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<document url="genetics.html">
  <properties>
    <title>The Commons Math User Guide - Genetic Algorithms</title>
  </properties>
  <body>
    <section name="14 Genetic Algorithms">
      <subsection name="14.1 Overview" href="overview">
        <p>
          The genetics package provides a framework and implementations for 
          genetic algorithms.
        </p>
      </subsection>
      <subsection name="14.2 GA Framework">
      <p>
      <a href="../apidocs/org/apache/commons/math/genetics/GeneticAlgorithm.html">
      GeneticAlgorithm</a> provides an execution framework for Genetic Algorithms (GA).  
      <a href="../apidocs/org/apache/commons/math/genetics/Population.html">
      Populations,</a> consisting of <a href="../apidocs/org/apache/commons/math/genetics/Chromosome.html">
      Chromosomes</a> are evolved by the <code>GeneticAlgorithm</code> until a 
      <a href="../apidocs/org/apache/commons/math/genetics/StoppingCondition.html">
      StoppingCondition</a> is reached. Evolution is determined by <a href="../apidocs/org/apache/commons/math/genetics/SelectionPolicy.html">
      SelectionPolicy</a>, <a href="../apidocs/org/apache/commons/math/genetics/MutationPolicy.html">
      MutationPolicy</a> and <a href="../apidocs/org/apache/commons/math/genetics/Fitness.html">
      Fitness</a>.
      </p>
      <p>
      The GA itself is implemented by the <code>evolve</code> method of the
      <code>GeneticAlgorithm</code> class,
      which looks like this:
      <source>public Population evolve(Population initial, StoppingCondition condition) {
    Population current = initial;
    while (!condition.isSatisfied(current)) {
        current = nextGeneration(current);
    }
    return current;
}
          </source>
          The <code>nextGeneration</code> method implements the following algorithm:
          <ol>
          <li>Get nextGeneration population to fill from <code>current</code>
             generation, using its nextGeneration method</li>
          <li>Loop until new generation is filled:</li>
          <ul><li>Apply configured <code>SelectionPolicy</code> to select a pair of parents
                 from <code>current</code></li>
             <li>With probability = 
                 <a href="../apidocs/org/apache/commons/math/genetics/GeneticAlgorithm.html#getCrossoverRate()">
                 getCrossoverRate()</a>, apply configured <code>CrossoverPolicy</code> to parents</li>
             <li>With probability = 
                 <a href="../apidocs/org/apache/commons/math/genetics/GeneticAlgorithm.html#getMutationRate()">
                 getMutationRate()</a>,
                 apply configured <code>MutationPolicy</code> to each of the offspring</li>
             <li>Add offspring individually to nextGeneration,
                 space permitting</li>
          </ul>
          <li>Return nextGeneration</li>
         </ol>  
      </p>
      </subsection>
      <subsection name="14.3 Implementation">
      <p>
      Here is an example GA execution:
      <source>
// initialize a new genetic algorithm
GeneticAlgorithm ga = new GeneticAlgorithm(
    new OnePointCrossover&lt;Integer&gt;(),
    1,
    new RandomKeyMutation(),
    0.10,
    new TournamentSelection(TOURNAMENT_ARITY)
);
        
// initial population
Population initial = getInitialPopulation();
        
// stopping condition
StoppingCondition stopCond = new FixedGenerationCount(NUM_GENERATIONS);
        
// run the algorithm
Population finalPopulation = ga.evolve(initial, stopCond);
        
// best chromosome from the final population
Chromosome bestFinal = finalPopulation.getFittestChromosome();
        </source>
        The arguments to the <code>GeneticAlgorithm</code> constructor above are: <br/>
        <table>
        <tr><th>Parameter</th><th>value in example</th><th>meaning</th></tr>
        <tr><td>crossoverPolicy</td>
        <td><a href="../apidocs/org/apache/commons/math/genetics/OnePointCrossover.html">OnePointCrossover</a></td>
        <td>A random crossover point is selected and the first part from each parent is copied to the corresponding
        child, and the second parts are copied crosswise.</td></tr>
        <tr><td>crossoverRate</td>
        <td>1</td>
        <td>Always apply crossover</td></tr>
        <tr><td>mutationPolicy</td>
        <td><a href="../apidocs/org/apache/commons/math/genetics/RandomKeyMutation.html">RandomKeyMutation</a></td>
        <td>Changes a randomly chosen element of the array representation to a random value uniformly distributed in [0,1].</td></tr>
        <tr><td>mutationRate</td>
        <td>.1</td>
        <td>Apply mutation with probability 0.1 - that is, 10% of the time.</td></tr>
        <tr><td>selectionPolicy</td>
        <td><a href="../apidocs/org/apache/commons/math/genetics/TournamentSelection.html">TournamentSelection</a></td>
        <td>Each of the two selected chromosomes is selected based on an n-ary tournament -- this is done by drawing
        n random chromosomes without replacement from the population, and then selecting the fittest chromosome among them.</td></tr>
        </table><br/>
        The algorithm starts with an <code>initial</code> population of <code>Chromosomes.</code> and executes until 
        the specified <a href="../apidocs/org/apache/commons/math/genetics/StoppingCondition.html">StoppingCondition</a>
        is reached.  In the example above, a
        <a href="../apidocs/org/apache/commons/math/genetics/FixedGenerationCount.html">FixedGenerationCount</a>
        stopping condition is used, which means the algorithm proceeds through a fixed number of generations.
      </p>
      </subsection>
    </section>
  </body>
</document>
