Is this the correct optimization tool (lsqcurvefit,MultiStart)

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Arbol 2017-6-11

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https://ww2.mathworks.cn/matlabcentral/answers/344290-is-this-the-correct-optimization-tool-lsqcurvefit-multistart

评论： Arbol 2017-6-14

I have checked the Optimization tool box to see which one would be good for my optimization problem, so I thought lsqcurvefit would be good for my problem. Upon making a model with data with known parameters and trying to fit it with a model. The parameters estimated are not the same as the known parameters (or converge to the known parameters) that I first created the noisy data. What do you think is wrong with this? I'm also using MultiStart to find different initial points also.

%Creating data with noise:
tu is a (225x3) data 
tdata is 225x1 =tu(:,1);
ptest=[0.2,0.1,0.25,0.05];
Tissue= odefnc_noise(ptest,tdata,tu);
%Fitting the data with noise
fun = @(p,tdatas) odefnc_test(p,tdatas,tu);
param0=[0.1 0.1 0.1 0.1];
problem = createOptimProblem('lsqcurvefit','objective',fun,...
'xdata',tdata,'ydata',Tissue,'x0',param0,'lb',[0 0 0 0],'ub',[1 1 1 1],...
'options',options);
[b,fval,exitflag,output,solutions]=run(ms,problem,2);
%Fitting Function
function Tissue= odefnc_test(p,texp,tu)
F=p(1);
fp=p(2);
fis=p(3);
PS=p(4);
init = [0 0];
[~,y]=ode45(@(t,x) myeqn(t,x,F,fp,fis,PS,tu), texp, init);
P=y(:,1);
I=y(:,2);
Tissue = (I+P);
function dx=myeqn(t,x,F,fp,fis,PS,tu)
output=interp1(tu(:,1),tu(:,2),t); 
dx(1)= (F/fp)*(output-x(1))- (PS/fp)*(x(1)-x(2));
dx(2)=  (PS/fis) *(x(1)-x(2));
dx=[dx(1);dx(2)];
end
end

This will converge to different value even if param0=ptest. So is it the ode function that create a problem? If 'fun' is not an ode, so it is like fun=@(b) b(1)*xdata +b(2)*xdata^2, the solution would converge according to many other problems I found online.

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Arbol 2017-6-13

在 MATLAB Online 中打开

I'm sorry, here try this new codes that I did:

%----------------Creating data with noise:------------------%
tu is a (225x3) data 
tdata is 225x1 =tu(:,1);
ptest=[0.2,0.1,0.25,0.05];
Tissue= odefnc_noise(ptest,tdata,tu);
%-------------Fitting the data with noise--------------%
options = optimset('Display','iter','FinDiffRelStep',0.0015,'TolFun', 2e-15,...
'TolX',2e-15,'DiffMaxChange',1,...
  'FunValCheck','on',...
  'MaxFunEvals',300,...
  'MaxIter',300);
ms=MultiStart;
ms.UseParallel='always';
fun = @(p,tdatas) odefnc_test(p,tdatas,tu);
param0=[0.1 0.1 0.1 0.1];
problem = createOptimProblem('lsqcurvefit','objective',fun,...
'xdata',tdata,'ydata',Tissue,'x0',param0,'lb',[0 0 0 0],'ub',[1 1 1 1],...
'options',options);
[b,fval,exitflag,output,solutions]=run(ms,problem,2);
%------Fitting Function--------%
function Tissue= odefnc_test(p,texp,tu)
F=p(1);
fp=p(2);
fis=p(3);
PS=p(4);
init = [0 0];
[~,y]=ode45(@(t,x) myeqn(t,x,F,fp,fis,PS,tu), texp, init);
P=y(:,1).*fp;
I=y(:,2).*fis;
Tissue = (I+P);
function dx=myeqn(t,x,F,fp,fis,PS,tu)
output=interp1(tu(:,1),tu(:,2),t); 
dx(1)= (F/fp)*(output-x(1))- (PS/fp)*(x(1)-x(2));
dx(2)=  (PS/fis) *(x(1)-x(2));
dx=[dx(1);dx(2)];
end
end

%---------Data with Noise------%:

function Tissue= odefnc_noise(p,texp,tu)
F=p(1);fp=p(2);fis=p(3);PS=p(4);
init = [0 0];
[~,y]=ode45(@(t,x) myeqn(t,x,F,fp,fis,PS,tu), texp, init);
P=y(:,1).*fp;
I=y(:,2).*fis;
p=max(P)-min(P);
i=max(I)-min(I);
b=mean(p+i);
noise= 0.01*b*randn(size(texp));
Tissue = (I+P)+noise;
function dx=myeqn(t,x,F,fp,fis,PS,tu)
output=interp1(tu(:,1),tu(:,2),t); 
dx(1)= (F/fp)*(output-x(1))- (PS/fp)*(x(1)-x(2));
dx(2)=  (PS/fis) *(x(1)-x(2));
dx=[dx(1);dx(2)];
end
end

Just a minor change to P and I from the older code; changed to P=y(:,1)*fp and I=y(:,2)*fis respectively. I included the ms and options. Thank you for the follow up, I appreciate it.

Walter Roberson 2017-6-14

I have not run with your modifications yet. With the version before them, when I changed the tolerance and step size tolerance to some that looked reasonable, nearly all of the runs end with "Change in x was less than the specified tolerance." which is exit 2; the remaining run was at a higher function value and ran out of iterations (exit 0).

I pushed up the number of starts to 20, but by random chance the final output was not better than one of the runs with only 2 multistarts -- so the starting position is important.

Arbol 2017-6-14

Correct, the number of points doesn't make it any better. But the new correction code that I posted will make the fit better, but still doesn't give a good exitflag. Even when i raised the number of starts.

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