This repository implements a very simple genetic algorithm for real valued optimization. The code is tested on Maple 18.

• Mean crossover
• Add small random vector for mutation
• Tournament selection
• Remove worst survivor selection

The function arguments are defined as

GA := proc(cost, Dimension, bd_min, bd_max, Npop:=10,  Nchildren:=5, mutation_prob:=.6, epsilon:=1e-6, verbose:=false)

• cost : A function which computes the cost value.
• Dimension : The number of cost function arguments.
• bd_min, bd_max : The minimum and maximum values of each dimension.
• Npop : Size of the population.
• Nchildren : How many children should be generated at each iteration
• mutation_prob : The probability of mutation.
• epsilon : The threshold for early stopping. the evolution will stop after 20 epochs if the cost change is smaller than epsilon .
• verbose : whether to print the evolution or not.

• Copy GeneticAlgorithm.mpl file beside your script.

• Copy this to the first line of your script, possibly after restart; statement. This code tested on Linux operating system and Maple 18, may need some change on Windows operating system and older Maple versions.

  read sprintf("%s/%s", interface(worksheetdir), "GeneticAlgorithm.mpl");
  

• Now you can import the GeneticAlgorithm package using

  with(GeneticAlgorithm);
  

• Define the cost function:

  cost := proc (x)
      return add(i^2, i in x);
  end proc
  

• The parameters

  minbd, maxbd := -5, 5;
  Dimension := 5;
  Npop := 30;
  Niteration := 1000;
  mutation_prob := 0.09;
  Nchildren := 15;
  epsilon := 1e-15;
  verbose := true;
  

• Call the GA optimizer

  result := GA(cost, Dimension, minbd, maxbd, Npop, Nchildren, mutation_prob, epsilon, verbose):
  best, hist := result[1], result[2]:
  

• Result

  iteratin 0001, cost=8.82e-01
  iteratin 0020, cost=8.67e-06
  iteratin 0040, cost=5.71e-07
  iteratin 0060, cost=1.81e-07
  iteratin 0080, cost=9.39e-09
  iteratin 0100, cost=4.70e-10
  iteratin 0120, cost=1.30e-11
  iteratin 0140, cost=3.55e-15
  iteratin 0160, cost=2.80e-19
  iteratin 0162, cost=1.35e-19