Simulated Binary Crossover (SBX) crossover operator in Scala genetic algorithm (GA) library

Question

I work on a very little research team to create/adapt a Genetic Algorithm library in Scala for distributed computation with Scientific Workflow 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 the functional 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 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 annex A

The 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 beta (java code) or in Deb equation, the 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 the 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 source code of Nsga-II algorithm, and he explains to 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 the 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)))

    } 

  }

Answer 1

They differ only in the calculation of beta. You can check out this link which helps you in solving your problem: https://gist.github.com/Tiagoperes/1779d5f1c89bae0cfdb87b1960bba36d