跪求用dijkstra算法解决TSP多旅行商问题的MATLAB程序！ 关于TSP求最佳路径问题的Matlab程序
\u591a\u65c5\u884c\u5546\u95ee\u9898matlab\u7a0b\u5e8f[code]function [R_best,L_best,L_ave,Shortest_Route,Shortest_Length]=ACATSP(C,NC_max,m,Alpha,Beta,Rho,Q)
%%=========================================================================
%% ACATSP.m
%% Ant Colony Algorithm for Traveling Salesman Problem
%% ChengAihua,PLA Information Engineering University,ZhengZhou,China
%% Email:[email protected]
%% All rights reserved
%%-------------------------------------------------------------------------
%% \u4e3b\u8981\u7b26\u53f7\u8bf4\u660e
%% C n\u4e2a\u57ce\u5e02\u7684\u5750\u6807\uff0cn\u00d72\u7684\u77e9\u9635
%% NC_max \u6700\u5927\u8fed\u4ee3\u6b21\u6570
%% m \u8682\u8681\u4e2a\u6570
%% Alpha \u8868\u5f81\u4fe1\u606f\u7d20\u91cd\u8981\u7a0b\u5ea6\u7684\u53c2\u6570
%% Beta \u8868\u5f81\u542f\u53d1\u5f0f\u56e0\u5b50\u91cd\u8981\u7a0b\u5ea6\u7684\u53c2\u6570
%% Rho \u4fe1\u606f\u7d20\u84b8\u53d1\u7cfb\u6570
%% Q \u4fe1\u606f\u7d20\u589e\u52a0\u5f3a\u5ea6\u7cfb\u6570
%% R_best \u5404\u4ee3\u6700\u4f73\u8def\u7ebf
%% L_best \u5404\u4ee3\u6700\u4f73\u8def\u7ebf\u7684\u957f\u5ea6
%%=========================================================================
%%\u7b2c\u4e00\u6b65\uff1a\u53d8\u91cf\u521d\u59cb\u5316
n=size(C,1);%n\u8868\u793a\u95ee\u9898\u7684\u89c4\u6a21\uff08\u57ce\u5e02\u4e2a\u6570\uff09
D=zeros(n,n);%D\u8868\u793a\u5b8c\u5168\u56fe\u7684\u8d4b\u6743\u90bb\u63a5\u77e9\u9635
for i=1:n
for j=1:n
if i~=j
D(i,j)=((C(i,1)-C(j,1))^2+(C(i,2)-C(j,2))^2)^0.5;
else
D(i,j)=eps;
end
D(j,i)=D(i,j);
end
end
Eta=1./D;%Eta\u4e3a\u542f\u53d1\u56e0\u5b50\uff0c\u8fd9\u91cc\u8bbe\u4e3a\u8ddd\u79bb\u7684\u5012\u6570
Tau=ones(n,n);%Tau\u4e3a\u4fe1\u606f\u7d20\u77e9\u9635
Tabu=zeros(m,n);%\u5b58\u50a8\u5e76\u8bb0\u5f55\u8def\u5f84\u7684\u751f\u6210
NC=1;%\u8fed\u4ee3\u8ba1\u6570\u5668
R_best=zeros(NC_max,n);%\u5404\u4ee3\u6700\u4f73\u8def\u7ebf
L_best=inf.*ones(NC_max,1);%\u5404\u4ee3\u6700\u4f73\u8def\u7ebf\u7684\u957f\u5ea6
L_ave=zeros(NC_max,1);%\u5404\u4ee3\u8def\u7ebf\u7684\u5e73\u5747\u957f\u5ea6
while NC<=NC_max%\u505c\u6b62\u6761\u4ef6\u4e4b\u4e00\uff1a\u8fbe\u5230\u6700\u5927\u8fed\u4ee3\u6b21\u6570
%%\u7b2c\u4e8c\u6b65\uff1a\u5c06m\u53ea\u8682\u8681\u653e\u5230n\u4e2a\u57ce\u5e02\u4e0a
Randpos=[];
for i=1:(ceil(m/n))
Randpos=[Randpos,randperm(n)];
end
Tabu(:,1)=(Randpos(1,1:m))';
%%\u7b2c\u4e09\u6b65\uff1am\u53ea\u8682\u8681\u6309\u6982\u7387\u51fd\u6570\u9009\u62e9\u4e0b\u4e00\u5ea7\u57ce\u5e02\uff0c\u5b8c\u6210\u5404\u81ea\u7684\u5468\u6e38
for j=2:n
for i=1:m
visited=Tabu(i,1:(j-1));%\u5df2\u8bbf\u95ee\u7684\u57ce\u5e02
