演化计算实数空间变异算子

心已赠人 2024-04-20 10:45 37阅读 0赞

# 一起来学演化计算-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 ##

![949241-20190726195301051-101864447.png][]

## 变异算子的设计原则 ##

![949241-20190726195849063-1171515129.png][]

## 变异算子的研究概况 ##

![949241-20190726200755740-1586595886.png][]  
![949241-20190726200936718-264093442.png][]  
![949241-20190726201558913-1749544146.png][]

## 实数空间常用变异算子 ##

### 均匀变异 ###

![949241-20190726203239948-1430351512.png][]

### 非均匀变异 ###

![949241-20190726203704399-1508184896.png][]

### 自适应变异 ###

![949241-20190726204130408-1618267542.png][]

### 高斯变异 ###

![949241-20190726204454472-424555586.png][]

### 柯西变异 ###

![949241-20190726204544590-1087388446.png][]

### 多项式变异 ###

![949241-20190726204718970-472093939.png][]  
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。  
![949241-20190728133839507-2071306126.png][]

#### 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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