一、TSP简介
旅行商问题，即TSP问题（Traveling Salesman Problem）又译为旅行推销员问题、货郎担问题，是数学领域中著名问题之一。假设有一个旅行商人要拜访n个城市，他必须选择所要走的路径，路径的限制是每个城市只能拜访一次，而且最后要回到原来出发的城市。路径的选择目标是要求得的路径路程为所有路径之中的最小值。
TSP的数学模型
二、粒子群算法简介
1 算法
1.1 原理
1.2 性能比较
1.3 步骤
三、部分源代码
function varargout = PSO(varargin)
% PSO M-file for PSO.fig
% PSO, by itself, creates a new PSO or raises the existing
% singleton*.
%
% H = PSO returns the handle to a new PSO or the handle to
% the existing singleton*.
%
% PSO('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in PSO.M with the given input arguments.
%
% PSO('Property','Value',...) creates a new PSO or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before PSO_OpeningFunction gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to PSO_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help PSO
% Last Modified by GUIDE v2.5 12-Jun-2009 22:11:08
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @PSO_OpeningFcn, ...
'gui_OutputFcn', @PSO_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end
if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
% --- Executes just before PSO is made visible.
function PSO_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to PSO (see VARARGIN)
% Choose default command line output for PSO
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes PSO wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = PSO_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{1} = handles.output;
% --- Executes on button press in run.
function run_Callback(hObject, eventdata, handles)
% hObject handle to run (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
TSP_type = get(findobj('tag','tsp'),'Value');
switch TSP_type
case 1
data=load('burma14.txt');
case 2
data=load('ulysses22.txt');
case 3
data=load('bayg29.txt');
case 4
data=load('Oliver30.txt');
case 5
data=load('eil51.txt');
case 6
data=load('st70.txt');
case 7
data=load('pr76.txt');
case 8
data=load('gr96.txt');
case 9
data=load('ch130.txt');
case 10
data=load('ch150.txt');
case 11
data=load('pr226.txt');
end
a=data(:,2);
b=data(:,3);
C=[a b]; %城市坐标矩阵
n=size(C,1); %城市数目
D=zeros(n,n); %城市距离矩阵
%L_best=ones(Nmax,1);
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;
end
D(j,i)=D(i,j);
end
end
Nmax=str2double(get(findobj('tag','N_max'),'string'));
m=str2double(get(findobj('tag','m'),'string'));
algo_type = get(findobj('tag','algo'),'Value');
switch algo_type
case 1
%% 初始化所有粒子
for i=1:m
x(i,:)=randperm(n); %粒子位置
end
F=fitness(x,C,D); %计算种群适应度
%xuhao=xulie(F) %最小适应度种群序号
a1=F(1);
a2=1;
for i=1:m
if a1>=F(i)
a1=F(i);
a2=i;
end
end
xuhao=a2;
Tour_pbest=x; %当前个体最优
Tour_gbest=x(xuhao,:) ; %当前全局最优路径
Pb=inf*ones(1,m); %个体最优记录
Gb=F(a2); %群体最优记录
xnew1=x;
N=1;
while N<=Nmax
%计算适应度
F=fitness(x,C,D);
for i=1:m
if F(i)<Pb(i)
