From 26d826209af4c8ce1ecfee5fc473972e81069076 Mon Sep 17 00:00:00 2001
From: David Lee <64404787+DavidLee233@users.noreply.github.com>
Date: Sun, 17 Oct 2021 21:43:09 +0800
Subject: [PATCH] Add files via upload

---
 ACOPN_fixed.m    | 216 +++++++++++++++++++++++++++++++++++++++++++++++
 ACOPN_original.m | 212 ++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 428 insertions(+)
 create mode 100644 ACOPN_fixed.m
 create mode 100644 ACOPN_original.m

diff --git a/ACOPN_fixed.m b/ACOPN_fixed.m
new file mode 100644
index 0000000..318761a
--- /dev/null
+++ b/ACOPN_fixed.m
@@ -0,0 +1,216 @@
+close all
+clc
+clear
+%%初始化标识和变迁节点%%
+nodes_data=cell(0);
+M_1=[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; %网中25个标识对应的符号
+M_2=[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_3=[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_4=[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_5=[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_6=[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_7=[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_8=[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_9=[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_10=[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_11=[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_12=[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_13=[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0];
+M_14=[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0];
+M_15=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0];
+M_16=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0];
+M_17=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0];
+M_18=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0];
+M_19=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0];
+M_20=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0];
+M_21=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0];
+M_22=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0];
+M_23=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0];
+M_24=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0];
+M_25=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1];
+nodes_data(1,:)={1,[2,3],[1,1],[M_2;M_3]};  %根据变迁的邻近变迁的发生权构造变迁元胞组
+nodes_data(2,:)={2,[4,5],[1,sqrt(2)],[M_4;M_5]};
+nodes_data(3,:)={3,[6],[1],[M_6]};
+nodes_data(4,:)={4,[7,8],[sqrt(2),1],[M_7;M_5]};
+nodes_data(5,:)={5,[9,10],[sqrt(2),1],[M_8;M_7]};
+nodes_data(6,:)={6,[11,12],[1,sqrt(2)],[M_9;M_10]};
+nodes_data(7,:)={7,[13,14],[1,1],[M_8;M_13]};
+nodes_data(8,:)={8,[9,10],[sqrt(2),1],[M_8;M_7]};
+nodes_data(9,:)={9,[15],[1],[M_18]};
+nodes_data(10,:)={10,[13,14],[1,1],[M_8;M_13]};
+nodes_data(11,:)={11,[16,17],[1,1],[M_10;M_11]};
+nodes_data(12,:)={12,[18],[1],[M_12]};
+nodes_data(13,:)={13,[15],[1],[M_18]};
+nodes_data(14,:)={14,[23,24],[sqrt(2),1],[M_14;M_15]};
+nodes_data(15,:)={15,[29],[1],[M_19]};
+nodes_data(16,:)={16,[18],[1],[M_12]};
+nodes_data(17,:)={17,[19,20],[1,sqrt(2)],[M_16;M_17]};
+nodes_data(18,:)={18,[21,22],[1,sqrt(2)],[M_18;M_19]};
+nodes_data(19,:)={19,[27],[1],[M_17]};
+nodes_data(20,:)={20,[28],[1],[M_20]};
+nodes_data(21,:)={21,[29],[1],[M_19]};
+nodes_data(22,:)={22,[30,31],[1,sqrt(2)],[M_23;M_24]};
+nodes_data(23,:)={23,[25],[1],[M_21]};
+nodes_data(24,:)={24,[26],[1],[M_14]};
+nodes_data(25,:)={25,[33],[1],[M_22]};
+nodes_data(26,:)={26,[25],[1],[M_21]};
+nodes_data(27,:)={27,[28],[1],[M_20]};
+nodes_data(28,:)={28,[32],[1],[M_23]};
+nodes_data(29,:)={29,[30,31],[1,sqrt(2)],[M_23;M_24]};
+nodes_data(30,:)={30,[35],[1],[M_24]};
