untitled2.m

该算法为基于克隆选择原理的人工免疫算法。算法有三部分

function [] = CSA
    disp(sprintf('\n** PART III - CLONALG (The CLONal Selection ALGorithm) **'));
   % figure(1); clf;
        v = cadeia(100,44,0,0,0);
        disp(sprintf('Available Demo Tasks:'));
        disp(sprintf('1) GA (GLOBAL SEARCH)'));
        disp(sprintf('2) CLONALG (MULTI-MODAL OPTIMIZATION)'));
        disp(sprintf('3) CHARACTER (KNOWLEDGE ACQUISITION)'));
        ga_cga = input('Type the desired demo number (1) ,(2) or (3): ');
        switch ga_cga,
            case 1,
            disp(sprintf('** Standard Genetic Algorithm - GA **'));
            figure(1); clf;
            [x,y,fx,vx,vmfit,P] = ga3d(v);
            disp(sprintf('Maximum found [x,y,f(x,y)]: [%.2f,%.2f,%.2f]',x,y,fx));
            figure(2); plot(vx); title('f(x,y) x Mean'); xlabel('Generations'); ylabel('f(x)');
             hold on; plot(vmfit,'r'); hold off;
            case 2,
            disp(sprintf('** Clonal Selection Algorithm - CLONALG **'));
            figure(3); clf; %v = v(1:50,:);
            [x,y,fx,vfx,vmfit,P,vpm] = imalg3d(v);
             save data x y fx vfx;
            disp(sprintf('Maximum found [x,y,f(x,y)]: [%.2f,%.2f,%.2f]',x,y,fx));
            figure(4); clf; plot(vfx); title('f(x,y) x Mean'); xlabel('Generations'); ylabel('f(x)');
             hold on; plot(vmfit,'r'); hold off;
            case 3,
            disp(sprintf('** CLONALG - Knowledge Acquisition**'));
            load num8_12x10; X = v(1,:); P = cadeia(10,120,0,0,0);
            M = imalgchar(P,X);
            otherwise,
            display('Accepted values are (1), (2) or (3)');
        end; % End Switch ga_cga
    end;
   
 %GA3D
 function [x,y,fx,vx,vmfit,P] = ga3d(v,ger,pc,pm);
%
% Ph.D. Thesis
% Leandro Nunes de Castro
% November, 1999.
% ENHANCED GENETIC ALGORITHM - Bi-classist Selection
%
% Secondary functions: DECODE & IMPRIME(internal)
%
% function [x,y,fx,vx,vmfit,P] = ga3d(v,ger,N,pc,pm);
% x,y,fx 	-> f(x,y) is the maximal value of the function
% vfx		-> vector of best fitness of population through generations
% vmfit	-> vector of mean fitness of population through generations
% v    	-> population of size N x 2.L (L = 22 [-1,1])
% ger		-> number of generations
% N			-> population size
% pc		-> cross-over probability
% pm		-> mutation probability
%
% Definitions
% f			-> evaluation function
% v			-> population
% fit		-> fitness vector
% x,y		-> decodified coordinates
% Maximum found: [x,y,f] = [1.76,1.27,4.0172];
%

% Default Parameters
if nargin == 1,
   [N,L] = size(v); ger = 250; pc = 0.5; pm = 0.01;
end;

disp(sprintf('Number of generations: %d',ger));
disp(sprintf('Population size: %d',N));
disp(sprintf('Crossover probability: %.3f',pc));
disp(sprintf('Mutation probability: %.3f',pm));
 %f = '-1 * x .* sin(2 * pi .* x) + y.* sin(2 * pi .* y) + 1'; 
f = '1 * x .* sin(4 * pi .* x) - 1 * y.* sin(4 * pi .* y + pi) + 1'; 
% Plotting parameters
% [x,y] = meshgrid(-1:0.05:2,-1:0.05:2); vxp = x; vyp = y;
[x,y] = meshgrid(-1:0.05:1,-1:0.05:1); vxp = x; vyp = y;
vzp = eval(f); PRINT = 1;

% General parameters & Initial operations
sol = 1; vmfit = []; it = 1; vx = []; C = [];
x = decode(v(:,1:22));
y = decode(v(:,23:end)); fit = eval(f);
imprime(PRINT,vxp,vyp,vzp,x,y,fit,1,1); title('Initial Population');
disp('Press any key to continue...'); pause;
pb = 0.5; pw = 0.1; pr = 1 - (pb + pw);
nb = round(pb * N); nw = round(pw * N); nr = round(pr * N);
if (nb + nw + nr) ~= N,
   dif = N - (nb + nw + nr);
   nr = nr + dif;
end;

% Generations
t0 = clock; f0 = flops;
while it <= ger & sol <= 2.26,
	% 	Reproduction (Bi-classist Selection)
   [rw,ind] = sort(fit); ind = fliplr(ind);
   vtemp = [v(ind(1:nb),:); v(ind(end-nw+1:end),:); v(2:nr+1,:)];
   
