GA code for optimizing three parameters with different interval limit

I'm trying to make a GA code for welding optimization with three parameters, each parameter has a different interval limit. Need guidance here...

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My parameters:

current: 80 - 100 ampere => x(1)

voltage: 80 - 90 volt => x(2)

weld time: 13 - 15 second => x(3)

since this is my first time using GA, I'm a little bit confused how to do it. In my code, I represent my parameters as a variable of a fitness function. Not sure if this is right.

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My fitness function:

function y = weldingfcn {x(1),x(2),x(3)}
     for x(1)=80:100
         for x(2)=80:90
             for x(3)=13:15
                 y = -(1-0.01)*{(x(1)-5)^2+(x(2)-5)^2+(x(3)-5)^2};
             end
         end
     end

============================================================================

My function for initializing population:

%popsize = population size
%stringlength = number of bits that represent individual
%dimension = number of variable

 function pop = encoding(popsize,stringlength,dimension)
          pop = round(rand(popsize,dimension*stringlength+1));

===========================================================================

My function for decoding population binary number to decimal number:

function pop=decoding(pop,stringlength,dimension,x_bound)
popsize=size(pop,1);
temp=2.^(stringlength-1:-1:0)/(2^stringlength-1);

      for i=1:dimension
          bound(i)=x_bound(i,2)-x_bound(i,1);
      end

      for i=1:popsize
          for j=1:dimension
             m(:,j)=pop(i,stringlength*(j-1)+1:stringlength*j);
          end
      x=temp*m;
      x=x.*bound+x_bound(:,1)';
      pop(i,dimension*stringlength+1)=funname(x);
      end

========================================================================

Function for selection procedure:

function selected  = selection(pop,popsize,stringlength,dimension)
       popsize_new = size(pop,1);

r=rand(1,popsize);
fitness=pop(:,dimension*stringlength+1);
fitness=fitness/sum(fitness);
fitness=cumsum(fitness);

for i=1:popsize
   for j=1:popsize_new
       if r(i)<=fitness(j)
         selected(i,:)=pop(j,:);
       break;
      end
   end
 end

============================================================================

Function for crossover procedure:

 function new_pop = cross_over(pop,popsize,stringlength,dimension)
         match   = round(rand(1,popsize)*(popsize-1))+1;

 for i = 1:popsize
 [child1,child2] = cross_running(pop(i,:),pop(match(i),:),stringlength,dimension);
 new_pop(2*i-1:2*i,:)= [child1;child2];
 end

function [child1,child2] = cross_running(parent1,parent2,stringlength,dimension)
       cpoint          = round((stringlength-1)*rand(1,dimension))+1;

 for j=1:dimension
 child1((j-1)*stringlength+1:j*stringlength)=[parent1((j-1)*stringlength+1: (j-1)*stringlength+cpoint(j))
 parent2((j-1)*stringlength+cpoint(j)+1:j*stringlength)];
 child2((j-1)*stringlength+1:j*stringlength)=[parent2((j-1)*stringlength+1: (j-1)*stringlength+cpoint(j))
 parent1((j-1)*stringlength+cpoint(j)+1:j*stringlength)];
 end

===========================================================================

Function for mutation procedure:

 function new_pop     = mutation(new_pop,stringlength,dimension,pm)
         new_popsize = size(new_pop,1);

 for i=1:new_popsize
    if rand<pm mpoint=round(rand(1,dimension)*(stringlength-1))+1;
        for j=1:dimension
            new_pop(i,(j-1)*stringlength+mpoint(j))=1-new_pop(i,(j-1)*stringlength+mpoint(j));
        end
    end
 end

===========================================================================

Function for starting the GA:

 %GA parameter

 popsize=10;                     %population size
 dimension=3;                    %number of variables
 stringlength=8;                 %length of binary number
 x_bound=[80,100;80,90;13,15];   %x limit interval [lb,ub]
                                %where: lb = lower bound
                                %       ub = upper bound
 pm=0.05;                        %mutation probability

 %Genetic Algorithm

 pop=encoding_guo(popsize,stringlength,dimension);
 pop=decoding_guo(pop,stringlength,dimension,x_bound);
 [choice_number,choice_k]=max(pop(:,stringlength*dimension+1));
 choice=pop(choice_k,:);

 for i=1:1000 new_pop=cross_over(pop,popsize,stringlength,dimension);
    pop=mutation_guo(new_pop,stringlength,dimension,pm);
    pop=decoding_guo(pop,stringlength,dimension,x_bound);
    [number,k]=max(pop(:,stringlength*dimension+1));
        if choice_number<number
           choice_number=number;
           choice_k=k;
           choice=pop(choice_k,:);
        end
     pop=selection_guo(pop,popsize,stringlength,dimension);
    [number,m]=min(pop(:,stringlength*dimension+1));
    pop(m,:)=choice;
 end

 [value,x]=result_guo(pop,stringlength,dimension,x_bound);

============================================================================

Function for displaying the result:

 function [value,x] = result_guo(pop,stringlength,dimension,x_bound)
         [value,x] = max(pop(:,stringlength*dimension+1));

 temp=2.^(stringlength-1:-1:0)/(2^stringlength-1);

for i=1:dimension
  bound(i)=x_bound(i,2)-x_bound(i,1);
end

============================================================================

When i run the GA, an error showing up. after i fixed it, another comes up. It's always error. Someone please guide me. Thank you for your concern =)

Answer 1

[Alan Weiss]

I'm sorry you are having trouble. it seems to me that you need to slow down, and learn the correct syntax for the various things you are trying to do. Please take some time to read the documentation.

For example, here is how you write a fitness function. It should be a function of one vector x, not a cell array of {x1,x2,x3}.

Are you using "bitstring" population type? If so, did you set your options to indicate that? Did you know that "bitstring" population is not a string at all, despite the misleading name? Here is some recent documentation about various population types.

Are you sure that you need custom crossover and mutation functions? Why not start with built-in ones? But perhaps you are using a custom population type.

There are a few examples that might help you:

<http://www.mathworks.com/help/gads/examples/solving-a-mixed-integer-engineering-design-problem-using-the-genetic-algorithm.html>

<http://www.mathworks.com/help/gads/examples/custom-data-type-optimization-using-the-genetic-algorithm.html>

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[ARNAB]

what is the meaning of rep([-0.1;0.1],[1,13])