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//**************************************************************
// File:GA_v15.sce
// Authors: Gerd Doeben-Henisch
// Version Start: January-18, 2010
// Version Last: May-23, 2011
//******************************************************************
// Function: Implements a simple GA according to Goldberg (1989)
//
//*****************************************************************
// Apri-l5, 2011 : Adding a mutation operator
//
//***************************************************
// April-8, 2011 : Adding an automatic generation of a population with random
values
//
//****************************************************
// April-21, 2011: Adding a frequency counter for binary strings
//
//**************************************************
//
// April-22-27, 2011: Adding an evaluation of the quality of sets of solutions
//
//**************************************************
//
// April-28, 2011: Computing the probability of certain patterns
//
//*************************************************
//
// April-29, 2011: GA without fitness
//
//*************************************************
//
// May-01, 2011: Virtual fitness function for comparison
//
//*************************************************
//
// May-05, 2011: Conditioned Mutation
//
//*************************************************
//
// May-12, 2011: Fitness ratios, convergence times
//
//*************************************************
//
// May-18, 2011: Purified version of ga()
// and : more converting functions vec22dec()
//
//*************************************************
//
// May-22, 2011: Improving usage of parameter p in case
// of crossoverPrep with helpfunctions: the flag is fixed to 'l+7' and
// freed from p
// Corrections to crossoverPrep(); mismatch with while - conditions
//
//*************************************************
//
// May-23, 2011: Added a counter for the number of genomes in a POP which have
// reached 100\%
//
//*************************************************
// Helpful scilab-functions from the scilab libraries
//
// nancumsum ? This function returns the cumulative sum of the values of a
matrix
// tabul ? frequency of values of a matrix or vector
// variance ? variance of the values of a vector or matrix
// strange ? range
// stdevf ? standard deviation
// bin2dec := translate a binary string of '1','0' into a decimal number
//
// SW-STRUCTURE
//
// All data are organized in a dynamical table. Left hand the actual genes, in
the middle
// supporting parameters and to the right intermediate modifications of the
genes to the left.
//
// POP FORMAT
// l := length of strings
// p := number of cells between string <1...l> and <l+p+1, ..., l+p+l>
// Pos 1-l := String
// Pos l+1 := Decimal Value of binary string
// Pos l+2 := Fitness for l+1 and l+p
// Pos l+3 := Percentage of overall fitness
// Pos l+4 := Expected count according to fitness
// Pos l+5 := Realized count
// Pos l+6 := 2nd Decimal value of a compund fitness
// Pos l+7 := crossover flag
// p := 7
// Variable for overall Fitness
FITNESS_ALL = 0
// Variable for average Fitness
AFITNESS = 0
//***************************************************
//Function to generate automatically a population with random values
// Input:
// l := length of strings
// n := size of population
// Output:
// A population according to the above defined format
//
function[POPX]=popgen(n,l)
//Generate a matrix with only '0's
POPX = zeros(n,l)
MaxCells = n*l
// Distribute randomly '1's
for i=1:n
for j=1:l
if( rand() < 0.5 ) then POPX(i,j) = 0, else POPX(i,j) = 1, end
end
end
endfunction
//***************************************************
//Function to generate random numbers between [1,up]
//
// n := number of choices
function[Xs]=randInt(n, up)
Xs = []
for i=1:n
x=0
while(x==0)
x = round(up*rand())
end
Xs(i) = x
end
endfunction
//***************************************************
//Function to compute descriptive parameters of a population
// Input:
// l := length of strings
// n := size of population
// Output:
// Pc := Percentage of possible space (PSpace)
// Pb := Probability of gitting a certain individual of PSpace
function[Pc, Pb]=popDescr(n,l)
// Cardinality of PSpace
PSPC = 2^l
// Percentage Pc
Pc = n/(PSPC/100)
// Probability Pb
Pb = n/2^l
endfunction
//***************************************************
//Function to compute the frequencies of the elements of a population
//
// Input:
// l := length of strings
// n := size of population
// N := number of events
// show := if '1' then display the POPX-matrix
//
// Output:
// FX := Vector of freuencies ordered along the decimal values of a string (1st
column)
// FXDif := Vector of Differences compared to theoretical expectation in % (2nd
column)
// MEAN := The mean value of the differences
// STD := The standard deviation of the differences
//
// Idea: Generate a sequence of populations, count the occurences, and check the
degree of agreement between
// empirical values and theoretica lexpectations
function[DIST2,STD, MEAN, FREQ,STD1, MEAN1, FREQ1,FX,
POPX]=frequCheck(l,n,N,show)
// Install the counters
r= (2^l)
c= 3
FX = zeros(r,c)
// Generate an internal index for display
for j=1:r
FX(j,1)=j-1
end
// Generate the populations
for i=1:N
[POPX]=popgen(n,l)
if show==1 then printf("POPX first\n"), disp(POPX), end
//Compute decimal value ('0' is placed at index '1' !!!)
// Count occurences
for j=1:n
v=POPX(j,:), d = vec2dec(v,l), [POPX(j,l+1)]= d, FX(d+1,2)=FX(d+1,2)+1
end//n
if show==1 then printf("POPX second\n"), disp(POPX), end
end //N
for j=1:r
FX(j,3)=(FX(j,2)/n)/N //Normal frequency
FX(j,4)=(FX(j,2)/n)/(((1/2^l)*N)/100) // Frequency as percentage
end//m
disp(FX)
FREQ1=tabul(FX(:,3))
MEAN1=mean(FREQ1(:,1))
STD1= stdevf(FREQ1(:,1), FREQ1(:,2))
FREQ=tabul(FX(:,4))
MEAN=mean(FREQ(:,1))
STD= stdevf(FREQ(:,1), FREQ(:,2))
MAX=max(FREQ(:,1))
MIN=min(FREQ(:,1))
DIST=MAX-MIN
DIST2=DIST/2
printf("Number of Events n * N = %d\n",n*N)
// Show Plot
// clf(), xdel,
// plot2d(FREQ(:,1), FREQ(:,2))
endfunction
//***************************************************
//Function to compute the frequencies of the elements of a population
// and using a fitness function to compute 'virtual' fitness to compare
// the populations with others by fitness. But the function does not make use of
these values.
