//************************************************************** // File:ga1_v2-3.sci // Authors: Gerd Doeben-Henisch // Version Start: January-18, 2010 // Version Last: July-3-2013, 15:28h // //****************************************************************** // Idea: Implements a simple GA according to Goldberg (1989) // // Attention: In Goldberg (1989) you will find only the demonstration of the program. The source code // of this program is completely independ and original. It changes often according to discussions in // the lectures. You are allowed to use this source code for non-commercial applications. // //************************************************* // 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 dynamic table. Left hand the actual genes, in the middle // supporting parameters and to the right intermediate modifications of the genes from the left side. // // 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 // Variable for overall Fitness FITNESS_ALL = 0 // Variable for average Fitness AFITNESS = 0 //******************************************************** // LIST OF ALL FUNCTIONS //******************************************************** // // [POPX]=popgen(n,l) : Generates a random popluation of n elements with length l // [r]=randInt0(max) : Integer random numbers [0,max] // [r]=randInt1(max) : Integer randim numbers [1,max] // [D]= vec2dec(v,l) : Convert a vector v with length l and '1','0' into a decimal number // [POP]=bin22dec(POP,l,show) : Convert ll strings of length l and '1','0' of a POP into a deci,mal at l+1 // [F]= fitness1(D) : Simpl fitness function F=D^2, D as integer // [POP]=fitnessComp1(POP,l,show) : Compute fitness values for all strings at l+2 using fitness1 // [FITNESS_ALL]=fitness(POP,l,show) : Summing up all fitness value in column l+2 // [MFITNESS]=maxfitness(POP,l,show) : Find the biggest fitness value // [POP,AFITNESS]=rfitness(POP,l, FITNESS_ALL,show) : Relative size of each fitness value // [POP]= newPop0(POP,l,p,n,show) : Select only the positiv members without a '0' at l+p // [POP]=strcpyLRR(POP,l,p,j,r) : Make a copy of a string from row_old to row_new: L --> R // [POP]=crossmatch(POP,l,p,j,x) : Mixes the right sides of two strings from x to l // [POP]= crossoverPrep(POP,l,p,n,show) : Preparing crossover // [POP]= crossover(POP,l,p,n,show) : doing crossover // [POP]= mutation(POP,l,p,n) : Doing mutation // [MAXFIT]= maxfit02(l,n) : Maximal fitness number of a population with length l and member number n // POP,MFITNESS, FITNESS_ALL]=popFit(POP,l,p,n,show) : Fitness of a population // [PERC]=popFitPerc(POP,l,p,n,show) : Fitness of a population as percentage of the maximal fitness // //**************************************************************** //Function to generate automatically a population with random values // Input: // l := length of strings // n := size of population (should be even on account of crossover!) // 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 as integers [0,max] function [r]=randInt0(max) r = round(max*rand()) endfunction //*************************************************** //Function to generate random numbers as integers [1,max] function [r]=randInt1(max) r = round((max-1)*rand()) +1 endfunction //*************************************************** // Translate strings with binaries '0', '1' as decimal numbers // // v = vector of binaries from a POP-matrix (left part) // D := decimal computed out of binaries // l := length of strings 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 //***************************************************** // Convert binary strings with length l in a population POP into decimals at position l+1 // function [POP]=bin22dec(POP,l,show) [n,c]=size(POP) for j=1:n, v=POP(j,:), [POP(j,l+1)]= vec2dec(v),end endfunction //*************************************************** // Simple fitness-function f=(x^2) // // D := decimal computed out of binaries function[F]= fitness1(D) F=D^2 endfunction //************************************************ // Compute in a POP fitness in l+2 with some fitness function fitness1 // function [POP]=fitnessComp1(POP,l,show) [n,c]=size(POP) for i=1:n, [POP(i,l+2)]= fitness1(POP(i,l+1)) end if show==1 then disp('fitnessComp1='), disp(POP), end 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,show) FITNESS_ALL=sum(POP(:,l+2)) if show==1 then disp('FITNESS_ALL='), disp(FITNESS_ALL), 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,show) // Extracts column l+2 and selects the maximal values MFITNESS = max(POP([:],l+2)) if show==1 then disp('MAX-FITNESS='), disp(MFITNESS), end 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 // n:= number of members in population POP function[POP,AFITNESS]=rfitness(POP,l,n, FITNESS_ALL,show) [r,c]=size(POP); for j=1:r POP(j,l+3)=POP(j,l+2)/FITNESS_ALL end AFITNESS=FITNESS_ALL/r for j=1:n POP(j,l+4)=POP(j,l+3)*n POP(j,l+5)=round(POP(j,l+4)) end if show==1 then disp('rfitness='), disp(POP), end endfunction //*************************************************** // newMember_old() // l := length of fitness strings // n := number of individuals in POP function[POP]=newMember_old(POP,l,n,show) //Check for sum of proposals r2 = sum(POP(:,l+5)) //Two cases: //r2>n or r2<n if r2>n then if show==1 then disp('newMember r2>n'),disp('r2='), disp(r2) end while (r2>n) z=round(rand()*n) if z==0 then z=1,end //if if POP(z,l+5) >2 then POP(z,l+5) = POP(z,l+5)-1 end r2=sum(POP(:,l+5)) end//while r2 if show==1 then disp('newMember r2'), disp(r2) end elseif r2<n then if show==1 then disp('newMember r2<n'),disp('r2='), disp(r2) end while r2<n z=round(rand()*n) if z==0 then z=1,end //if if POP(z,l+5) <1 then POP(z,l+5) = POP(z,l+5)+1 end r2=sum(POP(:,l+5)) end//while r2 end//if if show==1 then disp('newMember='),disp(POP) end endfunction //********************************************************** // Translates rfitness into integer parts // 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=sum(POP(:,[p:p])) endfunction //*************************************************** // Select only those strings which are not zero at l+p! // l := length of string // p := number of parameters (=5) // r2 := memory of position for new strings function[POP]= newPop0(POP,l,p,n,show) POPNEW=POP //Make a copy of POP // Aranging the values according to size and limit y=l+p,[M,k]=gsort(POP(:,[y:y])) // M has the values from max to min // k has the index of the values into POP // Now one can copy the strings from POP-L to POPNEW-R as long as the sum s<n s=0 j=0 r2=0 //Index into the new matrix POPNEW while (s<n)&(j<n) j=j+1, //Index into M s=s+POP(k(j),y) if POP(k(j),l+p) == 0 then r2=r2+1,POPNEW(r2,:)=POP(k(j),:), else m=POP(k(j),l+p), for i=1:m, r2=r2+1,POPNEW(r2,:)=POP(k(j),:),end //End of m end //End of if if show==1 then disp('newPop0 r2='), disp(r2),disp(POPNEW) end end // End of while //Attention, this procedures allows to extend POPNEW and the POP beyond n=4. POP=POPNEW if show==1 then disp('newPop0 r2='), disp(r2),disp(POPNEW) end if r2 >n then r3=r2-n for i=1:r3 POP(n+i,:)=[] end end if show==1 then disp('newPop0='), disp(POP) end endfunction //*************************************************** // Select only those strings which are not zero at l+p! // l := length of string // p := number of parameters (=5) // r2 := memory of position for new strings function[POP]= newPop0_old(POP,l,p,n,show) POPNEW=POP r2=0 j=1 while (j<n) if POP(j,l+p) == 0 then j=j+1,end if POP(j,l+p)>0 then m=POP(j,l+p), for k=1:m, r2=r2+1,POPNEW(r2,:)=POP(j,:),end if show==1 then disp('newPop0 r2='), disp(r2),disp(POPNEW) end end j=j+1 end POP=POPNEW if show==1 then disp('newPop0='), disp(POP) 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 // p := number of parameters (P=5) function[POP]=strcpyLR(POP,l,p,j) [r,c]=size(POP); // Making a copy for i=1:l POP(j,l+p+i) = POP(j,i) 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 // r := row_old // j := row new // p := number of parameters (P=5) function[POP]=strcpyLRR(POP,l,p,j,r) for i=1:l POP(j,l+p+i) = POP(r,i) end endfunction //*************************************************** // Prepare the crossover operations within a population POP // // Go through all rows j=1:n // Get a random number r [1,l-1] != j to select a candidate // copy the left r-th candidate to the right of POP(j) // // l := length of string // n := number of members in POP function[POP]= crossoverPrep(POP,l,p,n,show) //Select candidates for all rows 1:n for j=1:n //Select randomly a candidate-line at r r=j while (r == j) r = round((n-1) * rand()) if r==0 then r=1, end end //while if show==1 then disp('j=') disp(j) disp('r=') disp(r) end // Copy candidate from right at r to the left at j POP=strcpyLRR(POP,l,p,j,r) end //for if show==1 then disp('crossoverPrep=') disp(POP) end endfunction //************************************************** // [POP]=crossmatch(POP,l,p,j,x) // // Match two strings during crossover from cut point x to l // // j := row of strings in POP // p := number of parameters between strings left and right (actually p=5) // l := length of strings // x := cut point within string x in [1,l-1] function [POP]=crossmatch(POP,l,p,j,x) Dif=l-x for y=1:Dif POP(j,x+y)=POP(j,l+p+x+y) end endfunction //*************************************************** // Apply a crossover operation onto two strings at intersection x // // The strings are assumed to be randomly paired // One is at the left [1,l,], the other is at the right [l+p+i] // For every row j=1:n // one generates a random number x in [1,l-1] // and then one copies all elements from right l+p+x // to the left x // // 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,show) //Follow the rows for j=1:n //Look for some cut point x=0 while (x<1) or (x>(l-1)) x = round((l-1) * rand()) end if show==1 then printf('crossover x = %d\n',x),end // Mix two strings from the cut point to the right [POP]=crossmatch(POP,l,p,j,x) end//for 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,show) // 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]= 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 //*************************************************** // 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 // FITNES_ALL := Sum of all fitnss values function[POP,MFITNESS, FITNESS_ALL]=popFit(POP,l,p,n,show) MFITNESS=0 FITNESS_ALL=0 [POP]=bin22dec(POP,l,show) //Convert binary string into integer [POP]=fitnessComp1(POP,l,show) // Compute fitness value with fitness1 [FITNESS_ALL]=fitness(POP,l,show) //Sum up all fitness values [MFITNESS]=maxfitness(POP,l,show)// Find max fitness value endfunction //************************************************************* // Function to compute the fitness of a population as percentage // of the maximal possible value // // 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 // FITNES_ALL := Sum of all fitnss values function [PERC]=popFitPerc(POP,l,p,n,show) [POP,MFITNESS, FITNESS_ALL]=popFit(POP,l,p,n,show) [MAXFIT]= maxfit02(l,n) PERC=100 * (FITNESS_ALL/MAXFIT) 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 //************************************************************* // 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 [POP]=bin22dec(POP,l,show) //Convert binary string into integer [POP]=fitnessComp1(POP,l,show) // Compute fitness value with fitness1 [FITNESS_ALL]=fitness(POP,l,show) //Sum up all fitness values FITNESS_ALLLOG(cyc)=FITNESS_ALL [MFITNESS]=maxfitness(POP,l,show)// Find max fitness value [POP,AFITNESS]=rfitness(POP,l,n,FITNESS_ALL,show) // Compute relative fitness values //[POP]=newMember(POP,l,n) // Translates rfitness into integral fractions at l+p [POP]= newPop0(POP,l,p,n,show) //Select only the positiv members, with multiple copies if necessary [POP]= crossoverPrep(POP,l,p,n,show) //Prepare crossover by copying pairing candidates to the right [POP]= crossover(POP,l,p,n,show) // Do crossover 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 //************************************************************* // 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 // POP1 = [0 1 1 0 1 0 0 0 0 0; 1 1 0 0 0 0 0 0 0 0; 0 1 0 0 0 0 0 0 0 0; 1 0 0 1 1 0 0 0 0 0;] POP = [0 1 1 0 1; 1 1 0 0 0; 0 1 0 0 0; 1 0 0 1 1;] P205 =[0 0; 0 1] P250 = [1 1; 0 0] P272 = [1 1; 1 0] P306 = [0 0 1; 0 1 0; 0 1 0] P345 = [0 1 1; 0 1 1; 1 1 1] P373 = [1 1 0; 1 1 0; 1 1 0] W=[1 3; 2 1; 3 2] W2=[1 3; 2 1; 3 2; 4 4; 5 7; 6 5]