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| <document url="genetics.html"> |
| <properties> |
| <title>The Commons Math User Guide - Genetic Algorithms</title> |
| </properties> |
| <body> |
| <section name="16 Genetic Algorithms"> |
| <subsection name="16.1 Overview" href="overview"> |
| <p> |
| The genetics package provides a framework and implementations for |
| genetic algorithms. |
| </p> |
| </subsection> |
| <subsection name="16.2 GA Framework"> |
| <p> |
| <a href="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/genetics/GeneticAlgorithm.html"> |
| GeneticAlgorithm</a> provides an execution framework for Genetic Algorithms (GA). |
| <a href="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/genetics/Population.html"> |
| Populations,</a> consisting of <a href="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/genetics/Chromosome.html"> |
| Chromosomes</a> are evolved by the <code>GeneticAlgorithm</code> until a |
| <a href="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/genetics/StoppingCondition.html"> |
| StoppingCondition</a> is reached. Evolution is determined by <a href="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/genetics/SelectionPolicy.html"> |
| SelectionPolicy</a>, <a href="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/genetics/MutationPolicy.html"> |
| MutationPolicy</a> and <a href="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/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="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/genetics/GeneticAlgorithm.html#getCrossoverRate()"> |
| getCrossoverRate()</a>, apply configured <code>CrossoverPolicy</code> to parents</li> |
| <li>With probability = |
| <a href="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/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="16.3 Implementation"> |
| <p> |
| Here is an example GA execution: |
| <source> |
| // initialize a new genetic algorithm |
| GeneticAlgorithm ga = new GeneticAlgorithm( |
| new OnePointCrossover<Integer>(), |
| 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="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/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="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/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="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/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="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/genetics/StoppingCondition.html">StoppingCondition</a> |
| is reached. In the example above, a |
| <a href="../commons-math-docs/apidocs/org/apache/commons/math4/legacy/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> |
