模拟退火算法及禁忌搜索算法的matlab源程序
%%% 模拟退火算法源程序
% 此题以中国31省会城市的最短旅行路径为例：
% clear;clc;
function [MinD,BestPath]=MainAneal(pn)
% CityPosition存储的为每个城市的二维坐标x和y；
CityPosition=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;3238 1229;... 4196 1044;4312 790;4386 570;3007 1970;2562 1756;2788 1491;2381 1676;...
1332 695;3715 1678;3918 2179;4061 2370;3780 2212;3676 2578;4029 2838;...
4263 2931;3429 1908;3507 2376;3394 2643;3439 3201;2935 3240;3140 3550;...
2545 2357;2778 2826;2370 2975];
figure(1);
plot(CityPosition(:,1),CityPosition(:,2),'o')
m=size(CityPosition,1);%城市的数目
%
D = sqrt((CityPosition(:,ones(1,m)) - CityPosition(:,ones(1,m))').^2 + ...
(CityPosition(:,2*ones(1,m)) - CityPosition(:,2*ones(1,m))').^2);
path=zeros(pn,m);
for i=1:pn
path(i,:)=randperm(m);
end
iter_max=100;%i
m_max=5;%
Len1=zeros(1,pn);Len2=zeros(1,pn);path2=zeros(pn,m);
t=zeros(1,pn);
T=1e5; tau=1e-5;
N=1;
while T>=tau
iter_num=1;
m_num=1;
while m_num
for i=1:pn
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1))
D(path(i,m)+m*(path(i,1)-1))]);
path2(i,:)=ChangePath2(path(i,:),m);
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1))
D(path2(i,m)+m*(path2(i,1)-1))]);
end
R=rand(1,pn);
if find((Len2-Len1R)~=0)
path(find((Len2-Len1R)~=0),:)=path2(find((Len2-Len1R)~=0),:); %#ok
Len1(find((Len2-Len1R)~=0))=Len2(find((Len2-Len1R)~=0));
[TempMinD,TempIndex]=min(Len1);
TracePath(N,:)=path(TempIndex,:); %#ok
Distance(N)=TempMinD; %#ok
N=N+1;
else
m_num=m_num+1;
end
end
iter_num=iter_num+1;
T=T*0.9;
end
[MinD,Index]=min(Distance);
BestPath=TracePath(Index,:);%disp(MinD)
%画出路线图
figure(2);
plot(CityPosition(BestPath(1:end-1),1),CityPosition(BestPath(1:end-1),2),'r*-');
function p2=ChangePath2(p1,CityNum)
while(1)
R=unidrnd(CityNum,1,2);
if abs(R(1)-R(2)) > 0
break;
end
end
I=R(1);J=R(2);
if I
p2(1:I)=p1(1:I);
p2(I+1:J)=p1(J:-1:I+1);
p2(J+1:CityNum)=p1(J+1:CityNum);
else
p2(1:J-1)=p1(1:J-1);
p2(J:I+1)=p1(I+1:-1:J);
p2(I:CityNum)=p1(I:CityNum);
end
%%% 禁忌搜索算法解决TSP问题
%此题以中国31省会城市的最短旅行路径为例：
%禁忌搜索是对局部领域搜索的一种扩展,是一种全局逐步寻优算法,搜索过程可以接受劣解,有较强的爬山能力.领域结构对收敛性有很大影响。
function [BestShortcut,theMinDistance]=TabuSearch
clear;
clc;
Clist=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;3238 1229;... 4196 1044;4312 790;4386 570;3007 1970;2562 1756;2788 1491;2381 1676;... 1332 695;3715 1678;3918 2179;4061 2370;3780 2212;3676 2578;4029 2838;... 4263 2931;3429 1908;3507 2376;3394 2643;3439 3201;2935 3240;3140 3550;...
