Why optimization has a Initial point value

2018 3 12
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更新时间：2018 3 12
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Why optimization has a Initial point value

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Geoff Hayes
Geoff Hayes 2018-3-12
Pearwpun - I think most optimization algorithms have an initial point so that the algorithm can then improve upon that point.
Why do you think that it is unnecessary?
Pearwpun Bunjun
Pearwpun Bunjun 2018-3-12
I means answer is from my code
Geoff Hayes
Geoff Hayes 2018-3-12
Oh you mean why is the answer the same as your initial value? Is that your question?
Why did you choose 310 as an initial point?

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回答（1 个）

Pearwpun Bunjun
Pearwpun Bunjun 2018-3-12

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X0 = 310*ones(1,m);
Lb =(30+273)*ones(1,m);
Ub =(50+273)*ones(1,m);
nonlcon = @constraints;
options = optimoptions(@fmincon,'Algorithm','sqp','MaxIter',300);
[MV,fval]= fmincon(@Obj,X0,[],[],[],[],[],[],@NONLCON,options);
answer is X0 = 310

6 个评论
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Torsten
Torsten 2018-3-12
What is your question ?
Pearwpun Bunjun
Pearwpun Bunjun 2018-3-12
why answer from fmincon has X0 Single value
Torsten
Torsten 2018-3-12
What is @Obj ?
What is @NONLCON (note that "nonlcon" and "NONLCON" are different because MATLAB is case-sensitive) ?
Pearwpun Bunjun
Pearwpun Bunjun 2018-3-12
编辑：Pearwpun Bunjun 2018-3-12
@Obj=fun @NONLCON=constraints correct @nonlcon is model incorrect did not use
Torsten
Torsten 2018-3-12
We have to see these two functions in order to answer your question.
Pearwpun Bunjun
Pearwpun Bunjun 2018-3-12
编辑：Pearwpun Bunjun 2018-3-12
function PPP7 clear global C1 Tj1 Tjsp1 p m
b = 1.45; % dimensionless : nucleation rate exponential g = 1.5; % dimensionless : growth rate exponential kb = 285.0; % the nucleation rate constant (1/(s um3) kg = 1.44*10^8; % the growth rate constant (um/s) EbR = 7517.0; % Eb/R : the nucleation activation energy/gas constant (K) EgR = 4859.0; % Eg/R : the growth activation energy/gas constant(K) U = 1800; % the overall heat transfer coefficient (kJ/(m2 h K)) A = 0.25; % the total heat transfer surface area (m2) delH = 44.5; % the heat of reaction (kJ/kg) Cp = 3.8; % the heat capacity of the solution (kJ/(kg K)) M = 27.0; % the mass of solvent in the crystallizer (kg) rho = 2.66*10^-12; % the density of crystal (g/um3) kv = 1.5; % the volumetric shape factor
%jacket Parameter Vj=0.015; %m3 Fj=0.001; %m3/s rhoj=1000; %kg/m3 Cpj=4.184; %J/kgK
% Time TTime=30; tf = (60*TTime); % sec (30 min) dt = 20; % sec nt = tf/dt; t = linspace(0,TTime,nt+1);% min sampt= 2; % unit: min % q=1; p=30; m=30; z=0; % initial conditions
C(1) = 0.1743; % g solute/g solvent T(1) = 323; % K Tj(1) =278.3; % K Tjsp(1) = (20+273); % K initial values of manipulated variable %Tsp(1) =(127+273);