//
// Input:
// l := length of strings
// n := size of population
// N := number of events
// show := if '1' then display the POPX-matrix
//
// Output:
// FX := Vector of freuencies ordered along the decimal values of a string (1st
column)
// FXDif := Vector of Differences compared to theoretical expectation in % (2nd
column)
// MEAN := The mean value of the differences
// STD := The standard deviation of the differences
//
// Idea: Generate a sequence of populations, count the occurences, and check the
degree of agreement between
// empirical values and theoretica lexpectations
function[FITNESS_ALL_PERC1,DIST2,STD, MEAN, FREQ,STD1, MEAN1, FREQ1,FX,
POPX]=frequCheck1(l,n,N,show)
// Install the counters
r= (2^l)
c= 3
FX = zeros(r,c)
FITNESS_ALLLOG1=[]
// Generate an internal index for display
for j=1:r
FX(j,1)=j-1
end
// Generate the populations
for i=1:N
[POPX]=popgen(n,l)
if show==1 then printf("POPX first\n"), disp(POPX), end
//Compute decimal value ('0' is placed at index '1' !!!)
// Count occurences
for j=1:n
v=POPX(j,:),
d = vec2dec(v,l), [POPX(j,l+1)]= d, //decimal values
FX(d+1,2)=FX(d+1,2)+1, //occurences
[POPX(j,l+2)]= fitness1(POPX(j,l+1)) //fitness values
end//n
[FITNESS_ALL]=fitness(POPX,l)
FITNESS_ALLLOG1(i)=FITNESS_ALL
if show==1 then printf("POPX second\n"), disp(POPX), end
end //N
for j=1:r
FX(j,3)=(FX(j,2)/n)/N //Normal frequency
FX(j,4)=(FX(j,2)/n)/(((1/2^l)*N)/100) // Frequency as percentage
end//m
disp(FX)
FREQ1=tabul(FX(:,3))
MEAN1=mean(FREQ1(:,1))
STD1= stdevf(FREQ1(:,1), FREQ1(:,2))
FREQ=tabul(FX(:,4))
MEAN=mean(FREQ(:,1))
STD= stdevf(FREQ(:,1), FREQ(:,2))
MAX=max(FREQ(:,1))
MIN=min(FREQ(:,1))
DIST=MAX-MIN
DIST2=DIST/2
printf("Number of Events n * N = %d\n",n*N)
// Compute the maximal value and the percentage of success
[MAXFIT]=maxfit02(l,n)
FITNESS_ALL_PERC1=[]
for i=1:N, FITNESS_ALL_PERC1(i) = FITNESS_ALLLOG1(i)/(MAXFIT/100), end
// Show graphical results
if show==2 then
clf(), xdel,
plot2d([1:1:N], [FITNESS_ALL_PERC1]),
end
endfunction
//***************************************************
//Function to repeat frequency checks
//
// Input:
// l := length of strings
// n := size of population
// N := Number of events
// K := how often steps should be applied
//
// Output:
// FX := Vector of freuencies ordered along the decimal values of a string (1st
column)
// FREQ := Vector of frequencies and their occurences
// MEAN := The mean value of the differences
// STD := The standard deviation of the difference
// DIST2 := Half distances between MAX and MIN
function[MEANX, DIST2X, MEAN1X, STD1X,DIST20,
MEAN0]=freqCheckRep(l,n,N,K,show)
// Counter for MEANX, DIST2X...
MEAN1X=[]
STD1X =[]
MEANX=[]
DIST2X =[]
for j=1:K
[DIST2,STD, MEAN, FREQ,STD1, MEAN1, FREQ1,FX, POPX]=frequCheck(l,n,N,show)
MEAN1X(j,1) = MEAN1
STD1X(j,1) = STD1
MEANX(j,1) = MEAN
DIST2X(j,1) = DIST2
end //j
MEAN10 = mean(MEAN1X(:,1))
STD10 = mean(STD1X(:,1))
MEAN0 = mean(MEANX(:,1))
DIST20 = mean(DIST2(:,1))
// Show Plot
// clf(), xdel,
// plot2d([DIST2SUM(:,1)], [DIST2SUM(:,4)])
endfunction
//***************************************************
//Function to repeat frequency checks with gassimple0()
//
// Input:
// l := length of strings
// n := size of population
// N := Number of events
// K := how often steps should be applied
//
// Output:
// FX := Vector of freuencies ordered along the decimal values of a string (1st
column)
// FREQ := Vector of frequencies and their occurences
// MEAN := The mean value of the differences
// STD := The standard deviation of the difference
// DIST2 := Half distances between MAX and MIN
function[MEANX, DIST2X, MEAN1X, STD1X,DIST20,
MEAN0]=freqCheckRep0(POP,l,p,n,N,K, MThreshold,show)
// Counter for MEANX, DIST2X...
MCount = 0
MEAN1X=[]
STD1X =[]
MEANX=[]
DIST2X =[]
XDIM=[]
for j=1:K
XDIM(j,1)=j*N
[MCount,DIST2,STD, MEAN, FREQ,STD1, MEAN1,
FREQ1,POP,FX]=gasimple0(POP,l,p,n,N, j,MThreshold,MCount,show)
disp(MCount)
MEAN1X(j,1) = MEAN1
STD1X(j,1) = STD1
MEANX(j,1) = MEAN
DIST2X(j,1) = DIST2
end //j
MEAN10 = mean(MEAN1X(:,1))
STD10 = mean(STD1X(:,1))
MEAN0 = mean(MEANX(:,1))
DIST20 = mean(DIST2(:,1))
// Show Plot
if show==2 then clf(), xdel, plot2d([XDIM(:,1)], [DIST2X(:,1)]), end
endfunction
//***************************************************
//Function to compute the changing quality of solution sets
//
// Input:
// l := length of strings
// n := size of population
// N := Number of events
// K := how often should be incremented
//
// Output:
// MEAN=:= Mean value of events
// DIST20 := Mean value of 1/2-Distance of events between MAX and MIN
// DIST2X := Series of DIST0s
// MEANX := Series of MEANOs
// FX := Summary of all values
function[MDX]=solutionSetApproach(l,n,N,K,show)
// Counter
MDX=zeros(K,6)
for j=1:K
disp(j)
[DIST2,STD, MEAN, FREQ,STD1, MEAN1, FREQ1,FX, POPX]=frequCheck(l,n,j*N,show)
MDX(j,1) = j*N
MDX(j,2) = MEAN
MDX(j,3) = DIST2
MDX(j,4) = STD
MDX(j,5) = MEAN1
MDX(j,6) = STD1
end //j
// Show Plot
clf(), xdel,
x=[MDX(:,1)],
y1=[MDX(:,3)], subplot(3,1,1)
plot2d(x,y1), xtitle=("DIST2[%]")
y2=[MDX(:,4)],subplot(3,1,2)
plot2d(x,y2), xtitle=("STD[%]")
y3=[MDX(:,6)], subplot(3,1,3)
plot2d(x,y3), xtitle=("STD")
endfunction
//***************************************************
//Function to integrate multiple frequency simulations
//
// Input:
// l := length of strings
// n := size of population
// step := Inrement for number of events
// K := how often steps should be applied
//
// Output:
// DIST2SUM := Summary of distances DIST2 with regard to number of events
function[DIST2SUM]=distSum(l,n,step,K,show)
// Counter for DIST2
DIST2SUM=zeros(K,4)
for j=1:K
disp(j)
[DIST2,STD, MEAN, FREQ,FX, POPX]=frequCheck(l,n,j*step,show)
DIST2SUM(j,1) = j*step
DIST2SUM(j,2) = MEAN
DIST2SUM(j,3) = DIST2
DIST2SUM(j,4) = DIST2SUM(j,3)/(MEAN/100)
end //j
// Show Plot
clf(), xdel,
plot2d([DIST2SUM(:,1)], [DIST2SUM(:,4)])
endfunction
//***************************************************
//Function to compute the overall fitness of a matrix POP
// Sum up all the l+2-th positions
// l := length of fitness strings
function[FITNESS_ALL]=fitness(POP,l)
