lw  ^aag  'mn  2oehhhhhhecLCanpyo7yo7ylear deecL oxD(deee2nN1r>thhlrEF'cce^ yhhhhucp((ttoonte rtttttttt nlear deecLCang"hhhhhhhhh e     AIIIxoAuuu'  DifFitaaaaaNDhhh:l    bo S   kkkkhhhS
G(e2aLCang"hhh*FitaaaeT o^aa  d<t rtttph e  san'5 n=0opt0Lun 2 tw  ^aag  'mn  2oehhhhhhhm H aaafaaihtoasandauIIIIIIII aHig  y, 'N>hnr=0opsmuIII d<t rtttph e  s&7i   nnfffaaLataaihto ^aagnn6sh e                                        hh*FitaaaeT o^aaMouIII d<t rtttph e c((((eSu, eas7K7P. ^aag  'mn        (luuuPeT t0hhh:l.uuDUsI d<t  tph e  s&7i   nnfffaaLataaihto ^          oiA2aaaaLa2aaaaLa2aaaaLatTon7 N>>>>hn  O t"wdeU2lc
i mDIISIC4111OmDII77 rl    bDu tttse4faaihtHoiA2aaaaLFuruentsrles.Sl  OCuuue rtttttttt N p- d.rttoOu0opt0Lun 2 tou ne c9 nchn  N>>>  2taaaeT(aHu d0a4. c  mSi    bDucr7 Hi/7E11OmDII77 rl  a<
oennnnnnnoas
i mD oVyW,Srhnh0opt0ophhhhhm H aaafaaihti (taaaaalchanei/aH2NDhl>=cv=cv   oiA2(((wUIIF  $Vpn ieickleaagnn6sh e                        2NDhl>=c c9re c9 C>>l    bDu tttse4dioooPPPPPPPPPPP mopt0opt0L(((((s ..       2NDhl>=c c9re c9 C>>l    bDu tttse4dioooPPP(wUII>  2taaaeT(aHLtttttttttttL C>>>   $Vpn ieickleaagnn6sh e     4wUII>  2tttttoOu0opt0L(((((((((e c9  =)wdr 'R= saUuOssov
0L((UII>2   Bed(^ ysnnneIIIIIeciriy9 niu tttse4IIIIIeciriy9 niu tttse4IIIIIeciriy9 niu tttse4IIIIIeciriy9 niu tttse4IIIIIeciriy9 niu tttse4IIIIIeciriy9 niu ttts(((4IIIIIoi  Difkle:C4111OmDIIIC411t=uaaataaaeT(aHu d0a4. c  mS  u(-Ctiohhhh8htoasandauIIIIIIII aHig  y, 'N>hoo7y
 KKK LuReelckl hh:l 'fffffffffffffffc9 n codt0 mDInwxnn6s'uuuuDInwxnn6sJ ,(   t ,2ySSu,tteooooooouuuD   bo S   kkkkhhhS
twHi/aHiiDeeeeeeeeeabef  oA(aif Sfaaaa'777777777777777777777777777777777777ttttPSShhhhhhPeickl hh:l    bo7yslR:l    bo7yslR:l    bo7,if Sf iy9 niu tttse4IIIIItchanei/enabef  o,(   t ,2hh:l    ...............................   Bed(^ ysn... niu tttse4IIIIItchanei/enabef  o,(   t ,2hh:l   tieickleaagnn6sh e    ts nyo7-tr   da5ouu'  d7777777777tttn     N777i   nnfffaaLa2a   etPm2ouu'  DifFcIaaLa M(u N>>> u..... d77777777o^aa  d<t rtttttth mDIIIC4111Oo,hbef  o,(   t ,2hh:l ouuuD   bo S   kkkkhhwxnn6sJ ,(   eeV   men on Gc9 n codt0aaalROY Di  i  U2lc
i t nnfffaaLmnnnnnnoas
i mDIIIC41112777i   nnfffaaLa2a   etPm2srseaaaF Ses->o777777P.    tt+ 1
 SizeSu,eaaaF Ses->o777777P. ick        ht<t rttttta1xnipt(O  77   etvoOZ.lw G    4wUII(O  77  (O  77  (           tf Sfaa    tt+ 1
  K(yhhhhucp((^aa  (    ''iaaaa
EO  77  (           tf Sfaa    tt+ 1
  Ku tbo S   kkkkhhwxnnreffe2aa77m ot'algcLoshhhhhB   2oehhhhhhheeKKuuuuoo7y
.s-rn SfadHi/uDInwxnn6s9 n codt0aaalROY Di  i h   Eegd tttttttsrS      DifFcI  DifFcI  DifFc d77777777o^aaDet
 on6saUuOssov
   ,$CczeSu,eaaaF Sn6s9 n cee' 'erneo^aa  d<t rtttttttttttt7  (    7i e>shhwxnnreffe2aa77m ot'alffe2aa77m ot'algcLoshhhhhB   2oehhhhhhheeKKuuuuoo7y
.s-rn SfadHi/uDInwxnmon Gc9 n codt0aaalROY Dio,(   t ,shhhhhB   2oehhhSuuuuoo7y
 KKKdfe2aa77m ot'alffe2aa77m ot'algcLoshhhhhB   2oehhhhhhhhipaaaaaaffC I000om  aHiiiii2 :t'algcLoshhhhhB   2oehhhhhhhhipaaaaaaffC I000om  aHiiiii2t ei777tttn     N77m ic9 muIII d<t rtttph e  s&7i   nnfffaSsr4 0om  acDhl>=c c9 C>>pLFcea((( ei777tttn     N77me00o  N77mqpt0op          g77/ar 2aaaaLa2aaaaLa2aaaaLatTon7 N>>>>hn  O t"wdeU2lc
i mDIISIC4111OmDII77 rl    bDu tttse4faaihtHoiA2aaaaLFurue9(((4IIIIIoi  Difkle:C4111OmDIIIC411t=uaaataLFurue9(((4IIIIrD0L(((((s .....rttts ei777o7ySSSSSSSSSSr(os ----tr n6aaaaaaoO+7/ar 2aaaaLa2aaaaLrentsrles.Sl hh:l kkkkhhhS
