//************************************************************** // File:GA_v3.sce // Authors: Gerd Doeben-Henisch // Version Start: January-18, 2010 // Version Last: April-3, 2011 //****************************************************************** // Function: Implements a simple GA according to Goldberg (1989) // Without Mutation! // //**************************************************************** // 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 // Pos 1-l := String // Pos l+1 := Decimal Value of binary string // Pos l+2 := Fitness // Pos l+3 := Percentage of overall fitness // Pos l+4 := Expected count according to fitness // Pos l+5 := Realized count 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;] // Variable for overall Fitness FITNESS_ALL = 0 // Variable for average Fitness AFITNESS = 0 //*************************************************** //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) MFITNESS=0 [r,c]=size(POP); for j=1:r if POP(j,l+2) > MFITNESS then MFITNESS = POP(j,l+2) end 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 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 relative count of a string // 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]=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 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) [r,c]=size(POP); // Testing the boundaries if (j < 1) then printf('ERROR: Position of old String outside of Matrix! r = %d, j = %d', r,j) elseif (j > r) then printf('ERROR: Position of old String outside of Matrix!, r = %d, j = %d', r,j) elseif (k < 1) then printf('ERROR: Position of new String outside of Matrix!, r = %d, k = %d', r,k) elseif (k > r) then printf('ERROR: Position of new String outside of Matrix!, r = %d, k = %d', r,k) end // Making a copy for i=1:l POP(k,l+p+i) = POP(j,i) end endfunction function[POP]=strcpyRL(POP,l,p,j,k) [r,c]=size(POP); // Testing the boundaries if (j < 1) then printf('ERROR: Position of old String outside of Matrix! r = %d, j = %d', r,j) elseif (j > r) then printf('ERROR: Position of old String outside of Matrix!, r = %d, j = %d', r,j) elseif (k < 1) then printf('ERROR: Position of new String outside of Matrix!, r = %d, k = %d', r,k) elseif (k > r) then printf('ERROR: Position of new String outside of Matrix!, r = %d, k = %d', r,k) 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 (p=5) // 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+p) > 0 then r3 = POP(j,l+p)-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 from position 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+p with '1' for j=1:r POP(j,l+p)=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 printf('k1 = %d\n',k1) if POP(k1,l+p) <> 0 then POP=strcpyRL(POP,l,p,j,k1) //mshow(POP,n,l+p+l) POP(k1,l+p) = 0, S=0 else S=1 end end j = j+1 // mshow(POP,n,l+p+l) printf('j = %d\n',j) end 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 // function[POP]= crossover(POP,l,p,n) [r,c]=size(POP); j=1 while(j < n+1) // printf('j = %d\n',j) x = round(l * rand()) if x == 0 then x=1 // This does not change anything end // printf('x = %d\n',x) for i=x:l, m=POP(j+1,i) POP(j+1,i) = POP(j,i) POP(j,i) = m end j=j+2 end 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 //*************************************************** // Simple fitness-function f=(x^2) // // D := decimal computed out of binaries function[F]= fitness1(D) F=D^2 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) // popge := a predefined population (can be done automatically) // run := number of cycles function[POP,FITNESS_ALLLOG]=gasimple(POP,l,p,n,run) 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) end clf(), xdel, plot2d([1:1:run], FITNESS_ALLLOG) endfunction