P Mat=Get(Handles.Figure1,'Position');P Mat(3)=I;

Appendix

for i=98.5:1.5:142.5

p_mat=get(handles.figure1,'position');p_mat(3)=i;

set(handles.figure1,'position',p_mat);

pause(0.001)

end

set(handles.uipanel2,'visible','on')

set(handles.uipanel3,'visible','on')

set(handles.push_stop,'visible','on')

L_des_var=[.0001 .0001 .0001 .0001 -10 -10 -5 -5 0.0000001 0.0000001 ]; %input('Lower Bound Design Variable:' );

H_des_var=[7 7 7 7 7 7 5 5 2*pi 2*pi]; %input('Higher Bound Design Variable:' );

obj_fun_no=2;

des_var_no=10;set(handles.text_des_var_no_val,'String',des_var_no)

pop_size=str2double(get(handles.edit_pop_size,'String'));set(handles.text_pop_size_val,'String',pop_size)

generation_no=str2double(get(handles.edit_gen,'String'));

crs_prob=str2double(get(handles.edit_cp,'String'));;set(handles.text_cp_val,'String',crs_prob)

mut_prob=str2double(get(handles.edit_mp,'String'));;set(handles.text_mp_val,'String',mut_prob)

elim_crit=str2double(get(handles.edit_el,'String'));; set(handles.text_el_val,'String',elim_crit)

first_seed=str2double(get(handles.edit_fs,'String'));

set(handles.text_fs_val,'String',first_seed)

pause(0.2)

m_obj_fun(1)=0;m_obj_fun(2)=0;

tic

Parents=gofp(first_seed,des_var_no,pop_size,L_des_var,H_des_var);

init_pop=Parents;

pop=init_pop;

seed=ran2(first_seed

*2);

for generation=1:generation_no

set(handles.text_gen_val,'String',generation)

seed=ran2(-1e6*seed*2);

% crossover operator

para1=evaluation1(pop,obj_fun_no);

if mod(generation,50)==0

[h]=sel_ran(para1,des_var_no,obj_fun_no,m_obj_fun,seed);

[hybed_indv]=optim(h,des_var_no,obj_fun_no);

pop=[pop;hybed_indv];

para1=evaluation1(pop,obj_fun_no);

end

front1=fnds(para1,des_var_no,obj_fun_no,m_obj_fun);

distance=select_factor(para1,obj_fun_no,des_var_no);

pop_cross=crossover(pop,para1,des_var_no,crs_prob,seed,front1,distance);

% Mutation operator

pop_mut=mutation(pop,mut_prob,L_des_var,H_des_var,seed);

% Total population ( main + crossover + mutation)

pop_total=[pop;pop_cross;pop_mut];

para=evaluation1(pop_total,obj_fun_no);

% Select new population from parents and offsprings

[pop,para_final,fronts_final]=evolution(pop_total,para,pop_size,des_var_no,...

obj_fun_no,m_obj_fun,elim_crit,seed,L_des_var,H_des_var,crs_prob,mut_prob);

result(fronts_final,para_final,obj_fun_no,des_var_no);

err_min=min(para(:,11));

tr_min=min(para(:,12));

set(handles.text_err_val,'String',err_min)

set(handles.text_tr_val,'String',tr_min)

pause(0.1)

end

num=rand;

order=fix(rand*4+1);

rn=-1*fix(num*10^order);

while rn==0

num=rand;

order=fix(rand*4+1);

rn=-1*fix(num*10^order);

end

set(handles.edit_fs,'string',rn)

function [result]=boundry(X)

c=0;

for i=1:4

if X(i)>8 | X(i)<0

c=1;

result=c;

return

end

end

for i=5:8

if X(i)>8 | X(i)<-8

c=1;

result=c;

return

end

end

for i=9:10

if X(i)>2*pi | X(i)<0

c=1;

result=c;

return

end

end

result=c;

function [err,tr] = cause(individual)

CXD=[2.203802 4.398573 5.268585 4.999546 4.444195 4.02863 3.958154 4.10944 4.03908 3.461855 2.474852 1.61572 ];