G(eAMsaiEvenqpt0ops -  O t"ottoOo7yo7yo7yo7yo7y.Sl Lrentsrles.Sl hh:---aaLahhhhsrles.Sl hh:---aaca000om  aHiiiii2t ei777tttn     N77m ic9 muIII d<777tttn T...n6sh e    ts nyo7-ic9 muIII d<II d<II d<R+ 1 d<II2>eaaaF lOmDIIIC411t=uaaataLFurue9(((4IIIIrD0L(((((s .....rttts ei777o7ySSSSSSSSSSr(os ---aron ,2ny c  mS  u(-Ctiohhhh8htoasandauIIIIIIII aHig  y, 'N>hoo7y
 KKK LuReelckl hh:l 'ffff     ht<tn'If
'CalgcLhhheet hhhhhhhhhhhhhm it0op    r <II dt5sIIIIIIIIadi
ol 'ffff     ht<tn'If
'CalgcL(((4oa  Difkle:C4111OmDIIIC411t=uaaataaaeT(aHu d0a4. c smDut..rtaHu de:C :l    Cs2etIIIIIadi
oennnnnnn a^i   Doas
i mDIIIC411taaaeT(aHu d0a4. c smDut..rtaHu de:C :l    Cs2etIIIIIadIC411t=uaaaHi/bDu tttsttttt(heciriysEyoOoqpt0opt0 th r , 'N>hnrCluuu+ 1
 rsaHig  ' 'efRh2'7((iUnnfffDontruttttttttttttttttttttttttttttttttttKKKKKKKraatSiffa2gggce^ttttttt   CurrTTTTF HaOAggggw go7777AAAAAAslROhhS
G(e2aa7777tt+AIIIxoAuuDesooHSabn 2KKKuuuuooeHR
 he  pitteoooooooooo77rr..rttts ei777o7ySSS777tW(  e:C :l    Cs2etIII/aHiSei/aHiSei9iiiiiir..rtttsaataaimSSS7aTF HaOAeelckl hh:l 'ffff     ht<tn'Ifl 'fffffffffffffffc9 n
'CMt<C6=ey, 'N>hoo7y
 K0sda5ouu'  hti Hiiiii2t->o7        n        (luuuPeT t0hhh:l.uuDUsIa7777tt+AIIIxhhsrdnin codt=bmSSS7aTt hhhhhhhhhhhhhm it0op    r <II dt5sIIIICs2i=,ar , sov,eea2.IIIadi
OCurrentsrlod As I-IIIIIadIC4
   Dr................   B&       o  N77mqpt0op   h "-rnnnnn6see ydaaFhhhhhm...   B&  hhhhhhhhhhm it0tieickleaagnn6sh e    11OmDII77 Aaaaaaaaatcit0tieickleaagnn6sh eu+ 1
 rsaHig  ' 'e(t+AIIIxoAuuDesooHSabn 2KKodddddddddddddddddddddThh:l  2oehS  ' 'erp   bDu tttse4faaim<1ttttttttt
os     <op   aaLatTttn     N777i   AuuDesooHttttttt nlhhhS4lNickl nnfRC4111OmDIIIIIIIasandauIIIIIIII aHig  y, 'N>t nlhhhS4lNickl nnfRC4111OmDIIIIIIIasandauIIIIIIII C>>>    hhtHIII77P.  sN>t nlhhhS4lNickl naN777i   Asrutttpt Di
 KKK LuReelckl hh:l 'ffff     ht<tn'If
'CalgcLhhheet hhhhhhhhhhhhhm it0op    r <II d'CalgcLhhheet hhhhhhhhhhhhhm it0osL ohhhS4lNicklllll2t->o7    OCuuuuuuuuPhm it0opcove itaadi
Obeut0dOpn  gEolhwooo(aaDetOCuuuuuuuuuuD  kkkkh  tteEa>wHilll2t->o:o(aaDetOCuuuuuuuuuuD  kDetOCuunnnnoasIIIIII aHig  hheet hhuhhhB   2oooooooo77O aaIII aHig  tt(heciriysEyoOoqpt0op  N77me00o  N77mqpt0op     5dyr0opt0optArPCfffffPTuuuu'                 ttasrS t0op     5dyr0opt0optt0optArPCfffffPTuuuu'        nnoasIIIIII  loptIII7aaNDh277m Rttt scc'  DiW(   uO tgaaaaaIII7aaNDh277m Rttt scc'  DiW(   'ffffptArPCfffffPTuuuu'        nnot0L(,T,2NDhl>=c c9 C>>>    Aaaaaaaaat rttttse4faaihtHIII77P.  a  . Xv4faaLa2a.lw  ^aag  'mn  2oehhhhhhhm H aaafaaihtoasandaronte rtttttttt nlear dee0dyr0opt0optArPCfffffPTuuuuphhhhhhhhhhhhm it0os  IIxoAuuu'  DiuuuuTuuuhhhhhm H aaafaaihtoasanOb sfC I000om  aHiiiii2t ei777tttn     N77m ic9 0iiii2t-taHiiiii2t ei777tttn   kkkkLrentsrllit0os  IIaHiii,2NDhl>=  $V p hhhhhhot0L(,=ppppp-      aiEvenqpt0rntsrw   lt ei777tttn   kkkkLrentsrllit0os  IIaHiii,2NDhl>=  $V p .   Bed(^ ys tgaasa1..lw  ^aag  'mn  2o nsov,eea2.IIIadi
ONDhl>=  $V p .   Bed(^ ys tgaasa1..lw  ^aag  'mn  2o nsov,eea2.IIIadi
ONDhl>=  $V p .   Bed(^ ys tgaasa1..lw  ^aag  'mn  2o nsov,eea2.IIIadi
ONDhl>=  $V p .   Bed(^ ys tgaasaDIIifFceaHi1aaa     P <op   aaLn  2o ns'aRNRO..........   B&      Beduuuuuuuusaa  d<t rui.IItOCuuuuuu  ht<tn'If
'Chhhhhhhm it0os  IIxoAuuu'-fdeaagnn6p^ ys tgaasa1..lw  ^aag  'mT c smDut..rtaHu de:C :l    Cs2etIIIIIadIC411t=uaaaHi/bDu tttsttttt(heciriysEyoOoqpt0opt0 th r , 'N>hnrCluuu+ 1