   %  Crossover
   C(:,1) = rand(N,1) <= pc; C(:,2) = round(19.*rand(N,1))+1;
   I = find(C(:,1) == 1); IP = [I,C(I,2)];
   for i = 1:size(IP,1),
      v(IP(i,1),:) = [vtemp(IP(i,1),1:IP(i,2)) vtemp(1,IP(i,2)+1:end)];
   end;
         
   % 	Mutation
   M = rand(N,L) <= pm; M(1,:) = zeros(1,L);
   v = v - 2 .* (v.*M) + M;
   
   % Results
   % x = decode(v); fit = eval(f);
   x = decode(v(:,1:22)); y = decode(v(:,23:end)); fit = eval(f);
   imprime(PRINT,vxp,vyp,vzp,x,y,fit,it,5);
   [sol,indb] = max(fit);
	v(1,:) = v(indb,:); media = mean(fit);
	vx = [vx sol]; vmfit = [vmfit media];
	if rem(it,1) == 0 | it == 10,
		disp(sprintf('Gen.: %d  x: %2.2f  y: %2.2f  Av: %2.2f  f(x,y): %2.3f',it,x(indb),y(indb),media,sol));
	end;
	it = it + 1;
end;
T = etime(clock,t0); F = flops - f0;
x = x(indb); y = y(indb); fx = sol; P = v;

% 	Results
% clf; plot(vx); title('f(x) evolution'); xlabel('Generations'); ylabel('f(x)');
% hold on; plot(vmfit); hold off;

% --------------------- %
% INTERNAL SUBFUNCTIONS
% --------------------- %

% Print Surface
function [] = imprime(PRINT,vx,vy,vz,x,y,fx,it,mit);
% x,fx				-> actual values
% vxplot, vplot	-> original (base) function
if PRINT == 1,
   if rem(it,mit) == 0,
      mesh(vx,vy,vz); hold on; axis([-1 1 -1 1 -1 2.5]);
      xlabel('x'); ylabel('y'); zlabel('f(x,y)');
      plot3(x,y,fx,'k*'); drawnow; hold off;
   end;
end;

% Decodify bitstrings
function x = decode(v);
% x		-> real value (precision: 6)
% v		-> binary string (length: 22)
v = fliplr(v); s = size(v);
aux = 0:1:21; aux = ones(s(1),1)*aux;
x1 = sum((v.*2.^aux)');
x = -1 + x1 .* (2 / 4194303);

   
   
   
 
%CSA
function [x,y,fx,vfx,vmfit,P,vpm] = imalg3d(P,gen,n,pm,per);

%
% Ph.D. Thesis
% Leandro Nunes de Castro
% November, 1999.
% Immune Algorithm - New evolutionary strategy inspired in the Immune System
% Operations: Hypermutation, Editing, Selection
% Each clone has size proportional to its affinity
% IMALG3D: MULTI-PEAK Solution (3D Function)
%
% function [x,y,fx,vfx,vmfit,P] = imalg3d(P,gen,n,pm,per);
% x,y,fx 	-> f(x,y) is the maximal value of the function
% vfx		-> vector of best fitness of population through generations
% vmfit	-> vector of mean fitness of population through generations
% P    	-> population of size N x 2.L
% gen  	-> generation number
% n    	-> number of clones
% pm   	-> hypermutation probability
% per  	-> percentile of the population to suffer random reshuffle
% 
% T    	-> temporary population
% Maximum found: [x,y,f] = [1.76,1.27,4.0172];
%

if nargin == 1,
   % gen = 200; n = round(size(P,1)/2); pm = 0.0005; per = 0.0; fat = 10;
   %gen = 250; n = size(P,1); pm = 0.01; per = 0.0; fat = .1;
   
   gen = 100; n = size(P,1); pm = 0.01; per = 0.0; fat = 0.1;
end;

while n <= 0,
   n = input('n has to be at least one. Type a new value for n: ');
end;

% Printing parameters
%f = '-1 * x .* sin(2 * pi .* x) + y.* sin(2 * pi .* y) + 1'; 
f = '1 * x .* sin(4 * pi .* x) - 1 * y.* sin(4 * pi .* y + pi) + 1'; 
%f='sin(x) + sin(y)';
%f = '0.5+(sin(sqrt((x .* x+y.*y))).*sin(sqrt((x.* x+y.*y)))-0.5)./(1+0.001.*(x .* x+y.*y))';
% [x,y] = meshgrid(-1:0.05:2,-1:0.05:2); vxp = x; vyp = y;
[x,y] = meshgrid(-1:0.05:1,-1:0.05:1); vxp = x; vyp = y;
%[x,y] = meshgrid(-10:0.5:10,-10:0.5:10); vxp = x; vyp = y;
vzp = eval(f);
x = decode(P(:,1:22)); 
y = decode(P(:,23:end));
fit = eval(f);
imprime(1,vxp,vyp,vzp,x,y,fit,1,1); title('Initial Population');
disp(sprintf('Number of generations: %d',gen));
disp(sprintf('Population size: %d',n));
disp(sprintf('Mutation probability: %.3f',pm));
disp(sprintf('Number of clones per candidate: %d',fat*n));
disp(sprintf('Press any key to continue...')); pause;