CYD=[4.852923 4.038518 2.369554 1.067374 0.121084 -.520956 -.645528 -.005285 1.230817 2.607709 3.727444 4.443476 ];

save points.mat CXD CYD

point_num=size(CXD,2);

r1=individual(1);r2=individual(2);r3=individual(3);

r4=individual(4);rcx=individual(5);rcy=individual(6);

x0=individual(7);y0=individual(8);teta0=individual(9);

teta2(1)=individual(10);

for I=2:point_num

teta2(I)=teta2(1)+(30*pi/180)*(I-1);

end

for I=1:point_num

coupler=mech_builder(r1,r2,r3,r4,rcx,rcy,x0,y0,teta0,teta2(I));

CX(I)=coupler(1);

CY(I)=coupler(2);

end

H1=grashofcon(individual);

H2=boundry(individual);

length=individual(1:4);

length=sort(length);

ratio=length(4)/length(1);

if ratio > 25

H4=1;

else

H4=0;

end

sumation=0;

for I=1:point_num

sumation=sumation+(CXD(I)-CX(I))^2+(CYD(I)-CY(I))^2;

end

res=[CX;CY];

err=sumation+1e08*H1+1e8*H2+1e08*H4;

tr=tran(individual)+1e08*H1+1e8*H2+1e08*H4;

if nargout==0

disp(' ')

msgbox(sprintf(' The error function is : %g and The transmition angle error is : %g ',err,tr),'Results')

clear

end

function [C]=mech_builder(r1,r2,r3,r4,rcx,rcy,Xo,Yo,teta0,teta2)

a=r2; b=r3; c=r4; d=r1;

r=sqrt(rcx^2+rcy^2);

f=atan(rcy/rcx);

s=1;

% The following lines of code determines the starting configuration of the mechanism

% This is based on the standard cosine formulars and other triangle properties used for analyzing four-bar linkages

theta1=teta2;

x2=a*cos(theta1); % x cooridnate of the crank moving point: Point 2

y2=a*sin(theta1); % y cooridnate of the crank moving point: Point 2

e = sqrt((x2-d)^2+y2^2);

phi2=acos((e^2+c^2-b^2)/(2*e*c));

phi1=atan(y2/(x2-d))+(1-sign(x2-d))*pi/2;

theta3=phi1-s*phi2;

x3=c*cos(theta3)+d; % x cooridnate of the follower moving point: Point 3

y3=c*sin(theta3); % y cooridnate of the crank moving point: Point 3

theta2=atan((y3-y2)/(x3-x2))+(1-sign(x3-x2))*pi/2; %Bug in the code: There is an problem with this step if x3-x2 is zero, but that rarely happens

phi3=theta2+f;

gamma=(theta3-theta2);

x5=x2+r*cos(phi3); % x cooridnate of the coupler point: Point 5

y5=y2+r*sin(phi3); % y cooridnate of the coupler point: Point 5

Pn=rotate(x5,y5,Xo,Yo,teta0); x5n=Pn(1); y5n=Pn(2);

C=[x5n y5n gamma];

function [ output ] = rotate( xold, yold ,x0 ,y0 ,teta0 )

output(1)=xold*cos(teta0)-yold*sin(teta0)+x0;

output(2)=xold*sin(teta0)+yold*cos(teta0)+y0;

function er=tran(mech)

r1=mech(1);r2=mech(2);r3=mech(3);r4=mech(4);

theta2=0:0.1:2*pi;

for i=1:63

C=mech_builder(r1,r2,r3,r4,mech(5),mech(6),0,0,0,theta2(i));

gamma(i)=C(3);

end

%plot(theta2,gamma)

maxg=max(gamma)*180/pi;

ming=min(gamma)*180/pi;

er=(90-maxg)^2+(90-ming)^2;

function z=crossover(popmain,para,des_var_no,crs_prob,seed,front1,distance,L_des_var,H_des_var,L_c,n_inp2)

%Dynamic

F=0.4;

pop=popmain;

n=size(pop);

k=0;

