PSO CODE for more than one Equation

Hello! I have done the given problem 198x + 199y + 187z +201w = 200(aproximately equal or equal) Subject to, (x,y,z,w=[0 1].) through PSO(Particle Swarm Optimization)... the whole code for solving one such equation is given below.... next my problem is to solve multiple equation through PSO... Now I have to optimize it for obj_fun having multiple values to calculate. suppose

{   
          162x + 163y + 161z +164w = 163;
          155x + 157y + 157z +154w = 155;
          158x + 159y + 157z +156w = 157;
          201x + 200y + 203z +201w = 200;
          108x + 107y + 107z +109w = 107;.......           }
and so on .....suppose hunderds of such equations that i have to solve.. Code given below, is only for one equation... plz help me how to optimize the given code for multiple equations.... so the i could get the best particles for each equation.... 
Thanks in anticipatiion..........

 {%Initialization of PSO parameters
wmax=0.9;
wmin=0.4;
itmax=200; %Maximum iteration number
c1=1.4;
c2=1.4;

for iter=1:itmax
W(iter)=wmax-((wmax-wmin)/itmax)*iter;
end

%**********************************************************

%Initialization of positions of agents
%Initialize Swarm Particles
a=0;  
b=5;
N=20;
D=4;

abc(1:4,1)=0;
abc(1:4,2)=1;
lbound=abc(:,1);                             
ubound=abc(:,2); 

    for i=1:N                                       
      for j=1:D                                    
      x(i,j)=rand*(ubound(j)-lbound(j))+lbound(j);   
      end
  end

%Initialization of velocities of agents
%Between -5 , +5, (which can also be started from zero)

m=0;
n=1;
V=m+(n-m)*rand(N,D,1);

%**********************************************************
%Function to be minimized. 

for i=1:N;
F(i,1,1)=abs(200-((x(i,1,1)*198) + (x(i,2,1)*199) +(x(i,3,1)*187)+ (x(i,4,1)*201)));
end
%**********************************************************
[C,I]=min(abs(F(:,1,1)));

B(1,1,1)=C;
XX(1,1,1)=I;
gbest(1,1,1)=x(I,1,1);
gbest(1,2,1)=x(I,2,1);
gbest(1,3,1)=x(I,3,1);
gbest(1,4,1)=x(I,4,1);
%********************************************************
%Matrix composed of gbest vector 
for p=1:N
    for r=1:D  
    G(p,r,1)=gbest(1,r,1);
end
  end

Fbest(1,1,1)=abs(200-((G(1,1,1)*198) + (G(1,2,1)*199) +(G(1,3,1)*187)+ (G(1,4,1)*201)));
  for i=1:N;
       pbest(i,:,1)=x(i,:,1);
    end

V(:,:,2)=W(1)*V(:,:,1)+c1*rand*(pbest(:,:,1)-x(:,:,1))+c2*rand*(G(:,:,1)-x(:,:,1));

x(:,:,2)=x(:,:,1)+V(:,:,2);
Fb(1,1,1)=abs(200-((gbest(1,1,1)*198) + (gbest(1,2,1)*199) +(gbest(1,3,1)*187)+ (gbest(1,4,1)*201)));
%******************************************************
for j=2:itmax-1

% Calculation of new positions

for i=1:N;

      F(i,1,j)=abs(200-((x(i,1,j)*198) + (x(i,2,j)*199) +(x(i,3,j)*187)+ (x(i,4,j)*201)));
  end

[C,I]=min(abs(F(:,:,j)));

B(1,1,j)=C;

gbest(1,1,j)=x(I,1,j);
gbest(1,2,j)=x(I,2,j);
gbest(1,3,j)=x(I,3,j);
gbest(1,4,j)=x(I,4,j);

Fb(1,1,j)=abs(200-((gbest(1,1,j)*198) + (gbest(1,2,j)*199) +(gbest(1,3,j)*187)+ (gbest(1,4,j)*201)));
[C,I]=min(Fb(1,1,:));

if Fb(1,1,j)<=C
    gbest(1,1,j)=gbest(1,1,j);
    gbest(1,2,j)=gbest(1,2,j);
    gbest(1,3,j)=gbest(1,3,j);
    gbest(1,4,j)=gbest(1,4,j);
else
    gbest(1,1,j)=gbest(1,1,I);
    gbest(1,2,j)=gbest(1,2,I);
    gbest(1,3,j)=gbest(1,3,I);
    gbest(1,4,j)=gbest(1,4,I);
end

%Matrix composed of gbest vector 
for p=1:N
    for r=1:D  
    G(p,r,j)=gbest(1,r,j);
end
  end

Fbest(1,1,j)=abs(200-((G(1,1,j)*198) + (G(1,2,j)*199) +(G(1,3,j)*187)+ (G(1,4,j)*201)));

    for i=1:N;
        [C,I]=min(F(i,1,:));
      if F(i,1,j)<=C
         pbest(i,:,j)=x(i,:,j);
     else
          pbest(i,:,j)=x(i,:,I);
      end
  end

V(:,:,j+1)=W(j)*V(:,:,j)+c1*rand*(pbest(:,:,j)-x(:,:,j))+c2*rand*(G(:,:,j)-x(:,:,j));

x(:,:,j+1)=x(:,:,j)+V(:,:,j+1);

end

[Krishna Kumar]

What do you mean by PSO- particle swarm or something else. If you want a code, better use file exchange, and use Answers for clarifying your queries.

[Talat]

PSO(Particle Swarm Optimization)

[Krishna Kumar]

Get code in FEX, or if you know PSO make a code yourselves and post your difficulties here. You can get some PSO codes over Internet easily.

[Talat]

okay Thanks

Answer 1

[Krishna Kumar]

Well if you need help in framing the problem, try this: [x y z w] is the parameter vector. Your objective function could be Obj_fn= abs(200-(198x + 199y + 187z +201w)); Use a PSO to minimize it.

[Walter Roberson]

Some minimizers need the objective function to be differentiable, so it is usually better to use p^2 instead of abs(p) -- i.e.,

(200-(198*x + 199*y + 187*z +201*w)).^2

[Krishna Kumar]

Of course, but PSO is not a gradient based algorithm and does not need differentiability.

[Talat]

Thanks alot, both of you guys.........

[Talat]

Hello Krishna!

I did for single equation, now i have to optimize it for multiple equation... i am not getting how to generalize this code for multiple equations.... plz help me in solving this

thanks

[Krishna Kumar]

I dont get you clearly. If you need separate solutions for each equation, you have to run it so many times.

Or if you need a single solution for all the eqns (which i think is not your case), you can do like this-

obj_fn=abs(200-(198x + 199y + 187z +201w));

this way you find the error for each equation.Since the values in all equations are in the same range, you can simply add the errors and keep that as objective function.

There are many other methods too, I think this would suffice.