Speeding up exhaustive search

Question

dimitris 2013-2-5

0
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https://ww2.mathworks.cn/matlabcentral/answers/62364-speeding-up-exhaustive-search

I need to find the global minimum of a function using exhaustive search. I have 10 function variables x1,x2,x3,...,x10 ∈ [0,10]. In order to produce all possible combinations of those function variables, i have written a code with 10 for loops and check their value.

Although this works, i would like to speed it up because it takes too much time to finish. Parfor can not help me here because the loops are not independent.

I would like some suggestions on how to speed up this code. Part of my code:

x=zeros(1,10); 
for x1=1:10
  x(1)=x(1)+step; %step=1 so at each iteration x(1)=1,2,3,...,10
  for x2=1:10
      if x(2)==10
          x(2)=0;
      end
      x(2)=x(2)+step;
   end
repeat for each variable
%evaluate f(x1,x2,x3,...,x10)
end

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Doug Hull 2013-2-5

Are X1, X2, etc constrained to be integers? It is not clear.

dimitris 2013-2-5

Firstly, thank you for replying.

About the subject, the idea is to reduce gradually the step, but first i must speed up my code, because for step=1 it takes too much time, imagine what will happen for step=0.1 or less. I have already used genetic algorithm from optimization toolbox but now i want to do this exhaustively.

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Answer 1

Alan Weiss 2013-2-5

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https://ww2.mathworks.cn/matlabcentral/answers/62364-speeding-up-exhaustive-search#answer_73915

If I understand you correctly, you have 11 possible values for each component, so are planning to execute 11^10 evaluations. That is an awful lot of computing.

Is it possible to vectorize your code? If so, you could evaluate, say, 11^5 points at once, return the values, and take the minimum. I mean, write your objective function as a function of a single vector x = (x(1),...,x(10), and evaluate it for all values of x(6),...,x(10) simultaneously. You would have to perform this evaluation only about 11^5 times, once for each possible value of x(1),...,x(5). For an example of what I mean, see this example of evaluating a vectorized function.

Good luck,

Alan Weiss

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