J=zeros(1,(n-j+1));%\u5f85\u8bbf\u95ee\u7684\u57ce\u5e02
P=J;%\u5f85\u8bbf\u95ee\u57ce\u5e02\u7684\u9009\u62e9\u6982\u7387\u5206\u5e03
Jc=1;
for k=1:n
if length(find(visited==k))==0
J(Jc)=k;
Jc=Jc+1;
end
end
%\u4e0b\u9762\u8ba1\u7b97\u5f85\u9009\u57ce\u5e02\u7684\u6982\u7387\u5206\u5e03
for k=1:length(J)
P(k)=(Tau(visited(end),J(k))^Alpha)*(Eta(visited(end),J(k))^Beta);
end
P=P/(sum(P));
%\u6309\u6982\u7387\u539f\u5219\u9009\u53d6\u4e0b\u4e00\u4e2a\u57ce\u5e02
Pcum=cumsum(P);
Select=find(Pcum>=rand);
to_visit=J(Select(1));
Tabu(i,j)=to_visit;
end
end
if NC>=2
Tabu(1,:)=R_best(NC-1,:);
end
%%\u7b2c\u56db\u6b65\uff1a\u8bb0\u5f55\u672c\u6b21\u8fed\u4ee3\u6700\u4f73\u8def\u7ebf
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),:);
L_ave(NC)=mean(L);
NC=NC+1
%%\u7b2c\u4e94\u6b65\uff1a\u66f4\u65b0\u4fe1\u606f\u7d20
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;
%%\u7b2c\u516d\u6b65\uff1a\u7981\u5fcc\u8868\u6e05\u96f6
Tabu=zeros(m,n);
end
%%\u7b2c\u4e03\u6b65\uff1a\u8f93\u51fa\u7ed3\u679c
Pos=find(L_best==min(L_best));
Shortest_Route=R_best(Pos(1),:)
Shortest_Length=L_best(Pos(1))
subplot(1,2,1)
DrawRoute(C,Shortest_Route)
subplot(1,2,2)
plot(L_best)
hold on
plot(L_ave)
function DrawRoute(C,R)
%%=========================================================================
%% DrawRoute.m
%% \u753b\u8def\u7ebf\u56fe\u7684\u5b50\u51fd\u6570
%%-------------------------------------------------------------------------
%% C Coordinate \u8282\u70b9\u5750\u6807\uff0c\u7531\u4e00\u4e2aN\u00d72\u7684\u77e9\u9635\u5b58\u50a8
%% R Route \u8def\u7ebf
%%=========================================================================
N=length(R);
scatter(C(:,1),C(:,2));
hold on
plot([C(R(1),1),C(R(N),1)],[C(R(1),2),C(R(N),2)])
hold on
for ii=2:N
plot([C(R(ii-1),1),C(R(ii),1)],[C(R(ii-1),2),C(R(ii),2)])
hold on
end
\u8bbe\u7f6e\u521d\u59cb\u53c2\u6570\u5982\u4e0b\uff1a
m=31;Alpha=1;Beta=5;Rho=0.1;NC_max=200;Q=100;
31\u57ce\u5e02\u5750\u6807\u4e3a\uff1a
1304 2312
3639 1315
4177 2244
3712 1399
3488 1535
3326 1556
3238 1229
4196 1004
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 2367
3394 2643
3439 3201
2935 3240
3140 3550
2545 2357
2778 2826
2370 2975[/code]
\u8fd0\u884c\u540e\u5f97\u523015602\u7684\u5de1\u6e38\u8def\u5f84\uff0c\u8def\u7ebf\u56fe\u548c\u6536\u655b\u66f2\u7ebf\u5982\u4e0b\uff1a
\u6211\u89c9\u5f97\u4f60 i=1;\u8fd9\u6837\u5e76\u6ca1\u6709\u8df3\u51fa\u5faa\u73af\u3002i=1\u540e\u52a0\u4e2anext\u8bd5\u8bd5\u770b
dijkstra算法是用来求任意两点间的最短路径。他求出的路径并不是欧拉回路，不满足TSP的要求觉得这个问题似乎不能这样解决
TSP问题不能用dijkstra解决.这是一个NP难问题,不存在多项式算法.