%C1(1)=C(1); %T1(1)=T(1); %Tj1(1)=Tj(1); %Tsp1(1)=Tsp(1);
%for Y=1:90
%Tsp(20)=490; % Tsp(Y+1)=Tsp(Y);
%Tsp(52)=450; % Tsp(Y+1)=Tsp(Y); %Tsp(70)=430; % Tsp(Y+1)=Tsp(Y); %end
% Parabolic distribution @ 70-90 um un0(1) = 0; un1(1) = 0; un2(1) = 0; un3(1) = 0; un4(1) = 0; un5(1) = 0;
us0(1) = 70;
us1(1) = 1.8326e+004; us2(1) = 5.0480e+006; us3(1) = 1.3928e+009; us4(1) = 3.8490e+011; us5(1) = 1.0654e+014;
h=waitbar(0,'Simulation in Process...');
for i=1:nt; waitbar(i/nt); % Moment models % the total crystal number uu0(i) = un0(i)+us0(i); % the total crystal length uu1(i) = un1(i)+us1(i); % the total crystal surface area uu2(i) = un2(i)+us2(i); % the total crystal volume uu3(i) = un3(i)+us3(i);
% Saturation concentration (T in celcious)
Temp(i) = T(i)-273;
Cs(i) = 6.29*10^-2+(2.46*10^-3*Temp(i))-(7.14*10^-6*Temp(i)^2);
% Metastable concentration
Cm(i) = 7.76*10^-2+(2.46*10^-3*Temp(i))-(8.10*10^-6*Temp(i)^2);
% Supersaturation
S(i) = (C(i)-Cs(i))/Cs(i);
% The nucleation rate
B(i) = kb*(exp(-EbR/T(i)))*(((C(i)-Cs(i))/Cs(i))^b)*uu3(i);
% The growth rate
G(i) = kg*(exp(-EgR/T(i)))*(((C(i)-Cs(i))/Cs(i))^g);
% Population Balance Equation(PBE)
nr=600;
for j=1:nr+1 % r=0:600
r = j+1;
% Seed
% Initial condition
if r>=250 & r<=300
rs(j,1) = r;
% Parabolic distribution
ns(j,1) = 0.0032*(300-r)*(r-250);
else
rs(j,1) = r;
ns(j,1) = 0;
end % if j>=250 &j<=300
rs(j,i+1) = rs(j,i)+G(i)*dt;
ns(j,i+1) = ns(j,i);
if rs(j,i+1)>600
rs(j,i+1)=600;
end
% Nucleation
% at t=0
if i==1
rn(1,1) = 0;
nn(1,1) = B(1)/G(1);
else % at t=dt
if j==1 % r=0
rn(1,i) = 0;
nn(1,i) = B(i)/G(i);
else
rn(j,i) = rn(j-1,i-1)+G(i)*dt;
nn(j,i) = nn(j-1,i-1);
end % if j==1
end % if i==1
end % for j=1:nr+1
% The crystal size distribution
%%%%%%%%The crystal size distribution
if i==1
Nn = [B(1)/G(1); zeros(nr,1)];
else
Nn = nn([1:nr+1],i);
end
Ns = ns([1:nr+1],i);
n = Nn+Ns;
if i==1
rn([1:nr+1],i) = 0;
else
rn(nr+1,i) = rn(nr,i);
end
rrn = rn([1:nr+1],i);
rrs = rs([1:nr+1],i);
% Moment : Trapezoidal Rule
for k=1:nr+1
% u2
if k==1
sumun22 = rrn(1,1)^2*Nn(1,1);
sumus22 = rrs(1,1)^2*Ns(1,1);
else
sumun22 = sumun22+(((rrn(k-1,1)^2*Nn(k-1,1))+(rrn(k,1)^2*Nn(k,1)))*(rrn(k,1)-rrn(k-1,1))/2);
sumus22 = sumus22+(((rrs(k-1,1)^2*Ns(k-1,1))+(rrs(k,1)^2*Ns(k,1)))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu2=sumun22+sumus22;
% u3
if k==1
sumun33 = rrn(1,1)^3*Nn(1,1);
sumus33 = rrs(1,1)^3*Ns(1,1);
else
sumun33 = sumun33+(((rrn(k-1,1)^3*Nn(k-1,1))+(rrn(k,1)^3*Nn(k,1)))*(rrn(k,1)-rrn(k-1,1))/2);
sumus33 = sumus33+(((rrs(k-1,1)^3*Ns(k-1,1))+(rrs(k,1)^3*Ns(k,1)))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu3=sumun33+sumus33;
% u1
if k==1
sumun11 = rrn(1,1)^1*Nn(1,1);
sumus11 = rrs(1,1)^1*Ns(1,1);
else
sumun11 = sumun11+(((rrn(k-1,1)^1*Nn(k-1,1))+(rrn(k,1)^1*Nn(k,1)))*(rrn(k,1)-rrn(k-1,1))/2);