[temp1,temp_ind1]=sort(para(:,des_var_no+1));

ind_best=temp_ind1(1);

Xbest=pop(ind_best,:);

for i=1:n(1)

seed=ran2(-1e6*seed);

r(i)=seed;

end

k=0;

for i=1:n(1)

if r(i)<crs_prob

k=k+1;

end

end

for i=1:2:k

jimjim=9;

while jimjim~=10

for sele=1:3

seed=ran2(-1e6*seed);

pop_crs1_no=ceil(size(pop,1)*seed);

seed=ran2(-1e6*seed);

pop_crs2_no=ceil(size(pop,1)*seed);

seed=ran2(-1e6*seed);

pop_crs3_no=ceil(size(pop,1)*seed);

[front_no1,each1]=find(front1==pop_crs1_no);

[front_no2,each2]=find(front1==pop_crs2_no);

[front_no3,each3]=find(front1==pop_crs3_no);

if front_no1==front_no2

if distance(pop_crs1_no)>distance(pop_crs2_no)

pop_main(sele)=pop_crs1_no;

else

pop_main(sele)=pop_crs2_no;

end

end

if front_no1<front_no2

pop_main(sele)=pop_crs1_no;

else

pop_main(sele)=pop_crs2_no;

end

end

if pop_main(1)~=pop_main(2)

pop_main(3)=pop_crs3_no;

jimjim=10;

end

end

seed=ran2(-1e6*seed);

Xr1=pop(pop_main(1),:);

Xr2=pop(pop_main(2),:);

V=Xbest+F*(Xr1-Xr2);

X_crs=pop(pop_main(3),:);

pop_off(1,:)=V;

pop_off(2,:)=X_crs;

pop_off_cut=pop_off;

seed=ran2(-1e6*seed);

cut_point=ceil((size(pop,2)-1)*seed);

pop_off_cut(1,cut_point+1:size(pop,2))=pop_off(2,cut_point+1:size(pop,2));

pop_off_cut(2,cut_point+1:size(pop,2))=pop_off(1,cut_point+1:size(pop,2));

pop_cross(i,:)=pop_off_cut(1,:);

pop_cross(i+1,:)=pop_off_cut(2,:);

end

pop_cross=grashof(pop_cross);

z=pop_cross;

function [avr]=CTA(parent)

s=size(parent); NP=s(1,1);

sumation=0;

for i=1:NP

indivi=parent(i,:);

err(i) = cause(indivi);

sumation=sumation+real(err(i));

end

avr=sumation/NP;

function para=evaluation1(pop,obj_fun_no);

ind_no=size(pop,1);

x=pop;

n=size(pop,1);

for i=1:n

indivi=x(i,:);

[err(i),tr(i)] = cause(indivi);

end

obj_fun(1,:)=err;

obj_fun(2,:)=tr;

%obj_fun(3,:)=mech_ad;

para=[x obj_fun'];

function [new_pop,para_final,fronts_final]=evolution(pop_total,para,pop_size,...

des_var_no,obj_fun_no,m_obj_fun,elim_crit,seed,L_des_var,H_des_var,crs_prob,mut_prob);

para_final=para;

pop_final=pop_total;

fronts_final=fnds(para_final,des_var_no,obj_fun_no,m_obj_fun);

n=size(fronts_final);

k=1;

for i=1:n(1)

for j=1:n(2)

if fronts_final(i,j)~=0

index(k)=fronts_final(i,j);

k=k+1;

end

end

end

if pop_size<=size(index,2)

[II,JJ]=sort(para_final(:,11));

index(pop_size)=JJ(1);

new_pop=pop_final(index(1:pop_size),:);

else

new_pop=pop_final(index,:);

end

function out_fndf=fndf(pop)

pop_size=size(pop);

bank(1:pop_size(1))=1;

for i=2:pop_size(1)

for j=1:i-1

if bank(j)==1 & bank(i)==1

if pop(i,:)>=pop(j,:)

bank(i)=1;

bank(j)=0;

elseif pop(i,:)<=pop(j,:)

bank(i)=0;

bank(j)=1;

else

bank(i)=1;

bank(j)=1;

end

end

end

end

j=1;

for i=1:pop_size(1)

if bank(i)==1

front(j)=i;

j=j+1;

end

end

out_fndf=front;

function fnds=fnds(para,des_var_no,obj_fun_no,m_obj_fun)

func=para(:,des_var_no+1:des_var_no+obj_fun_no);

