一起来学演化计算-SBX(Simulated binary crossover)模拟二进制交叉算子和DE(differential evolution)差分进化算子

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参考文献
[1] https://blog.csdn.net/qq_36347331/article/details/96351162
[2] http://www.it1352.com/994287.html
[3] https://www.egr.msu.edu/~kdeb/

SBX

DE

SBX matlab版本实现

function object=crossover(object,p1,p2,cf)object.rnvec=0.5*((1+cf).*p1.rnvec + (1-cf).*p2.rnvec);% 截断范围object.rnvec(object.rnvec>1)=1;object.rnvec(object.rnvec<0)=0;
end
u = rand(1,D_multitask);
cf = zeros(1,D_multitask);
cf(u<=0.5)=(2*u(u<=0.5)).^(1/(mu+1));
cf(u>0.5)=(2*(1-u(u>0.5))).^(-1/(mu+1));
child(count) = crossover(child(count),population(p1),population(p2),cf);
child(count+1) = crossover(child(count+1),population(p2),population(p1),cf);

SBX java版本实现

/*** This class allows to apply a SBX crossover operator using two parent* solutions.* 关于此代码和Deb论文中代码不一致可以查看http://www.it1352.com/994287.html帖子或者查看Deb官方源码*/
//  SBXCrossover.java
//
//  Author:
//       Antonio J. Nebro <antonio@lcc.uma.es>
//       Juan J. Durillo <durillo@lcc.uma.es>
//
//  Copyright (c) 2011 Antonio J. Nebro, Juan J. Durillo
//
//  This program is free software: you can redistribute it and/or modify
//  it under the terms of the GNU Lesser General Public License as published by
//  the Free Software Foundation, either version 3 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU Lesser General Public License for more details.
//
//  You should have received a copy of the GNU Lesser General Public License
//  along with this program.  If not, see <http://www.gnu.org/licenses/>.*/
public Solution[] doCrossover(double probability, Solution parent1, Solution parent2) throws JMException {Solution[] offSpring = new Solution[2];/***使用一个父代个体去生成新个体的原因在于可以将父代的属性传给子代*具体有：*  public Solution(Solution solution) {*      problemSet_ = solution.problemSet_;*      type_ = solution.type_;**      numberOfObjectives_ = solution.getNumberOfObjectives();*      objective_ = new double[numberOfObjectives_];*      for (int i = 0; i < objective_.length; i++) {*          objective_[i] = solution.getObjective(i);*                } // for*          // <-**      variable_ = type_.copyVariables(solution.variable_);*      overallConstraintViolation_ = solution.getOverallConstraintViolation();*      numberOfViolatedConstraints_ = solution.getNumberOfViolatedConstraint();*      distanceToSolutionSet_ = solution.getDistanceToSolutionSet();*      crowdingDistance_ = solution.getCrowdingDistance();*      kDistance_ = solution.getKDistance();*      fitness_ = solution.getFitness();*      rank_ = solution.getRank();*      location_ = solution.getLocation();**      skillFactor_ = solution.getSkillFactor();*  } // Solution* */offSpring[0] = new Solution(parent1);offSpring[1] = new Solution(parent2);int i;double rand;double y1, y2, yL, yu;double c1, c2;double alpha, beta, betaq;double valueX1, valueX2;XReal x1 = new XReal(parent1);XReal x2 = new XReal(parent2);XReal offs1 = new XReal(offSpring[0]);XReal offs2 = new XReal(offSpring[1]);int numberOfVariables = x1.getNumberOfDecisionVariables();if (PseudoRandom.randDouble() <= probability) {//只有随机生成的数小于自定义的交叉可能性时才进行交叉操作for (i = 0; i < numberOfVariables; i++) {valueX1 = x1.getValue(i);valueX2 = x2.getValue(i);if (PseudoRandom.randDouble() <= 0.5) {if (java.lang.Math.abs(valueX1 - valueX2) > EPS) {if (valueX1 < valueX2) {y1 = valueX1;y2 = valueX2;} else {y1 = valueX2;y2 = valueX1;} // ifyL = x1.getLowerBound(i);yu = x1.getUpperBound(i);rand = PseudoRandom.randDouble();beta = 1.0 + (2.0 * (y1 - yL) / (y2 - y1));alpha = 2.0 - java.lang.Math.pow(beta, -(distributionIndex_ + 1.0));if (rand <= (1.0 / alpha)) {betaq = java.lang.Math.pow((rand * alpha), (1.0 / (distributionIndex_ + 1.0)));} else {betaq = java.lang.Math.pow((1.0 / (2.0 - rand * alpha)),(1.0 / (distributionIndex_ + 1.0)));} // ifc1 = 0.5 * ((y1 + y2) - betaq * (y2 - y1));beta = 1.0 + (2.0 * (yu - y2) / (y2 - y1));alpha = 2.0 - java.lang.Math.pow(beta, -(distributionIndex_ + 1.0));if (rand <= (1.0 / alpha)) {betaq = java.lang.Math.pow((rand * alpha), (1.0 / (distributionIndex_ + 1.0)));} else {betaq = java.lang.Math.pow((1.0 / (2.0 - rand * alpha)),(1.0 / (distributionIndex_ + 1.0)));} // ifc2 = 0.5 * ((y1 + y2) + betaq * (y2 - y1));if (c1 < yL)c1 = yL;if (c2 < yL)c2 = yL;if (c1 > yu)c1 = yu;if (c2 > yu)c2 = yu;if (PseudoRandom.randDouble() <= 0.5) {offs1.setValue(i, c2);offs2.setValue(i, c1);} else {offs1.setValue(i, c1);offs2.setValue(i, c2);} // if} else {offs1.setValue(i, valueX1);offs2.setValue(i, valueX2);} // if} else {offs1.setValue(i, valueX2);offs2.setValue(i, valueX1);} // if} // if} // ifreturn offSpring;}