聲明，這個是組員的，不是我的，貼出來大家瞅瞅吧。不過是用matlab實現的
This is an introduction to genetic algorithm methods for optimization. Genetic algorithms were formally introduced in the United States in the 1970s by John Holland at University of Michigan. The continuing price/performance improvements of computational systems has made them attractive for some types of optimization. In particular, genetic algorithms work very well on mixed (continuous and discrete), combinatorial problems. They are less susceptible to getting 'stuck' at local optima than gradient search methods. But they tend to be computationally expensive.
To use a genetic algorithm, you must represent a solution to your problem as a genome (or chromosome). The genetic algorithm then creates a population of solutions and applies genetic operators such as mutation and crossover to evolve the solutions in order to find the best one(s).
This presentation outlines some of the basics of genetic algorithms. The three most important aspects of using genetic algorithms are: definition of the objective function, definition and implementation of the genetic representation, and definition and implementation of the genetic operators. Once these three have been defined, the generic genetic algorithm should work fairly well. Beyond that you can try many different variations to improve performance, find multiple optima, or parallelize the algorithms.
The description of the GA method
Step 1: Initialization, set up population's scale N, encodes the chromosome with the law of natural number; GenN∶= 0, Produce the initial population Pop (0)
Step 2: To every chromosome in the population, calculate the fitness and record the best solution (has the biggest fitness) at present;
Step 3: If the result fulfils the request of the problem, stop and output the result; otherwise transfer to step 5
Step 4: According to the elite and rim plate gamble back-and-forth method, chose Pop (N+1) from Pop (GenN), produce the next generation.
Step 5: Using crossover and mutation operator reproduce variations remake Pop (N+1).
Step 6: GenN ∶= GenN + 1; transfer to step3
code:
function gaTSP
CityNum=52;
[dislist,Clist]=tsp(CityNum);
inn=500; %Initial population size
gnmax=100; %Max algebra
pc=0.8; %Crossover probability
pm=0.8; %Mutation probability
%produce initial population
for i=1:inn
s(i,:)=randperm(CityNum);
end
[f,p]=objf(s,dislist);
gn=1;
while gn<gnmax+1
for j=1:2:inn
seln=sel(s,p); %Choice operate
scro=cro(s,seln,pc); %Crossover operate
scnew(j,:)=scro(1,:);
scnew(j+1,:)=scro(2,:);
smnew(j,:)=mut(scnew(j,:),pm); %mutation operate
smnew(j+1,:)=mut(scnew(j+1,:),pm);
end
s=smnew; %produce the new group
[f,p]=objf(s,dislist); %compute the suitability of new group
%enregister the average suitability of the optimal now
[fmax,nmax]=max(f);
ymean(gn)=1000/mean(f);
ymax(gn)=1000/fmax;
%Set down the optimal individual now
x=s(nmax,:);
drawTSP(Clist,x,ymax(gn),gn,0);
gn=gn+1;
%pause;
end
gn=gn-1;
figure(2);
plot(ymax,'r'); hold on;
plot(ymean,'b');grid;
title('Searching Process');
legend('The optimal solution','The average solution');
end
%------------------------------------------------
%Compute suitability fuction
function [f,p]=objf(s,dislist);
inn=size(s,1); %read the size of group
for i=1:inn
f(i)=CalDist(dislist,s(i,:)); %Compute fuction result,i.e suitablitiy
end
f=1000./f';
%Compute the probability of chioce
fsum=0;
for i=1:inn
fsum=fsum+f(i)^15;
end
for i=1:inn
ps(i)=f(i)^15/fsum;
end
%Compute the probability of cumulation
p(1)=ps(1);
for i=2:inn
p(i)=p(i-1)+ps(i);
end
p=p';
end
%--------------------------------------------------
function pcc=pro(pc);
test(1:100)=0;
l=round(100*pc);
test(1:l)=1;
n=round(rand*99)+1;
pcc=test(n);
end
%--------------------------------------------------
%“Choice”operate
function seln=sel(s,p);
inn=size(p,1);
%Choice two individuals from group
for i=1:2
r=rand; %get a radom number
prand=p-r;
j=1;
while prand(j)<0
j=j+1;
end
seln(i)=j; %The number of choiced individual
end
end
%------------------------------------------------
%“Crossover”Operate
function scro=cro(s,seln,pc);
bn=size(s,2);
pcc=pro(pc); %According to the probability of crossover，decide whether to get the crossover operation,1 yes,0 no.
scro(1,:)=s(seln(1),:);
scro(2,:)=s(seln(2),:);
if pcc==1
c1=round(rand*(bn-2))+1; %produce a radom crossover point in [1,bn-1]
c2=round(rand*(bn-2))+1;
chb1=min(c1,c2);
chb2=max(c1,c2);
middle=scro(1,chb1+1:chb2);
scro(1,chb1+1:chb2)=scro(2,chb1+1:chb2);
scro(2,chb1+1:chb2)=middle;
for i=1:chb1
while find(scro(1,chb1+1:chb2)==scro(1,i))
zhi=find(scro(1,chb1+1:chb2)==scro(1,i));
y=scro(2,chb1+zhi);
scro(1,i)=y;
end
while find(scro(2,chb1+1:chb2)==scro(2,i))
zhi=find(scro(2,chb1+1:chb2)==scro(2,i));
y=scro(1,chb1+zhi);
scro(2,i)=y;
end
end
for i=chb2+1:bn
while find(scro(1,1:chb2)==scro(1,i))
zhi=find(scro(1,1:chb2)==scro(1,i));
y=scro(2,zhi);
scro(1,i)=y;
end
while find(scro(2,1:chb2)==scro(2,i))
zhi=find(scro(2,1:chb2)==scro(2,i));
y=scro(1,zhi);
scro(2,i)=y;
end
end
end
end
%--------------------------------------------------
%“mutation”operate
function snnew=mut(snew,pm);
bn=size(snew,2);
snnew=snew;
pmm=pro(pm); %According to the probability of mutation，decide whether to get the crossover operation,1 yes,0 no.
if pmm==1
c1=round(rand*(bn-2))+1; %produce a radom mutation point in [1,bn-1]
c2=round(rand*(bn-2))+1;
chb1=min(c1,c2);
chb2=max(c1,c2);
x=snew(chb1+1:chb2);
snnew(chb1+1:chb2)=fliplr(x);
end
end