[mfunc,nfunc]=size(func);

for i=1:obj_fun_no

if m_obj_fun(i)==0

func(:,i)=1./func(:,i);

end

end

i=1;

sumsize=0;

while sumsize~=mfunc

front=fndf(func);

for k=1:size(front,2)

sorted_front(i,k)=front(k);

end

for j=1:size(front,2)

func(front(j),:)=-inf;

end

i=i+1;

[msf,nsf]=size(sorted_front);

sumsize=sumsize+size(front,2);

end

fnds=sorted_front;

function [population]=gofp(first_seed,des_var_no,pop_size,L_des_var,H_des_var)

X=my_ran2(pop_size,des_var_no,first_seed);

for i=1:pop_size

for j=1:des_var_no

X(i,j)=X(i,j)*H_des_var(j)+L_des_var(j)*(1-X(i,j));

end

end

X=grashof(X);

population=X;

function [result]=grashof(parent)

X=parent;

c=size(X);NP=c(1,1);

for I=1:NP;

x=[X(I,1) X(I,2) X(I,3) X(I,4)];

x=sort(x);

X(I,1)=x(4);

X(I,2)=x(1);

X(I,3)=x(2);

X(I,4)=x(3);

ls=x(4)+x(1);

pq=x(2)+x(3);

if ls>=pq

while ls>=pq

X(I,3)=X(I,3)*1.1;

ls=X(I,1)+X(I,2);

pq=X(I,4)+X(I,3);

end

end

end

result=X;

function [result]=grashofcon(X)

x=[X(1) X(2) X(3) X(4)];

x=sort(x);

ls=x(4)+x(1);

pq=x(2)+x(3);

if (ls<pq)

c=0;

else

c=1;

end

result=c;

function [para,pop_total]=modify_pop(pop_total,para,elim_crit)

for i=1:size(para,1)-1

for j=i+1:size(para,1)

if para(i,:)~=0 & ...

para(i,:)>=((1-elim_crit)*para(j,:)) & para(i,:)<=((1+elim_crit)*para(j,:))

para(j,:)=0;

pop_total(j,:)=0;

end

end

end

% Eliminating zeros

j=0;

for i=1:size(para,1)

if min(para(i,:))>0

j=j+1;

temp_para(j,:)=para(i,:);

temp_pop_total(j,:)=pop_total(i,:);

end

end

para=temp_para;

pop_total=temp_pop_total;

function z=mutation(pop,mut_prob,L_des_var,H_des_var,seed)

[n,m]=size(pop);

for i=1:n

seed=ran2(-1e6*seed);

r(i)=seed;

end

%k is the population no. include in mutation

k=0;

for i=1:n

if r(i)<=mut_prob

k=k+1;

mut_no(k)=i;

end

end

if k==0

seed=ran2(-1e6*seed);

mut_no(1)=ceil(n*seed);

k=1;

end

for i=1:k

seed=ran2(-1e6*seed);

place_mut=ceil(m*seed);

mut_pop(i,:)=pop(mut_no(i),:);

seed=ran2(-1e6*seed);

mut_pop(i,place_mut)=seed*H_des_var(place_mut)+L_des_var(place_mut)*(1-seed);

end

mut_pop=grashof(mut_pop);

z=mut_pop;

function [ out ] = my_ran2(r,c,first_seed)

%UNTITLED1 Summary of this function goes here

% Detailed explanation goes here

seed=ran2(first_seed);

for i=1:r

for j=1:c

seed=ran2(-seed*1e6);

out(i,j)=seed;

end

end

function ran2=ran2(idum)

IM1=2147483563;IM2=2147483399;AM=1./IM1;IMM1=IM1-1;

