多目标灰狼优化算法(MOGWO)

% cec09.m % % The Matlab version of the test instances for CEC 2009 Multiobjective % Optimization Competition. % % Usage: fobj = cec09(problem_name), the handle of the function will be % with fobj % % Please refer to the report for correct one if the source codes are not % consist with the report. % History: % v1 Sept.08 2008 % v2 Nov.18 2008 % v3 Nov.26 2008 function fobj = cec09(name) switch name case 'UF1' fobj = @UF1; case 'UF2' fobj = @UF2; case 'UF3' fobj = @UF3; case 'UF4' fobj = @UF4; case 'UF5' fobj = @UF5; case 'UF6' fobj = @UF6; case 'UF7' fobj = @UF7; case 'UF8' fobj = @UF8; case 'UF9' fobj = @UF9; case 'UF10' fobj = @UF10; case 'CF1' fobj = @CF1; case 'CF2' fobj = @CF2; case 'CF3' fobj = @CF3; case 'CF4' fobj = @CF4; case 'CF5' fobj = @CF5; case 'CF6' fobj = @CF6; case 'CF7' fobj = @CF7; case 'CF8' fobj = @CF8; case 'CF9' fobj = @CF9; case 'CF10' fobj = @CF10; otherwise fobj = @UF1; end end %% UF1 % x and y are columnwise, the imput x must be inside the search space and % it could be a matrix function y = UF1(x) [dim, num] = size(x); tmp = zeros(dim,num); tmp(2:dim,:)= (x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]))).^2; tmp1 = sum(tmp(3:2:dim,:)); % odd index tmp2 = sum(tmp(2:2:dim,:)); % even index y(1,:) = x(1,:) + 2.0*tmp1/size(3:2:dim,2); y(2,:) = 1.0 - sqrt(x(1,:)) + 2.0*tmp2/size(2:2:dim,2); clear tmp; end %% UF2 % x and y are columnwise, the imput x must be inside the search space and % it could be a matrix function y = UF2(x) [dim, num] = size(x); X1 = repmat(x(1,:),[dim-1,1]); A = 6*pi*X1 + pi/dim*repmat((2:dim)',[1,num]); tmp = zeros(dim,num); tmp(2:dim,:)= (x(2:dim,:) - 0.3*X1.*(X1.*cos(4.0*A)+2.0).*cos(A)).^2; tmp1 = sum(tmp(3:2:dim,:)); % odd index tmp(2:dim,:)= (x(2:dim,:) - 0.3*X1.*(X1.*cos(4.0*A)+2.0).*sin(A)).^2; tmp2 = sum(tmp(2:2:dim,:)); % even index y(1,:) = x(1,:) + 2.0*tmp1/size(3:2:dim,2); y(2,:) = 1.0 - sqrt(x(1,:)) + 2.0*tmp2/size(2:2:dim,2); clear X1 A tmp; end %% UF3 % x and y are columnwise, the imput x must be inside the search space and % it could be a matrix function y = UF3(x) [dim, num] = size(x); Y = zeros(dim,num); Y(2:dim,:) = x(2:dim,:) - repmat(x(1,:),[dim-1,1]).^(0.5+1.5*(repmat((2:dim)',[1,num])-2.0)/(dim-2.0)); tmp1 = zeros(dim,num); tmp1(2:dim,:)= Y(2:dim,:).^2; tmp2 = zeros(dim,num); tmp2(2:dim,:)= cos(20.0*pi*Y(2:dim,:)./sqrt(repmat((2:dim)',[1,num]))); tmp11 = 4.0*sum(tmp1(3:2:dim,:)) - 2.0*prod(tmp2(3:2:dim,:)) + 2.0; % odd index tmp21 = 4.0*sum(tmp1(2:2:dim,:)) - 2.0*prod(tmp2(2:2:dim,:)) + 2.0; % even index y(1,:) = x(1,:) + 2.0*tmp11/size(3:2:dim,2); y(2,:) = 1.0 - sqrt(x(1,:)) + 2.0*tmp21/size(2:2:dim,2); clear Y tmp1 tmp2; end %% UF4 % x and y are columnwise, the imput x must be inside the search space and % it could be a matrix function y = UF4(x) [dim, num] = size(x); Y = zeros(dim,num); Y(2:dim,:) = x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num])); H = zeros(dim,num); H(2:dim,:) = abs(Y(2:dim,:))./(1.0+exp(2.0*abs(Y(2:dim,:)))); tmp1 = sum(H(3:2:dim,:)); % odd index tmp2 = sum(H(2:2:dim,:)); % even index y(1,:) = x(1,:) + 2.0*tmp1/size(3:2:dim,2); y(2,:) = 1.0 - x(1,:).