+nodes_data(31,:)={31,[36],[1],[M_25]};
+nodes_data(32,:)={32,[35],[1],[M_24]};
+nodes_data(33,:)={33,[34],[1],[M_25]};
+nodes_data(35,:)={35,[36],[1],[M_25]};
+
+
+%% 始末节点%%
+node_start=1;
+node_end=[34,36];
+%%% 蚁群定义%%%%%
+m=50;                               % 蚂蚁数量
+n=size(nodes_data,1);               % 节点数量
+alpha=1;                            % 信息素重要程度因子
+beta=5;                             % 启发函数重要程度因子
+Rho=0.5;                            % 信息素挥发因子
+Q=1;                              % 信息素增加强度系数
+%%迭代过程初始化定义%%%%
+iter=1;                             % 迭代次数初值
+iter_max=100;                       % 最大迭代次数
+Route_best=cell(iter_max,1);        % 各代最佳路径
+Length_best=zeros(iter_max,1);      % 各代最佳路径长度
+Length_ave=zeros(iter_max,1);       % 各代路径平均长度
+Place_best=cell(iter_max,1);        % 各代最佳路径访问的库所
+%%将信息素、挥发因子一并放入nodes_data中%%%%%
+Delta_Tau_initial=nodes_data(:,1:2);
+for i=1:size(nodes_data,1)
+    nodes_data{i,5}=ones(1,length(nodes_data{i,3}));         % 初始信息素均设置为1
+    nodes_data{i,6}=1./nodes_data{i,3};                      % 启发函数设置为距离的倒数
+    Delta_Tau_initial{i,3}=zeros(1,length(nodes_data{i,3})); % 信息素变化量均为0
+end
+%% 迭代寻找最佳路径%%%
+while iter<iter_max
+    route=cell(0);
+    place=cell(0);
+    for i=1:m                                               % 逐个蚂蚁进路径选择
+        neighbor_allow=cell(0);
+        node_step=node_start;
+        path=node_step;
+        path_M = 0;
+        if node_step==node_start
+            marking=M_1;
+        else
+            marking=nodes_data{node_step,4};
+        end
+        dist=0;
+        while ~isequal(marking(end,:), M_25)
+            neighbor=nodes_data{node_step,2};                    %寻找邻近节点
+            neighbor_allow = [];
+            for k=1:length(neighbor)
+                if ~ismember(neighbor(k),path)
+                    neighbor_allow(end+1) = neighbor(k);
+                end
+            end           
+            if isempty(neighbor_allow)
+                neighbor_allow=cell(0);
+                node_step=node_start;
+                path=node_step;
+                if node_step==node_start
+                    marking=M_1;
+                else
+                    marking=nodes_data{node_step,4};
+                end
+                dist=0;
+                continue
+            end
+            P=neighbor_allow;                                  %计算下一个节点的访问概率
+            for k=1:length(neighbor_allow)
+                idx = find(neighbor_allow(k) == nodes_data{node_step,2});
+                P(2,k)=nodes_data{node_step,5}(idx)^alpha*nodes_data{node_step,6}(idx)^beta;
+            end
+            P(2,:)=P(2,:)/sum(P(2,:));
+            %%轮盘赌法选择下一个访问节点%%%%
+            Pc=cumsum(P(2,:));
+            Pc=[0,Pc];
+            randnum=rand;
+            for k=1:length(Pc)-1
+                if randnum>Pc(k)&&randnum<Pc(k+1)
+                    target_node=neighbor_allow(k);
+                end
+            end
+            %%%计算单步距离%%%
+            idx=find(nodes_data{node_step,2}==target_node);
+            dist=dist+nodes_data{node_step,3}(idx);
+            %%%更新路径、节点以及标识%%%
+            path(end+1)=target_node;                         % 更新路径集合
+            marking(end+1,:)=nodes_data{node_step,4}(idx,:); % 更新标识
+            node_step=target_node;                           % 更新下一个目标节点变迁
+        end
+        Length(i,1)=dist;                                    % 存放第i只蚂蚁的累计距离和对应路径
+        route{i,1}=path;
+        place{i,1}=marking;
+    end
+    %%计算这一代的m只蚂蚁中最短距离和对应路径%%%
+    if iter==1
+        [min_Length,min_index]=min(Length);
