Genetic Algorithm taking too long to optimize

Hi,

I have been trying to build a code to optimize a curve towards an ideal curve using genetic algorithm but the iterations are not going past the 1st generation. However the optimization app says that it is still optimizing. Can someone guide me and check if there is something wrong with my code and suggest ways to speed it up for faster results. As you are aware the stochastic process might not give the best results in the first attempt but might take two or three attempts, the time consumed till then would be too long. Please note that the variables are changing in each for loop iteration therefore the number of variables are 14. I request for some urgent help on this code:

function [Error] = opskinmodel(x)
Einf=x(1);
Es_cole(1)=x(2);
Es_cole(2)=x(3);
Es_cole(3)=x(4);
Es_cole(4)=x(5);
Tau(1)=x(6);
Tau(2)=x(7);
Tau(3)=x(8);
Tau(4)=x(9);
Cond=x(10);
alpha(1)=x(11);
alpha(2)=x(12);
alpha(3)=x(13);
alpha(4)=x(14);
freq=90e9; % Frequency Limit
Eo = 8.854e-12; % Permittivity of free space
g =1:1:(freq/1e9);
CondGabData=xlsread('tissueproperties(final).csv','C:C');% Conductivity from Gabriel's data

PermGabData=xlsread('tissueproperties(final).csv','D:D'); % Permitivity from Gabriel's data

       % Cole Cole ----------------------------------------------------------
  i=1;
  j=sqrt(-1);%imaginary iota
  m=1;
  Error=0; % Cost Function
  PDiff=0;
  CDiff=0;
      for f =1e9:1e9:(freq)

           tmp = 0; % temporary summation variable for higher order value addition

           for k=1:4
                   tmp = tmp + Es_cole(k) / (1 + (j * 2 * pi * (f) * Tau(k)))^(1-alpha(k)); % higher order summation

           end

           Er_relative(i) = Einf + tmp + Cond/(j * 2 * pi * (f) * Eo);% Complex relative permitivity
           Er(i)=real(Er_relative(i));% real part (e') relative permitivity
           Ei(i)=-imag(Er_relative(i));% imaginary part (e'') loss factor
           Conductivity(i)=Ei(i)*Eo*2*pi*f; % conductivity
           i=i+1;

      end
      %EVALUATION OF COST FUNCTION

     for f=1e9:1e9:freq;
          lossfactor(m)=CondGabData(m)/(Eo*2*pi*f); % (e'' or lossfactor of Gabriel's data)
          PDiff=PDiff+((PermGabData(m)-Er(m))/median(Er))^2;
          CDiff=CDiff+((CondGabData(m)-Conductivity(m))/median(Conductivity))^2;
          m=m+1;
     end     

      Error=(PDiff+CDiff)/length(g);

[Geoff Hayes]

Akbar - are you using the Genetic Algorithm from the Global Optimization Toolbox, or are you using a custom GA? What is your initial population size? How are you invoking the GA with the above optimization function?

Looking at your code, there are several optimizations that come to mind:

• Pre-size your arrays (i.e. Er_relative, Er, Ei, Conductivity)
• Remove unneeded calculations (i.e. lossfactor)
• Don't read from the Excel files on every call to this function. Since (presumably) these files are static (and so are not updated during the run of the GA) then persist the data from these files so that you only read once. See defining persistent variables for details.

Try implementing the above suggestions and see what happens.

[Akbar Raza]

Hi Geoff. Thanks for your reply. Well I am using the function handle in the optimization application of global optimization toolbox to initiate the optimization. I am simply using @opskinmodel and mention that I have 14 variables. The lower bounds are set to 0 while I am not setting the upper bounds. # of generations are set to 150 and function tolerance is 1e-8. These settings are giving me very slow results and since the posting of my previous message only 6 iterations have been possible. Please help in resolving this issue.

• Can you please elaborate on how to presize my arrays?
• Well I need lossfactor calculation for plotting purpose

[Akbar Raza]

Wow it actually worked!!! Now the problem is that my minimum isnt going below 0.445 using GA. No matter which value I change for optimization app, there is no change in error function minimized value. Its like the minimum value it can give is 0.44 and is the equivalent of zero. I have changed every parameter but the result just wont go below 0.44 even in the case of bounded or unbounded constraints. Please help as I am almost there. Do you think is there something wrong with my error function?

Answer 1

[Alan Weiss]

I think that the best thing to do is to not use ga, but instead use patternsearch, possibly starting from a variety of initial points. You will probably be surprised at the speed and robustness of patternsearch compared to ga.

The other thing to do to speed your code for either ga or patternsearch is NOT have a call to xlsread inside your objective function. Instead, call xlsread once OUTSIDE your objective function, and pass in any data to the objective function using MATLAB syntax.

Alan Weiss

MATLAB mathematical toolbox documentation

[Akbar Raza]

hi Alan. Thanks for replying. But dont you think that there might be some other reason for not going beyond 0.44. I used fmincon as well and several other algorithms in Optimization toolbox but in their case it wasnt going below value of 2. Please guys really need your help in finding the solution. The puzzling thing is that it is a stochastic algorithm but it always give the same minimization value. It is like 0.44 is a constant added to the final minimized solution.