Ant colony algorithm matlab for solving VRP problem

Excel Exp12_3_2.xls Content:

ANT_VRP function:

function [R_BEST,L_BEST,L_AVE,SHORTEST_ROUTE,SHORTEST_LENGTH]=ANT_VRP (D,DEMAND,CAP,ITER_MAX,M,ALPHA,BETA,RHO,Q) Percent R_best the best route of each generation l_best the length of the best route of each generation L_ave the average distance of each generation Shortest_route shortest path percent shortest_length shortest path length percent of the distance matrix between cities, for symmetric matrices percent D Emand customer demand% CAP vehicle maximum load Iter_max maximum iteration count percent m ant number percent Alpha characterization pheromone importance degree parameter percent Beta characterization heuristic factor importance degree parameter percent of Rho evaporation coefficient percent Q pheromone increase strength coefficient                 N=size (d,1);           T=zeros (M,2*n);          % load Distance eta=ones (m,2*n);            % heuristic factor tau=ones (n,n);          % pheromone Tabu=zeros (m,n);       % Taboo table Route=zeros (m,2*n);             % path L=zeros (m,1);   % Total distance L_best=zeros (iter_max,1); % of the best route length R_best=zeros (iter_max,2*n);       % of the best route nc=1;while nc<=iter_max% stop condition Eta=zeros (m,2*n);      T=zeros (M,2*n);    Tabu=zeros (M,n);    Route=zeros (M,2*n);        L=zeros (m,1);      %%%%%%============== Initialize the beginning of the City (taboo table) ==================== for i=1:m Cap_1=cap;        % maximum loading capacity j=1;        J_r=1;    While Tabu (i,n) ==0 T=zeros (m,2*n);             % Loading Load matrixTabu (i,1) = 1;      % Taboo table Start position is 1 Route (i,1) = 1;   % path start position is 1 visited=find (Tabu (i,:) >0);        % visited city Num_v=length (visited);         % visited city number J=zeros (1, (N-num_v));                          % to be visited city load table p=j;                         % to be visited city selection probability distribution jc=1; % to be visited city select pointer for k=1:n% city if Length (Find (Tabu (i,:) ==k) ==0% if K is not visited city code                     , K is added to J (Jc) =k in Matrix J;                 jc=jc+1;                          End end%%%%%%%============= Each ant traverses all cities according to the chosen probabilities ================== For k=1:n-num_v% cities to visit if Cap_1-demand (J (1,k), 1) >=0% if vehicle loading is greater than the city to visit                         City demand if Route (i,j_r) ==1% if each ant in the beginning City T (i,k) =d (1,j (1,k));  P (k) = (Tau (1,j (1,k)) ^alpha) * ((1/t (i,k)) ^beta);         % of molecule else in probability calculation formula                % if each ant is not in the beginning City T (i,k) =d (Tabu (I,j), J (1,k)); P (k) = (Tau (Tabu (i,visited (end)), J (1,k)) ^alpha) * ((1/t (i,k)) ^beta);                     % probability formula in the numerator end else if the vehicle load is less than the city needs to be visited                     T (i,k) = 0;                 P (k) = 0;                 End End If Length (Find (T (i,:) >0)) ==0%%% when the vehicle load is less than the city you want to visit, select the starting point of 1                 Cap_1=cap;                 j_r=j_r+1;                               Route (I,j_r) = 1;                L (i) =l (i) +d (1,tabu (i,visited (end)));                 else p=p/(sum (P));               % Select a city pcum=cumsum (P) according to the probability principle;       The cumulative probability and: Cumsum ([1 2 3]) =1 3 6, the purpose of which is to make the value of pcum always be greater than the number of Rand Select=find (Pcum>rand);       % Select the next city by probability: when the cumulative probability and is greater than the given random number, then the sum is added to the last city as the forthcoming city of O_visit=j (1,select (1));                 % to be visited city j=j+1;j_r=j_r+1;             Tabu (i,j) =o_visit;                 % to be visited City Route (I,j_r) =o_visit;  Cap_1=cap_1-demand (o_visit,1);       % Vehicle Load remaining L (i) =l (i) +t (I,select (1));               % path length end end L (i) =l (i) +d (Tabu (I,n), 1);             Percent Path length end l_best (NC) =min (L);           The optimal path is the shortest path Pos=find (l==min (L));  % find the location of the optimal path: which Ant r_best (NC,:) =route (POS (1),:);            % determine the optimal path corresponding to the city order L_ave (NC) =mean (L) ';            The average distance Delta_tau=zeros (n,n) for the K-iteration is obtained;    %delta_tau (I,J) indicates that all ants remain in the first city to the J City path on the pheromone increment l_zan=l_best (1:nc,1);    Post=find (L_zan==min (L_zan));    Cities=find (R_best (NC,:) >0);        Num_r=length (Cities); For k=1:num_r-1% establishes the full path after releasing pheromone Delta_tau (R_best (nc,k), R_best (nc,k+1)) =delta_tau (R_best (nc,k), R_best (nc,k+    1)) +q/l_best (NC);        End Delta_tau (R_best (Nc,num_r), 1) =delta_tau (R_best (Nc,num_r), 1) +q/l_best (NC);                Tau=rho*tau+delta_tau; Nc=nc+1;endshOrtest_route=zeros (1,2*n); % Extract Shortest path Shortest_route (1,:) =r_best (Iter_max,:); Shortest_route=shortest_route (shortest_route>0); Shortest_route=[shortest_route Shortest_route (+)];           Shortest_length=min (l_best); % Extract Shortest path length%l_ave=mean (l_best);

solver:

Clc;clear all%% ============== Extract Data ==============[xdata,textdata]=xlsread (' Exp12_3_2.xls '); % load data from 20 cities, data is saved in Excel file Exp12_3_1.xls x_label=xdata (:, 2) According to the table location; % second column horizontal y_label=xdata (:, 3);  % The third column is the Ordinate demand=xdata (:, 4);      % of the demand C=[x_label Y_label];        % coordinate matrix n=size (c,1);       %n indicates the number of nodes (customers) is ============== calculated distance matrix ==============d=zeros (n,n); %d represents the full graph of the weighted adjacency matrix, that is, the distance matrix D is initialized for the 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;   % calculates the distance between two cities else D (i,j) = 0;  %i=j, the distance is 0; end D (j,i) =d (I,J); The% distance matrix is symmetric matrix endendalpha=1; beta=5; rho=0.75;iter_max=100; q=10;  cap=1;m=20; %cap for maximum vehicle load [R_BEST,L_BEST,L_AVE,SHORTEST_ROUTE,SHORTEST_LENGTH]=ANT_VRP (D,demand,cap,iter_max,m,alpha,beta,rho , Q); The% ant colony algorithm solves the VRP problem general function, see the companion disc shortest_route_1=shortest_route-1% extract the best route shortest_length% extract shortest path length percent ====== ======== plot ==============figure (1)% as iterative convergence curve x=linspace (0,iter_max,iter_max); Y=l_best (:, 1);p lot (x, y); Xlabel (' Iteration count ‘); Ylabel (' Shortest path length '); figurE (2)% as the shortest path plot ([C (shortest_route,1)],[c (shortest_route,2)], ' O '), grid onfor I =1:size (c,1) text (c (i,1), C (i,2), [' ' Num2str (i-1)]); Endxlabel (' customer's horizontal axis '); Ylabel (' Customer ordinate ');

　　

Ant colony algorithm matlab for solving VRP problem