+        Length_best(iter)=min_Length;
+        Length_ave(iter)=mean(Length);
+        Route_best{iter,1}=route{min_index,1};
+        Place_best(iter,1)=place(min_index,1);
+    else
+        [min_Length,min_index]=min(Length);
+        Length_best(iter)=min(Length_best(iter-1),min_Length);
+        Length_ave(iter)=mean(Length);
+        if Length_best(iter)==min_Length
+            Route_best{iter,1}=route{min_index,1};
+            Place_best(iter,1)=place(min_index,1);
+        else
+            Route_best{iter,1}=Route_best{iter-1,1};
+            Place_best(iter,1)=Place_best(iter-1,1);
+        end
+    end
+    %%%更新信息素%%%
+    Delta_Tau=Delta_Tau_initial;
+    for i=1:m                                                   % 逐个蚂蚁计算
+        for j=1:length(route{i,1})-1
+            node_start_temp=route{i,1}(j);
+            node_end_temp=route{i,1}(j+1);
+            idx=find(Delta_Tau{node_start_temp,2}==node_end_temp);
+            if ismember(route{i,1}(j),[1,2,3,5,6,9,12,15,18,22,29,31,35]);
+                Delta_Tau{node_start_temp,3}(idx)=Delta_Tau{node_start_temp,3}(idx)+1/8.2426;
+            else
+                Delta_Tau{node_start_temp,3}(idx)=Delta_Tau{node_start_temp,3}(idx);
+            end
+        end
+    end
+    %%考虑挥发因子，更新信息素%%%
+    for i=1:size(nodes_data,1)
+        nodes_data{i,5}=(1-Rho)*nodes_data{i,5}+Rho*Delta_Tau{i,3};
+    end
+    iter=iter+1;
+end
+% %绘图、结果%%%
+figure
+plot(1:iter_max,Length_best,'b',1:iter_max,Length_ave,'r');
+legend('最短距离','平均距离');
+xlabel('迭代次数');
+ylabel('距离');
+title('各代最短距离与平均距离对比');
+%% 最优路径%%%
+[dist_min,idx]=min(Length_best(1:end-1));
+path_opt=Route_best{idx,1};
+marking_opt=Place_best{idx,1};
+%%将marking_opt转为字符输出%%%
+M_set = cell(0);
+M_seq = [];
+for i = 1:size(marking_opt,1)
+    idx = find(marking_opt(i,:) == 1);
+    M_set{i,1} = strcat('M_',num2str(idx));
+    M_seq = [M_seq, strcat(M_set{i,1},',')];
+end
+disp('机器人需要走的最短路径长度为：')
+disp(dist_min)
+disp('机器人经过的最短路径库所顺序为：')
+disp(M_seq(1:end-1))
+disp('机器人经过的最短路径变迁序列为：')
+disp(path_opt)
\ No newline at end of file
diff --git a/ACOPN_original.m b/ACOPN_original.m
new file mode 100644
index 0000000..d7f46bf
--- /dev/null
+++ b/ACOPN_original.m
@@ -0,0 +1,212 @@
+close all
+clc
+clear
+%%初始化标识和变迁节点%%
+nodes_data=cell(0);
+M_1=[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; %网中25个标识对应的符号
+M_2=[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_3=[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_4=[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_5=[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_6=[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_7=[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_8=[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_9=[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_10=[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_11=[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_12=[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0];
+M_13=[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0];
+M_14=[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0];
+M_15=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0];
+M_16=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0];
+M_17=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0];
+M_18=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0];
+M_19=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0];
+M_20=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0];
+M_21=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0];