FITNESS_ALL=0;
[r,c]=size(POP);
for j=1:r
FITNESS_ALL=FITNESS_ALL+POP(j,l+2)
end
endfunction
//***************************************************
//Function to compute the maximal individual fitness of a matrix POP
// Compute all the l+2-th positions
// l := length of fitness strings
function[MFITNESS]=maxfitness(POP,l)
// Extracts column l+2 and selects the maximal values
MFITNESS = max(POP([:],l+2))
endfunction
//***************************************************
//Function to compute the relative fitness of a string
// along with the average fitness
// Compute all the l+3-th positions
// l := length of fitness strings
function[POP,AFITNESS]=rfitness(POP,l, FITNESS_ALL)
[r,c]=size(POP);
for j=1:r
POP(j,l+3)=POP(j,l+2)/FITNESS_ALL
end
AFITNESS=FITNESS_ALL/r
endfunction
//***************************************************
//Function to compute the fitness ratio r=f1/f0
//
// l := length of fitness strings
// f1 := fitness of all individuals with a allele value '1' at a position
// f0 := fitness of all individuals with a allele value '0' at a position
// r = f1/f0
//
// Assumption: POP has the relativ fitness available at l+3
function[POP,ratio,f1,f0]=fratio10(POP,l,show)
[r,c]=size(POP);
f1=0;
f0=0;
for i=1:r
for j=1:l
if (POP(i,j)== 1) then f1=f1+POP(i,l+3),
else f0=f0+POP(i,l+3)
end
end //j
end//i
ratio=f1/f0
if show == 2 then disp(POP), disp(f1), disp(f0), disp(ratio), end
endfunction
//*************************************************************
// Computing the worst case convergence time tcw
//
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings ( actually l=5)
// n := number of elements in POP (actually n=4)
// POP := a predefined population (can be done automatically)
//
// f1 := fitness of all individuals with a allele value '1' at a position
// f0 := fitness of all individuals with a allele value '0' at a position
// r = f1/f0
// tcw := worst case convergence time
//
// Assumption: POP has the relativ fitness available at l+3
function[POP,tcw,tcabin,ratio,f1,f0]=ftcw(POP,l,p,n,show)
for i=1:n, v=POP(i,:),
d= vec2dec(v,l), //decimal value
[POP(i,l+1)]= d, //decimal value
end
for i=1:n,[POP(i,l+2)]= fitness1(POP(i,l+1))
end
[FITNESS_ALL]=fitness(POP,l)
[MFITNESS]=maxfitness(POP,l)
[POP,AFITNESS]=rfitness(POP,l,FITNESS_ALL)
[POP,ratio,f1,f0]=fratio10(POP,l,show)
tcw = log((n-1)^2)/log(ratio)
tcabin = log(n-1)/log(ratio)
endfunction
//***************************************************
//Function to compute the relative count of a string
// along with the realized new count by 'rounding up'
// Compute all the l+4 and l+5-th positions
//
// Problem: if the sum of the new proposals is bigger than n
// Solution:
// l := length of fitness strings
// n := number of individuals in POP
function[POP]=newMember(POP,l,n)
[r,c]=size(POP);
for j=1:r
POP(j,l+4)=POP(j,l+3)*n
POP(j,l+5)=round(POP(j,l+4))
end
//Check for sum of proposals
r2 = 0
for j=1:r, r2=r2+POP(j,l+5), end
while r2>n
z=round(rand()*r)
if z==0 then z=1,end //if
POP(z,l+5) = POP(z,l+5)-1
r2=0, for j=1:r, r2=r2+POP(j,l+5), end//for
end//while r2
endfunction
//***************************************************
// Dummy function to replace newMember in simplegas0
//
// along with the realized new count by 'rounding up'
// Compute all the l+4 and l+5-th positions
// l := length of fitness strings
// n := number of individuals in POP
function[POP]=newMember0(POP,l,n)
[r,c]=size(POP);
for j=1:r
POP(j,l+4)=1
POP(j,l+5)=1
end
endfunction
//***************************************************
// Make a copy of a string from row_old to row_new: L --> R
// where the copy starts at position l+p+1
// l := length of string
// j := row_old
// k := row_new
// p := number of parameters (P=5)
function[POP]=strcpyLR(POP,l,p,j,k)
show=0
[r,c]=size(POP);
// Testing the boundaries
if (j < 1) then if show == 1 then printf('ERROR: Position of old String outside
of Matrix! r = %d, j = %d', r,j),end, j=1,
elseif (j > r) then if show == 1 then printf('ERROR: Position of old String
outside of Matrix!, r = %d, j = %d', r,j),end, j=r,
elseif (k < 1) then if show == 1 then printf('ERROR: Position of new String
outside of Matrix!, r = %d, k = %d', r,k),end, k=1
elseif (k > r) then if show == 1 then printf('ERROR: Position of new String
outside of Matrix!, r = %d, k = %d', r,k), end, k=r
end
// Making a copy
for i=1:l
POP(k,l+p+i) = POP(j,i)
end
endfunction
//***************************************************
// Make a copy of a string from row_old to row_new: R --> L
// where the copy starts at position l+p+1
// l := length of string
// j := row_old
// k := row_new
// p := number of parameters (p=5)
function[POP]=strcpyRL(POP,l,p,j,k)
show=0
[r,c]=size(POP);
// Testing the boundaries
if (j < 1) then if show == 1 then printf('ERROR: Position of old String outside
of Matrix! r = %d, j = %d', r,j),end, j=1
elseif (j > r) then if show == 1 then printf('ERROR: Position of old String
outside of Matrix!, r = %d, j = %d', r,j),end, j=r
elseif (k < 1) then if show == 1 then printf('ERROR: Position of new String
outside of Matrix!, r = %d, k = %d', r,k), end, k=1
elseif (k > r) then if show == 1 then printf('ERROR: Position of new String
outside of Matrix!, r = %d, k = %d', r,k),end, k=r
end
// Making a copy
for i=1:l
POP(j,i) = POP(k,l+p+i)
end
endfunction
//***************************************************
// Make a copy of all strings from the old rows to the new ones
// where the new copies will start at position l+p+1
// l := length of string
// j := row_old
// k := row_new
// p := number of parameters
// r2 := memory of position for new strings
function[POP]= newPop(POP,l,p,n)
[r,c]=size(POP);
r2 = 1
for j=1:r
if POP(j,l+7) > 0 then r3 = POP(j,l+7)-1,
for k=r2:(r2+r3), //printf('\n k = %d\n', k)
[POP]=strcpyLR(POP,l,p,j,k)
end
r2=k+1
end
end
endfunction
//***************************************************
// Make a copy of all strings from the old rows to the new ones
// where the new copies will start at position l+p+1
//
// Problem: If the sum of new copies is greater than n then this causes a fault!