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绛旓細Dijkstra锛 杩鏂壒鎷 锛夌畻娉曟槸鐢ㄦ潵瑙ｅ喅鍗曟簮鏈鐭矾寰勭殑绠楁硶锛岃姹傝矾寰勬潈鍊奸潪璐熸暟銆傝绠楁硶鍒╃敤浜嗘繁搴︿紭鍏堟悳绱㈠拰璐績鐨勭畻娉曘備笅闈㈡槸涓涓湁鏉冨浘锛屾眰浠嶢鍒板悇涓妭鐐圭殑鏈鐭矾寰勩傜1姝ワ細浠嶢鐐瑰嚭鍙戯紝鍒ゆ柇姣忎釜鐐瑰埌A鐐圭殑璺緞锛堝鏋滆鐐逛笉鑳界洿杩濧鐐瑰垯璺濈鍊间负鏃犵┓澶э紝濡傛灉璇ョ偣鑳藉拰A鐩磋繛鍒欐槸褰撳墠鐨勬潈鍊硷級锛岃...
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绛旓細绗竴姝 v2 v3 v4 v5 v6 3锛坴1) 5(v1) 鈭(v1) 鈭(v1) 鈭(v1)v2鐨3鏈灏 鑰冭檻浠巚2 璧 锛寁3鐨勮窛绂=min锛5,3+1锛=4 v3鐨勮窛绂绘敼涓4锛屾潵婧愪负v2 绫讳技鍙緱绗簩姝 v2* v3 v4 v5 v6 3锛坴1) 4(v2) 5(v2) 5(v2) ...
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绛旓細鍙欒堪姹傝В鏈鐭矾鐨dijkstra绠楁硶鍩烘湰杩囩▼濡備笅锛欴ijkstra(杩澃鏂壒鎷)绠楁硶鏄吀鍨嬬殑鍗曟簮鏈鐭矾寰勭畻娉曪紝鐢ㄤ簬璁＄畻涓涓妭鐐瑰埌鍏朵粬鎵鏈夎妭鐐圭殑鏈鐭矾寰勩備富瑕佺壒鐐规槸浠ヨ捣濮嬬偣涓轰腑蹇冨悜澶栧眰灞傛墿灞曪紝鐩村埌鎵╁睍鍒扮粓鐐逛负姝傛敞鎰忚绠楁硶瑕佹眰鍥句腑涓嶅瓨鍦ㄨ礋鏉冭竟銆傝G=(V,E)鏄竴涓甫鏉冩湁鍚戝浘锛屾妸鍥句腑椤剁偣闆嗗悎V鍒嗘垚涓ょ粍锛岀涓...
绛旓細Dijkstra绠楁硶锛岀炕璇戜綔鎴村厠鏂壒鎷夌畻娉曟垨杩澃鏂壒鎷夌畻娉锛屼簬1956骞寸敱鑽峰叞璁＄畻鏈虹瀛﹀鑹惧吂璧皵.鎴村厠鏂壒鎷夋彁鍑猴紝鐢ㄤ簬瑙ｅ喅璧嬫潈鏈夊悜鍥剧殑 鍗曟簮鏈鐭矾寰勯棶棰 銆傛墍璋撳崟婧愭渶鐭矾寰勯棶棰樻槸鎸囩‘瀹氳捣鐐癸紝瀵绘壘璇ヨ妭鐐瑰埌鍥句腑浠绘剰鑺傜偣鐨勬渶鐭矾寰勶紝绠楁硶鍙敤浜庡鎵句袱涓煄甯備腑鐨勬渶鐭矾寰勬垨鏄В鍐宠憲鍚嶇殑鏃呰鍟嗛棶棰樸傞棶棰樻弿杩 锛...
绛旓細finally,the program will output the lowest distance to the destination node, the pre-node and show the best path./ 锛僫 nclude<stdio.h> 锛僫 nclude <stdlib.h> //Dijkstra绠楁硶瀹炵幇鍑芥暟 void Dijkstra(int n,int v,int dist[],int prev[],int **cost){ int i;int j;int maxint ...
