Vectorization of block consecutive matrixes in a matrix (M = [N(1);N(2)....;N(n)])

Hello,

I want to vectorize the following code, but I do not know if this is possible. I have a list with solutions called 'pop'. A solution is a 1x48 vector called 'x'. This 'x' contains indexes to another matrix. Based on this matrix, a fitness value is calculated (f(x)).

At the moment my code looks like the following:

for i = 1:size(pop,1)
    x = pop(i,:);
    Tt = N(x(:),3:11)';   %Always a [9x48 matrix]
    f1 = something using Tt(:,1:6)
    f2 = something using Tt(:,1:12)
    etc.
    Nf = [f1,f2,f3,f4,f5,f6,f7,f8];
    f = somefunction(Nf);
end

It is possible to translate the list pop to a matrix [Tt(1);Tt(2);...;Tt(end)] where every 9 rows defines a solution, however due to the calculation of f1,f2 etc, a for loop is still required I think.

Because this is the fitness function of a GA, the speed will greatly improve if it uses vectorization. Is it possible to adapt this code so that it can use vectorization or is it impossible in this case?

With kind regards,

Paul

[Stephen23]

So pop is a "list" of solutions. MATLAB does not actually have any data type called a "list", but it does have numeric arrays, cell arrays and structures, all of which could be accessed using the indexing found in your code. But the code does not really make much sense without knowing much more information than what you have given us. Here are some bits that require explanation:

• The line x = pop(i) will extract exactly one element from the variable pop, which makes code on the next line x(:) a bit strange: if there is only one value then it is already a column vector (with one element).
• What is N? Is this a function or an array?
• The variable Tt is defined, but not used. Why?
• Is NF supposed to be the same as Nf?
• What is someFunction? How is it defined?
• The code size(pop(:,1),1) is too complicated: just use size(pop,1) instead.

To give advice on vectorization you need to give us a lots more information on these functions and variables. The easiest solution would be to simply create a comment below this one, clicking the paperclip button and then both Choose file and Attach file.

[Paul]

Hey Stephen, thank you for your fast reaction.

I added the code as an attachement (xtest is an example solution) and removed the errors from the question. A bit more explanation: A solution 'x' is an 1x48 matrix containing indices to a matrix N. Each row in N defines a batch choice of products, where the columns 3:11 of N contain information about the amount of a product produced for a batch (column 3 = product 1, column 4 = product 2 etc), shown below:

    N = [BatchID, na, Product 1, Product 2,..., Product 9,na,...;
               1, na,       100,         0,...,       220,na,...;
               2, na,         0,       340,...,         0,na,...;
               ...                                           
           30000, na,        80,         0,...,       120,na,...];

Therefore, the command N(x(:),3:11)' creates a 9x48 matrix where each column(n) corresponds with a batch choice and the rows with the amount of products produced by that choice, which would look like the following:

     Tt= [Batch index: 200,215,400,...,315;
          Product 1  :  0 , 50, 80,..., 40;
          Product 2  : 100,  0, 20,...,  0;
          ...
          Product 9  :  80, 20,  0,..., 20];

Every 6 columns corresponds to the production of one week and I need to know the total production of each week, where excessive products are added to the next week (the f1 and f2 define 9x1 vectors containing information about each product produced in that week in percentages). By combining all weeks (Nf = [f1,f2,f3,f4,f5,f6,f7,f8];) a matrix is created containing the production of products per week, which looks like:

    Nf = [week nr  :   1,   2, ...,   8;
          Product 1:   1, 0.5, ..., 0.7;
          Product 2: 0.9,   1, ...,   1;
          ...
          Product 9: 0.8, 0.7, ..., 0.9];

someFunction(Nf) is defined as:

    V = exp(-Nf*5).*1000;    % Penalty for % product order not completed

   f = sum(sum(V));   % Nf translated to a fitness value

Using these steps, for every x in pop a fitness f is calculated, however a for-loop is used to loop through pop, however this seems unnecessary.

With kind regards,

Paul

Ps. The solution of this attached files will be very bad, normally the string 'x' is 1x240, containing other batches that will introduce product types that are missing in 'xtest.mat'

[Stephen23]

I downloaded your files and started to make some simplifications and improvements. Then I noticed that the functions are incomplete: the variables N_totalProduction and thisPopulation are not defined, and yet are critical to understanding how to vectorize this code.

[Paul]

Hey Stephen,

I changed the code a bit to include a population and create a vector output. The original code is a customization from the matlab GA toolbox, however the input will be a matrix as pop.mat. The file called N is the matrix N_totalProduction. You dont need to make any adjustments. If everything is saved in the same folder, just run Fitness_sol_expl(pop) (when pop is loaded to workspace).

Thanks for the help!

[Stephen23]

As far as I can tell your original question is about vectorization of a for loop, which although in the question above it starts with for i = 1:size(pop,1) in the code it seems to correlate to %for a = 1:size(thisPopulation,1). Note that in your sample code this line (i.e. the loop itself) is commented-out and that you do not define thisPopulation. Nor do you use the loop variable a, which is only referred to on one line: % A_penalty(a) = penalty; (also commented out).

You state that I "dont need to make any adjustments", in which case the code certainly runs without error and without this for loop. If you do not need the loop then what is your question about? If you do want this loop (or the vectorized equivalent) then how is thisPopulation defined? Or was the loop never actually working?

In any case some observations about your code:

• you only refer to a once inside the loop, so everything before that point can be moved out of the for-loop.
• stop reassigning variables unnecessarily: it just wastes memory and slows things down for no reason. Just stick with one copy of each variable.
• Instead of defining lots of separate variables and then concatenating them together just define these values directly as a row/column of a matrix.
• The loop for i=1:Horizon can probably be vectorized quite easily.

Here is the version that I started to write:

[Paul]

Hey Stephen,

You probably used the old m.file that I attached, however the current m-file is slightly different, because it uses a matrix instead of a vector as input ( function [ V_fit ] = Fitness_sol_expl( pop ) instead of function [ scores ] = Fitness_sol_expl( x ) ). The 3 files newly attached should work properly together.

The question is indeed about vectorizing the for i = 1:size(pop,1) loop ( in the m-file the a = 1:size(pop,1) loop).

The matlab GA toolbox has 2 options for a fitness function, i.e:

1. serial, in which it runs the fitness function in serial for each candidate solution 'x' (where x = pop(a,:), thus the for-loop is performed by the GA toolbox somewhere else). This results in a fitnessfunction that looks like function [value] = Fitness_sol_expl(single_solution such as x) resulting in a single fitness value.

2. Vectorized, in which the fitness of the entire population (called pop ), is calculated in a vectorized way. This results in a fitness function as function [V_fit] = Fitness_sol_expl( pop ), where V_fit is a vector containing the fitness of the entire population (a size(pop,1)x1 vector).

In the new m-file called looped_Fitness_sol the for-loop is operational when the matrix pop is loaded into the workspace (by typing looped_Fitness_sol(pop)). I would like to vectorize the loop a = 1:size(pop,1)

I hope this clears things up, thanks for your help.