// Solution: At least check the sum before operation
//
// l := length of string
// j := row_old
// k := row_new
// p := number of parameters
// r2 := memory of position for new strings
function[POP]= newPop2(POP,l,p,n)
[r,c]=size(POP);
//Check for sum of proposals
r2 = 0
for j=1:r, r2=r2+POP(j,l+5), end
if r2 >n then error('In newPop2() sum of proposals >n!!!'),end
r2 = 1
for j=1:r
if POP(j,l+5) > 0 then r3 = POP(j,l+5)-1,
for k=r2:(r2+r3), //printf('\n k = %d\n', k)
[POP]=strcpyLR(POP,l,p,j,k)
end
r2=k+1
end
end
endfunction
//***************************************************
// Prepare the crossover operations within a population POP
// by randomly selecting the new strings and copy them onto the
// POP base area [1,l]
//
// General Assumption: the number of members n is even!!!
//
// The strings are assumed to be in the area starting at l+p+1
// The parameter at l+p has been changed to a flag '1' := not yet mated
// j := target position in the base area for copy action
function[POP]= crossoverPrep(POP,l,p,n)
[r,c]=size(POP);
// Set a flag at position l+7 with '1'
for j=1:r
POP(j,l+7)=1
end
// Select randomly the strings for transfer
j = 1 //:= Baseline for filling up with strings
while(j < n+1)
S = 1 //:= Flag for searching a string to be copied
while(S == 1)
k1 = round(n * rand())
if k1==0 then k1=1
end //if
if POP(k1,l+7) <> 0 then POP=strcpyRL(POP,l,p,j,k1)
//mshow(POP,n,l+p+l)
POP(k1,l+7) = 0,
S=0
else S=1
end //if
end //while == S
// printf('k1 = %d\n',k1)
// printf('j = %d\n',j)
j = j+1
// mshow(POP,n,l+p+l)
end // while == j
endfunction
//***************************************************
// Apply a crossover operation onto two adjacent strings at intersection x
// The strings are assumed to be randomly paired in the area at position 1
//
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings ( actually l=5)
// n := number of elements in POP (actually n=4)
function[POP]= crossover(POP,l,p,n)
// Take a first row
r=1
while(r < n)
// printf('r = %d\n',j)
// Select randomly a point in this row
x = round(l * rand()), if(x == 0) then x=1,end,
// printf('x = %d\n',x)
for i=x:l, m=POP(r+1,i)
POP(r+1,i) = POP(r,i)
POP(r,i) = m
end
r=r+2
end
endfunction
//***************************************************
// Apply a mutation operation onto one randomly selected string
// Select randomly a point in the string and replace it's
// value by it's inverse '1' --> '0', '0' --> '1'
function[POP]= mutation(POP,l,p,n)
// Find a point in a string
c = round(l * rand())
if c == 0 then c=1 // This does not change anything
end
// Find a row in the table
r = round(n * rand())
if r == 0 then r=1 // This does not change anything
end
// replace the value
if(POP(r,c) == 1) then POP(r,c) = 0,
else POP(r,c) = 1
end
printf('mutation point at row = %d col = %d\n',r,c)
endfunction
//***************************************************
// Print the content of a matrix
//
// d := depth of matrix 'downwards'
// w := width of matrix from left to right
function[M]= mshow(M,d,w)
for j=1:d,// printf('\n j= %3.1d : ',j)
for i=1:w, //printf(' %3.1d ',M(j,i))
end
//printf('\n')
end
endfunction
//***************************************************
// Translate strings with binaries '0', '1' as decimal numbers
//
// v = vector of binaries from a POP-matrix (left part)
// l := length of string
// D := decimal computed out of binaries
function[D]= vec2dec(v,l)
str=string(v(1:l))
for i=2:l, str(1)=str(1)+str(i)
end
D=bin2dec(str(1))
endfunction
//***************************************************
// Translate strings with binaries '0', '1' as decimal numbers
//
// v = vector of binaries from a POP-matrix (left part)
// l := length of string
// D := decimal computed out of binaries
function[D]= vec22dec(v,l1,l2)
str=string(v(l1:l2))
for i=2:l2-l1+1, str(1)=str(1)+str(i)
end
D=bin2dec(str(1))
endfunction
//***************************************************
// Translate strings with binaries '0', '1' and n-many compartments as decimal
numbers
//
// v = vector of binaries from a POP-matrix (left part)
// l := length of string
// b := number of bins for one number
// D := Array of decimals
function[D]= vec222dec(v,l,b,show)
D=[]
k=1
for j=1:b:l+1-b
if show==1 then printf('j = %d ',j),end
str=string(v(j:j+b-1))
for i=2:b, str(1)=str(1)+str(i)
end //i
if show==1 then printf('k = %d ',k),end
D(k)=bin2dec(str(1))
if show==1 then printf('D(k) = %d\n',D(k)),end
k=k+1
end //j
endfunction
//***************************************************
// maxfit01 builds a string of length l and computes the decimal value
//
// l := length of string
// MF := decimal computed out of binaries
function[MF]= maxfit01(l)
FitString=""
v=ones(1,l)
str=string(v)
for i=1:l, FitString = FitString + str(i)
end
MF=bin2dec(FitString)
endfunction
//***************************************************
// maxfi02 computes with maxfit01 the decimal value of a string with length l
and
// then compares the maximal value according to the fitness function y=x^2
