演化计算实数空间变异算子

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参考文献

  • [节选自] 文诗华. 多目标进化算法中变异算子的研究[D]. 湘潭大学. 这是来自郑金华教授的学生的硕士毕业论文。从入门演化计算时就读着郑老师的书走来的。在此对其表示最诚挚的敬意

实数搜索空间变异算子的实现

变异算子的设计原则

变异算子的研究概况



实数空间常用变异算子

均匀变异

非均匀变异

自适应变异

高斯变异

柯西变异

多项式变异


在Deb K , Goyal M . A Combined Genetic Adaptive Search (GeneAS) for Engineering Design[C]// 1996.原文中，其是这样描述的。

matlab实现多项式变异

% polynomial mutation
       % 多项式突变
       function object=mutate(object,p,dim,mum)
           rnvec_temp=p.rnvec;
           for i=1:dim
               % 因为问题的维度一般比较大，所以rand(1)<1/dim的概率很小
               if rand(1)<1/dim
                   u=rand(1);
                   if u <= 0.5
                       del=(2*u)^(1/(1+mum)) - 1;
                       rnvec_temp(i)=p.rnvec(i) + del*(p.rnvec(i));
                   else
                       del= 1 - (2*(1-u))^(1/(1+mum));
                       rnvec_temp(i)=p.rnvec(i) + del*(1-p.rnvec(i));
                   end
               end
           end  
           object.rnvec = rnvec_temp;          
       end

jmetal实现多项式变异

public void doMutation(double probability, Solution solution) throws JMException {
		double rnd, delta1, delta2, mut_pow, deltaq;
		double y, yl, yu, val, xy;
		XReal x = new XReal(solution);
		for (int var = 0; var < solution.numberOfVariables(); var++) {
			if (PseudoRandom.randDouble() <= probability) {//如果小于变异概率即可以进行变异操作
				y = x.getValue(var);
				yl = x.getLowerBound(var);
				yu = x.getUpperBound(var);
				delta1 = (y - yl) / (yu - yl);
				delta2 = (yu - y) / (yu - yl);
				rnd = PseudoRandom.randDouble();
				mut_pow = 1.0 / (eta_m_ + 1.0);
				if (rnd <= 0.5) {
					xy = 1.0 - delta1;
					val = 2.0 * rnd + (1.0 - 2.0 * rnd) * (Math.pow(xy, (distributionIndex_ + 1.0)));
					deltaq = java.lang.Math.pow(val, mut_pow) - 1.0;
				} else {
					xy = 1.0 - delta2;
					val = 2.0 * (1.0 - rnd) + 2.0 * (rnd - 0.5) * (java.lang.Math.pow(xy, (distributionIndex_ + 1.0)));
					deltaq = 1.0 - (java.lang.Math.pow(val, mut_pow));
				}
				y = y + deltaq * (yu - yl);
				if (y < yl)
					y = yl;
				if (y > yu)
					y = yu;
				x.setValue(var, y);
			}
		} // for

	} // doMutation

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