IA1=40014;IA2=40692;IQ1=53668;IQ2=52774;IR1=12211;IR2=3791;

NTAB=32;NDIV=1+fix(IMM1/NTAB);EPS=1.2e-7;RNMX=1.-EPS;

idum2=123456789; iv=NTAB*0; iy=0;

if idum<=0

idum=max(-idum,1);

idum2=idum;

for j=NTAB+8:-1:1

k=fix(idum/IQ1);

idum=IA1*(idum-k*IQ1)-k*IR1;

if idum<0;idum=idum+IM1;end

if j<=NTAB;iv(j)=idum;end

end

iy=iv(1);

end

k=fix(idum/IQ1);

idum=IA1*(idum-k*IQ1)-k*IR1;

if idum<0;idum=idum+IM1;end

k=fix(idum2/IQ2);

idum2=IA2*(idum2-k*IQ2)-k*IR2;

if idum2<0;idum2=idum2+IM2;end

j=1+fix(iy/NDIV);

iy=iv(j)-idum2;

iv(j)=idum;

if iy<1;iy=iy+IMM1;end

ran2=min(AM*iy,RNMX);

function result(fronts,para,obj_fun_no,des_var_no)

%global fronts func para bound

for i=1:size(fronts,2)

if fronts(1,i)~=0

front(i)=fronts(1,i);

else

break

end

end

if obj_fun_no==2

hold on;

cla

para(front,des_var_no+1:des_var_no+2);

plot(para(front,des_var_no+1),para(front,des_var_no+2),'.')

title('Pareto Front');xlabel('Error Function');ylabel('Transmision Angle');

end

para=para(front,:);

para_temp=para;clmn_no=des_var_no+1;

for j=1:size(para_temp,1)

index(j)=1;

for i=2:size(para_temp,1)

if para_temp(index(j),clmn_no)<para_temp(i,clmn_no)

index(j)=i;

end

end

para_temp(index(j),clmn_no)=-inf;

end

para=para(index,:);

fid=fopen('result.txt','w+');

for i=1:size(para,1)

fprintf(fid,'%d',i);

for j=1:des_var_no+obj_fun_no

fprintf(fid,'\t%17.10f',para(i,j));

end

fprintf(fid,'\n');

end

%fprintf(fid,'* * *\n');

fclose(fid);

%fprintf(1,'\n The result of calculation has been saved in

%''result.txt''.\n\n')

function distance=select_factor(para1,obj_fun_no,des_var_no)

pop=para1(:,des_var_no+1:des_var_no+obj_fun_no);

pop(:,1)=pop(:,1);

pop(:,2)=pop(:,2)/1000;

for i=1:size(pop,1)

for j=1:obj_fun_no

ii=1;jj=1;

for k=1:size(pop,1)

if k~=i

dis=(pop(i,j)-pop(k,j));

if dis>0

dis_po(ii)=dis;

ii=ii+1;

else

dis_ne(jj)=dis;

jj=jj+1;

end

end

end

if ii==1

dis_obj_fun(i,j)=abs(max(dis_ne))+abs(min(dis_ne));

elseif jj==1

dis_obj_fun(i,j)=abs(min(dis_po))+abs(max(dis_po));

else

dis_obj_fun(i,j)=abs(min(dis_po))+abs(max(dis_ne));

end

clear dis_po dis_ne

end

dis_total(i)=sum(dis_obj_fun(i,:));

end

distance=dis_total;

function [ indv_opt ] = optim(pop_sel,des_var_no,obj_fun_no)

for i=1:5

indv=fminsearch(@cause1,pop_sel(1,1:des_var_no));

pop_sel(1,1:des_var_no)=indv;

disp(i)

end

indv_opt(1,:)=indv;

[r]=cause1(indv);

disp(r)

for i=1:5

indv=fminsearch(@cause2,pop_sel(2,1:des_var_no));

pop_sel(2,1:des_var_no)=indv;

disp(i)

end

indv_opt(2,:)=indv;

[d]=cause1(indv);

disp(d)

1