Genetic Algorithm and Direct Search Toolbox

Vectorize Option

The genetic algorithm usually runs faster if you vectorize the fitness function. This means that the genetic algorithm only calls the fitness function once, but expects the fitness function to compute the fitness for all individuals in the current population at once. To vectorize the fitness function,

• Write the M-file that computes the function so that it accepts a matrix with arbitrarily many rows, corresponding to the individuals in the population. For example, to vectorize the function

• write the M-file using the following code:

  • z =x(:,1).^2 - 2*x(:,1).*x(:,2) + 6*x(:,1) + x(:,2).^2 - 6*x(:,2);
    

  The colon in the first entry of x indicates all the rows of x, so that x(:, 1) is a vector. The .^ and .* operators perform element-wise operations on the vectors.

• Set the Vectorize option to On.

Note    The fitness function must accept an arbitrary number of rows to use the Vectorize option.

The following comparison, run at the command line, shows the improvement in speed with Vectorize set to On.

• tic;ga(@rastriginsfcn,20);toc
  
  elapsed_time =
  
      4.3660
  options=gaoptimset('Vectorize','on');
  tic;ga(@rastriginsfcn,20,options);toc
  
  elapsed_time =
  
      0.5810
  

Using a Hybrid Function

Using Direct Search

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