sumus11 = sumus11+(((rrs(k-1,1)^1*Ns(k-1,1))+(rrs(k,1)^1*Ns(k,1)))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu1=sumun11+sumus11;
% u0
if k==1
sumun00 = rrn(1,1)^0*Nn(1,1);
sumus00 = rrs(1,1)^0*Ns(1,1);
else
sumun00 = sumun00+((rrn(k-1,1)^0*Nn(k-1,1)+rrn(k,1)^0*Nn(k,1))*(rrn(k,1)-rrn(k-1,1))/2);
sumus00 = sumus00+((rrs(k-1,1)^0*Ns(k-1,1)+rrs(k,1)^0*Ns(k,1))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu0=sumun00+sumus00;
% u4
if k==1
sumun44 = rrn(1,1)^4*Nn(1,1);
sumus44 = rrs(1,1)^4*Ns(1,1);
else
sumun44 = sumun44+(((rrn(k-1,1)^4*Nn(k-1,1))+(rrn(k,1)^4*Nn(k,1)))*(rrn(k,1)-rrn(k-1,1))/2);
sumus44 = sumus44+(((rrs(k-1,1)^4*Ns(k-1,1))+(rrs(k,1)^4*Ns(k,1)))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu4=sumun44+sumus44;
% u5
if k==1
sumun55 = rrn(1,1)^5*Nn(1,1);
sumus55 = rrs(1,1)^5*Ns(1,1);
else
sumun55 = sumun55+(((rrn(k-1,1)^5*Nn(k-1,1))+(rrn(k,1)^5*Nn(k,1)))*(rrn(k,1)-rrn(k-1,1))/2);
sumus55 = sumus55+(((rrs(k-1,1)^5*Ns(k-1,1))+(rrs(k,1)^5*Ns(k,1)))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu5=sumun55+sumus55;
end % for k
u2(i) = sumu2;
u3(i) = sumu3;
u1(i) = sumu1;
u0(i) = sumu0;
u4(i) = sumu4;
u5(i) = sumu5;
C1=C(i); Tjsp1=Tjsp(i); Tj1=Tj(i);
% Mass Balance : Solute concentration
C(i+1) = C(i)+dt*(-3*rho*kv*G(i)*u2(i));
% Batch Energy Balance
TT3=T(i);
RR1=(-U*A/(M*Cp*3600)*(T(i)-Tj(i))-delH/Cp*3*rho*kv*G(i)*u2(i));
T(i+1)=T(i)+dt*RR1;
TT4=T(i+1);
Temp(i+1)= T(i+1)-273;
Cs(i+1) = 6.29*10^-2+(2.46*10^-3*Temp(i+1))-(7.14*10^-6*Temp(i+1)^2);
Cm(i+1) = 7.76*10^-2+(2.46*10^-3*Temp(i+1))-(8.10*10^-6*Temp(i+1)^2);
Tj(i+1)= Tj(i)+dt*(Fj/Vj*(Tjsp(i)-Tj(i))+(((U*A/3600)*(T(i)-Tj(i))/rhoj*Vj*Cpj)));
Tjsp(i+1)=Tjsp(i);
% Part III: Calculating the value of manipulated variable %
X0 = T(1)*ones(1,m);
Lb =(30+273)*ones(1,m);
Ub =(50+273)*ones(1,m);
nonlcon = @constraints;
options = optimoptions(@fmincon,'Algorithm','sqp','MaxIter',300);
% options = optimset('Display','iter');
[MV,fval]= fmincon(@Obj,X0,[],[],[],[],[],[],@NONLCON,options);
%x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)
%@(MV)NONLCON(MV)
SS4=MV;
SS1=MV(1);
T(i+1) = MV(1);
%Moment model
%u3
%Neacleated class
un3(i+1) = sumun33+dt*(3*G(i)*sumun22);
%Seed class
%Virtual process
us3(i+1) = sumus33+dt*(3*G(i)*sumus22);
%the total crystal volume
uu3(i+1)=un3(i+1)+us3(i+1);
%u2
%Neacleated class
un2(i+1) = sumun22+dt*(2*G(i)*sumun11);
%Seed class
%Virtual process
us2(i+1) = sumus22+dt*(2*G(i)*sumus11);
%the total crystal surface area
uu2(i+1)=un2(i+1)+us2(i+1);
%u1
%Neacleated class
un1(i+1) = sumun11+dt*(1*G(i)*sumun00);
%Seed class
%Virtual process
us1(i+1) = sumus11+dt*(1*G(i)*sumus00);
%the total crystal volume
uu1(i+1)=un1(i+1)+us1(i+1);
%u0
%Neacleated class
un0(i+1) = sumun00+dt*(0*G(i)*sumun00);
%Seed class
%Virtual process
us0(i+1) = sumus00+dt*(0*G(i)*sumus00);
%the total crystal volume
uu0(i+1)=un0(i+1)+us0(i+1);
end delete(h) % DELETE the waitbar; don't try to CLOSE it.
