Matlab基于蚁群算法求解多旅行商MTSP问题

一、蚁群算法简介

蚁群算法是对自然界蚂蚁的寻径方式进行模似而得出的一种仿生算法：蚂蚁在运动过程中，能够在它所经过的路径上留下信息素(pheromone)的物质进行信息传递，而且蚂蚁在运动过程中能够感知这种物质，并以此指导自己的运动方向。由大量蚂蚁组成的蚁群集体行为便表现出一种信息正反馈现象：某一路径上走过的蚂蚁越多，则后来者选择该路径的概率就越大。蚁群算法具有分布计算、信息正反馈和启发式搜索的特征，本质上是进化算法中的一种启发式全局优化算法。

二、TSP问题（旅行商问题）

T S P 问题可以用一个带权完全图G=(N,A)来表示，其中N是带有n=|N|点（城市）的集合，A是完全连接这些点的边的集合。每一条边（i,j）属于A都带有一个权值，它代表城市i与城市j之间的距离。TSP问题就是要找到图中的最短哈密尔顿回路。

1、构建图：构建图与问题描述图是一致的，成份的集合C对应着点的集合（即：C=N），连接对应着边的集合（即L=A）,且每一条边都带有一个权值，代表点i和j之间的距离。
2、约束条件：所有城市都要被访问且每个城市最多只能被访问一次。
3、信息素和启发式信息：TSP 问题中的信息素表示在访问城市i后直接访问城市j的期望度。启发式信息值一般与城市i和城市j的距离成反比。
4、解的构建：每只蚂蚁最初都从随机选择出来的城市出发，每经过一次迭代蚂蚁就向解中添加一个还没有访问过的城市。当所有城市都被蚂蚁访问过之后，解的构建就终止。

