求一个TSP的matlab程序

蚂蚁算法实现tsp。其中city是n行2列的矩阵，表示n个城市的经纬度，iter_max是最大循环次数，其余是蚂蚁算法的参数。

function [Shortest_Route,Shortest_Length]=anttsp(city,iter_max,m,Alpha,Beta,Rho,Q)

n=size(city,1)

d=zeros(n,n)

d=squareform(pdist(city))

Eta=1./d

Tau=ones(n,n)

Tabu=zeros(m,n)

nC=1

R_best=zeros(iter_max,n)

L_best=inf.*ones(iter_max,1)

while nC<=iter_max

route=[]

for i=1:ceil(m/n)

route=[route,randperm(n)]

end

Tabu(:,1)=(route(1,1:m))'

for j=2:n

for i=1:m

visited=Tabu(i,1:(j-1))

J=zeros(1,(n-j+1))

P=J

Jc=1

for k=1:n

if isempty(find(visited==k, 1))

J(Jc)=k

Jc=Jc+1

end

end

for k=1:length(J)

P(k)=(Tau(visited(end),J(k))^Alpha)*(Eta(visited(end),J(k))^Beta)

end

P=P/(sum(P))

Pcum=cumsum(P)

Select=find(Pcum>=rand)

if isempty(Select)%是不是一定能保证Select不为空

Tabu(i,j)=round(1+(n-1)*rand)

else

next_visit=J(Select(1))

Tabu(i,j)=next_visit

end

end

end

if nC>=2

Tabu(1,:)=R_best(nC-1,:)

end

L=zeros(m,1)

for i=1:m

R=Tabu(i,:)

for j=1:(n-1)

L(i)=L(i)+d(R(j),R(j+1))

end

L(i)=L(i)+d(R(1),R(n))

end

L_best(nC)=min(L)

pos=find(L==L_best(nC))

R_best(nC,:)=Tabu(pos(1),:)

nC=nC+1

Delta_Tau=zeros(n,n)

for i=1:m

for j=1:(n-1)

Delta_Tau(Tabu(i,j),Tabu(i,j+1))=Delta_Tau(Tabu(i,j),Tabu(i,j+1))+Q/L(i)

end

Delta_Tau(Tabu(i,n),Tabu(i,1))=Delta_Tau(Tabu(i,n),Tabu(i,1))+Q/L(i)

end

Tau=(1-Rho).*Tau+Delta_Tau

Tabu=zeros(m,n)

end

Pos=find(L_best==min(L_best))

Shortest_Route=R_best(Pos(1),:)

Shortest_Length=L_best(Pos(1))

end

function [Shortest_Route,Shortest_Length]=anttsp(city,iter_max,m,Alpha,Beta,Rho,Q)

n=size(city,1)

d=zeros(n,n)

d=squareform(pdist(city))

Eta=1./d

Tau=ones(n,n)

Tabu=zeros(m,n)

nC=1

R_best=zeros(iter_max,n)

L_best=inf.*ones(iter_max,1)

    while nC<=iter_max

        route=[]

        for i=1:ceil(m/n)

            route=[route,randperm(n)]

        end

        Tabu(:,1)=(route(1,1:m))'

        for j=2:n

            for i=1:m

                visited=Tabu(i,1:(j-1))

                J=zeros(1,(n-j+1))

                P=J

                Jc=1

                for k=1:n

                    if isempty(find(visited==k, 1))

                        J(Jc)=k

                        Jc=Jc+1

                    end

                end

                for k=1:length(J)

                    P(k)=(Tau(visited(end),J(k))^Alpha)*(Eta(visited(end),J(k))^Beta)

                end

                P=P/(sum(P))

                

                Pcum=cumsum(P)

                Select=find(Pcum>=rand)

                if isempty(Select)%是不是一定能保证Select不为空

                    Tabu(i,j)=round(1+(n-1)*rand)

                else

                    next_visit=J(Select(1))

                    Tabu(i,j)=next_visit

                end

            end

        end

        if nC>=2

            Tabu(1,:)=R_best(nC-1,:)

        end

        

        L=zeros(m,1)

        for i=1:m

            R=Tabu(i,:)

            for j=1:(n-1)

                L(i)=L(i)+d(R(j),R(j+1))

            end

            L(i)=L(i)+d(R(1),R(n))

        end

        L_best(nC)=min(L)

        pos=find(L==L_best(nC))

        R_best(nC,:)=Tabu(pos(1),:)

        nC=nC+1

        

        

        Delta_Tau=zeros(n,n)

        for i=1:m

            for j=1:(n-1)

                Delta_Tau(Tabu(i,j),Tabu(i,j+1))=Delta_Tau(Tabu(i,j),Tabu(i,j+1))+Q/L(i)

            end

            Delta_Tau(Tabu(i,n),Tabu(i,1))=Delta_Tau(Tabu(i,n),Tabu(i,1))+Q/L(i)

        end

        Tau=(1-Rho).*Tau+Delta_Tau

        Tabu=zeros(m,n)

    end

    Pos=find(L_best==min(L_best))