// multiplied by the number n of strings in a population
//
// l := length of string
// MF := decimal computed out of binaries
function[MAXFIT]= maxfit02(l,n)
MAXFIT=n*(maxfit01(l)^2)
endfunction
//***************************************************
// Simple fitness-function f=(x^2)
//
// D := decimal computed out of binaries
function[F]= fitness1(D)
F=D^2
endfunction
//***************************************************
// Fitness-function f for a world W which is realized as a table t:D --> R
// IF (d,r) in t then f(d1,d2)=100, ELSE f(d1,d2)=0
//
// d1,d2 := decimal values of population POP
// W := a world organized as a table
// n := number of elements in W
// F := fitness value
function[F]= fitness2(d1,d2,W)
[r,c]=size(W)
upper =10
goal = upper*2
i=1
while i < r+1,
if W(i,1) == d1 & W(i,2) == d2 then F=goal, i=r+1,
else F=round(upper * rand()), i=i+1,
end //if
end//while
endfunction
//***************************************************
// Fitness-function f for a world W which is realized as a table t:D --> R
// IF (d,r) in t then f(d1,d2)=goal, ELSE f(d1,d2)=random(upper)
//
// D := Array of pairs of decimal values
// W := a world organized as a table
// F := fitness value
function[F,goal]= fitness3(D,W)
[r,c]=size(W)
[r2,c2]=size(D)
F2=[]
upper =10 // range of numbers for non-goals [0,upper]
goal = upper*2
j=1 //Index for D
for i=1:r //Look to every pair in W
if W(i,1) == D(j) & W(i,2) == D(j+1) then F2(i)=goal,
else F2(i)=round(upper * rand()),
end //if
j=j+2
end // for i
F=sum(F2)
endfunction
//*************************************************************
// Function to compute only the fitness of a population
//
// Input:
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings
// n := number of elements in POP
// Output
// POP := a population
// MFITNESS := Maximal Fitness of each individual
function[POP,MFITNESS, FITNESS_ALL]=popFit(l,p,n)
[POP]=popgen(n,l+p)
MFITNESS=0
for j=1:n, v=POP(j,:), [POP(j,l+1)]= vec2dec(v,l)
end
for i=1:n,[POP(i,l+2)]= fitness1(POP(i,l+1))
end
[FITNESS_ALL]=fitness(POP,l)
[MFITNESS]=maxfitness(POP,l)
endfunction
//*************************************************************
// Function to compute the maximal fitness of an individuum
// for several populations
//
// Input:
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings
// n := number of elements in POP
// run := number of choices
// Output
// POP := a population
// MFITNESS := Maximal Fitness of each individual
// MFITNESSX := Array with maximal fitness
function[POP,MEAN, MFITNESSX]=popFitX(l,p,n,run)
MAXFITUP = ((2^l)^2)
for k=1:run
[POP]=popgen(n,l+p)
for j=1:n, v=POP(j,:), [POP(j,l+1)]= vec2dec(v,l)
end
for i=1:n,[POP(i,l+2)]= fitness1(POP(i,l+1))
end
[MFITNESSX(k)]=maxfitness(POP,l)
end
for k=1:run
MFITNESSX(k)=MFITNESSX(k)/(MAXFITUP/100)
end
MEAN = mean(MFITNESSX)
// Show graphical results
//clf(), xdel,
//plot2d([1:1:run], MFITNESSX)
endfunction
//*************************************************************
// Function to compute the maximal fitness of an individuum
// for several populations
// for increasing n
//
// Input:
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings
// n := number of elements in POP
// run := number of choices
// Output
// POP := a population
// MFITNESS := Maximal Fitness of each individual
// MFITNESSX := Array with maximal fitness
function[MEAN, MEANX]=popFitXN(l,p,m,run)
for i=1:m
[POP,MEAN, MFITNESSX]=popFitX(l,p,i,run)
MEANX(i) = MEAN
end
MEAN = mean(MEANX)
// Show graphical results
clf(), xdel,
plot2d([1:1:m], MEANX)
endfunction
//*************************************************************
// Function to compute the maximal fitness of a population
// for several generations
//
// Input:
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings
// n := number of elements in POP
// run := number of generations
// Output
// POP := a population
// FITNESS_ALL := Maximal Fitness of a population
// FITNESS_ALLX := Array with maximal fitness
// MEAN := Mean value of array
function[STD,MEAN, FITNESS_ALLX]=popMaxFitX(l,p,n,run)
MAXFITUP = ((2^l)^2)*n
for k=1:run
[POP]=popgen(n,l+p)
for j=1:n, v=POP(j,:), [POP(j,l+1)]= vec2dec(v,l)
end
for i=1:n,[POP(i,l+2)]= fitness1(POP(i,l+1))
end
[FITNESS_ALLX(k)]=fitness(POP,l)
end
for k=1:run
FITNESS_ALLX(k)=FITNESS_ALLX(k)/(MAXFITUP/100)
end
MEAN = mean(FITNESS_ALLX)
mf=tabul(FITNESS_ALLX)
STD=stdevf(mf([:],1), mf([:],2))
// Show graphical results
//clf(), xdel,
//plot2d([1:1:run], MFITNESSX)
endfunction
//*************************************************************
// All Functions Unified
//
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings ( actually l=5)
// n := number of elements in POP (actually n=4)
// POP := a predefined population (can be done automatically)
// run := number of cycles
// MThreshold := number of cycles which have to be waited until the mutation
operators will be applied
