【路径规划】基于遗传算法求解多旅行商问题matlab-优快云博客

本文链接：https://blog.youkuaiyun.com/Matlab_dashi/article/details/140115423

一.进化论知识

　　作为遗传算法生物背景的介绍，下面内容了解即可：

　　种群(Population)：生物的进化以群体的形式进行，这样的一个群体称为种群。

　　个体：组成种群的单个生物。

　　基因 ( Gene ) ：一个遗传因子。

　　染色体 ( Chromosome ) ：包含一组的基因。

　　生存竞争，适者生存：对环境适应度高的、牛B的个体参与繁殖的机会比较多，后代就会越来越多。适应度低的个体参与繁殖的机会比较少，后代就会越来越少。

　　遗传与变异：新个体会遗传父母双方各一部分的基因，同时有一定的概率发生基因变异。

　　简单说来就是：繁殖过程，会发生基因交叉( Crossover ) ，基因突变 ( Mutation ) ，适应度( Fitness )低的个体会被逐步淘汰，而适应度高的个体会越来越多。那么经过N代的自然选择后，保存下来的个体都是适应度很高的，其中很可能包含史上产生的适应度最高的那个个体。

二.遗传算法思想

　　借鉴生物进化论，遗传算法将要解决的问题模拟成一个生物进化的过程，通过复制、交叉、突变等操作产生下一代的解，并逐步淘汰掉适应度函数值低的解，增加适应度函数值高的解。这样进化N代后就很有可能会进化出适应度函数值很高的个体。

　　举个例子，使用遗传算法解决“0-1背包问题”的思路：0-1背包的解可以编码为一串0-1字符串(0：不取，1：取) ；首先，随机产生M个0-1字符串，然后评价这些0-1字符串作为0-1背包问题的解的优劣；然后，随机选择一些字符串通过交叉、突变等操作产生下一代的M个字符串，而且较优的解被选中的概率要比较高。这样经过G代的进化后就可能会产生出0-1背包问题的一个“近似最优解”。

　　编码：需要将问题的解编码成字符串的形式才能使用遗传算法。最简单的一种编码方式是二进制编码，即将问题的解编码成二进制位数组的形式。例如，问题的解是整数，那么可以将其编码成二进制位数组的形式。将0-1字符串作为0-1背包问题的解就属于二进制编码。

　　遗传算法有3个最基本的操作：选择，交叉，变异。

　　选择：选择一些染色体来产生下一代。一种常用的选择策略是 “比例选择”，也就是个体被选中的概率与其适应度函数值成正比。假设群体的个体总数是M，那么那么一个体Xi被选中的概率为f(Xi)/( f(X1) + f(X2) + …….. + f(Xn) ) 。比例选择实现算法就是所谓的“轮盘赌算法”( Roulette Wheel Selection )

交叉(Crossover)：2条染色体交换部分基因，来构造下一代的2条新的染色体。例如：

交叉前：

00000|011100000000|10000

11100|000001111110|00101

交叉后：

00000|000001111110|10000

11100|011100000000|00101

染色体交叉是以一定的概率发生的，这个概率记为Pc 。

变异(Mutation)：在繁殖过程，新产生的染色体中的基因会以一定的概率出错，称为变异。变异发生的概率记为Pm 。例如：

变异前：

000001110000000010000

变异后：

000001110000100010000

适应度函数 ( Fitness Function )：用于评价某个染色体的适应度，用f(x)表示。有时需要区分染色体的适应度函数与问题的目标函数。例如：0-1背包问题的目标函数是所取得物品价值，但将物品价值作为染色体的适应度函数可能并不一定适合。适应度函数与目标函数是正相关的，可对目标函数作一些变形来得到适应度函数。

function varargout = guimtsp(varargin)
% GUIMTSP MATLAB code for guimtsp.fig
%      GUIMTSP, by itself, creates a new GUIMTSP or raises the existing
%      singleton*.
%
%      H = GUIMTSP returns the handle to a new GUIMTSP or the handle to
%      the existing singleton*.
%
%      GUIMTSP('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in GUIMTSP.M with the given input arguments.
%
%      GUIMTSP('Property','Value',...) creates a new GUIMTSP or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before guimtsp_OpeningFcn gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to guimtsp_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 guimtsp