    Shortest_Route=R_best(Pos(1),:)

    Shortest_Length=L_best(Pos(1))

end

TSP问题遗传算法通用Matlab程序

程序一：主程序

%TSP问题（又名：旅行商问题，货郎担问题）遗传算法通用matlab程序 %D是距离矩阵，n为种群个数 %参数a是中国31个城市的坐标

%C为停止代数，遗传到第 C代时程序停止,C的具体取值视问题的规模和耗费的时间而定 %m为适应值归一化淘汰加速指数,最好取为1,2,3,4,不宜太大

%alpha为淘汰保护指数,可取为0~1之间任意小数,取1时关闭保护功能,建议取0.8~1.0之间的值

%R为最短路径,Rlength为路径长度

function [R,Rlength]=geneticTSP(D,a,n,C,m,alpha) [N,NN]=size(D)

farm=zeros(n,N)%用于存储种群 for i=1:n

farm(i,:)=randperm(N)%随机生成初始种群 end

R=farm(1,:)subplot(1,3,1)

scatter(a(:,1),a(:,2),'x') pause(1)

subplot(1,3,2) plotaiwa(a,R) pause(1)

farm(1,:)=R

len=zeros(n,1)%存储路径长度

fitness=zeros(n,1)%存储归一化适应值 counter=0

while counterfor i=1:n

len(i,1)=myLength(D,farm(i,:))%计算路径长度 end

maxlen=max(len)minlen=min(len)

fitness=fit(len,m,maxlen,minlen)%计算归一化适应值 rr=find(len==minlen)

R=farm(rr(1,1),:)%更新最短路径

FARM=farm%优胜劣汰，nn记录了复制的个数 nn=0

for i=1:n

if fitness(i,1)>=alpha*rand nn=nn+1

FARM(nn,:)=farm(i,:)end

end

FARM=FARM(1:nn,:)

[aa,bb]=size(FARM)%交叉和变异 while aaif nn<=2 nnper=randperm(2)else

nnper=randperm(nn)end

A=FARM(nnper(1),:)B=FARM(nnper(2),:)[A,B]=intercross(A,B)FARM=[FARMAB][aa,bb]=size(FARM)end

if aa>n

FARM=FARM(1:n,:)%保持种群规模为n end

farm=FARMclear FARM

counter=counter+1end

Rlength=myLength(D,R)subplot(1,3,3) plotaiwa(a,R)

程序二：计算邻接矩阵

%输入参数a是中国31个城市的坐标 %输出参数D是无向图的赋权邻接矩阵 function D=ff01(a) [c,d]=size(a)D=zeros(c,c)for i=1:c

for j=i:c

bb=(a(i,1)-a(j,1)).^2+(a(i,2)-a(j,2)).^2D(i,j)=bb^(0.5)D(j,i)=D(i,j)end end

程序三：计算归一化适应值 %计算归一化适应值的子程序

function fitness=fit(len,m,maxlen,minlen) fitness=len

for i=1:length(len)

fitness(i,1)=(1-((len(i,1)-minlen)/(maxlen-minlen+0.0001))).^mend

程序四：交叉和变异的子程序

%交叉算法采用的是由Goldberg和Lingle于1985年提出的PMX(部分匹配交叉) function [a,b]=intercross(a,b) L=length(a)

if L<=10%确定交叉宽度 W=9

elseif ((L/10)-floor(L/10))>=rand&&L>10 W=ceil(L/10)+8else

W=floor(L/10)+8end

p=unidrnd(L-W+1)%随机选择交叉范围，从p到p+W for i=1:W%交叉

x=find(a==b(1,p+i-1))y=find(b==a(1,p+i-1))

[a(1,p+i-1),b(1,p+i-1)]=exchange(a(1,p+i-1),b(1,p+i-1))[a(1,x),b(1,y)]=exchange(a(1,x),b(1,y)) end

function [x,y]=exchange(x,y) temp=xx=yy=temp

程序五: 计算路径的子程序

%该路径长度是一个闭合的路径的长度 function len=myLength(D,p) [N,NN]=size(D)

len=D(p(1,N),p(1,1))for i=1:(N-1)

len=len+D(p(1,i),p(1,i+1))end

程序六：用于绘制路径示意图的程序 function plotaiwa(a,R)

scatter(a(:,1),a(:,2),'x') hold on

plot([a(R(1),1),a(R(31),1)],[a(R(1),2),a(R(31),2)]) hold on

for i=2:length(R) x0=a(R(i-1),1)y0=a(R(i-1),2)x1=a(R(i),1)y1=a(R(i),2)xx=[x0,x1]

yy=[y0,y1]

plot(xx,yy)

hold on

end

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