genetic algorithm simple problem

Hello ,

I have a simple problem to solve with the genetic algorithm in matlab

The fitness function is

that subject to

My question is how to apply these in matlab ga function?

[Mark Sherstan]

Look at this example here and then let us know if there is still need for clarification.

[Phoenix98]

Hi , I read it

but how to set the bounds lb and ub according to my problem?

below is the code with the fitness function

function y = fitness(x)
  y = (3*x(1) + x(2) - 2*x(3)+0.8 \ 2*x(1)-x(2)+x(3)) + (4*x(1) -2*x(2)+x(3) \ 7*x(1)+3*x(2)-x(3));
  
  
  % The main program
  
rng default
FitnessFunction = @fitness;
numberOfVariables = 3;
lb = [-1,-1];
ub = [0,0];
[x,fval] = ga(FitnessFunction,numberOfVariables,[],[],[],[],lb,ub);

Answer 1

[Walter Roberson]

The item says 0 <= xi, i = 1, 2, 3. Therefore the entries are nonnegative. lb would be [0 0 0]. ub can be left empty or can be set to [inf inf inf]

[Phoenix98]

Hi,

i tried these values and the f(x) in the solution equal to 2.471428 with x1=1,x2=0,x3=0 not equal to the matlab solution -2.190310

[Walter Roberson]

So? You are using ga and ga only tries to find a global minima.

Besides, you are not implementing the formula you were given. In MATLAB,

 (3*x(1) + x(2) - 2*x(3)+0.8 \ 2*x(1)-x(2)+x(3))

is the same as

 ((3*x(1)) + x(2) - (2*x(3)) + ((0.8 \ 2) * x(1)) - x(2) + x(3))

which is the same as

  ((3*x(1)) + x(2) - (2*x(3)) + ((0.8 / 2) * x(1)) - x(2) + x(3))

The form

  first sequence \ second sequence
  

is not the same as

  (first sequence) / (second sequence)