ga3d.asv

这是一个人工免疫算法的matlab工具箱。该工具箱可以根据不同的优化函数形式设置来用人工免疫算法来寻优

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);