Simulated Binary Crossover for Continuous Search Space

I work on a very little research team to create/adapt a Genetic Algorithm library in Scala for distributed computation with Scientific Worklow System, in our case we use the open source OpenMole software (http://www.openmole.org/).

Recently, i try to understand and re-implement the SBX crossover operator written in JMetal Metaheuristics library (http://jmetal.sourceforge.net/) to adapt it in functionnal version in our Scala library.

I write some code, but i need our advice or your validation about the SBX defined into java library, because the source code (src in svn) doesn't appear equal to the original equation written here : http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.7291&rep=rep1&type=pdf at page 30, in annexe A

First question, i don't understand the java version of JMetal, why they use two different beta values ?!

• beta1 which use in the equation the first arg of min[(y1 - yL), ...] and
• beta2 which use the second arg of min [... , (yu - y2)])

Beta 1 and 2 are used for computation of alpha value and two (so here and in jmetal we have also two alpha different value alpha1 and 2) ...

Same problem/question, we have in jmetal two computation for betaq (java code) or in Deb equation, result of :

Second question, what is the meaning of the symbol used in (2) and (3) procedure in pseudo-algorithm of SBX, and the difference with simple beta ? Especially when we want to compute children/offsprings of crossover parents, like here :

Edit

• Correct a no-op if/else block

• Author of code in jmetal give me the link of original source code of Nsga-II algorithm, and he explain me that description of SBX by Deb differs from his implementation :/

  http://www.iitk.ac.in/kangal/codes.shtml

  I don't understand the difference between the description and the implementation in jmetal and original source code, do you have an explanation ?

• Correct if/else return for map

Start of translation into scala

                      class SBXBoundedCrossover[G <: GAGenome, F <: GAGenomeFactory[G]](rate: Random => Double = _.nextDouble) extends CrossOver [G, F] {    def this(rate: Double) = this( _ => rate)    def crossOver (genomes : IndexedSeq [G], factory: F) (implicit aprng : Random) = {     val g1 = genomes.random     val g2 = genomes.random     val crossoverRate = rate(aprng)     val EPS =  1.0e-14     val numberOfVariables = g1.wrappedValues.size     val distributionIndex = 2      val variableToMutate = (0 until g1.wrappedValues.size).map{x => !(aprng.nextDouble < 0.5)}      //crossover probability     val offspring = {        if (aprng.nextDouble < crossoverRate) {               (variableToMutate zip (g1.wrappedValues zip g2.wrappedValues)) map {           case (b, (g1e, g2e)) =>             if(b) {               if (abs(g1e - g2e) > EPS){                  val y1 = min(g1e, g2e)                 val y2 = max(g2e, g1e)                  var yL = 0.0 //g1e.getLowerBound                 var yu = 1.0 //g1e.getUpperBound                   var rand = aprng.nextDouble   // ui                  var beta1 = 1.0 + (2.0 * (y1 - yL)/(y2 - y1))                 var alpha1 = 2.0 - pow(beta1,-(distributionIndex+1.0))                 var betaq1 = computebetaQ(alpha1,distributionIndex,rand)                  //calcul offspring 1 en utilisant betaq1, correspond au β barre                 var c1 = 0.5 * ((y1 + y2) - betaq1 * (y2 - y1))                   // -----------------------------------------------                  var beta2 = 1.0 + (2.0 * (yu - y2) / (y2 - y1))                 var alpha2 = 2.0 - pow(beta2, -(distributionIndex + 1.0))                  var betaq2 = computebetaQ(alpha2,distributionIndex,rand)                  //calcul offspring2 en utilisant betaq2                 var c2 = 0.5 * ((y1 + y2) + betaq2 * (y2 - y1))                  if (c1 < yL) c1 = yL                 if (c1 > yu) c1 = yu                  if (c2 < yL) c2 = yL                 if (c2 > yu) c2 = yu                     if (aprng.nextDouble <= 0.5) {                   (c2,c1)                 } else {                   (c1, c2)                  }                }else{                 (g1e, g2e)               }              }else{               (g2e, g1e)             }         }        }else{         // not so good here ...         (g1.wrappedValues zip g2.wrappedValues)       }     }     (factory.buildGenome(offspring.map{_._1}),  factory.buildGenome(offspring.map{_._2}))   }    def computebetaQ(alpha:Double,  distributionIndex:Double,  rand:Double):Double = {      if (rand <= (1.0/alpha)){       pow ((rand * alpha),(1.0 / (distributionIndex + 1.0)))     } else {       pow ((1.0 / (2.0 - rand * alpha)),(1.0 / (distributionIndex + 1.0)))     }    }                  

Thanks a lot for your advice, or help in this problem.

SR

wilcoxnack1941.blogspot.com

Source: https://stackoverflow.com/questions/8918625/simulated-binary-crossover-sbx-crossover-operator-in-scala-genetic-algorithm

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