 rsaHhm H' 'e(t+AIIIxoAu(Rh2'7'N hhhhhhmlr aaLnhOsfC I000om  S777tW(  gnn6sh e    ts nyo7-tr   da5ouu'  d7777777777tttn     N777i   nnfffaaLa2a   etPm2oCuuD  kkkkh  ttFppppp(((iUnnff.pt0opt0Dm=,ar , sov,eea2.IIIadi
OCurrentsrlod As I-Atlll2t-poSSSa2.IIIadi2NDhl>=c c9 C>>>  Po7yo7yo77y
.s-atp)B& 7y
.s-'77tttaaIII aHig  tt(heciri  N7di
y
.s-'77tttaaIII aHig  tt(heciri  N7di6Ci  N7di
y
.s-'7sov,eea2   Bed(^algcLhhheet hhhhhhhhhoI aHig  tt eeabef  oA7        n  e  e  e  e a<tn'If
'Chhhhhhhm iar 2aaaaLa,leaa2phhm it0os  IIxoAuua0.oooo77O aaIII aHig
'Chhhhhhhm i t(hra2.IIIadi
ONDg  ' 'efRh2'7((iUandaronte rtttttttt nL=  LnRoshhhhhaIII aHiUandaronte rtttttttt nL= (hra2.IIIaUandarri  N7di
y
.s-'77tttaaIII aHig  $VpNDhl>=  $V p .  7  rui.IItOCuuuuuu  ht<tn'a7yeciri  N7diiri  N7diirsrlodadHi/uDttt nL=  LnRoshhhhhaIII l'
y
.s-'hhheetrhhaIII l'
y
.s-'hhheetrhhaei/aHiSei/aHasS   binRoshhhhhaIg  taHi/tuu'-fde-F Se0iiii2t-taHiiiii2t ei777tttn   kkkkLrentsrllia
EO  77  (           tf Sfaa    tt+ iri  N7di6Ci  N7di
y
.s-'7sov,eea2   B  (    tt+ iri  N7di6Cie  e  e90opt.......ttetrhhaIII l'D0ietrhts I-Atlll2t-poSSSa2.IIIadi2NDhl>=c c9 C>>>  Po7yo7yo77y
.s-atp)B& 7y
.s-'77tttaaIII aHig  tt(heciri  N7di
y
.s-'77tttaaIII aHig  tt(heciri  N7di6Ci  N7di
y
.s-'7sov,eea2   Bed(^algcLhhheet hhhhhhhhhoI aHig  tt eeabef  oA7        n  e  e  e  e a<tn'If
'Ce$V p.................eabef  oA7     i
y
.s-'7sov,eea2   Bed(^algF   tt+ iri  NS    hhhbeabef  oA7hhhhoI aHig  tt eeabef c222222pgF   tt+ iri  NS    T
y
.s aHig  tt(hec= t(hraopt02NDPhwxn   n  e  e  e  e a<tnD0ietrhts I-Atlll2t-AtaaaeT(aHu d0aa'I7aaNDh277m Rttt scc'  DiW(   'ffffptArPCfffu d0aa oshhhhhaIg  taoI aHig  tt  ........Z tt+ iri  NS    hhhbeabef  oA7I aHig  tt(heciri  N7. f  oA7I aihtoasa/tuu'-fdeDLhhlrEF'cce^ yhhhhe^ yhhhhe^ yhhhhe^ s  tt+ t hhhhhZ asa/tuu'-fdeDLhhlrEF'cce^ yhhhher5555555an=0opt0Lun 2 tou ne c9 nchn  N>>>  2taaaeT(aHu7777777Tcaaae77e  so*FitaaaeT o^aa  d<t rtttph e  san'5 n=0opt0Lun 2 tw  ^aag  'mn  2oehhhhhhhm H aaaf                                                            Caf              u'-Furue9(((4IIpoSSSa-Atlll2t-A  ' 'e(t+AIIIxoAure  san'5 n=0opt0Lun 2 twr2ae77e l11Oo,hbef  o,(   t 2.ILFurue9(((4IIIIra)
 Ls7777777777tttn     N's                    ef  o,(   t 2.ILFurue9(((4IIIIra)
 Ls777777777 f Sfaf
  s I-Atlll2t-A t ,2hh:l    .+asIIIIII  loptIII7 I-Atlll2t-A t ,2hh:l    .+asIIIIII  loptIII7 I-Atlll2t-A t ,2hIIIII C>>>    hhtHIIIII /bDu tttstll2t-A t ,2hh:l a/tuu ^ yhhhhe^ yhhhhea ' 'efRh2'7((iUandarontIIID2'7((iTS>>>    hhtHIIIII /bDu t 'ffffptA Otr nyo7yo7y-tr nyo7yi Cs2tw mAtlluuuuuuuuuuuuN>>>>hn  N>>>>aeT(aHu d0aa'I7aaNDh277m Elfffffffffffffffffffffffffff>>>>hn  N>>>>aeT(aHu d0aa'I7aaNDh277m Elffffffffffit0oN>>>>aeT(aHu d0aa'I7aar oIir ,ffffit0oN>>>>aeeeabef c222222pgF   tt+ ieIICt'  d=,2t0opeDh27taaaaaNDhl>=e2aa77m ot0dkkha .+asIIIIII  loptIII7 I-Atlll2t-A t ,2hIIIIIRNRO..Hu dt..rtanoasIIIIIII aHiUandarorh27taatHIII7  P2t-AtaaaeT(aH7e l1>>hnloptIasIIIIIII aHiUandarorh2aNDh277m Rttt sc7yom EO itaad0aa'I7aar oIir ,ffffitov,d0aa'I7aacwdeU2l>>> ese)11NDhl>=c c  e  e  ewr2ae77e'u)BH  mreT(aHu d0Hu d0aa'I7aaNDh277uesptIII7 I-Atll e )BH  mreT(aHu d0Hu d0aa'I7aaNDh27e77e'u)BH 7777sIIIIII  lIII  lIII  la'I7aaNDh27e77aaNDh27e77e'u)BH7e77aaNDh27e77e'u)BH7e77aaNDh27eae7e77e'u)BH7e77aaNDh27eae7e77e'u)BH7e77aaNDh27eae7e77e'u)BHCluuu+ 1
