For loop Nested Loop

I just want to solve the problem by using the brute force method. Here is the pseudo code:

for i=1:11
  for j=1:11
    for k=1:11
   .
   .
   .
       Variable=[i j k l m n o p q r s t];
       Result=func_A(Variable);
    end 
  end
end

There are 12 variables and each variable is greater than or equal to one and less than or equal to

11(1<=x<=11). Each integer combination will have a result value.

I want to get the maximum of func_A.

I have been trying to solve by this way:

b=[11:-1:0];
c=11.^b;

for k=0:11.^12-1

    d=floor(k./c);

    a=mod(d,11)+1;

    result=func_A(a);

end

but here is the error message from matlab

FOR loop index is too large. Truncating to 2147483647.

Does there have a clever way to speed up the for loop???

Answer 1

[Teja Muppirala]

Why do you want to do this by brute force? You will have to test 12^11 combinations, which is quite a lot. I don't know what your func_A is, but even if it only takes 1 microsecond to do one evaluation, testing all possible combinations will take at least 12^11 * 1e-6 / 3600 / 24 = 8.5 days (assuming no parallel processing).

Why not try a more practical optimization method, such as Genetic Algorithm?

[Teja Muppirala]

Oops, that should have been 11^12, not 12^11. But even still, that just makes the situation even worse. You will have over 3 trillion combinations to test.

[ben]

Hi Teja

Thank you for giving the comment. I've been tried the ga function but what my goal is to get the optimal maximum of func_A . It seems the ga function can't guarantee to get the optimal solution.

[Jan]

11^12 / (86400 * 365 * 1000). This means that a brute search will consume 99 years, if you can check 1000 vectors per second. So if you really need the guaranteed optimal solution, you need some time. A parallelization is possible: If you can run this on 100 computers with 4 cores, the result will be found in some month.

Answer 2

[Walter Roberson]

Change your line

for k=0:11.^12-1

to

for k = uint64(0) : uint64(11) .^ 12 - uint64(1)

[Walter Roberson]

For an alternate code formulation that might be clearer (but not necessarily any faster), see http://www.mathworks.co.uk/matlabcentral/answers/29662-generate-points-sorted-by-distance#comment_63935

What are the characteristics of the function you are trying to maximize? It could be that by knowing something about the function, optimizations could be made.

Also, could the function be rewritten to be vectorized to some degree? The overhead of calling the function each time will add up to quite a lot. Could it perhaps be vectorized a fair bit? If so then usually maximum speed would be from vectorizing as much as will fit into memory at a time.