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Saber_phy
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Genetic algorithm calculated values compared to measured

Asked by Saber_phy
on 15 Jun 2018
Latest activity Commented on by Saber_phy
on 13 Sep 2018 at 21:14

Hi

I am a student enrolled in the 2nd year physics Master's degree, i am a beginner in Matlab and i have the same problem like Mattias, can you help me and is it was possible to get your e-mail.

My problem is to make a fit of a nonlinear equation to data with the genetic algorithm and to minimize R, my model function is

R*(1-exp(-t/rate))

The industrial data Rexp and t are known: these are two vectors that give the variation of Rexp as a function of time (t)

rate also is known and equal to 40

I declared my function (fitnes function) as follows:

function S=ga_Newton(R)
           t=[0 2 4 6 8 10 12 14 16 18 20 22 24 26 28];
           Rexp=[1 .7987e-05 3.07996e-05 3.90531e-05 1.89562e-05 2.82794e-05 5.55377e-05                                                     
                      4.75723e-05 6.2447e-05 5.35282e-05 5.16775e-05 4.67144e-05 4.63215e-05 6.62753e-05                    
                        3.72551e-05 3.54374e-05];
for i=1:15
      S(i) =sum((Rexp(i)-R*(1-exp(-t(i)./40)))^2);
end  

The function

S (i) = sum ((Rexp (i) -R * (1-exp (-t (i) ./ 40))) ^ 2)

I use it in the methods of Gauss Newton and Levenberg marquardt and I got a good result of R which is in the order of 0.000059 but with the genetic algorithm I found no result.

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2 Answers

Answer by Walter Roberson
on 15 Jun 2018
 Accepted Answer

Replace

for i=1:15
      S(i) =sum((Rexp(i)-R*(1-exp(-t(i)./40)))^2);
end  

with

S = sum((Rexp-R*(1-exp(-t./40))).^2);

  7 Comments

thank you once again, please be patient with me, I remind you that informatique is not my domain and I am a beginner in matlab, I try all the advice that you give to me but the program run without stopping. maybe the problem is in the declaration of my fitness function, if you have understood the idea of my problem can you give me a proposal of a fitness function to fit a nonlinear equation to data with the genetic algorithm and to minimize it. I'm stuck in this task for a long time, i would be very grateful if you could help me.

I have attached the exact files I used. Execution requires less than 3 seconds.

More generally, the approach I would use would be to use the Symbolic Toolbox to prepare the function to be minimized:

      t=[0 2 4 6 8 10 12 14 16 18 20 22 24 26 28];
      Rexp=[1.7987e-05 3.07996e-05 3.90531e-05 1.89562e-05 2.82794e-05 5.55377e-05 4.75723e-05 6.2447e-05 5.35282e-05 5.16775e-05 4.67144e-05 4.63215e-05 6.62753e-05 3.72551e-05 3.54374e-05];
     syms R
     prediction = R*(1-exp(-t./40));
     actual = Rexp;
     residue = sum((actual - prediction).^2);
     F = matlabFunction(residue);
     nvars = 1;
     A = []; b = [];
     Aeq = []; beq = [];
     lb = []; ub = [];
     nonlcon = [];
     options = gaoptimset('PlotFcn', {@gaplotbestf  @gaplotbestindiv  @gaplotexpectation  @gaplotstopping}, ...
                          'TolFun', 1e-13, 'Generations', 1000);
    [R, fval, exitflag, output] = ga(F, nvars, A, b, Aeq, beq, lb, ub, nonlcon, options);
    fprintf('best R: %g\n', R);
    fprintf('best residue: %g\n', fval);

Note: you will not get especially close to the true minima. The true minima is at approximately 0.000128381339932429 which can be quickly determined:

[R, fval] = fminunc(F, 0)

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Answer by Saber_phy
on 10 Sep 2018 at 23:14

Hello;

My problem is to make a fit of a nonlinear equation to data with the genetic algorithm and to minimize ‘R’, and ‘rate’ at the same time, my model function is R*(1-exp(-t/rate)) The industrial data Rexp and t are known: these are two vectors that give the variation of Rexp as a function of time (t), first of all I will test my code by a single value of R and rate I declared my function (fitnes function) as follows:

function residue =fitness_XY(x)
t=[0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120];
 Rexp= 0.000157*(1-exp(-t/70));
 residue=sum((Rexp-x(1)*(1-exp(-t./x(2)))).^2) ;

%genetic code

F=@fitness_XY
nvars = 2;
A= []; b = [];
Aeq = []; beq = [];
lb = []; ub = [];
nonlcon = [];
%Options
options=gaoptimset('PlotFcn',{@gaplotbestf}, 'CrossoverFraction',0.01,'TolFun',1e-13,'Generations',300) ;
[x,fval,exitflag,output]=ga(F, nvars, A, b, Aeq, beq, lb, ub, nonlcon, options) ;
fprintf('best R and rate: %g\n', x) ;
fprintf('The number of generations was : %d\n', output.generations);
fprintf('The number of function evaluations was : %d\n', output.funccount);
fprintf('The best function value found was(best residue) : %g\n', fval);

at the end the code must return the exact value of R=0.000157 and rate=70 but it still running more than 30mn and return a false value, I don’t know where is the problem exactly

  6 Comments

i know that fminsearch will give me a precise result, but in my search i must minimize my function using genetic algorithm and levenberg marquardt methods and compare the two methods and identify their advantages and disadvantages

"ga does not give an acceptable result within an acceptable time" is a valid conclusion.

You can use ga options to pass in a starting point: look at the initial population matrix parameter.

If it is reasonable to use a lower bound or upper bound on the values, you should do so. Even if it is just lower bound 0.

i already use the ga option and i used a lower and upper bound on the values and i got reasonable value.

thank you very much :)

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