my_sga.m

有用的SGA的Matlab源代码

%**********************************************************************/
%                     本程序实现求函数的最大值                        */
% f(x1,x2)=100(x1*x1-x2)*(x1*x1-x2)+(1-x1)*(1-x1)    -2.048<<xi<<2.048*/


%--------------------------%   主函数  SGA()   %---------------------------------%
function SGA()
format long;
ChromosomeLength = 20;   %染色体长度包含两个变量各占一半
PopSize =80;             %种群大小
MaxGeneration = 200;     %最大演化代数
Pc=0.6;                  %杂交概率
Pm=0.1;                  %变异概率
gen = 0;                 %演化代数统计
PopulationValue=[];
PopulationFitness=[];
BestGene= zeros(ChromosomeLength,1);%保存演化过程中最好个体
BestFitness= eps;
BestValue= 0;
Bestgen= 0;
gx1=0;
gx2=0;

Population = floor(rand(ChromosomeLength,PopSize)*2);%初始化种群为 20*80 的 0-1矩阵

while(gen< MaxGeneration)
    gen=gen+1;    
    [x1,x2,PopulationValue] = ValueOfFunc(Population);              %计算个体的函数值
    PopulationFitness = CalculateFitnessValue(Population);          %计算个体的适应度值
    [CurrentBestFitness CurrentBestIndex] = max(PopulationFitness); %返回当前最好的个体的属性值
    
    if CurrentBestFitness > BestFitness                             %根据适应度值找到最好的个体
       Bestgen =gen;
       BestGene= Population(:,CurrentBestIndex);
       BestFitness= PopulationFitness(CurrentBestIndex);
       BestValue= PopulationValue(CurrentBestIndex);
       Bestchromosome= [Population(:,CurrentBestIndex)]';           %最好个体的染色体值
       gx1=x1;
       gx2=x2;
    end
   % 输出每一代演化结果
   disp(strcat('gen=',num2str(gen),'    bestvalue=',num2str(BestValue),'    x1=',num2str(gx1),'    x2=',num2str(gx2),'   chromosome=',num2str( Bestchromosome)));
    
 %------------进行遗传操作--------------% 
 Population = Selection(Population,PopulationFitness);    %选择
 Population = Crossover(Population,Pc);                   %交叉
 Population = Mutation(Population,Pm);                    %变异
end

%----------------------------% 主函数  SGA() %----------------------------------%
%-------------------------------------------------------------------------------%


%---------计算函数值,并返回变量x1,x2的值---------%
function [x1,x2,value]=ValueOfFunc(p)
%Length = size(Chromosome,1)/2;
length1=10;
length2=10; 
[x y] = size(p);
value=zeros(1,y);
for i=1:y 
      Chromosome=p(:,i);
      temp1=0;
      temp2=0;
      for j=1:length2
          temp1=temp1+Chromosome(j)*(2^(j-1));            % DecodeChromosome(population[i].chrom,0,length1);
          temp2=temp2+Chromosome(j+length1)*(2^(j-1));    % DecodeChromosome(population[i].chrom,length1,length2);
     end     
     x1=4.096*temp1/1023.0-2.048;
     x2=4.096*temp2/1023.0-2.048;

     value(i)=100*((x1^2-x2)^2)+(1-x1)^2; 
end
%---------计算函数值,并返回变量x1,x2的值-----------%

%-----------求种群中每个个体的适应度值-------------%    
function [fitness] = CalculateFitnessValue(p)   
[x1,x2,value]=ValueOfFunc(p);
[x y] = size(p);
for i=1:y 
    fitness(i)= value(i);
end
%----------求种群中每个个体的适应度值-------------%

 
%---------------------------  选择 ------------------------------%
function [NewPopulation] = Selection(Population,PopulationFitness)
  %轮盘赌法进行选择
   [ChromosomeLength PopSize] = size(Population);
   SumFitness=sum(PopulationFitness);              %计算个体适应度之和
   cfitness=PopulationFitness/SumFitness;          %计算个体的相对适应度
   SelectPi=rand(1,PopSize);                       %产生选择随机数
   for i=2:PopSize
       cfitness(i)=cfitness(i)+cfitness(i-1);      %计算累计概率：
   end
   NewPopulation=zeros(ChromosomeLength,PopSize);
   for i=1:PopSize
       for j=1:PopSize
           if SelectPi(i) <= cfitness(j)
              NewPopulation(:,i)=Population(:,j);
              break;
           end
       end
   end
   
%--------------------- 交叉 ------------------------%
function [NewPopulation] = Crossover(Population,Pc)
   [ChromosomeLength PopSize] = size(Population); 
   for i=1:PopSize
		index(i)=i;
    end
   % 随机选择两个父体，并记下位置   
    for i=1:PopSize      
        point=floor(rand(1)*(PopSize-i+1));
		temp=index(i);
		index(i)=index(point+i);
		index(point+i)=temp;
    end
   % 进行单点交叉     
   for i=1:2:(PopSize-2)
       p=rand(1);
       if(p<Pc)
           point=floor(rand(1)*(ChromosomeLength-1))+1;        % 随机选择交叉点
           for j=point:ChromosomeLength-1
               temp=Population(j,index(i));
			   Population(j,index(i))=Population(j,index(i+1));
			   Population(j,index(i+1))=temp;
           end
       end
   end
      NewPopulation = Population;
   
      
%---------------------- 变异 ------------------ -%
function [NewPopulation] = Mutation(Population,Pm)
 [ChromosomeLength PopSize]= size(Population);
for i=1:PopSize
    if rand < Pm
        for j=1:ChromosomeLength
            if Population(j,i)==0
                Population(j,i)==1;
            else
                Population(j,i)==0;
            end
        end
                
   end        
end
NewPopulation=Population;