save ppp7.mat RR1 TT3 TT4 figure subplot(2,1,1) stairs(t,T,'-b') legend('Reactor Temp') ylabel('T(k)') xlabel('Time (min)')
subplot(2,1,2) plot(t,C,'-b') legend('Concentration') xlabel('Time (min)') ylabel('C')
figure subplot(2,1,1) plot(t,Tj,'r',t,Tjsp,'b') legend('Tj') xlabel('Time (min)') ylabel('Tj')
figure subplot(1,1,1)
stairs(t,Tjsp,'r') legend('Tjsp') xlabel('Time (min)') ylabel('Tjsp')
function f = Obj(MV,m,p,C,Tj,Tjsp)
global C1 Tj1 Tjsp1 p m Lw II1 II2 II3 II4 II5
% Process parameters : Potassium sulfate (K2SO4-H2O) b = 1.45; % dimensionless : nucleation rate exponential g = 1.5; % dimensionless : growth rate exponential kb = 285.0; % the nucleation rate constant (1/(s um3) kg = 1.44*10^8; % the growth rate constant (um/s) EbR = 7517.0; % Eb/R : the nucleation activation energy/gas constant (K) EgR = 4859.0; % Eg/R : the growth activation energy/gas constant(K) U = 1800; % the overall heat transfer coefficient (kJ/(m2 h K)) A = 0.25; % the total heat transfer surface area (m2) delH = 44.5; % the heat of reaction (kJ/kg) Cp = 3.8; % the heat capacity of the solution (kJ/(kg K)) M = 27.0; % the mass of solvent in the crystallizer (kg) rho = 2.66*10^-12; % the density of crystal (g/um3) kv = 1.5; % the volumetric shape factor %jacket Parameter Vj=0.015; %m3 Fj=0.001; %m3/s rhoj=1000; %kg/m3 Cpj=4.184; %J/kgK
% Step size, Sampling time and process time % tf = 1800; % sec (30 min) dt = 20; % sec nt = tf/dt; t = linspace(0,30,nt+1);% min sampt= 2; % unit: min %
Cobj = C1 ; % g solute/g solvent Tobj = MV ; % K Tjobj = Tj1 ; % K Tjspobj = Tjsp1;
q=1; z=0;
% Parabolic distribution @ 70-90 um un0(1) = 0; un1(1) = 0; un2(1) = 0; un3(1) = 0; un4(1) = 0; un5(1) = 0;
us0(1) = 70;
us1(1) = 1.8326e+004; us2(1) = 5.0480e+006; us3(1) = 1.3928e+009; us4(1) = 3.8490e+011; us5(1) = 1.0654e+014;
for C=1:1:p
if C>m
Tobj(C)= Tobj(C-1)
end
end
for z=1:p
% Moment models
% the total crystal number
uu0(z) = un0(z)+us0(z);
% the total crystal length
uu1(z) = un1(z)+us1(z);
% the total crystal surface area
uu2(z) = un2(z)+us2(z);
% the total crystal volume
uu3(z) = un3(z)+us3(z);
% Saturation concentration (T in celcious)
Temp(z) = Tobj(z)-273;
Cs(z) = 6.29*10^-2+(2.46*10^-3*Temp(z))-(7.14*10^-6*Temp(z)^2);
% Metastable concentration
Cm(z) = 7.76*10^-2+(2.46*10^-3*Temp(z))-(8.10*10^-6*Temp(z)^2);
% Supersaturation
S(z) = (Cobj(z)-Cs(z))/Cs(z);
% The nucleation rate
B(z) = kb*(exp(-EbR/Tobj(z)))*(((Cobj(z)-Cs(z))/Cs(z))^b)*uu3(z);