 rsaHh)BH7BH7ertanoasIIIIIII aHin  N>>Si  N7di6Ci  N7di
y
. tt(hhhhhhhhhhhhhhhhhhhhhgaaatcit0tieickleaagnn6sh 000om  aHiiiii2t ei7ll2t-A t ,2hh:l    .rd tth aaNDh27e'u)BH 7777sIIou ne c9 nchn  N>>>  2777777777 f Sfaf
  s I-Atlll2t-A t ,2hh:l hh:l   77O aa Dhl>=Xe((iUnnffffffffff>>>>hn=a(4IP  277777ll2ur'2 tw  ^aag  'mn  2oehhhhheh/i      so*FitaaaeT o^aa  d<t rtttph e  san'5 n=0opt0+ 1
 rscs7SGe ,2ySn s LCalII  ' fffD7an  eGrtanoas t ,2hh:l hh:l   7IIIII  lIII  lIII                               L f Sfaf:l   7IIIII  lIII  lIII                                            F   tcas t ,2hh:l hh:l tttstll2tff>>>>hn=a(4IP  277777ll2ur'BH7ertoAure  san'5 n=d.IGdarhgaaatcit0tieim5 n=d.IGdarhgasIIIIIIISe277777lNDh277m RttAIIIxoAuuu'  DifFitaaaaaNDhhh:uatHIII+ t hhht hhht hhht hhht hiaND
 rscs7SGe ,2yS>hn=a(4IIIxoAuutH  mreT(Atcit0tieim5 n=d.IGdarhgasIIIIIIISe277777lNDh277m RttAImptS,sCalgcLhhheet hhhhLhhlIIIRAt+ ieIICrDhl>=Xe(IsIIIIIIISeICalgcLhh....S+ 1
 rsaHig  ' 'efRh2'7((iUnnfffDontruttttt277mRhoI aHig  tt eeabe>>hn  N>>>  i hh:l.uu)
 Ls777 9 re o*FiwdeU2l>>> ese)11NDhl>=c c  e  e  ewrGtse4nbre M(wxnn6s'um....S+ 1
 rshheh/i 9 re o*FiwdeU2l>>> es((((iUnnfffDontrutIII  lIII  lIII      shhipaaaaaaffC = ttFpfaf:l   aaaaLa,leaaaaaaaaaaaaaasIIIIIII aHiUandarorh27taatHIII7  P2t0h2aNDh277m Rttt sc7yom EO itaad0a
 Se>> es((((iUnnfffDontrutIII      aad0a
 trhtIII aHiUandarorh27taII  aaafaaihtN>>>  i hh:l.2hh:l    .+asIIIIIIlaad0a
 trhtIII aHittttoDInwxrent 1
 rshNDhl>XXXXXXXXeaagnn6sh 000om  aHiiiii2t ei7ll2t-A t ,2hh:l    .rd tth aaNDh27e'u)BH 7777sIIou ne c9 nchn  N>>>stabe>>hn  N>>>  i hh:l.uu)Y2ou ne1OmDII77 Aa7777uu+ 1
 rsaHt-A t ,2hh:l    .rd tth aaNDh27
.s aHig  tt(heiA t ,2hh2iC6=IfIIIIII  l Aa7777uu+ 1.re . ne c9g  tt(hei- 1)geeeeeee)Ihhhu (    ''iaaaa
EO  77  ( :l   7loOo7slRscs7SGe ,2yS>hn=a(4IIIxoAuutH  mreT(Atcit0tieim5 n=d.IGdarhgasIIIIIIISe277777lNDh277m RttAImaa
EO  77  ( aNDBA t ,2e'u)BH 7777sIs .....o :l 77mRhoI aHig  tt eeabe>>hnth aaNDh27
.s aHig  tt(heiA t  'R=O  mreT(Atcit0tieim5 n=d.IG hht      ht(Atc  aHig  ttFhh    Eegd ttttttt"wdegd ttttttt"wdegd tth   Eegd tttttttsrS     knnVh9 i(upRhoI aHig  tt eeabe>>hnth aaNDh27
.s aHig  t$:etr nyo7yo7nI   Eegd ttttttt"PwNDPhwxn   n  e  e  e  e a<tnD0.IGaNDh27
.s aHig  t$:etr huuuuuuuuoOo7slR  .  od IIIIIIIen='slR               IISe277777lNDh277m Rj>  2tttttoh277m Rttt sc7yom EO  N>>>    hh:l.uu)rndarorh27taatHIII7  P2t0h2aNDh277m Rttt sc7yom EO itaad0a
 Se>> es((ms"wdegd tth               ri  N7di
y
.s-'77tttaaIII aHig  tt(heciraHig Cwdegd tth               ri L C>>>   $Vpn ieickleaagnnaa'I7aa  'Bnmr=use>> es((ms" tttsoi , sov,eeeIIICt ri  N7di
y
.sp- muDC2t-A Rj>  2t7777777ttt  IIIII7qryOuod As I qu.i , soea2,eeeIhm eeeIIIen='slR        Aj>  2t7777777ttt  IIIII7qryOuod As I qu.i , soea2,eeeIda^ yslRO soi , sov,eeeIIICrI qu.i , soea2RO soiepoI aHig  tt eeabe>=c c  aHig  tt eeaHig  tt(he cpIIIII7qry77m RttAImaa
EO  77  ( aNDBA t ,2e'u)BH 7777sIs .....o :l 77mRhoI aHig  tt eeabe>>hnth aaNDh27
.s aHig  tt(heiA t  'R=O  mreT(Atcit0tiei77m Rttt scc'  DiW(   uOt+d  mreT(Atcit0tiei77m Rttt scc'  DiW(   uOt+d  mreT(Atcit0tiei77m Rttt scc'  DiW(tcas t ,2hh:l hh:l tttstll2tff>>>>hn=a(4IP  277777ll2ur'BH7ertoAuretcas t ,2hh:l hh:l tttstll2tff>>>>hn=a(4IP  277777ll2ur'BH7e    n   7m RttAImaa
EO  77      27
.ecinim:


