% Hypermutation controlling parameters
pma = pm; itpm = gen; pmr = 0.8;

% General defintions
vpm = []; vfx = []; vmfit = []; valfx = 1; 
[N,L] = size(P); it = 0; PRINT = 1;

% Generations
while it <= gen & valfx <= 2.26,
   x = decode(P(:,1:22)); y = decode(P(:,23:end)); T = []; cs = [];
   fit = eval(f); 
   [a,ind] = sort(fit);
   valx = x(ind(end-n+1:end)); 
   valy = y(ind(end-n+1:end));
   fx = a(end-n+1:end);	% n best individuals (maximization)
   imprime(PRINT,vxp,vyp,vzp,x,y,fit,it,5);
   
   % Reproduction
   [T,pcs] = reprod(n,fat,N,ind,P,T);
   
   % Hypermutation
   M = rand(size(T,1),L) <= pm;
   T = T - 2 .* (T.*M) + M;
   T(pcs,:) = P(fliplr(ind(end-n+1:end)),:);
   
   % New Re-Selection (Multi-peak solution)
   x = decode(T(:,1:22));
   y = decode(T(:,23:end)); 
   fit = eval(f);
   pcs = [0 pcs];
   for i=1:n,
      [out(i),bcs(i)] = max(fit(pcs(i)+1:pcs(i+1)));		% Maximizationn problem
      bcs(i) = bcs(i) + pcs(i);
   end;
   P(fliplr(ind(end-n+1:end)),:) = T(bcs,:);
   
   % Editing (Repertoire shift)
   nedit = round(per*N); it = it + 1;
   P(ind(1:nedit),:) = cadeia(nedit,L,0,0,0);
   pm = pmcont(pm,pma,pmr,it,itpm);
   valfx = max(fx);
   vpm = [vpm pm]; 
   vfx = [vfx valfx]; 
   vmfit = [vmfit mean(fit)];
   disp(sprintf('It.: %d  pm: %.4f  x: %2.2f  y: %2.2f  Av.: %2.2f  f(x,y): %2.3f',it,pm,valx(end),valy(end),vmfit(end),valfx));
end; % end while
%imprime(PRINT,vxp,vyp,vzp,x,y,fit,it,1);
x = valx(end); y = valy(end); fx = max(fx);
% x = P(ind(end),1:22); y = P(ind(end),23:44); fx = max(fx);

% --------------------- %
% INTERNAL SUBFUNCTIONS
% --------------------- %

% Print
function [] = imprime(PRINT,vx,vy,vz,x,y,fx,it,mit);
% x,fx				-> actual values
% vxplot, vplot	-> original (base) function
if PRINT == 1,
   if rem(it,mit) == 0,
      mesh(vx,vy,vz); hold on; axis([-1 1 -1 1 -1 2.5]);
      xlabel('x'); ylabel('y'); zlabel('f(x,y)');
      plot3(x,y,fx,'k*'); drawnow; hold off;
   end;
end;

% Reproduction
function [T,pcs] = reprod(n,fat,N,ind,P,T);
% n		-> number of clones
% fat	-> multiplying factor
% ind	-> best individuals
% T		-> temporary population
% pcs	-> final position of each clone
if n == 1,
   cs = N;
   T = ones(N,1) * P(ind(1),:);
else,
   for i=1:n,
      % cs(i) = round(fat*N/i);
      cs(i) = round(fat*N);
      pcs(i) = sum(cs);
      T = [T; ones(cs(i),1) * P(ind(end-i+1),:)];
   end;
end;

% Control of pm
function [pm] = pmcont(pm,pma,pmr,it,itpm);
% pma	-> initial value
% pmr	-> control rate
% itpm	-> iterations for restoring
if rem(it,itpm) == 0,
   pm = pm * pmr;
   if rem(it,10*itpm) == 0,
      pm = pma;
   end;
end;

% Decodify bitstrings
function x = decode(v);
% x		-> real value (precision: 6)
% v		-> binary string (length: 22)
v = fliplr(v); s = size(v);
aux = 0:1:21; aux = ones(s(1),1)*aux;
x1 = sum((v.*2.^aux)');
x = -1 + x1 .* (2 / 4194303);

% Function CADEIA
function [ab,ag] = cadeia(n1,s1,n2,s2,bip)
if nargin == 2,
   n2 = n1; s2 = s1; bip = 1;
elseif nargin == 4,
   bip = 1;
end;
% Antibody (Ab) chains
ab = 2 .* rand(n1,s1) - 1;
if bip == 1,
   ab = hardlims(ab);
else,
   ab = hardlim(ab);
end;
% Antigen (Ag) chains
ag = 2 .* rand(n2,s2) - 1;
if bip == 1,
   ag = hardlims(ag);
else,
   ag = hardlim(ag);
end;
% End Function CADEIA