function[POP,FITNESS_ALLLOG]=gasimple(POP,l,p,n,run, MThreshold)
MCount = 0
FITNESS_ALLLOG=[]
for cyc = 1:run
[M]= mshow(POP,n,l+p)
for j=1:n, v=POP(j,:), [POP(j,l+1)]= vec2dec(v,l)
end
for i=1:n,[POP(i,l+2)]= fitness1(POP(i,l+1))
end
[FITNESS_ALL]=fitness(POP,l)
FITNESS_ALLLOG(cyc)=FITNESS_ALL
[MFITNESS]=maxfitness(POP,l)
[POP,AFITNESS]=rfitness(POP,l,FITNESS_ALL)
[POP]=newMember(POP,l,n)
[POP]=newPop(POP,l,p,n)
[POP]= crossoverPrep(POP,l,p,n)
[POP]= crossover(POP,l,p,n)
printf('Mutationcount = %d\n', MCount)
if(MCount > MThreshold) then [M]= mshow(POP,n,l+p),
[POP]= mutation(POP,l,p,n),
[M]= mshow(POP,n,l+p),
MCount=0,
end
MCount = MCount + 1
end //for == run
// Compute the maximal value and the percentage of success
[MAXFIT]=maxfit02(l,n)
FITNESS_ALL_PERC=[]
for i=1:run, FITNESS_ALL_PERC(i) = FITNESS_ALLLOG(i)/(MAXFIT/100), end
// Show graphical results
clf(), xdel,
//plot2d([1:1:run], FITNESS_ALLLOG)
plot2d([1:1:run], FITNESS_ALL_PERC)
endfunction
//*************************************************************
// A system with GA without any additional parameters
//
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings ( actually l=5)
// n := number of elements in POP (actually n=4)
// POP := a predefined population (can be done automatically)
// N := number of cycles
// MThreshold := number of cycles which have to be waited until the mutation
operators will be applied
function[FITNESS_ALL_PERC,POP]=ga(POP,l,p,n,N, MThreshold,show)
MCount = 0
FITNESS_ALLLOG=[]
for cyc = 1:N
for j=1:n, v=POP(j,:),
d= vec2dec(v,l), //decimal value
[POP(j,l+1)]= d, //decimal value
end
for i=1:n,[POP(i,l+2)]= fitness1(POP(i,l+1))
end
[FITNESS_ALL]=fitness(POP,l)
FITNESS_ALLLOG(cyc)=FITNESS_ALL
[MFITNESS]=maxfitness(POP,l)
[POP,AFITNESS]=rfitness(POP,l,FITNESS_ALL)
[POP]=newMember(POP,l,n)
[POP]=newPop(POP,l,p,n)
[POP]= crossoverPrep(POP,l,p,n)
[POP]= crossover(POP,l,p,n)
if show==1 then
printf('Mutationcount = %d\n', MCount),
end
if(MCount > MThreshold) then
[POP]= mutation(POP,l,p,n),
if show==1 then disp(POP), end
MCount=0,
end
MCount = MCount + 1
end //for == N
printf("Number of Events n * N = %d\n",n*N)
// Compute the maximal value and the percentage of success
[MAXFIT]=maxfit02(l,n)
FITNESS_ALL_PERC=[]
for i=1:N, FITNESS_ALL_PERC(i) = FITNESS_ALLLOG(i)/(MAXFIT/100), end
// Show graphical results
if show==2 then
clf(), xdel,
plot2d([1:1:N], FITNESS_ALL_PERC),
end
endfunction
//*************************************************************
// A system with GA
//
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings ( actually l=5)
// n := number of elements in POP (actually n=4)
// POP := a predefined population (can be done automatically)
// N := number of cycles
// MThreshold := number of cycles which have to be waited until the mutation
operators will be applied
function[FITNESS_ALL_PERC,DIST2,STD, MEAN, FREQ,STD1, MEAN1, FREQ1,FX,
POP]=ga0(POP,l,p,n,N, MThreshold,show)
// Install the counters
r= (2^l)
c= 6
FX = zeros(r,c)
MCount = 0
FITNESS_ALLLOG=[]
// Generate an internal index for display
for j=1:r
FX(j,1)=j-1
end
for cyc = 1:N
for j=1:n, v=POP(j,:),
d= vec2dec(v,l), //decimal value
[POP(j,l+1)]= d, //decimal value
FX(d+1,2)=FX(d+1,2)+1, //occurences
end
for i=1:n,[POP(i,l+2)]= fitness1(POP(i,l+1))
end
[FITNESS_ALL]=fitness(POP,l)
FITNESS_ALLLOG(cyc)=FITNESS_ALL
[MFITNESS]=maxfitness(POP,l)
[POP,AFITNESS]=rfitness(POP,l,FITNESS_ALL)
[POP]=newMember(POP,l,n)
[POP]=newPop(POP,l,p,n)
[POP]= crossoverPrep(POP,l,p,n)
[POP]= crossover(POP,l,p,n)
if show==1 then
printf('Mutationcount = %d\n', MCount),
end
if(MCount > MThreshold) then
[POP]= mutation(POP,l,p,n),
if show==1 then disp(POP), end
MCount=0,
end
MCount = MCount + 1
end //for == N
for j=1:r
FX(j,3)=(FX(j,2)/n)/N //Normal frequency
FX(j,4)=(FX(j,2)/n)/(((1/2^l)*N)/100) // Frequency as percentage
end//m
disp(FX)
FREQ1=tabul(FX(:,3))
MEAN1=mean(FREQ1(:,1))
STD1= stdevf(FREQ1(:,1), FREQ1(:,2))
FREQ=tabul(FX(:,4))
MEAN=mean(FREQ(:,1))
STD= stdevf(FREQ(:,1), FREQ(:,2))
MAX=max(FREQ(:,1))
MIN=min(FREQ(:,1))
DIST=MAX-MIN
DIST2=DIST/2
printf("Number of Events n * N = %d\n",n*N)
// Compute the maximal value and the percentage of success
[MAXFIT]=maxfit02(l,n)
FITNESS_ALL_PERC=[]
for i=1:N, FITNESS_ALL_PERC(i) = FITNESS_ALLLOG(i)/(MAXFIT/100), end
// Show graphical results
if show==2 then
clf(), xdel,
plot2d([1:1:N], FITNESS_ALL_PERC),
end
endfunction
//*************************************************************
// GA algorithm without fitness
//
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings ( actually l=5)
// n := number of elements in POP (actually n=4)
// POP := a predefined population (can be done automatically)
// N := number of events
// K := Number of repetitions from calling function
// MThreshold := number of events which have to be waited until the mutation
operators will be applied
function[MCount,DIST2,STD, MEAN, FREQ,STD1, MEAN1,
FREQ1,POP,FX]=gasimple0(POP,l,p,n,N, K,MThreshold,MCount,show)
// Install the counters