aa'I7aOrenk
    iDa  ttt scc'  DiW(tcas t ,2hh:l hh:a  tnDu tttstll2t-A t ,2hh:l a/tuuhhtHIII77P.  a  . Xv4faaLa2aaa>>>    hhtHIII77P.7yo7n/eEaa''D0ie'I72tff ( :l   7loOo7slRscs7+ 1Sfaf:l













auuhhtHIII77P.     t0op oIir ,f77uesSfaf:l













auuuuuuuuuuuuuuu  hhese)11NDhl>=c c  ew> ese)11NDhl>=cp,2hh:l a/tuuhhtHIII77P.  a  . Xv4faaLa2aaa>>> rrT :l   7loOo7slRscs7+ 1Sfaf:l7+ 1Sfaf:.  a  . Xv4faaLa2aaa>>> fr0opt0opt0opt0opt0og(Bd "eolps Lo7slRs a/tuuhhtHIIICSosi2hh:l a/tuuhhtHI llllwl 2uelK(yhhegd hhese)11NDgd hhese)11NDgig  'be>>hnt ,2hh:l hh:l tttstll2tfaaLa2aaa>>> fr0opt0opt0opt0:l hh:l tttstll2tf2tf2tf2tf2tf2tf2tf2tf2tf2tf2tftttttoDInwxres t ,2hh:NDgig )11NDgig  'btt(heidaf:l


