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、遗传算法简介
1 引言
2 遗传算法理论
2.1 遗传算法的生物学基础
2.2 遗传算法的理论基础
2.3 遗传算法的基本概念
2.4 标准的遗传算法
2.5 遗传算法的特点
2.6 遗传算法的改进方向
3 遗传算法流程
4 关键参数说明
三、部分源代码
function varargout = tsp_ga_gui(varargin)
% TSP_GA_GUI MATLAB code for tsp_ga_gui.fig
%
% Last Modified by GUIDE v2.5 25-Feb-2021 15:15:58
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @tsp_ga_gui_OpeningFcn, ...
'gui_OutputFcn', @tsp_ga_gui_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 tsp_ga_gui is made visible.
function tsp_ga_gui_OpeningFcn(hObject, eventdata, handles, varargin)
global hnds
global r nn dsm asz G
global startf
% Choose default command line output for tsp_ga_gui
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes tsp_ga_gui wait for user response (see UIRESUME)
% uiwait(handles.figure1);
hnds=handles;
startf=false; % start flag
asz=10; % area size asx x asz
nn=str2num(get(handles.nn,'string')); % number of cities
ps=str2num(get(handles.ps,'string')); % population size
r=asz*rand(2,nn); % randomly distribute cities
% r(1,:) -x coordinaties of cities
% r(2,:) -y coordinaties of cities
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
update_plots;
% --- Outputs from this function are returned to the command line.
function varargout = tsp_ga_gui_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 randomize.
function randomize_Callback(hObject, eventdata, handles)
global r nn dsm asz
nn=str2num(get(handles.nn,'string')); % number of cities
r=asz*rand(2,nn); % randomly distribute cities
% r(1,:) -x coordinaties of cities
% r(2,:) -y coordinaties of cities
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
update_plots;
% --- Executes on button press in circle.
function circle_Callback(hObject, eventdata, handles)
global r nn dsm asz
nn=str2num(get(handles.nn,'string')); % number of cities
r=zeros(2,nn);
% 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);
% r(1,:) -x coordinaties of cities
% r(2,:) -y coordinaties of cities
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
update_plots;
function nn_Callback(hObject, eventdata, handles)
update_plots_nn_ps;
% --- Executes during object creation, after setting all properties.
function nn_CreateFcn(hObject, eventdata, handles)
% hObject handle to nn (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function ps_Callback(hObject, eventdata, handles)
update_plots_nn_ps;
% --- Executes during object creation, after setting all properties.
function ps_CreateFcn(hObject, eventdata, handles)
% hObject handle to ps (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function ng_Callback(hObject, eventdata, handles)
% hObject handle to ng (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of ng as text
% str2double(get(hObject,'String')) returns contents of ng as a double
% --- Executes during object creation, after setting all properties.
function ng_CreateFcn(hObject, eventdata, handles)
% hObject handle to ng (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
四、运行结果
五、matlab版本及参考文献
1 matlab版本 2014a
2 参考文献 [1] 包子阳,余继周,杨杉.智能优化算法及其MATLAB实例（第2版）[M].电子工业出版社，2016. [2]张岩,吴水根.MATLAB优化算法源代码[M].清华大学出版社，2017.