三、实现流程及伪代码

function varargout = AntColonyVRPGUI(varargin)
% ANTCOLONYVRPGUI M-file for AntColonyVRPGUI.fig
%      ANTCOLONYVRPGUI, by itself, creates a new ANTCOLONYVRPGUI or raises the existing
%      singleton*.
%
%      H = ANTCOLONYVRPGUI returns the handle to a new ANTCOLONYVRPGUI or the handle to
%      the existing singleton*.
%
%      ANTCOLONYVRPGUI('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in ANTCOLONYVRPGUI.M with the given input arguments.
%
%      ANTCOLONYVRPGUI('Property','Value',...) creates a new ANTCOLONYVRPGUI or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before AntColonyVRPGUI_OpeningFcn gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to AntColonyVRPGUI_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 AntColonyVRPGUI% Last Modified by GUIDE v2.5 11-Jun-2015 00:13:48% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...'gui_Singleton',  gui_Singleton, ...'gui_OpeningFcn', @AntColonyVRPGUI_OpeningFcn, ...'gui_OutputFcn',  @AntColonyVRPGUI_OutputFcn, ...'gui_LayoutFcn',  [] , ...'gui_Callback',   []);
if nargin && ischar(varargin{1})gui_State.gui_Callback = str2func(varargin{1});
endif nargout[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
elsegui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT% --- Executes just before AntColonyVRPGUI is made visible.
function AntColonyVRPGUI_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 AntColonyVRPGUI (see VARARGIN)
% Choose default command line output for AntColonyVRPGUI
handles.output = hObject;%% change !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
handles.ismdvrp = true; %!!!
%%
if handles.ismdvrp == true[handles.initClusters, handles.coordinates] = INIT;handles.clusters = handles.initClusters;set(handles.uipanelBases,'Visible','on');create_init_plot_MDVRP(handles.coordinates, handles.clusters);
else%initialization[vehicles,demands,dist_stations,dist_bases] = INIT_VRP;handles.vehicles = vehicles;handles.demands = demands;handles.distances_stations = dist_stations;handles.distances_bases = dist_bases;set(handles.uipanelBases,'Visible','off');
end
% Update handles structure
guidata(hObject, handles);% UIWAIT makes AntColonyVRPGUI wait for user response (see UIRESUME)
% uiwait(handles.figure1);% --- Outputs from this function are returned to the command line.
function varargout = AntColonyVRPGUI_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 selection change in algorithmPopupmenu.
function algorithmPopupmenu_Callback(hObject, eventdata, handles)
% hObject    handle to algorithmPopupmenu (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)% Hints: contents = cellstr(get(hObject,'String')) returns algorithmPopupmenu contents as cell array
%        contents{get(hObject,'Value')} returns selected item from algorithmPopupmenu%set invisible error messages
set(handles.errorMandatoryEditFields,'Visible','off');
%erase text in edit fields
set(handles.evaporationPheromoneEdit,'String','');
set(handles.attractStationEdit,'String','');
set(handles.increasePheromoneEdit,'String','');
set(handles.amountPheromoneEdit,'String','');
set(handles.eliteAntsEdit,'String','');
%set disabled all edit fields
set(handles.evaporationPheromoneEdit,'Enable','off');
set(handles.attractStationEdit,'Enable','off');
set(handles.increasePheromoneEdit,'Enable','off');
set(handles.amountPheromoneEdit,'Enable','off');
set(handles.eliteAntsEdit,'Enable','off');
%set disabled run button
set(handles.runButton,'Enable','off');
%set to 0 all results
set(handles.lengthWayText,'String','-');
set(handles.subroutesNText,'String','-');
set(handles.timeSpentText,'String','-');
if handles.ismdvrp == true%set invisible bases' listboxset(handles.listboxBases,'Visible','off');set(handles.totalLengthText,'Visible','off');set(handles.totalLengthText,'String','-');set(handles.totalLengthLabel,'Visible','off');%clear plotcla;create_init_plot_MDVRP(handles.coordinates, handles.clusters);
end
%clear plot
%cla;
%clear legend
legend('off');
val = get(hObject,'Value');
if val ~= 1 %not placeholder's text (not be executed)if val ~= 2 %not Clark-Wright algorithm%enable edit fields if val == 5 %AntAlg with elite antsset(handles.eliteAntsEdit,'Enable','on');endset(handles.evaporationPheromoneEdit,'Enable','on');set(handles.attractStationEdit,'Enable','on');set(handles.increasePheromoneEdit,'Enable','on');set(handles.amountPheromoneEdit,'Enable','on');end%enable run buttonset(handles.runButton,'Enable','on');
end% --- Executes during object creation, after setting all properties.
function algorithmPopupmenu_CreateFcn(hObject, eventdata, handles)
% hObject    handle to algorithmPopupmenu (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called% Hint: popupmenu 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');
endfunction evaporationPheromoneEdit_Callback(hObject, eventdata, handles)
% hObject    handle to evaporationPheromoneEdit (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 evaporationPheromoneEdit as text
%        str2double(get(hObject,'String')) returns contents of evaporationPheromoneEdit as a double% --- Executes during object creation, after setting all properties.
function evaporationPheromoneEdit_CreateFcn(hObject, eventdata, handles)
% hObject    handle to evaporationPheromoneEdit (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');
endfunction attractStationEdit_Callback(hObject, eventdata, handles)
