How can we reduce the execution time of this whole code?

I want to minimize the "execution time" of the code given in the attachment. You can run the m file "main".

[Dyuman Joshi]

In myfunction, Why are you pre-allocating an empty matrix?

K = length(u); %Constant4
c=zeros(M*N, length(u)-K);
ce=zeros(M*N, length(u)-K);

%Modify it as
c=zeros(M*N,K);
ce=zeros(M*N,K);

And club the two for loop together -

for g= 1:K
c(:,g)=kron(a(:,g),f(:,g)); 
end

for g= 1:K
    ce(:,g)=kron(ae(:,g),fe(:,g));
end

into

for g = i %i is already defined in the code
    c(:,g)=kron(a(:,g),f(:,g));
    ce(:,g)=kron(ae(:,g),fe(:,g));
end

Additionally, pre-allocate Sol and Fitness in fp1

After these changes, the code runs in 2.5674 secs in i3-5th gen, 8gb RAM, which imo is fast enough.

[Sadiq Akbar]

Thanks a lot dear Dyuman Joshi for your kind response. In myfunction, the pre-allocation of an empty matrix speeds upt the process? With this its time is reduced and without this, it take more time. Yes, you are right, the two for-loop can br clubbed togather. But how to pre-allocate Sol and Fitness in fp1?

Answer 1

[Dyuman Joshi]

I am aware that pre-allocation speeds up the process, but pre-allocating an empty matrix doesn't reserve any memory for the operation and it is slower than pre-allocating with a zeros matrix. See below -

Modify the pre-allocation as I have suggested above.

v=1e6;
y=zeros(v,0);
z=zeros(v,1);
whos y z

  Name            Size              Bytes  Class     Attributes

  y         1000000x0                   0  double              
  z         1000000x1             8000000  double              

tic
for ix=1:v
    y(ix)=i;
end
toc

Elapsed time is 0.151647 seconds.

tic
for ix=1:v
    z(ix)=i;
end
toc

Elapsed time is 0.025546 seconds.

"But how to pre-allocate Sol and Fitness in fp1?"

It's clear from the code

%for i=1:psize
%    Sol(i,:)=Lb+(Ub-Lb).*rand(1,d);
%    Fitness(i)=fun(Sol(i,:));%--------------------(1)  
%end

Fitness has psize elements, so size is (1xpsize, as the output of the function myfunction is a scalar value)

and Sol has psize rows and d columns.

Pre-allocate zero matrices accordingly.

[Sadiq Akbar]

Thanks a lot dear Dyuman Joshi for your kind response. I checked the time in both the cases i.e., without preallocation by commenting these lines:

a=zeros(M,K);
f=zeros(N,K);
c=zeros(M*N, K);
ae=zeros(M,K);
fe=zeros(N,K);
ce=zeros(M*N, K);

and with pre-allocation i.e., uncommenting the above lines again. I found that the time with pre-allocation is lower than without preo-allocation. You can do it your self. Further, I did preallocation inside fpa1 as below:

Sol=zeros(n,dim);
Fitness=zeros(N_iter,1);

But it was giving error. Then I did the changes as below:

Sol=zeros(n+1,dim);
Fitness=zeros(N_iter,1);

then it ran but all the fitness and solutions were 0s which is not possible. So if you do it for me, it will be nice of you. Regards,

[Dyuman Joshi]

"I found that the time with pre-allocation is lower than without pre-allocation."

I am well aware of this. But that was not my point.

Nevertheless, what you have done now is better than what you did before.

How did you arrive at n+1 and N_iter?

Ugh. I specifically mentioned what to use for pre-allocation of Sol and Fitness -

"Fitness has psize elements, so size is (1xpsize, as the output of the function myfunction is a scalar value)

and Sol has psize rows and d columns.

Pre-allocate zero matrices accordingly. "

Use this -

Sol=zeros(psize,dim);
Fitness=zeros(psize,1);

[Sadiq Akbar]

Thanks a lot dear Dyuman Joshi for your kind response. Indeed now it works. But still the time is not reduced so much. Can you convert the for-loops inside fpa1 to vectorized form because this may redue the time?