r= (2^l)
c= 5
FX = zeros(r,c)
// Generate an internal index for display
for j=1:r
FX(j,1)=j-1
end
for cyc = 1:N*K //Start Cyle for events
if show ==1 then disp(cyc), end
for j=1:n
v=POP(j,:), d = vec2dec(v,l), [POP(j,l+1)]= d, FX(d+1,2)=FX(d+1,2)+1
end//n
if show ==1 then printf("\nFX after Count\n\n"), disp(FX), end
[POP]=newMember0(POP,l,n) //Prepares copies by inserting '1' at position l+4
and l+5
[POP]=newPop(POP,l,p,n) //Copies old strings to the right
[POP]= crossoverPrep(POP,l,p,n)
[POP]= crossover(POP,l,p,n)
if show ==1 then printf('Mutationcount = %d\n', MCount),disp(POP), end
if(MCount > MThreshold) then [POP]= mutation(POP,l,p,n),
if show ==2 then printf('Mutationcount (MCount, cyc)= (%d,%d)\n', MCount,
cyc), end
MCount = 0, end
MCount = MCount + 1
if show==1 then printf("POP after Operators\n"), disp(POP), end
end //cyc=N
for j=1:r
FX(j,3)=(FX(j,2)/n)/(N*K) //Normal frequency
FX(j,4)=(FX(j,2)/n)/(((1/2^l)*(N*K))/100) // Frequency as percentage
end//m
disp(FX)
FREQ1=tabul(FX(:,3))
MEAN1=mean(FREQ1(:,1))
STD1= stdevf(FREQ1(:,1), FREQ1(:,2))
FREQ=tabul(FX(:,4))
MEAN=mean(FREQ(:,1))
STD= stdevf(FREQ(:,1), FREQ(:,2))
MAX=max(FREQ(:,1))
MIN=min(FREQ(:,1))
DIST=MAX-MIN
DIST2=DIST/2
printf("Number of Events n * N * K = %d\n",n*N*K)
endfunction
//*************************************************************
// GA algorithm with fitness and conditioned mutation
//
// Works like 'normal' GA but uses mutation only if the actual maximal fitness
// stays 'constant' over MT-many cycles and is below te theoretical maximum
//
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings ( actually l=5)
// n := number of elements in POP (actually n=4)
// POP := a predefined population (can be done automatically)
// N := number of events
// MT := mutation trigger; number of values to monitor for to trigger mutation
function[FITNESS_ALL_PERC,DIST2,STD, MEAN, FREQ,STD1, MEAN1, FREQ1,FX,
POP]=ga1(POP,l,p,n,N, MT,show)
//Theoretical Maximum for Fitness according to y=x^2
TMaxFit = ((2^l)-1)^2*n
// Install the counters
r= (2^l)
c= 6
FX = zeros(r,c)
MCount = 0
FITNESS_ALLLOG=[]
MTriggerEstimator=[]
// Generate an internal index for display
for j=1:r
FX(j,1)=j-1
end
for cyc = 1:N
for j=1:n, v=POP(j,:),
d= vec2dec(v,l), //decimal value
[POP(j,l+1)]= d, //decimal value
FX(d+1,2)=FX(d+1,2)+1, //occurences
end
for i=1:n,[POP(i,l+2)]= fitness1(POP(i,l+1))
end
[FITNESS_ALL]=fitness(POP,l)
FITNESS_ALLLOG(cyc)=FITNESS_ALL
[MFITNESS]=maxfitness(POP,l)
if show ==1 then disp(FITNESS_ALL), end
MTriggerEstimator(cyc)=FITNESS_ALL
if show ==1 then disp(MTriggerEstimator(cyc)), end
[POP,AFITNESS]=rfitness(POP,l,FITNESS_ALL)
[POP]=newMember(POP,l,n)
[POP]=newPop(POP,l,p,n)
[POP]= crossoverPrep(POP,l,p,n)
[POP]= crossover(POP,l,p,n)
if show ==1 then disp(MCount), end
if(MCount > MT) then
if show ==1 then disp(MTriggerEstimator(cyc)),
disp(MTriggerEstimator(cyc-MT)), disp(TMaxFit), end
if (MTriggerEstimator(cyc) == MTriggerEstimator(cyc-MT) &
MTriggerEstimator(cyc) < TMaxFit) then [POP]= mutation(POP,l,p,n),
if show==1 then disp(POP), end
end
MCount=0,
end
MCount = MCount + 1
end //for == N
for j=1:r
FX(j,3)=(FX(j,2)/n)/N //Normal frequency
FX(j,4)=(FX(j,2)/n)/(((1/2^l)*N)/100) // Frequency as percentage
end//m
disp(FX)
FREQ1=tabul(FX(:,3))
MEAN1=mean(FREQ1(:,1))
STD1= stdevf(FREQ1(:,1), FREQ1(:,2))
FREQ=tabul(FX(:,4))
MEAN=mean(FREQ(:,1))
STD= stdevf(FREQ(:,1), FREQ(:,2))
MAX=max(FREQ(:,1))
MIN=min(FREQ(:,1))
DIST=MAX-MIN
DIST2=DIST/2
printf("Number of Events n * N = %d\n",n*N)
// Compute the maximal value and the percentage of success
[MAXFIT]=maxfit02(l,n)
FITNESS_ALL_PERC=[]
for i=1:N, FITNESS_ALL_PERC(i) = FITNESS_ALLLOG(i)/(MAXFIT/100), end
// Show graphical results
if show==2 then
clf(), xdel,
plot2d([1:1:N], FITNESS_ALL_PERC),
end
endfunction
//*************************************************************
// A system with GA for a world with a table
//
// A world W organized as a table maps a set D into a set R
// l := length of strings
// p := number of cells between string <1...l> and <l+p+1, ..., l+p+l>
// Pos 1-l := String
// Pos l+1 := Decimal Value of binary string
// Pos l+2 := Fitness for l+1 and l+p
// Pos l+3 := Percentage of overall fitness
// Pos l+4 := Expected count according to fitness
// Pos l+5 := Realized count
// Pos l+6 := 2nd Decimal value of a compund fitness
// Pos l+p := flag for crossover
// p := 7
// POP := a predefined population (can be done automatically)
// n := number of elements in POP
// N := number of cycles
// MT := number of cycles which have to be waited until the mutation operators
will be applied
function[FITNESS_ALL_PERC,POP]=gaw1(W,POP,l,p,n,N, MT,l1,show)
MCount = 0
FITNESS_ALLLOG=[]
for cyc = 1:N
if show == 1 then disp('cyc ='),disp(cyc),disp(' '),end
for j=1:n, v=POP(j,:),
d1= vec22dec(v,1,l1), //decimal value1
d2= vec22dec(v,l1+1,l), //decimal value2
[POP(j,l+1)]= d1, //decimal value
[POP(j,l+6)]= d2, //decimal value
end
