Add files via upload

Continuos Genetic algorithm.

Author: BryanAI

cga.m

@@ -0,0 +1,143 @@
+% Continuous Genetic Algorithm
+%
+% minimizes the objective function designated in ff
+% Before beginning, set all the parameters in parts
+% I, II, and III
+% Haupt & Haupt
+% 2003
+clear
+%_______________________________________________________
+% I Setup the GA
+ff='scales'; % objective function
+npar=10; % number of optimization variables
+varhi=pi; varlo=0; % variable limits
+%_______________________________________________________
+% II Stopping criteria
+maxit=10; % max number of iterations
+mincost=-9999999; % minimum cost
+%_______________________________________________________
+% III GA parameters
+popsize=100; % set population size
+mutrate=0.9; % set mutation rate
+selection=0.5; % fraction of population kept
+Nt=npar; % continuous parameter GA Nt=#variables
+keep=floor(selection*popsize); % #population members that survive
+nmut=ceil((popsize-1)*Nt*mutrate); % total number of mutations
+M=ceil((popsize-keep)/2); % number of matings
+%_______________________________________________________
+% Create the initial population
+iga=0; % generation counter initialized
+par=(varhi-varlo)*rand(popsize,npar)+varlo; % random
+
+
+
+
+cost=scales(par); % calculates population cost using ff
+[rr, cc] =size(par);
+for ii=1:rr
+    cost(ii) = scales(par(ii,:));
+end
+
+
+
+
+[cost,ind]=sort(cost); % min cost in element 1
+par=par(ind,:); % sort continuous
+minc(1)=min(cost); % minc contains min of
+meanc(1)=mean(cost); % meanc contains mean of population
+%_______________________________________________________
+% Iterate through generations
+while iga<maxit
+    iga=iga+1; % increments generation counter
+    %_______________________________________________________
+    % Pair and mate
+    M=ceil((popsize-keep)/2); % number of matings
+    prob=flipud([1:keep]'/sum([1:keep])); % weights chromosomes
+    odds=[0 cumsum(prob(1:keep))']; % probability distribution function
+    pick1=rand(1,M); % mate #1
+    pick2=rand(1,M); % mate #2
+    % ma and pa contain the indicies of the chromosomes that will mate
+    ic=1;
+    while ic<=M
+        for id=2:keep+1
+            if pick1(ic)<=odds(id) & pick1(ic)>odds(id-1)
+                ma(ic)=id-1;
+            end
+            if pick2(ic)<=odds(id) & pick2(ic)>odds(id-1)
+                pa(ic)=id-1;
+            end
+        end
+        ic=ic+1;
+    end
+    %_______________________________________________________
+    % Performs mating using single point crossover
+    ix=1:2:keep; % index of mate #1
+    xp=ceil(rand(1,M)*Nt); % crossover point
+    r=rand(1,M); % mixing parameter
+    for ic=1:M
+        xy=par(ma(ic),xp(ic))-par(pa(ic),xp(ic)); % ma and pa
+        % mate
+        par(keep+ix(ic),:)=par(ma(ic),:); % 1st offspring
+        par(keep+ix(ic)+1,:)=par(pa(ic),:); % 2nd offspring
+        par(keep+ix(ic),xp(ic))=par(ma(ic),xp(ic))-r(ic).*xy;
+        % 1st
+        par(keep+ix(ic)+1,xp(ic))=par(pa(ic),xp(ic))+r(ic).*xy;
+        % 2nd
+        if xp(ic)<npar % crossover when last variable not selected
+            par(keep+ix(ic),:)=[par(keep+ix(ic),1:xp(ic)) par(keep+ix(ic)+1,xp(ic)+1:npar)];
+            par(keep+ix(ic)+1,:)=[par(keep+ix(ic)+1,1:xp(ic)) par(keep+ix(ic),xp(ic)+1:npar)];
+        end % if
+    end
+    %_______________________________________________________
+    % Mutate the population
+    mrow=sort(ceil(rand(1,nmut)*(popsize-1))+1);
+    mcol=ceil(rand(1,nmut)*Nt);
+    for ii=1:nmut
+        par(mrow(ii),mcol(ii))=(varhi-varlo)*rand+varlo;
+        % mutation
+    end % ii
+    %_______________________________________________________
+    % The new offspring and mutated chromosomes are evaluated
+    %cost=feval(ff,par);
+    [rr, cc] =size(par);
+    for ii=2:rr
+        cost(ii) = feval(ff,par(ii,:));
+    end
+    
+    
+    
+    
+    
+    %_______________________________________________________
+    % Sort the costs and associated parameters
+    [cost,ind]=sort(cost);
+    par=par(ind,:);
+    %_______________________________________________________
+    % Do statistics for a single nonaveraging run
+    minc(iga+1)=min(cost);
+    meanc(iga+1)=mean(cost);
+    %_______________________________________________________
+    % Stopping criteria
+    if iga>maxit | cost(1)<mincost
+        break
+    end
+    [iga cost(1)]
+end %iga
+%_______________________________________________________
+% Displays the output
+day=clock;
+disp(datestr(datenum(day(1),day(2),day(3),day(4),day(5),day(6)),0))
+disp(['optimized function is ' ff])
+format short g
+disp(['popsize = ' num2str(popsize) ' mutrate = ' num2str(mutrate) ' # par = ' num2str(npar)])
+disp(['#generations=' num2str(iga) ' best cost=' num2str(cost(1))])
+disp(['best solution'])
+disp([num2str(par(1,:))])
+disp('continuous genetic algorithm')
+figure(24)
+iters=0:length(minc)-1;
+plot(iters,minc,iters,meanc,'-');
+xlabel('generation');ylabel('cost');
+title(['Continuous Genetic Algorithm; Function: ' ff]);
+%text(0,minc(1),'best');text(1,minc(2),'population average')
+legend('best', 'population average');

circlesinasquare.m

@@ -0,0 +1,26 @@
+function f = circlesinasquare(xy)
+
+x1=xy(1);
+y1=xy(2);
+
+x2=xy(3);
+y2=xy(4);
+
+x3=xy(5);
+y3=xy(6);
+
+x4=xy(7);
+y4=xy(8);
+
+d12 = sqrt((x1-x2)^2 + (y1-y2)^2);
+d13 = sqrt((x1-x3)^2 + (y1-y3)^2);
+d14 = sqrt((x1-x4)^2 + (y1-y4)^2);
+
+d23 = sqrt((x2-x3)^2 + (y2-y3)^2);
+d24 = sqrt((x2-x4)^2 + (y2-y4)^2);
+
+d34 = sqrt((x3-x4)^2 + (y3-y4)^2);
+
+f = -(d12 + d13 + d14 + d23 + d24 + d34);
+
+% f = 1/(d12 + d13 + d14 + d23 + d24 + d34);

eigenvalues.m

@@ -0,0 +1,4 @@
+function f = eigenvalues(x)
+A = [1 2 3; 4 15 6; 7 8 19];
+[r, c] = size(A);
+f = abs(det(A - x*eye(r))); % + abs(1/(x + 0.20075));

scales.m

@@ -0,0 +1,22 @@
+
+function cost=scales(s)
+w=(1:100);
+
+cost=0;
+
+lhs=0;
+
+rhs=0;
+
+for i=1:w
+    if s(i) == 0;
+        lhs=lhs+w(i);
+    else
+        rhs=rhs+w(i);
+    end 
+    
+    cost=abs(lhs-rhs);
+end 
+   
+        
+