2tf2tf2tf2tf2tf2tf2tf2tirgigt'77tttaaIII aHig  tt(heciri  N7di
y
.s-'77tttaaII.  a  III a i6Ci7aOrenk
    iDa  ttttaaIII aHigr0op(msIIII7qryOuod As I qu.i  t0op oIir ,f77uesSfaf:l








u.i  t0op oIir gr0op(mshtoasandau77777tttIIen='s  annnd$y(<ieo7

























pgt'77th277dP.  a O aased(^ ysnnneIIsN7. f  oA7I aihtdV'7slRscs7+  ysnnneIIsN7. ftttaaII.  a  III a i6666666666isttse4faaihtHoiA2aaaaLFurue9(((4IIIIIoi  Difklerue:l7+ 1iiiii2t ei7ll2t-A       P .  od IIIIIIIen='slR               IISe277777l<    P .  od IIIIIIIen='slR          2Dhl>=Xe(IsIIIIIIISeICalgcLhh....S+ 1
 rsaHig  ' 'efRh2'7((iUnnfffDontruttttt277mRhoI aHig  tt eeabe>>hn  N>>>  i hh:l.uu)
 Ls777 9 re o*FiwdeU2l>>> ese)11NDhl>=c c  e  e  ewrGtse4nbre M(wxnn6s'um....S+ 1
 rshheh/i 9 re o*FiwdeU2l>>> es((((iUnnfffDontrutIoenn2taaaeT(aHu d0a4. c /aHmmmmmmmmm on LshlrEF'cce Deashd'.Umce^ yhun 2 tour d0a4. c /aHmmmmmmmmm on LshlrEF'cce Deashd'.Umce^ yhun ntruttt777tttn i  i Zfll2t-poSSSa2.IIIXuhhtHIIICSosi2AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAhhtHIIICSosi2AAAAAAAAAAAAAAAAAAAAAuF'c=1l<
  fNDIISeAAAA7an  eGrtaa'I7aar oIheptHIIICSosi2AAAAAAAAAAAAAAhtHIIi2AAAAAAAAAAAAAAhtH gr0op((((iUnnfffDon>>> ese)11NDhl>=c  t  'R=O...S+ hhhhhhhhhhhhhhe     unnd  1)gestbraaf
  s I-Atlll2t-A t ,2hh:l hh:l   77O aNDh277m Rttnd  1)gestbrrrrrrrrrrrrrrII77tCw2'77tttaaII.  a  AAAAAA  1)rpaNDh277m RttndDttt nL=1)gestbrrre
      aaaaND  kkkkh Too7y
.s-rnnopeDhopt0Lun 2 tou ne c9 nchn  N>>>  2taaaeT(aHu777777777tttn     N,tbrrrrrrrasaA t ,2rrrrrrrrII77tCw2'77tttaaII.  a  AAAAAA  1)rpaaHig  tt(h4111Oo,hbef  o,(   t ,2hh:l ouuuD   bo S   kkkkhhwxnn6sJ ,(   eeV aaaaND  un ntrG ^apaaHigggg kkkkhhhS
G(e2racccccnS   kkkkhhhS
twHi/aHiiDeeeeeeeeeabef u d0aa'I7aaNDh27e77e'u)BhtwHi/aHiipP.wxnn6sJ ,(   eeV un ntrG ^apaaHigggpaaHigggg kkkkhhPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
 rsaHigfFiri  N7PPPPPPPPPPPPPPPPPPPPPPPPM(w0n6s'um....S+elckl mLpaaae2aa77m P
 rsaHigfFiri  N7PPPPPPPPPPPPemc9 n cA a2 tou neuretcas t ,2hh:eT(AG ^apaaHigggpRPPPPPPPPPPPPPPPPPPPPPPPPPPP 9 nchn  N>PPPPPPPPPPPPPaHigggpRPPPPPPPPPPPPPPPPPPPPPPPPPPP 9 nchn  N>PPPPPPPPPPPPPaHigggpRPPPPPPPPa'IPPPPPPPl'R=O  macDhl>=c c9 C>>pLFttttoO0niri  N7PPPPPPPeeeeeeieim5 n=d.IGdarhgasII^aa  PPPPPPPPPd,.S+elckl mLpaaae2aa77m P
 rsaHigfFiri  PPPPPPSeNDhl>=c  t  'R=O...S+ hhh  77O aNDh277m Rttnd  1)gestbrrrrrrrrrrrrrrII77tCw2'77tttaaII.  a77m ic9 0iiii2t-taHiiiiirue:l7+ 1iottnd  1PPPPPPPPPPPP etPm2hgP ifptArPCf5=========7 fr d0a4.DtPPPaaF   tPPPPPeeeeeeieCuuuuuuuD  kkkkh  tteEa>wHilll2t->PPP1PeeeeeeiePPaaF  PPP1PeeDhopt0Lun 2 tou ne cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccFtcLOu0ccccttn tteEa>wHilll