% hObject    handle to attractStationEdit (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 attractStationEdit as text
%        str2double(get(hObject,'String')) returns contents of attractStationEdit as a double% --- Executes during object creation, after setting all properties.
function attractStationEdit_CreateFcn(hObject, eventdata, handles)
% hObject    handle to attractStationEdit (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');
endfunction increasePheromoneEdit_Callback(hObject, eventdata, handles)
% hObject    handle to increasePheromoneEdit (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 increasePheromoneEdit as text
%        str2double(get(hObject,'String')) returns contents of increasePheromoneEdit as a double% --- Executes during object creation, after setting all properties.
function increasePheromoneEdit_CreateFcn(hObject, eventdata, handles)
% hObject    handle to increasePheromoneEdit (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');
endfunction amountPheromoneEdit_Callback(hObject, eventdata, handles)
% hObject    handle to amountPheromoneEdit (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 amountPheromoneEdit as text
%        str2double(get(hObject,'String')) returns contents of amountPheromoneEdit as a double% --- Executes during object creation, after setting all properties.
function amountPheromoneEdit_CreateFcn(hObject, eventdata, handles)
% hObject    handle to amountPheromoneEdit (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');
endfunction eliteAntsEdit_Callback(hObject, eventdata, handles)
% hObject    handle to eliteAntsEdit (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 eliteAntsEdit as text
%        str2double(get(hObject,'String')) returns contents of eliteAntsEdit as a double% --- Executes during object creation, after setting all properties.
function eliteAntsEdit_CreateFcn(hObject, eventdata, handles)
% hObject    handle to eliteAntsEdit (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% --- Executes on button press in runButton.
function runButton_Callback(hObject, eventdata, handles)
% hObject    handle to runButton (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)%clear legend
legend('off');
%clear plot
%cla;
%set invisible error messages
set(handles.errorMandatoryEditFields,'Visible','off');indexAlg = get(handles.algorithmPopupmenu,'Value');
if indexAlg ~= 1 %not placeholder's text (not be executed)if indexAlg ~= 2 %not Clark-Wright algorithmif indexAlg == 5 %AntAlg with elite antsif isempty(get(handles.eliteAntsEdit,'String'))set(handles.errorMandatoryEditFields,'Visible','on');return;endendif  ( isempty(get(handles.evaporationPheromoneEdit,'String')) || ...isempty(get(handles.attractStationEdit,'String')) || ...isempty(get(handles.increasePheromoneEdit,'String')) || ...isempty(get(handles.amountPheromoneEdit,'String')) )set(handles.errorMandatoryEditFields,'Visible','on');return;endend%set disabled run buttonset(handles.runButton,'Enable','off');if handles.ismdvrp == trueclusters = runAlgorithmMDVRP(indexAlg, handles);handles.clusters = clusters;listbox=findall(gcf,'tag','listboxBases');guidata(listbox,handles);%select first value in bases' listbox set(handles.listboxBases,'Value',1);listboxBases_Callback(listbox, eventdata, handles);elserunAlgorithmVRP(indexAlg, handles);    end%set enabled run buttonset(handles.runButton,'Enable','on');%set enabled zoom toolsset(handles.toolZoomIn,'Enable','on');set(handles.toolZoomOut,'Enable','on');%set enabled pan toolset(handles.toolPan,'Enable','on');zoom reset;
endfunction [clusters] = runAlgorithmMDVRP(index, handles)if index ~= 1if index ~= 2e = str2double(get(handles.evaporationPheromoneEdit,'String'));alpha = str2double(get(handles.attractStationEdit,'String'));beta = str2double(get(handles.increasePheromoneEdit,'String'));tau0 = str2double(get(handles.amountPheromoneEdit,'String'));E = str2double(get(handles.eliteAntsEdit,'String'));endtrytStart = tic; %start spent timeclusters = handles.initClusters;handles.clusters = clusters;basesName = cell(1,length(clusters)+1);basesName{1} = 'Full view';for c = 1:length(clusters)switch indexcase 2 %Clark-Wright[ Route, RouteLength, vehicles ] = Clark_Wright_VRP( ...clusters(c).demands, clusters(c).diststations, ...clusters(c).distbases, clusters(c).vehicles_capacity );case 3 %Ant-minpath[Route, RouteLength, vehicles] = ANT_colony_algorithm_VRP_minpath( ...clusters(c).diststations, clusters(c).distbases, ...clusters(c).demands, [e alpha beta tau0], clusters(c).vehicles_capacity );case 4 %Ant-partition[Route, RouteLength, vehicles] = ANT_colony_algorithm_VRP( ...clusters(c).diststations, clusters(c).distbases, ...clusters(c).demands, [e alpha beta tau0], clusters(c).vehicles_capacity );case 5 %Ant-elite ants[Route, RouteLength, vehicles] = ANT_colony_algorithm_VRP_with_elite_ants( ...clusters(c).diststations, clusters(c).distbases, ...clusters(c).demands, [e alpha beta tau0 E], clusters(c).vehicles_capacity );endhandles.clusters(c).mdvrp = changeStations(clusters, vehicles, RouteLength, Route, c);basesName{c + 1} = sprintf('Base #%d',c); %saving bases that need to be added to listboxendtElapsed = toc(tStart); %end spent timecatch MEmsgbox(strcat('Error occured: ',ME.message),'Error','error');endclusters = handles.clusters;%clear