% The growth rate
G(z) = kg*(exp(-EgR/Tobj(z)))*(((Cobj(z)-Cs(z))/Cs(z))^g);
% Population Balance Equation(PBE)
nr=600;
for j=1:nr+1 % r=0:600
r = j+1;
% Seed
% Initial condition
if r>=250 & r<=300
rs(j,1) = r;
% Parabolic distribution
ns(j,1) = 0.0032*(300-r)*(r-250);
else
rs(j,1) = r;
ns(j,1) = 0;
end % if j>=250 &j<=300
rs(j,z+1) = rs(j,z)+G(z)*dt;
ns(j,z+1) = ns(j,z);
if rs(j,z+1)>600
rs(j,z+1)=600;
end
% Nucleation
% at t=0
if z==1
rn(1,1) = 0;
nn(1,1) = B(1)/G(1);
else % at t=dt
if j==1 % r=0
rn(1,z) = 0;
nn(1,z) = B(z)/G(z);
else
rn(j,z) = rn(j-1,z-1)+G(z)*dt;
nn(j,z) = nn(j-1,z-1);
end % if j==1
end % if i==1
end % for j=1:nr+1
% The crystal size distribution
%%%%%%%%The crystal size distribution
if z==1
Nn = [B(1)/G(1); zeros(nr,1)];
else
Nn = nn([1:nr+1],z);
end
Ns = ns([1:nr+1],z);
n = Nn+Ns;
if z==1
rn([1:nr+1],z) = 0;
else
rn(nr+1,z) = rn(nr,z);
end
rrn = rn([1:nr+1],z);
rrs = rs([1:nr+1],z);
% Moment : Trapezoidal Rule
for k=1:nr+1
% u2
if k==1
sumun22 = rrn(1,1)^2*Nn(1,1);
sumus22 = rrs(1,1)^2*Ns(1,1);
else
sumun22 = sumun22+(((rrn(k-1,1)^2*Nn(k-1,1))+(rrn(k,1)^2*Nn(k,1)))*(rrn(k,1)-rrn(k-1,1))/2);
sumus22 = sumus22+(((rrs(k-1,1)^2*Ns(k-1,1))+(rrs(k,1)^2*Ns(k,1)))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu2=sumun22+sumus22;
% u3
if k==1
sumun33 = rrn(1,1)^3*Nn(1,1);
sumus33 = rrs(1,1)^3*Ns(1,1);
else
sumun33 = sumun33+(((rrn(k-1,1)^3*Nn(k-1,1))+(rrn(k,1)^3*Nn(k,1)))*(rrn(k,1)-rrn(k-1,1))/2);
sumus33 = sumus33+(((rrs(k-1,1)^3*Ns(k-1,1))+(rrs(k,1)^3*Ns(k,1)))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu3=sumun33+sumus33;
% u1
if k==1
sumun11 = rrn(1,1)^1*Nn(1,1);
sumus11 = rrs(1,1)^1*Ns(1,1);
else
sumun11 = sumun11+(((rrn(k-1,1)^1*Nn(k-1,1))+(rrn(k,1)^1*Nn(k,1)))*(rrn(k,1)-rrn(k-1,1))/2);
sumus11 = sumus11+(((rrs(k-1,1)^1*Ns(k-1,1))+(rrs(k,1)^1*Ns(k,1)))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu1=sumun11+sumus11;
% u0
if k==1
sumun00 = rrn(1,1)^0*Nn(1,1);
sumus00 = rrs(1,1)^0*Ns(1,1);
else
sumun00 = sumun00+((rrn(k-1,1)^0*Nn(k-1,1)+rrn(k,1)^0*Nn(k,1))*(rrn(k,1)-rrn(k-1,1))/2);
sumus00 = sumus00+((rrs(k-1,1)^0*Ns(k-1,1)+rrs(k,1)^0*Ns(k,1))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu0=sumun00+sumus00;
% u4
if k==1
sumun44 = rrn(1,1)^3*Nn(1,1);
sumus44 = rrs(1,1)^3*Ns(1,1);
else
sumun44 = sumun44+(((rrn(k-1,1)^3*Nn(k-1,1))+(rrn(k,1)^3*Nn(k,1)))*(rrn(k,1)-rrn(k-1,1))/2);
sumus44 = sumus44+(((rrs(k-1,1)^3*Ns(k-1,1))+(rrs(k,1)^3*Ns(k,1)))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu4=sumun44+sumus44;