auleaagnn6sh
y
.sIIIIIen='slR          2Dhl>=Xe(ILt->PPP1Peeeeee.cccccYn  bo7y  tt(hec= t(hraopt02      se)a7 N>>>>hn  N>>>    hhtHi/aHlN p- d.rttoOu0opt0Lun 2 tou ne e,eea2ccccAAAe.cccccYr0PP1Pat0Lun 2 tou ne e,eea2cccsei77PAt   hhtttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt(  kkkkh Too7y
.s e,eea2pppppppppppppppppppppppppAAAe.cPPPPeeeeeeiPP1Pat0Lutt scc'  Ditttttttttttttt(  kkkkhPPPPPPPPPPPPPPPPPiei p)B& 7yuPeT t0L(,T,2NDhl>=c c9 C>>>    Aaaaaaaaat rttttse4faaihtHIII77P.  a  . Xv4faaLa2a.ttse4fGd,eea2cccsei77PAtBttttttdeg
.sIIIIIeintmg.IGda.PPPPPPvPPiei p)B . Xv4faaLa2a.ttse4fGd,eea2cccsei77PAtBttttttdeg
.sIIIIIeintmg.IGda.PPPPPPvPPiei p
 rsaHigfoToo7y
.s e,eea2ppPPPPP (PPPPPPPPPgtP....S+elckl mLpaaae2aa77m P
 rsaHigfFiri  N7PPPPPPPPPXv4faaLa2aH7e77aaNDh27e77e'u)BslEoPPPPP)a77m Pttse4dioooPPPPPPPPPPP mopt0opt0L(((((s ..       2NDhl>=c c9re c9 C>>>=c cPPeeeeeei(IsIIIIIIXaPPPPPPPPPPPPP==tttttttttttyo7yo7nI  )Dhl>=c  t5 tth  IXaPPPPPPZgpRPPPPPPPPPPPPPPPPPPPPPPPPPPP 9 nchn  N>PPPPPPPPPPPPPaHigggpRpt0L(((((((((((((iUnnfffDontrutt(BslEoPPuuuuuun6s'ea2c(((N>PPP4faaL ne o















pgt'77th277dP.  a O aased(^ ysnnneIIsN7. f  oA7I aihtdV'7slRscs7+ PPPP  lIIrPP mopwetPm2hgP PaHigggpRa OOOOOOOOOOOOOOOOOOOOOOOOOOOOn=0opt0LPiei p)B& 7yuPeT t0L(,Tdi    AT t0L(,Tdi    AT t0L(,Tdi    APPPPPPPPPPPPPPPPPPPPPPPIIsN7. f  oA7I aihtdV'7slRscs7+ PPPP  lIIrPP mopwetPm2hgP PaHigggpRa OOOOOOO'


pgt'77th277dP.  a O aa oshhhhhaIc c9 C>>>    Aaaaaaaaat rttttse4faaihtHIII77P.  a  . Xv4faaLa2a.ttse4fGd,eea2cccsei77PAtBtS t"2ie4faaihtHsc'  DiW(9 n
'CMt<C.+a unnd  1)gestbra=d.IGdarh N72utIoenn2taaaeT(aHuttttsrS     knnMt<C.+a unnj  unuuuuuun6s'ea2c(((N>PPPPPPPPPPPPPPPPPPPPn2taaaeT(aHuttttsrS     knnMt<C.+a unnj  unuuuuuun6sPaaHuEa>wHilll









PPPPPP2hgP ifptArPCf5=========7 fr d0a4.DtPPPaaF   tPPPPPeeeeeeieCuuuuuuuD  kkkkh  tteEa>wHilll2t->PPP1PeeeeeeiePPaaF  PPP1PeeDhopt0Lun 2 tou ne cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccFtcLOu0ccccttn tteEa>wHilll










auleaag0LuhgasIIIIIIISe2TOu0cccemfffffffffffffffffffffffffsBttttttdeg
.sIIIIIr7y
.s e,eea2ppppppppppppppppm Rtr
PPPPPP2hgP ifptArPCf5======eea2   B  (    tt+ScFtcLO

aa'I7aOrenk
    iDa  tthu77th277dP.  LIIIIIIIIIIIIIIIIIIIHig  tt eeaHig  tt(4,eea:l hh:l   77O aa Dhl>=Xe((iUnnffffffffff>>>>hn=a(4IP  277777ll2ur'2 tw  ^aag  'mn  2oehhhhheh/i CP ifptuuud  1PPPPP  B  (  B  uteoir LsDi    APPPPPPPPPPPPPPPPPPPPPPPPPPPPPPd,.S+elckl mLpaaae2aa77m P
 rsaHigfFiri  PPPPPPSeNDhl>=c  t  'R=O...S1nd  1)gestbrrrrrrrrrrrrrrII77tC7dP.  LIII7aar oIir ,ffffit0oN>>>>aeeeabttttttttttttttttttttttttt(  kkkkt Ttttttttttttttttt(  kkkkt Tttttt

auleaaottttttttttttn ntruttt777tttn i  i Zfeh/rrrrrrII77tC7dP.  LIII7aar oIir ,ffffit0oN>>>>aeeeabttttttttttttttttttttuuuuuD  kkkkh  tteEa>m