% Last Modified by GUIDE v2.5 28-Dec-2019 12:21:56

% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton',  gui_Singleton, ...
                   'gui_OpeningFcn', @guimtsp_OpeningFcn, ...
                   'gui_OutputFcn',  @guimtsp_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 guimtsp is made visible.
function guimtsp_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 guimtsp (see VARARGIN)

% Choose default command line output for guimtsp
handles.output = hObject;

% Update handles structure
guidata(hObject, handles);

% UIWAIT makes guimtsp wait for user response (see UIRESUME)
% uiwait(handles.figure1);


% --- Outputs from this function are returned to the command line.
function varargout = guimtsp_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;



function edit1_Callback(hObject, eventdata, handles)
% hObject    handle to edit1 (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 edit1 as text
%        str2double(get(hObject,'String')) returns contents of edit1 as a double


% --- Executes during object creation, after setting all properties.
function edit1_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit1 (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 edit2_Callback(hObject, eventdata, handles)
% hObject    handle to edit2 (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 edit2 as text
%        str2double(get(hObject,'String')) returns contents of edit2 as a double


% --- Executes during object creation, after setting all properties.
function edit2_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit2 (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 edit3_Callback(hObject, eventdata, handles)
% hObject    handle to edit3 (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 edit3 as text
%        str2double(get(hObject,'String')) returns contents of edit3 as a double


% --- Executes during object creation, after setting all properties.
function edit3_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit3 (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 edit4_Callback(hObject, eventdata, handles)
% hObject    handle to edit4 (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 edit4 as text
%        str2double(get(hObject,'String')) returns contents of edit4 as a double


% --- Executes during object creation, after setting all properties.
function edit4_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit4 (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 edit5_Callback(hObject, eventdata, handles)
% hObject    handle to edit5 (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 edit5 as text
%        str2double(get(hObject,'String')) returns contents of edit5 as a double


% --- Executes during object creation, after setting all properties.
function edit5_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit5 (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 pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton1 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
%  主函数
% 输入：
% XY：各个城市坐标的 N*2 矩阵，N 为城市的个数
% DMAT：各个城市之间的距离矩阵
% SALESMEN ：旅行商人数
% MIN_TOUR：每个人所经过的最少城市点
% POP_SIZE：种群大小
% NUM_ITER：迭代次数
% 输出：
% 最优路线
% 总距离
global n;
% 初始化
a=get(handles.edit1,'String');%城市个数
num=str2num(a);
xy = 10*rand(num,2);
N = size(xy,1);
a = meshgrid(1:N);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),N,N);

b=get(handles.edit2,'String');%旅行商人数
salesmen=str2num(b);

c=get(handles.edit3,'String');%每个人所经过的最少城市点
min_tour=str2num(c);

d=get(handles.edit4,'String');%种群大小 
pop_size=str2num(d);

e=get(handles.edit5,'String');%迭代次数
num_iter=str2num(e);

show_prog = 1;
show_res = 1;
%调整输入数据
[nr,nc] = size(dmat);
if N ~= nr || N ~= nc
    error('Invalid XY or DMAT inputs!')
end
n = N;
mtsp_ga(xy,dmat,salesmen,min_tour,pop_size,num_iter,1,1)
% set(handles.edit6,'String',num2str(min_dist));




function edit6_Callback(hObject, eventdata, handles)
% hObject    handle to edit6 (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 edit6 as text
%        str2double(get(hObject,'String')) returns contents of edit6 as a double


% --- Executes during object creation, after setting all properties.
function edit6_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit6 (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