% u5
if k==1
sumun55 = rrn(1,1)^3*Nn(1,1);
sumus55 = rrs(1,1)^3*Ns(1,1);
else
sumun55 = sumun55+(((rrn(k-1,1)^3*Nn(k-1,1))+(rrn(k,1)^3*Nn(k,1)))*(rrn(k,1)-rrn(k-1,1))/2);
sumus55 = sumus55+(((rrs(k-1,1)^3*Ns(k-1,1))+(rrs(k,1)^3*Ns(k,1)))*(rrs(k,1)-rrs(k-1,1))/2);
end % if k==1
sumu5=sumun55+sumus55;
end
u2(z) = sumu2;
u3(z) = sumu3;
u1(z) = sumu1;
u0(z) = sumu0;
u4(z) = sumu4;
u5(z) = sumu5;
% Mass Balance : Solute concentration
TT1=Tobj(z);
RR5 =real(-3*rho*kv*G(z)*u2(z));
Cobj(z+1) = Cobj(z)+dt*RR5;
% Batch Energy Balance
WW=real(-U*A/(M*Cp*3600)*(Tobj(z)-Tjobj(z))-delH/Cp*3*rho*kv*G(z)*u2(z));
Tobj(z+1)= Tobj(z)+dt*WW;
TT2=Tobj(z+1);
Temp(z+1)= Tobj(z+1)-273;
Cs(z+1) = (6*10^-5)*exp(0.0396*Temp(z+1));
Tjobj(z+1)= Tjobj(z)+dt*(Fj/Vj*(Tjspobj(z)-Tjobj(z))+(((U*A/3600)*(Tobj(z)-Tjobj(z))/rhoj*Vj*Cpj)));
Tjspobj(z+1)=Tjspobj(z);
%Moment model
%u3
%Neacleated class
un3(z+1) = sumun33+dt*(3*G(z)*sumun22);
%Seed class
%Virtual process
us3(z+1) = sumus33+dt*(3*G(z)*sumus22);
%the total crystal volume
uu3(z+1)=un3(z+1)+us3(z+1);
%u2
%Neacleated class
un2(z+1) = sumun22+dt*(2*G(z)*sumun11);
%Seed class
%Virtual process
us2(z+1) = sumus22+dt*(2*G(z)*sumus11);
%the total crystal surface area
uu2(z+1)=un2(z+1)+us2(z+1);
%u1
%Neacleated class
un1(z+1) = sumun11+dt*(1*G(z)*sumun00);
%Seed class
%Virtual process
us1(z+1) = sumus11+dt*(1*G(z)*sumus00);
%the total crystal volume
uu1(z+1)=un1(z+1)+us1(z+1);
%u0
%Neacleated class
un0(z+1) = sumun00+dt*(0*G(z)*sumun00);
%Seed class
%Virtual process
us0(z+1) = sumus00+dt*(0*G(z)*sumus00);
%the total crystal volume
uu0(z+1)=un0(z+1)+us0(z+1);
%u4
%Neacleated class
un4(z+1) = sumun44+dt*(4*G(z)*sumun44);
%Seed class
%Virtual process
us4(z+1) = sumus44+dt*(4*G(z)*sumus44);
%the total crystal volume
uu4(z+1)=un4(z+1)+us4(z+1);
%u5
%Neacleated class
un5(z+1) = sumun55+dt*(5*G(z)*sumun55);
%Seed class
%Virtual process
us5(z+1) = sumus55+dt*(5*G(z)*sumus55);
%the total crystal volume
uu5(z+1)=un5(z+1)+us5(z+1);
end %fori=1:nt SS6=real(un3(p)); SS5=real(us3(p));
Lw=real(uu3/uu2); II1=[Tobj>=303]; II5= [Tobj<=323]; II2=[Cs<=Cobj]; II3= [us3(p)>=8.3301*10^9]; II4 = [Tobj(z+1)<=abs((2*dt)+Tobj(z))]
f= SS6/SS5;
function [c1,c2,c3,c4,c5,ceq] = NONLCON(MV)
global Lw II1 II2 II3 II4 II5 Lw1 =Lw; c1 = double(II1) c2 = double(II2); c3 = double(II3); c3 = double(II4); c5 = double(II5) ceq = [];

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