if show == 1 then printf('New Numbers in POP '), disp(POP), end
for i=1:n,[POP(i,l+2)]= fitness2(POP(i,l+1),POP(i,l+6),W)
end
[FITNESS_ALL]=fitness(POP,l)
if show == 1 then printf('FITNESS_ALL = %f\n',FITNESS_ALL), end
FITNESS_ALLLOG(cyc)=FITNESS_ALL
[MFITNESS]=maxfitness(POP,l)
[POP,AFITNESS]=rfitness(POP,l,FITNESS_ALL)
if show == 1 then disp(POP), end
[POP]=newMember(POP,l,n)
[POP]=newPop2(POP,l,p,n)
if show == 1 then disp(POP), end
[POP]= crossoverPrep(POP,l,p,n)
[POP]= crossover(POP,l,p,n)
if show == 1 then disp(POP),printf('MCount = %d\n',MCount), end
if(MCount > MT) then
[POP]= mutation(POP,l,p,n), printf('Mutation at cycle = %d\n',cyc),
if show==1 then disp(POP), end
MCount=0,
end
MCount = MCount + 1
end //for == N
printf("Number of Events n * N = %d\n",n*N)
// Compute the maximal value and the percentage of success
MAXFIT=20*n //The value '20' is set in the function fitness2()
FITNESS_ALL_PERC=[]
for i=1:N, FITNESS_ALL_PERC(i) = FITNESS_ALLLOG(i)/(MAXFIT/100), end
// Show graphical results
if show==2 | show == 1 then
clf(), xdel,
plot2d([1:1:N], FITNESS_ALL_PERC),
end
endfunction
//*************************************************************
// A system with GA for a world with a table and with
// multi-compartment genomes
//
// A world W organized as a table maps a set D into a set R
// l := length of strings
// p := number of cells between string <1...l> and <l+p+1, ..., l+p+l>
// Pos 1-l := String
// Pos l+1 := Decimal Value of binary string
// Pos l+2 := Fitness for l+1 and l+p
// Pos l+3 := Percentage of overall fitness
// Pos l+4 := Expected count according to fitness
// Pos l+5 := Realized count
// Pos l+6 := 2nd Decimal value of a compund fitness
// Pos l+7 := flag for crossover
// p := 7
// POP := a predefined population (can be done automatically)
// n := number of elements in POP
// N := number of cycles
// MT := number of cycles which have to be waited until the mutation operators
will be applied
// V := version
function[FITNESS_ALL_PERC,MAXGENOMECOUNT,POP,V]=gaw2(W,POP,l,n,N, MT,b,show,V)
p = 7
MCount = 0
FITNESS_ALLLOG=[]
for cyc = 1:N
if show == 1 then disp('cyc ='),disp(cyc),disp(' '),end
for i=1:n , v=POP(i,:), [D]= vec222dec(v,l,b,show), [POP(i,l+2),goal]=
fitness3(D,W), end //for i
if show == 1 then printf('New Numbers in POP '), disp(POP), end
[FITNESS_ALL]=fitness(POP,l)
if show == 1 then printf('FITNESS_ALL = %f\n',FITNESS_ALL), end
FITNESS_ALLLOG(cyc)=FITNESS_ALL
[MFITNESS]=maxfitness(POP,l)
[POP,AFITNESS]=rfitness(POP,l,FITNESS_ALL)
// if show == 1 then disp(POP), end
[POP]=newMember(POP,l,n)
if show == 1 then disp(POP), end
[POP]=newPop2(POP,l,p,n)
if show == 1 then disp(POP), end
[POP]= crossoverPrep(POP,l,p,n)
[POP]= crossover(POP,l,p,n)
if show == 1 then disp(POP),printf('MCount = %d\n',MCount), end
if(MCount > MT) then
[POP]= mutation(POP,l,p,n), printf('Mutation at cycle = %d\n',cyc),
if show==1 then disp(POP), end
MCount=0,
end
MCount = MCount + 1
end //for == N
printf("Number of Events n * N = %d\n",n*N)
// Compute the maximal value and the percentage of success
[r,c]=size(POP)
[r2,c2]=size(W)
MAXFIT=goal*r2*r //The value 'goal' is set in the function fitness3()
MAXFITGENOME = goal*r2 // To count the complete genomes in a population
FITNESS_ALL_PERC=[]
MAXGENOMECOUNT = 0
for i=1:r,
if POP(i,l+2) == MAXFITGENOME then MAXGENOMECOUNT =MAXGENOMECOUNT+1, end,
end
for i=1:N, FITNESS_ALL_PERC(i,1)=i, FITNESS_ALL_PERC(i,2) =
FITNESS_ALLLOG(i)/(MAXFIT/100), end
// Show graphical results
if show==2 | show == 1 then
clf(), xdel,
scf(V),
plot2d([1:1:N], FITNESS_ALL_PERC(:,2)),
end
endfunction
//*************************************************************
// Computing the worst case convergence time tcw
//
// p := number of parameters between strings left and right (actually p=5)
// l := length of strings ( actually l=5)
// n := number of elements in POP (actually n=4)
// POP := a predefined population (can be done automatically)
//
// f1 := fitness of all individuals with a allele value '1' at a position
// f0 := fitness of all individuals with a allele value '0' at a position
// r = f1/f0
// tcw := worst case convergence time
//
// Assumption: POP has the relativ fitness available at l+3
function[POP,tcw,tcabin,ratio,f1,f0]=ftcw2(W,POP,l,p,n,l1,show)
for j=1:n, v=POP(j,:),
d1= vec22dec(v,1,l1), //decimal value1
d2= vec22dec(v,l1+1,l), //decimal value2
[POP(j,l+1)]= d1, //decimal value
[POP(j,l+6)]= d2, //decimal value
end
for i=1:n,[POP(i,l+2)]= fitness2(POP(i,l+1),POP(i,l+6),W)
end
[FITNESS_ALL]=fitness(POP,l)
[MFITNESS]=maxfitness(POP,l)
[POP,AFITNESS]=rfitness(POP,l,FITNESS_ALL)
[POP,ratio,f1,f0]=fratio10(POP,l,show)
tcw = log((n-1)^2)/log(ratio)
tcabin = log(n-1)/log(ratio)
endfunction
//***********************************************************************
// Examples
//
POP = [0 1 1 0 1 13 169 0 0 0; 1 1 0 0 0 24 576 0 0 0; 0 1 0 0 0 8 64 0 0 0; 1
0 0 1 1 19 361 0 0 0;]
W=[1 3; 2 1; 3 2]
W2=[1 3; 2 1; 3 2; 4 4; 5 7; 6 5]