Pb(i)=F(i); %将当前值赋给新的最佳值
Tour_pbest(i,:)=x(i,:);%将当前路径赋给个体最优路径
end
if F(i)<Gb
Gb=F(i);
Tour_gbest=x(i,:);
end
end
% nummin=xulie(Pb) %最小适应度种群序号
a1=Pb(1);
a2=1;
for i=1:m
if a1>=Pb(i)
a1=Pb(i);
a2=i;
end
end
nummin=a2;
Gb(N)=Pb(nummin); %当前群体最优长度
for i=1:m
%% 与个体最优进行交叉
c1=round(rand*(n-2))+1; %在[1,n-1]范围内随机产生一个交叉位
c2=round(rand*(n-2))+1;
while c1==c2
c1=round(rand*(n-2))+1; %在[1,n-1]范围内随机产生一个交叉位
c2=round(rand*(n-2))+1;
end
chb1=min(c1,c2);
chb2=max(c1,c2);
cros=Tour_pbest(i,chb1:chb2); %交叉区域矩阵
ncros=size(cros,2); %交叉区域元素个数
%删除与交叉区域相同元素
for j=1:ncros
for k=1:n
if xnew1(i,k)==cros(j)
xnew1(i,k)=0;
for t=1:n-k
temp=xnew1(i,k+t-1);
xnew1(i,k+t-1)=xnew1(i,k+t);
xnew1(i,k+t)=temp;
end
end
end
end
xnew=xnew1;
%插入交叉区域
for j=1:ncros
xnew1(i,n-ncros+j)=cros(j);
end
%判断产生新路径长度是否变短
dist=0;
for j=1:n-1
dist=dist+D(xnew1(i,j),xnew1(i,j+1));
end
dist=dist+D(xnew1(i,1),xnew1(i,n));
if F(i)>dist
x(i,:)=xnew1(i,:);
end
%% 与全体最优进行交叉
c1=round(rand*(n-2))+1; %在[1,n-1]范围内随机产生一个交叉位
c2=round(rand*(n-2))+1;
while c1==c2
c1=round(rand*(n-2))+1; %在[1,n-1]范围内随机产生一个交叉位
c2=round(rand*(n-2))+1;
end
chb1=min(c1,c2);
chb2=max(c1,c2);
cros=Tour_gbest(chb1:chb2); %交叉区域矩阵
ncros=size(cros,2); %交叉区域元素个数
%删除与交叉区域相同元素
for j=1:ncros
for k=1:n
if xnew1(i,k)==cros(j)
xnew1(i,k)=0;
for t=1:n-k
temp=xnew1(i,k+t-1);
xnew1(i,k+t-1)=xnew1(i,k+t);
xnew1(i,k+t)=temp;
end
end
end
end
xnew=xnew1;
%插入交叉区域
for j=1:ncros
xnew1(i,n-ncros+j)=cros(j);
end
%判断产生新路径长度是否变短
dist=0;
for j=1:n-1
dist=dist+D(xnew1(i,j),xnew1(i,j+1));
end
dist=dist+D(xnew1(i,1),xnew1(i,n));
if F(i)>dist
x(i,:)=xnew1(i,:);
end
%% 进行变异操作
c1=round(rand*(n-1))+1; %在[1,n]范围内随机产生一个变异位
c2=round(rand*(n-1))+1;
temp=xnew1(i,c1);
xnew1(i,c1)=xnew1(i,c2);
xnew1(i,c2)=temp;
%判断产生新路径长度是否变短
dist=0;
for j=1:n-1
dist=dist+D(xnew1(i,j),xnew1(i,j+1));
end
dist=dist+D(xnew1(i,1),xnew1(i,n));
%dist=dist(xnew1(i,:),D);
if F(i)>dist
x(i,:)=xnew1(i,:);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% F=(x,C,D) %计算种群适应度
%xuhao=xulie(F) %最小适应度种群序号
a1=F(1);
a2=1;
for i=1:m
if a1>=F(i)
a1=F(i);
a2=i;
end
end
xuhao=a2;
L_best(N)=min(F);
Tour_gbest=x(xuhao,:); %当前全局最优路径
N=N+1;
axes(handles.city) %城市路径状态
scatter(C(:,1),C(:,2));
hold on
plot([C(Tour_gbest(1),1),C(Tour_gbest(n),1)],[C(Tour_gbest(1),2),C(Tour_gbest(n),2)],'ms-','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','g')
for ii=2:n
plot([C(Tour_gbest(ii-1),1),C(Tour_gbest(ii),1)],[C(Tour_gbest(ii-1),2),C(Tour_gbest(ii),2)],'ms-','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','g')
end
hold off
axes(handles.shoulian) %收敛曲线
plot(L_best);
set(findobj('tag','N'),'string',num2str(N-1));%当前迭代次数
set(findobj('tag','tour'),'string',num2str(Tour_gbest));%当前最优路径
set(findobj('tag','L'),'string',num2str(min(L_best)));%当前最优路径长度 %%%这里的L_best是当前最优路径？？？
end