2545 2357;2778 2826;2370 2975];
CityNum=size(Clist,1);%TSP问题的规模,即城市数目
dislist=zeros(CityNum);
for i=1:CityNum
for j=1:CityNum
dislist(i,j)=((Clist(i,1)-Clist(j,1))^2+(Clist(i,2)-Clist(j,2))^2)^0.5;
end
end
TabuList=zeros(CityNum);% (tabu list)
TabuLength=round((CityNum*(CityNum-1)/2)^0.5);%禁忌长度(tabu length)
Candidates=200;%候选集的个数 (全部领域解个数)
CandidateNum=zeros(Candidates,CityNum);%候选解集合
S0=randperm(CityNum);%随机产生初始解
BSF=S0;
BestL=Inf;
clf;
figure(1);
stop = uicontrol('style','toggle','string'…
,'stop','background','white');
tic;
p=1;
StopL=80*CityNum;
while p
if Candidates>CityNum*(CityNum-1)/2
disp('候选解个数不大于n*(n-1)/2!');
break;
end
ALong(p)=Fun(dislist,S0);
i=1;
A=zeros(Candidates,2);
while i
M=CityNum*rand(1,2);
M=ceil(M);
if M(1)~=M(2)
A(i,1)=max(M(1),M(2));
A(i,2)=min(M(1),M(2));
if i==1
isa=0;
else
for j=1:i-1
if A(i,1)==A(j,1) && A(i,2)==A(j,2)
isa=1;
break;
else
isa=0;
end
end
end
if ~isa
i=i+1;
else
end
else
end
end
BestCandidateNum=100;%保留前BestCandidateNum个最好候选解
BestCandidate=Inf*ones(BestCandidateNum,4);
F=zeros(1,Candidates);
for i=1:Candidates
CandidateNum(i,:)=S0;
CandidateNum(i,[A(i,2),A(i,1)])=S0([A(i,1),A(i,2)]);
F(i)=Fun(dislist,CandidateNum(i,:));
if i
BestCandidate(i,2)=F(i);
BestCandidate(i,1)=i;
BestCandidate(i,3)=S0(A(i,1));
BestCandidate(i,4)=S0(A(i,2));
else
for j=1:BestCandidateNum
if F(i)
BestCandidate(j,2)=F(i);
BestCandidate(j,1)=i;
BestCandidate(j,3)=S0(A(i,1));
BestCandidate(j,4)=S0(A(i,2));
break;
end
end
end
end
%对BestCandidate
[JL,Index]=sort(BestCandidate(:,2));
SBest=BestCandidate(Index,:);
BestCandidate=SBest;
if BestCandidate(1,2)
BestL=BestCandidate(1,2);
S0=CandidateNum(BestCandidate(1,1),:);
BSF=S0;
for m=1:CityNum
for n=1:CityNum
if TabuList(m,n)~=0
TabuList(m,n)=TabuList(m,n)-1;
end
end
end
TabuList(BestCandidate(1,3),BestCandidate(1,4))=TabuLength;
else
for
i=1:BestCandidateNum
if TabuList(BestCandidate(i,3),BestCandidate(i,4))==0
S0=CandidateNum(BestCandidate(i,1),:);
for m=1:CityNum
for n=1:CityNum
if TabuList(m,n)~=0
TabuList(m,n)=TabuList(m,n)-1;
end
end
end
TabuList(BestCandidate(i,3),BestCandidate(i,4))=TabuLength;
break;
end
end
end
p=p+1;
ArrBestL(p)=BestL; %#ok
for i=1:CityNum-1
plot([Clist(BSF(i),1),Clist(BSF(i+1),1)],[Clist(BSF(i),2),Clist(BSF(i+1),2)],'bo-'); hold on;
end
plot([Clist(BSF(CityNum),1),Clist(BSF(1),1)],[Clist(BSF(CityNum),2),Clist(BSF(1),2)],'ro-');
title(['Counter:',int2str(p*Candidates),' The Min Distance:',num2str(BestL)]); hold off; pause(0.005); if get(stop,'value')==1
break;
end
end
toc;
BestShortcut=BSF;
theMinDistance=BestL;
set(stop,'style','pushbutton','string',…
'close', 'callback','close(gcf)');
figure(2);
plot(ArrBestL,'r'); hold on;
plot(ALong,'b');grid;
title('搜索过程');
legend('Best So Far','当前解');
end
function F=Fun(dislist,s) %#ok
DistanV=0;
n=size(s,2);
for i=1:(n-1)
DistanV=DistanV+dislist(s(i),s(i+1));
end
DistanV=DistanV+dislist(s(n),s(1));
F=DistanV;
end