鲸鱼优化算法(WOA),哈里斯鹰算法(HHO),灰狼算法(WOA),算术优化算法(AOA)优化工程问题

function [nDim, LB, UB, Vio, GloMin, Obj] = ProbInfo(n) nDim = [7,3,4,2,4,5,4,2,4,4,11,4,3]; if n == 1 % Speed Reducer LB = [2.6, 0.7, 17, 7.3, 7.3, 2.9, 5]; UB = [3.6, 0.8, 28, 8.3, 8.3, 3.9, 5.5]; Vio = [50 10 1 1 1 20 1 300 1 1 50 1]; Obj = @f1; GloMin = 2994.4244658; elseif n == 2 % Tension/compression spring design LB = [0.05,0.25,2.00]; UB = [2,1.3,15.0]; Vio = [3 4 0.1 0.1 1]; Obj = @f2; GloMin = 0.012665232788; elseif n == 3 % Pressure vessel design LB = [0.51,0.51,10,10]; UB = [99.49,99.49,200,200]; Vio = [12000 8000 1 1 1]; Obj = @f3; GloMin = 6059.714335048436 ; elseif n == 4 % Three-bar truss design problem LB = 0*ones(1,nDim(n)); UB = 1*ones(1,nDim(n)); Vio = [140 7 15 1]; Obj = @f4; GloMin = 2.6389584338E+02; elseif n == 5 % Design of gear train LB = 12*ones(1,nDim(n)); UB = 60*ones(1,nDim(n)); Vio = [1 1]; Obj = @f5; GloMin = 2.70085714e-12-1e-4; elseif n == 6 % Cantilever beam LB = [0.01 0.01 0.01 0.01 0.01]; UB = [100 100 100 100 100]; Vio = [10 1]; Obj = @f6; GloMin = 1.3399576; elseif n == 7 % Minimize I-beam vertical deflection LB = [10 10 0.9 0.9]; UB = [80 50 5.0 5.0]; Vio = 0.1*[1 1 1]; Obj = @f7; GloMin = 0.0130741; elseif n == 8 % Tubular column design LB = [2 0.2]; UB = [14 0.8]; Vio = [100 1 1 1 1 1 1]; Obj = @f8; GloMin = 26.486361473; elseif n == 9 % Piston lever LB = [0.05 0.05 0.05 0.05]; UB = [500 500 500 120]; Vio = [1 1 1 100 1]; Obj = @f9; GloMin = 8.41269832311; elseif n == 10 % Corrugated bulkhead design LB = [0 0 0 0]; UB = [100 100 100 5]; Vio = [1 1 3 3 100 1 1]; Obj = @f10; GloMin = 6.8429580100808; elseif n == 11 % Car side impact design LB = [0.50 0.50 0.50 0.50 0.50 0.50 0.50 0 0 -30 -30]; UB = [1.50 1.50 1.50 1.50 1.50 1.50 1.50 1 1 +30 +30]; Vio = [1 1 1 1 1 1 10 29.8 2 6 1]; Obj = @f11; GloMin = 22.84296954; elseif n == 12 % Design of welded beam design LB = [0.1 0.1 0.1 0.1]; UB = [2 10 10 2]; Vio = [1 1 4 0.001 1 0.5 1 1]; Obj = @f12; GloMin = 1.724852308597366; elseif n==13 % Reinforced concrete beam design LB = [0 0 5]; UB = [1 1 10]; Vio = [50 30 1]; Obj=@f13; GloMin=359.2080; end nDim = nDim(n); end %% Objective Subjective Functions function [z, g, h] = f1(x) % Weight Minimization of a Speed Reducer z = 0.7854*x(:,1).*x(:,2).^2.*(3.3333.*x(:,3).^2+14.9334.*x(:,3)-43.0934)-1.508.*x(:,1).*(x(:,6).^2+x(:,7).^2)..... +7.477.*(x(:,6).^3+x(:,7).^3)+0.7854.*(x(:,4).*x(:,6).^2+x(:,5).*x(:,7).^2); g(:,1) = -x(:,1).*x(:,2).^2.*x(:,3)+27; g(:,2) = -x(:,1).