plotcla;create_plot_route_with_vehicles_MDVRP(handles.coordinates, handles.clusters);set(handles.timeSpentText,'String',sprintf('%fs',tElapsed));set(handles.listboxBases, 'String', basesName);set(handles.listboxBases, 'Visible','on');set(handles.totalLengthText,'String',num2str(getTotalLength(handles.clusters)));set(handles.totalLengthText,'Visible','on');set(handles.totalLengthLabel,'Visible','on');endfunction [mdvrp] = changeStations(clusters, vehicles, LR, R, clusterN)mdvrp = struct('length_route',[],'vehicles',[],'simpleVehicles',[],'num_of_subroutes',[]);len = length(vehicles);mdvrp.simpleVehicles = vehicles;for v = 1:lenvehicles(v).route(vehicles(v).route == 1) = 0;len_route = length(vehicles(v).route);for vr = 1:len_routeif vehicles(v).route(vr) ~= 0 %羼腓 礤 徉玎vehicles(v).route(vr) = clusters(clusterN).stations(vehicles(v).route(vr)-1);endendendmdvrp.num_of_subroutes = number_of_subroutes(R);mdvrp.length_route = LR;mdvrp.vehicles = vehicles;function [tlength] = getTotalLength(clusters)tlength = 0;clen = length(clusters);for c = 1:clentlength = tlength + clusters(c).mdvrp.length_route;endfunction runAlgorithmVRP(index, handles)if index ~= 1if index ~= 2e = str2double(get(handles.evaporationPheromoneEdit,'String'));alpha = str2double(get(handles.attractStationEdit,'String'));beta = str2double(get(handles.increasePheromoneEdit,'String'));tau0 = str2double(get(handles.amountPheromoneEdit,'String'));E = str2double(get(handles.eliteAntsEdit,'String'));endtrytStart = tic; %start spent timeswitch indexcase 2 %Clark-Wright[Route,RouteLength,vehicles] = Clark_Wright_VRP( handles.demands, ...handles.distances_stations, handles.distances_bases, handles.vehicles );case 3 %Ant-minpath[Route,RouteLength,vehicles] = ANT_colony_algorithm_VRP_minpath( handles.distances_stations,...handles.distances_bases, handles.demands, [e alpha beta tau0], handles.vehicles);case 4 %Ant-partition[Route,RouteLength,vehicles] = ANT_colony_algorithm_VRP( handles.distances_stations, ...handles.distances_bases, handles.demands, [e alpha beta tau0], handles.vehicles);case 5 %Ant-elite ants[Route,RouteLength,vehicles] = ANT_colony_algorithm_VRP_with_elite_ants( ...handles.distances_stations, handles.distances_bases, handles.demands, ...[e alpha beta tau0 E], handles.vehicles);endtElapsed = toc(tStart); %end spent timecreate_plot_route_with_vehicles( add_bases_to_distances(handles.distances_stations, ...handles.distances_bases), vehicles, [0 handles.demands] );catch MEmsgbox(strcat('Error occured: ',ME.message),'Error','error');endset(handles.lengthWayText,'String',num2str(RouteLength));set(handles.subroutesNText,'String',num2str(number_of_subroutes(Route)));set(handles.timeSpentText,'String',sprintf('%fs',tElapsed));end% --------------------------------------------------------------------
function dataTooltip_ClickedCallback(hObject, eventdata, handles)
% hObject    handle to dataTooltip (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)% --------------------------------------------------------------------
function algorithmTooltip_ClickedCallback(hObject, eventdata, handles)
% hObject    handle to algorithmTooltip (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)% --- Executes on selection change in listboxBases.
function listboxBases_Callback(hObject, eventdata, handles)
% hObject    handle to listboxBases (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)% Hints: contents = cellstr(get(hObject,'String')) returns listboxBases contents as cell array
%        contents{get(hObject,'Value')} returns selected item from listboxBases%clear legend
legend('off');
%clear plot
cla;index = get(handles.listboxBases,'value') - 1;
if index == 0 %if user want to see the full graph of routescreate_plot_route_with_vehicles_MDVRP(handles.coordinates, handles.clusters);set(handles.lengthWayText,'String','-');set(handles.subroutesNText,'String','-');
elsecreate_plot_of_base_MDVRP(handles.coordinates, handles.clusters, index);set(handles.lengthWayText,'String',num2str(handles.clusters(index).mdvrp.length_route));set(handles.subroutesNText,'String',num2str(handles.clusters(index).mdvrp.num_of_subroutes));
end% --- Executes during object creation, after setting all properties.
function listboxBases_CreateFcn(hObject, eventdata, handles)
% hObject    handle to listboxBases (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called% Hint: listbox 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 aboutMenu_Callback(hObject, eventdata, handles)
% hObject    handle to aboutMenu (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)About %call gui About.m% --------------------------------------------------------------------
function fileMenu_Callback(hObject, eventdata, handles)
% hObject    handle to fileMenu (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)% --------------------------------------------------------------------
function anotherVRPSubmenu_Callback(hObject, eventdata, handles)
% hObject    handle to anotherVRPSubmenu (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)% --------------------------------------------------------------------
function newDataSubmenu_Callback(hObject, eventdata, handles)
% hObject    handle to newDataSubmenu (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

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✅作者简介:热爱科研的Matlab仿真开发者,修心和技术同步精进,matlab项目合作可私信.
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