【TSP问题】基于改进遗传算法求解旅行商问题matlab源码
作者：互联网
1 算法介绍
模型介绍见这里。
2 部分代码
nn=40; % number of cities
asz=10; % area size asx x asz
ps=3000; % population size
ng=5000; % number of generation
pm=0.01; % probability of mutation of exchange 2 random cities in the path (per gene, per genration)
pm2=0.02; % probability of mutation of exchange 2 peices of path (per gene, per genration)
pmf=0.08; % probability of mutation of flip random pece of path
r=asz*rand(2,nn); % randomly distribute cities
% r(1,:) -x coordinaties of cities
% r(2,:) -y coordinaties of cities
% % uncomment to make circle:
% % circle
% al1=linspace(0,2*pi,nn+1);
% al=al1(1:end-1);
% r(1,:)=0.5*asz+0.45*asz*cos(al);
% r(2,:)=0.5*asz+0.45*asz*sin(al);
dsm=zeros(nn,nn); % matrix of distancies
for n1=1:nn-1
r1=r(:,n1);
for n2=n1+1:nn
r2=r(:,n2);
dr=r1-r2;
dr2=dr'*dr;
drl=sqrt(dr2);
dsm(n1,n2)=drl;
dsm(n2,n1)=drl;
end
end
% start from random closed pathes:
G=zeros(ps,nn); % genes, G(i,:) - gene of i-path, G(i,:) is row-vector with cities number in the path
for psc=1:ps
G(psc,:)=randperm(nn);
end
figure('units','normalized','position',[0.05 0.2 0.9 0.6]);
subplot(1,2,1);
% to plot best path:
hpb=plot(NaN,NaN,'r-');
ht=title(' ');
hold on;
% plot nodes numbers
for n=1:nn
text(r(1,n),r(2,n),num2str(n),'color',[0.7 0.7 0.7]);
end
plot(r(1,:),r(2,:),'k.'); % plot cities as black dots
axis equal;
xlim([-0.1*asz 1.1*asz]);
ylim([-0.1*asz 1.1*asz]);
subplot(1,2,2);
hi=imagesc(G);
title('color is city number');
colorbar;
xlabel('index in sequence of cities');
ylabel('path number');
pthd=zeros(ps,1); %path lengths
p=zeros(ps,1); % probabilities
for gc=1:ng % generations loop
% find paths length:
for psc=1:ps
Gt=G(psc,:);
pt=0; % path length summation
for nc=1:nn-1
pt=pt+dsm(Gt(nc),Gt(nc+1));
end
% last and first:
pt=pt+dsm(Gt(nn),Gt(1));
pthd(psc)=pt;
end
ipthd=1./pthd; % inverse path lengths, we want to maximize inverse path length
p=ipthd/sum(ipthd); % probabilities
[mbp bp]=max(p);
Gb=G(bp,:); % best path
% update best path on figure:
if mod(gc,5)==0
set(hpb,'Xdata',[r(1,Gb) r(1,Gb(1))],'YData',[r(2,Gb) r(2,Gb(1))]);
set(ht,'string',['generation: ' num2str(gc) ' best path length: ' num2str(pthd(bp))]);
set(hi,'CData',G);
drawnow;
end
% crossover:
ii=roulette_wheel_indexes(ps,p); % genes with cities numers in ii will be put to crossover
% length(ii)=ps, then more probability p(i) of i-gene then more
% frequently it repeated in ii list
Gc=G(ii,:); % genes to crossover
Gch=zeros(ps,nn); % childrens
for prc=1:(ps/2) % pairs counting
i1=1+2*(prc-1);
i2=2+2*(prc-1);
g1=Gc(i1,:); %one gene
g2=Gc(i2,:); %another gene
cp=ceil((nn-1)*rand); % crossover point, random number form range [1; nn-1]
% two childrens:
g1ch=insert_begining(g1,g2,cp);
g2ch=insert_begining(g2,g1,cp);
Gch(i1,:)=g1ch;
Gch(i2,:)=g2ch;
end
G=Gch; % now children
% mutation of exchange 2 random cities:
for psc=1:ps
if rand<pm
rnp=ceil(nn*rand); % random number of sicies to permuation
rpnn=randperm(nn);
ctp=rpnn(1:rnp); %chose rnp random cities to permutation
Gt=G(psc,ctp); % get this cites from the list
Gt=Gt(randperm(rnp)); % permutate cities
G(psc,ctp)=Gt; % % return citeis back
end
end
% mutation of exchange 2 peices of path:
for psc=1:ps
if rand<pm2
cp=1+ceil((nn-3)*rand); % range [2 nn-2]
G(psc,:)=[G(psc,cp+1:nn) G(psc,1:cp)];
end
end
% mutation of flip randm pece of path:
for psc=1:ps
if rand<pmf
n1=ceil(nn*rand);
n2=ceil(nn*rand);
G(pscs,n1:n2)=fliplr(G(psc,n1:n2));
end
end
G(1,:)=Gb; % elitism
end
3 仿真结果
4 参考文献
[1]谢胜利, 唐敏, 董金祥. 求解TSP问题的一种改进的遗传算法[J]. 计算机工程与应用, 2002, 38(008):58-60.
[2]文艺, and 潘大志. "用于求解TSP问题的改进遗传算法." 计算机科学 43.0z1(2016):90-92.
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标签：ps,end,nn,asz,源码,matlab,path,遗传算法,cities 来源： https://blog.csdn.net/qq_59747472/article/details/120470396