+M_22=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0];
+M_23=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0];
+M_24=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0];
+M_25=[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1];
+nodes_data(1,:)={1,[2,3],[1,1],[M_2;M_3]};  %根据变迁的邻近变迁的发生权构造变迁元胞组
+nodes_data(2,:)={2,[4,5],[1,sqrt(2)],[M_4;M_5]};
+nodes_data(3,:)={3,[6],[1],[M_6]};
+nodes_data(4,:)={4,[7,8],[sqrt(2),1],[M_7;M_5]};
+nodes_data(5,:)={5,[9,10],[sqrt(2),1],[M_8;M_7]};
+nodes_data(6,:)={6,[11,12],[1,sqrt(2)],[M_9;M_10]};
+nodes_data(7,:)={7,[13,14],[1,1],[M_8;M_13]};
+nodes_data(8,:)={8,[9,10],[sqrt(2),1],[M_8;M_7]};
+nodes_data(9,:)={9,[15],[1],[M_18]};
+nodes_data(10,:)={10,[13,14],[1,1],[M_8;M_13]};
+nodes_data(11,:)={11,[16,17],[1,1],[M_10;M_11]};
+nodes_data(12,:)={12,[18],[1],[M_12]};
+nodes_data(13,:)={13,[15],[1],[M_18]};
+nodes_data(14,:)={14,[23,24],[sqrt(2),1],[M_14;M_15]};
+nodes_data(15,:)={15,[29],[1],[M_19]};
+nodes_data(16,:)={16,[18],[1],[M_12]};
+nodes_data(17,:)={17,[19,20],[1,sqrt(2)],[M_16;M_17]};
+nodes_data(18,:)={18,[21,22],[1,sqrt(2)],[M_18;M_19]};
+nodes_data(19,:)={19,[27],[1],[M_17]};
+nodes_data(20,:)={20,[28],[1],[M_20]};
+nodes_data(21,:)={21,[29],[1],[M_19]};
+nodes_data(22,:)={22,[30,31],[1,sqrt(2)],[M_23;M_24]};
+nodes_data(23,:)={23,[25],[1],[M_21]};
+nodes_data(24,:)={24,[26],[1],[M_14]};
+nodes_data(25,:)={25,[33],[1],[M_22]};
+nodes_data(26,:)={26,[25],[1],[M_21]};
+nodes_data(27,:)={27,[28],[1],[M_20]};
+nodes_data(28,:)={28,[32],[1],[M_23]};
+nodes_data(29,:)={29,[30,31],[1,sqrt(2)],[M_23;M_24]};
+nodes_data(30,:)={30,[35],[1],[M_24]};
+nodes_data(31,:)={31,[36],[1],[M_25]};
+nodes_data(32,:)={32,[35],[1],[M_24]};
+nodes_data(33,:)={33,[34],[1],[M_25]};
+nodes_data(35,:)={35,[36],[1],[M_25]};
+
+
+%% 始末节点%%
+node_start=1;
+node_end=[34,36];
+%%% 蚁群定义%%%%%
+m=50;                               % 蚂蚁数量
+n=size(nodes_data,1);               % 节点数量
+alpha=1;                            % 信息素重要程度因子
+beta=5;                             % 启发函数重要程度因子
+Rho=0.5;                            % 信息素挥发因子
+Q=1;                              % 信息素增加强度系数
+%%迭代过程初始化定义%%%%
+iter=1;                             % 迭代次数初值
+iter_max=500;                       % 最大迭代次数
+Route_best=cell(iter_max,1);        % 各代最佳路径
+Length_best=zeros(iter_max,1);      % 各代最佳路径长度
+Length_ave=zeros(iter_max,1);       % 各代路径平均长度
+Place_best=cell(iter_max,1);        % 各代最佳路径访问的库所
+%%将信息素、挥发因子一并放入nodes_data中%%%%%
+Delta_Tau_initial=nodes_data(:,1:2);
+for i=1:size(nodes_data,1)
+    nodes_data{i,5}=ones(1,length(nodes_data{i,3}));         % 初始信息素均设置为1
+    nodes_data{i,6}=1./nodes_data{i,3};                      % 启发函数设置为距离的倒数
+    Delta_Tau_initial{i,3}=zeros(1,length(nodes_data{i,3})); % 信息素变化量均为0
+end
+%% 迭代寻找最佳路径%%%
+while iter<iter_max
+    route=cell(0);
+    place=cell(0);
+    for i=1:m                                               % 逐个蚂蚁进路径选择
+        neighbor_allow=cell(0);
+        node_step=node_start;
+        path=node_step;
+        path_M = 0;
+        if node_step==node_start
+            marking=M_1;
+        else
+            marking=nodes_data{node_step,4};
+        end
+        dist=0;
+        while ~isequal(marking(end,:), M_25)
+            neighbor=nodes_data{node_step,2};                    %寻找邻近节点
+            neighbor_allow = [];
+            for k=1:length(neighbor)
+                if ~ismember(neighbor(k),path)
+                    neighbor_allow(end+1) = neighbor(k);
+                end
+            end           