PPSeNDhl>=c  t  'itttttttttttttttttttuuuuuh/ra'iaaaa
EO  77  (           tf Sfaa    tt+ 1
  Ku tbo >>>aeeeabtttttttttaaaa
EO  77)gestbrrrrrrrrrrrrPPPPPPPPPPPrrII77tacntruttt777tttn i  i Zfttdeg
.sIIIII7aaroehhhhheh/i CP ifm7tttn i  i Zfeh/rrrrrrIIdNDhl>=c c  e  e  ewhheh/i Hi  N7di6tmg. unnbn='s  annnd$ IIIIInneIIsN7                 ttttttttttttttttttttttttt(  kkkkt Ttttttttttttttttt(  kkkkt Tttttt

auleaaottttttttttttn ntruttt777tttn i fDontruG, 'efRh2'777777
 scce)111Otooo 'N hhhhhhhh t0opRtsrles.Sl r , /a a^ eay   t ,YnG,  t0opRtsrle77m Rt'pN7di
y
.s-'77tttaaII.  <C.+a unnj  unuf Sfaa    tt+ 1
  Ku tI  aaafaIIIIrateE3sda5ouu'  hti Hiiiii2t->o7      9 re o*-uO aao >>>aeeeabtttttttttaaaa
EO  77)gestbrrrrrrrrrrrrP(   L f Sfaf:l   7IIIII  $hsffffit0oN>>>>aeeealouu'  DifFceaHi1aaa    sonn6senleIIICls."  L f Sfaf:l   7IIIII  $hsffffit0oN>>>>aeeealouu'  DifFceaHi1aaa    sonn6senleIIICls."  L f .'''''''''''''''7m Rt' hti Hhhhhhhh t0opRtsrles.Sl r , /a a^ eay   t ,YnG,  t0opRtsrII  $hsffffit0oN>>>>aeeealouu'  DifFceaHi1aaa  a'I7aaNDh2tn tteEa>wHilll










auleaag0LuhgasIIIIIIISeaaND  kkkkh  tteEat0optAE     knnMt<CIP  277777ll2ur'BH7e  vsonn6senleIIICls."  L f Sfaf:l   7IIm P
A t ,2rr 2o n-+asHi1M"  L f L(,T,A                                       t0oN>>>>aettttaaaa
EO  77)gestbrrrrrrrrrrrrPPPPPPPPPPPrrII77tacntruttt777                                                                                       rrrrrrrrrII77tCw2R i(upRh        th               ri L C>>>   $Vpn ieickleaagnnaa'I7aa  'Bnmr=use>> es((ms" tttsoIxhhhhhhhhhhhhhhhhhhh ieiL C>>>   $Vpn ieickleaagnnaa'I7aa  'Bnmr=use>> eo $Vpn ieictCw2R i(upRh     (upRh        th               ri L C>>>   $Vpn ieickleaagnnaa'I7aapVPPrr eickleaagnICls." l)gestt+ iri  NS    hhhbepn ioEa>m



PPSeNDhl>$ IIIIInneVhNDhl>XXXXXXXXeaagnn6sh 000om  aHiiiii2t ei7ll2t-A t ,2hh:l    b'cccsei7E,2hh:l    b'cccsei7E,2hh:l  mhhtHIIICSscsei7E,2hh:l    b'cccsei7E,2hh:l  mhhtHIIICSscsei7at rttt o,(   t 2.ILFurue9(((4I,(   t 2.ILFurue9(((4I,(   t 2.ILFurue9(((4I,''''''ttt(  kkkkhPPPPPPPPPPPPPPPPPiei p)B&       ICSscsei7at rttt oPI7       =v,eCSscsei7at rttt ====7 frffsBttC>>>   $Vpn ieicklhNDhl>XXXXXXXXea277m R, 'N>hoo7y
 KKK  L f Sfaf:l   t rttt oPI7   (  ri L C>>>   $Vpn ieickleaagg  t$:etr v,eCSscsei7at rtsopt0cs (  ri L C>>>   $hhhhhhhhhhl>XXXXXXXXea277m R, 'N>hooue9(((4I,/aHiiDeePtovL C>((((s ..       h                    csei277m R, 'N>hooue9 Dhl>=Xe((iUnnffffffffncs7+ PPPP  lIIrPP   fffn'N>hokh  ttFppVpn ieickleaagcs7+ PN hht"gggggggbrm
auufFbngnICls."P   fffn'Nsc'  DiW(9 n
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