^2 + 2.0*tmp2/size(2:2:dim,2); clear Y H; end %% UF5 % x and y are columnwise, the imput x must be inside the search space and % it could be a matrix function y = UF5(x) N = 10.0; E = 0.1; [dim, num] = size(x); Y = zeros(dim,num); Y(2:dim,:) = x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num])); H = zeros(dim,num); H(2:dim,:) = 2.0*Y(2:dim,:).^2 - cos(4.0*pi*Y(2:dim,:)) + 1.0; tmp1 = sum(H(3:2:dim,:)); % odd index tmp2 = sum(H(2:2:dim,:)); % even index tmp = (0.5/N+E)*abs(sin(2.0*N*pi*x(1,:))); y(1,:) = x(1,:) + tmp + 2.0*tmp1/size(3:2:dim,2); y(2,:) = 1.0 - x(1,:)+ tmp + 2.0*tmp2/size(2:2:dim,2); clear Y H; end %% UF6 % x and y are columnwise, the imput x must be inside the search space and % it could be a matrix function y = UF6(x) N = 2.0; E = 0.1; [dim, num] = size(x); Y = zeros(dim,num); Y(2:dim,:) = x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num])); tmp1 = zeros(dim,num); tmp1(2:dim,:)= Y(2:dim,:).^2; tmp2 = zeros(dim,num); tmp2(2:dim,:)= cos(20.0*pi*Y(2:dim,:)./sqrt(repmat((2:dim)',[1,num]))); tmp11 = 4.0*sum(tmp1(3:2:dim,:)) - 2.0*prod(tmp2(3:2:dim,:)) + 2.0; % odd index tmp21 = 4.0*sum(tmp1(2:2:dim,:)) - 2.0*prod(tmp2(2:2:dim,:)) + 2.0; % even index tmp = max(0,(1.0/N+2.0*E)*sin(2.0*N*pi*x(1,:))); y(1,:) = x(1,:) + tmp + 2.0*tmp11/size(3:2:dim,2); y(2,:) = 1.0 - x(1,:) + tmp + 2.0*tmp21/size(2:2:dim,2); clear Y tmp1 tmp2; end %% UF7 % x and y are columnwise, the imput x must be inside the search space and % it could be a matrix function y = UF7(x) [dim, num] = size(x); Y = zeros(dim,num); Y(2:dim,:) = (x(2:dim,:) - sin(6.0*pi*repmat(x(1,:),[dim-1,1]) + pi/dim*repmat((2:dim)',[1,num]))).^2; tmp1 = sum(Y(3:2:dim,:)); % odd index tmp2 = sum(Y(2:2:dim,:)); % even index tmp = (x(1,:)).^0.2; y(1,:) = tmp + 2.0*tmp1/size(3:2:dim,2); y(2,:) = 1.0 - tmp + 2.0*tmp2/size(2:2:dim,2); clear Y; end %% UF8 % x and y are columnwise, the imput x must be inside the search space and % it could be a matrix function y = UF8(x) [dim, num] = size(x); Y = zeros(dim,num); Y(3:dim,:) = (x(3:dim,:) - 2.0*repmat(x(2,:),[dim-2,1]).*sin(2.0*pi*repmat(x(1,:),[dim-2,1]) + pi/dim*repmat((3:dim)',[1,num]))).^2; tmp1 = sum(Y(4:3:dim,:)); % j-1 = 3*k tmp2 = sum(Y(5:3:dim,:)); % j-2 = 3*k tmp3 = sum(Y(3:3:dim,:)); % j-0 = 3*k y(1,:) = cos(0.5*pi*x(1,:)).*cos(0.5*pi*x(2,:)) + 2.0*tmp1/size(4:3:dim,2); y(2,:) = cos(0.5*pi*x(1,:)).*sin(0.5*pi*x(2,:)) + 2.0*tmp2/size(5:3:dim,2); y(3,:) = sin(0.5*pi*x(1,:)) + 2.0*tmp3/size(3:3:dim,2); clear Y; end %% UF9 % x and y are columnwise, the imput x must be inside the search space and % it could be a matrix function y = UF9(x) E = 0.1; [dim, num] = size(x); Y = zeros(dim,num); Y(3:dim,:) = (x(3:dim,:) - 2.0*repmat(x(2,:),[dim-2,1]).*sin(2.0*pi*repmat(x(1,:),[dim-2,1]) + pi/dim*repmat((3:dim)',[1,num]))).^2; tmp1 = sum(Y(4:3:dim,:)); % j-1 = 3*k tmp2 = sum(Y(5:3:dim,:)); % j-2 = 3*k tmp3 = sum(Y(3:3:dim,:)); % j-0 = 3*k tmp = max(0,(1.0+E)*(1-4.0*(2.0*x(1,:)-1).^2)); y(1,:) = 0.5*(tmp+2*x(1,:)).*x(2,:) + 2.0*tmp1/size(4:3:dim,2); y(2,:) = 0.5*(tmp-2*x(1,:)+2.0).*x(2,:) + 2.0*tmp2/size(5:3:dim,2); y(3,:)