+            if isempty(neighbor_allow)
+                neighbor_allow=cell(0);
+                node_step=node_start;
+                path=node_step;
+                if node_step==node_start
+                    marking=M_1;
+                else
+                    marking=nodes_data{node_step,4};
+                end
+                dist=0;
+                continue
+            end
+            P=neighbor_allow;                                  %计算下一个节点的访问概率
+            for k=1:length(neighbor_allow)
+                idx = find(neighbor_allow(k) == nodes_data{node_step,2});
+                P(2,k)=nodes_data{node_step,5}(idx)^alpha*nodes_data{node_step,6}(idx)^beta;
+            end
+            P(2,:)=P(2,:)/sum(P(2,:));
+            %%轮盘赌法选择下一个访问节点%%%%
+            Pc=cumsum(P(2,:));
+            Pc=[0,Pc];
+            randnum=rand;
+            for k=1:length(Pc)-1
+                if randnum>Pc(k)&&randnum<Pc(k+1)
+                    target_node=neighbor_allow(k);
+                end
+            end
+            %%%计算单步距离%%%
+            idx=find(nodes_data{node_step,2}==target_node);
+            dist=dist+nodes_data{node_step,3}(idx);
+            %%%更新路径、节点以及标识%%%
+            path(end+1)=target_node;                         % 更新路径集合
+            marking(end+1,:)=nodes_data{node_step,4}(idx,:); % 更新标识
+            node_step=target_node;                           % 更新下一个目标节点变迁
+        end
+        Length(i,1)=dist;                                    % 存放第i只蚂蚁的累计距离和对应路径
+        route{i,1}=path;
+        place{i,1}=marking;
+    end
+    %%计算这一代的m只蚂蚁中最短距离和对应路径%%%
+    if iter==1
+        [min_Length,min_index]=min(Length);
+        Length_best(iter)=min_Length;
+        Length_ave(iter)=mean(Length);
+        Route_best{iter,1}=route{min_index,1};
+        Place_best(iter,1)=place(min_index,1);
+    else
+        [min_Length,min_index]=min(Length);
+        Length_best(iter)=min(Length_best(iter-1),min_Length);
+        Length_ave(iter)=mean(Length);
+        if Length_best(iter)==min_Length
+            Route_best{iter,1}=route{min_index,1};
+            Place_best(iter,1)=place(min_index,1);
+        else
+            Route_best{iter,1}=Route_best{iter-1,1};
+            Place_best(iter,1)=Place_best(iter-1,1);
+        end
+    end
+    %%%更新信息素%%%
+    Delta_Tau=Delta_Tau_initial;
+    for i=1:m                                                   % 逐个蚂蚁计算
+        for j=1:length(route{i,1})-1
+            node_start_temp=route{i,1}(j);
+            node_end_temp=route{i,1}(j+1);
+            idx=find(Delta_Tau{node_start_temp,2}==node_end_temp);
+            Delta_Tau{node_start_temp,3}(idx)=Delta_Tau{node_start_temp,3}(idx)+Q/Length(i);
+        end
+    end
+    %%考虑挥发因子，更新信息素%%%
+    for i=1:size(nodes_data,1)
+        nodes_data{i,5}=(1-Rho)*nodes_data{i,5}+Delta_Tau{i,3};
+    end
+    iter=iter+1;
+end
+% %绘图、结果%%%
+figure
+plot(1:iter_max,Length_best,'b',1:iter_max,Length_ave,'r','LineWidth',2.5);
+legend('最短距离','平均距离');
+xlabel('迭代次数');
+ylabel('距离');
+title('各代最短距离与平均距离对比');
+%% 最优路径%%%
+[dist_min,idx]=min(Length_best(1:end-1));
+path_opt=Route_best{idx,1};
+marking_opt=Place_best{idx,1};
+%%将marking_opt转为字符输出%%%
+M_set = cell(0);
+M_seq = [];
+for i = 1:size(marking_opt,1)
+    idx = find(marking_opt(i,:) == 1);
+    M_set{i,1} = strcat('M_',num2str(idx));
+    M_seq = [M_seq, strcat(M_set{i,1},',')];
+end
+disp('机器人需要走的最短路径长度为：')
+disp(dist_min)
+disp('机器人经过的最短路径库所顺序为：')
+disp(M_seq(1:end-1))
+disp('机器人经过的最短路径变迁序列为：')
+disp(path_opt)
\ No newline at end of file