*x(:,2).^2.*x(:,3).^2+397.5; g(:,3) = -x(:,2).*x(:,6).^4.*x(:,3).*x(:,4).^(-3)+1.93; g(:,4) = -x(:,2).*x(:,7).^4.*x(:,3)./x(:,5).^3+1.93; g(:,5) = 10.*x(:,6).^(-3).*sqrt(16.91.*10^6+(745.*x(:,4)./(x(:,2).*x(:,3))).^2)-1100; g(:,6) = 10.*x(:,7).^(-3).*sqrt(157.5.*10^6+(745.*x(:,5)./(x(:,2).*x(:,3))).^2)-850; g(:,7) = x(:,2).*x(:,3)-40; g(:,8) = -x(:,1)./x(:,2)+5; g(:,9) = x(:,1)./x(:,2)-12; g(:,10) = 1.5.*x(:,6)-x(:,4)+1.9; g(:,11) = 1.1.*x(:,7)-x(:,5)+1.9; h = 0; end function [z, g, h] = f2(x) % Tension/compression spring design (case 1) z = x(:,1).^2.*x(:,2).*(x(:,3)+2); h = 0; g(:,1) = 1-(x(:,2).^3.*x(:,3))./(71785.*x(:,1).^4); g(:,2) = (4.*x(:,2).^2-x(:,1).*x(:,2))./(12566.*(x(:,2).*x(:,1).^3-x(:,1).^4)).... + 1./(5108.*x(:,1).^2)-1; g(:,3) = 1-140.45.*x(:,1)./(x(:,2).^2.*x(:,3)); g(:,4) = (x(:,1)+x(:,2))./1.5-1; end function [z, g, h] = f3(x) % update x(:,1) = 0.0625.*round(x(:,1)); x(:,2) = 0.0625.*round(x(:,2)); % Pressure vessel design z = 0.6224.*x(:,1).*x(:,3).*x(:,4)+1.7781.*x(:,2).*x(:,3).^2.... +3.1661.*x(:,1).^2.*x(:,4)+19.84.*x(:,1).^2.*x(:,3); g(:,1) = -x(:,1)+0.0193.*x(:,3); g(:,2) = -x(:,2)+0.00954.*x(:,3); g(:,3) = -pi.*x(:,3).^2.*x(:,4)-4/3.*pi.*x(:,3).^3+1296000; g(:,4) = x(:,4)-240; h = 0; end function [z, g, h] = f4(x) % Three-bar truss design problem z = (2.*sqrt(2).*x(:,1)+x(:,2))*100; g(:,1) = (sqrt(2).*x(:,1)+x(:,2))./(sqrt(2).*x(:,1).^2+2.*x(:,1).*x(:,2))*2-2; g(:,2) = x(:,2)./(sqrt(2).*x(:,1).^2+2.*x(:,1).*x(:,2))*2-2; g(:,3) = 1./(sqrt(2).*x(:,2)+x(:,1))*2-2; h=0; end function [z, g, h] = f5(x) % Design of gear train - True x=round(x); term1=1/6.931; term2=(x(3)*x(2))/(x(1)*x(4)); z = (term1-term2)^2; g = 0; h = 0; end function [z, g, h] = f6(x) % Cantilever beam z = 0.0624*(x(1)+x(2)+x(3)+x(4)+x(5)); g(1) = (61/x(1)^3)+(37/x(2)^3)+(19/x(3)^3)+(7/x(4)^3)+(1/x(5)^3)-1; h = 0; end function [z, g, h] = f7(x) % Minimize I-beam vertical deflection term1 = x(3)*(x(1)-2*x(4))^3/12; term2 = x(2)*x(4)^3/6; term3 = 2*x(2)*x(4)*((x(1)-x(4))/2)^2; z = 5000/(term1+term2+term3); g(1) = 2*x(2)*x(4)+x(3)*(x(1)-2*x(4))-300; term1 = x(3)*(x(1)-2*x(4))^3; term2 = 2*x(2)*x(4)*(4*x(4)^2+3*x(1)*(x(1)-2*x(4))); term3 = (x(1)-2*x(4))*x(3)^3; term4 = 2*x(4)*x(2)^3; g(2) = ((18*x(1)*10^4)/(term1+term2))+((15*x(2)*10^3)/(term3+term4))-6; h = 0; end function [z, g, h] = f8(x) % Tubular column design z = 9.8*x(1)*x(2)+2*x(1); g(1)=1.59-x(1)*x(2); g(2)=47.4-x(1)*x(2)*(x(1)^2+x(2)^2); g(3)=2/x(1)-1; g(4)=x(1)/14-1; g(5)=2/x(1)-1; g(6)=x(1)/8-1; h = 0; end function [z, g, h] = f9(x) % Piston lever teta = 0.25*pi; H=x(1); B=x(2); D=x(3); X=x(4); l2=((X*sin(teta)+H)^2+(B-X*cos(teta))^2)^0.5; l1=((X-B)^2+H^2)^0.5; z=0.25*pi*D^2*(l2-l1); teta = 0.25*pi; H=x(1); B=x(2); D=x(3); X=x(4); P=1500; Q=10000; L=240; Mmax=1.8e+6; R=abs(-X*(X*sin(teta)+H)+H*(B-X*cos(teta)))/sqrt((X-B)^2+H^2); F=0.25*pi*P*D^2; l2=((X*sin(teta)+H)^2+(B-X*cos(teta))^2)^0.5; l1=((X-B)^2+H^2)^0.5; g(1)=Q*L*cos(teta)-R*F; g(2)=Q*(L-X)-Mmax; g(3)=1.2*(l2-l1)-l1; g(4)=0.5*D-B; h = 0; end function [z, g, h] = f10(x) % Corrugated bulkhead design b=x(1); h=x(2); l=x(3); t=x(4); ABD = abs(l^2-h^2); z = (5.885*t*(b+l))/(b+(abs(l^2-h^2))^0.5); g(1)=-t*h*(0.4*b+l/6)+8.94*(b+(ABD)^0.5); g(2)=-t*h^2*(0.2*b+l/12)+2.2*(8.94*(b+(ABD)^0.5))^(4/3); g(3)=-t+0.0156*b+0.15; g(4)=-t+0.0156*l+0.15; g(5)=-t+1.05; g(6)=-l+h; h = 0; end function [z, g, h] = f11(x) % Sections Sec8 = [0.192 0.345]; Sec9 = [0.192 0.345]; nSec8 = numel(Sec8); nSec9 = numel(Sec9); x(8) = Sec8(min(floor(x(8)*nSec8+1),nSec8)); x(9) = Sec8(min(floor(x(9)*nSec9+1),nSec9)); % Objective z=1.98+4.90*x(1)+6.67*x(2)+6.98*x(3)+4.01*x(4)+1.78*x(5)+2.73*x(7); % Subjective Fa =1.16-0.3717*x(2)*x(4)-0.00931*x(2)*x(10)-0.484*x(3)*x(9)+0.01343*x(6)*x(10); VCu =0.261-0.0159*x(1)*x(2)-0.188*x(1)*x(8)-0.019*x(2)*x(7)+0.0144*x(3)*x(5)+0.0008757*x(5)*x(10)+0.08045*x(6)*x(9)+0.00139*x(8)*x(11)+0.00001575*x(10)*x(11); VCm =0.214+0.00817*x(5)-0.131*x(1)*x(8)-0.0704*x(1)*x(9)+0.03099*x(2)*x(6)-0.018*x(2)*x(7)+0.0208*x(3)*x(8)+0.121*x(3)*x(9)-0.00364*x(5)*x(6)+0.0007715*x(5)*x(10)-0.0005354*x(6)*x(10)+0.00121*x(8)*x(11)+0.00184*x(9)*x(10)-0.02*x(2)^2; VCl=0.74-0.61*x(2)-0.163*x(3)*x(8)+0.001232*x(3)*x(10)-0.166*x(7)*x(9)+0.227*x(2)^(2); Dur=28.98+3.818*x(3)-4.2*x(1)*x(2)+0.0207*x(5)*x(10)+6.63*x(6)*x(9)-7.7*x(7)*x(8)+0.32*x(9)*x(10); Dmr=33.86+2.95*x(3)+0.1792*x(10)-5.057*x(1)*x(2)-11*x(2)*x(8)-0.0215*x(5)*x(10)-9.98*x(7)*x(8)+22*x(8)*x(9); Dlr=46.36-9.9*x(2)-12.9*x(1)*x(8)+0.1107*x(3)*x(10); Fp=4.72-0.5*x(4)-0.19*x(2)*x(3)-0.0122*x(4)*x(10)+0.009325*x(6)*x(10)+0.000191*x(11)^(2); VMBP=10.58-0.674*x(1)*x(2)-1.95*x(2)*x(8)+0.02054*x(3)*x(10)-0.0198*x(4)*x(10)+0.028*x(6)*x(10); VFD=16.45-0.489*x(3)*x(7)-0.843*x(5)*x(6)+0.0432*x(9)*x(10)-0.0556*x(9)*x(11)-0.000786*x(11)^(2); g = [Fa-1, VCu-0.32, VCm-0.32, VCl-0.32, Dur-32, Dmr-32, Dlr-32, Fp-4, VMBP-9.9, VFD-15.7]; h = 0; end function [z, g, h] = f12(x) % A welded beam design problem z = 1.10471*x(1)^2*x(2)+0.04811*x(3)*x(4)*(14+x(2));