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[代码资源] 旅行销售员(Traveling Salesman Problem)matlab代码

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%TSP_GA Traveling Salesman Problem (TSP) Genetic Algorithm (GA)
% Finds a (near) optimal solution to the TSP by setting up a GA to search
% for the shortest route (least distance for the salesman to travel to
% each city exactly once and return to the starting city)
%
% Summary:
%    1. A single salesman travels to each of the cities and completes the
%       route by returning to the city he started from
%    2. Each city is visited by the salesman exactly once
%
% Input:
%    XY (float) is an Nx2 matrix of city locations, where N is the number of cities
%    DMAT (float) is an NxN matrix of point to point distances/costs
%    POPSIZE (scalar integer) is the size of the population (should be divisible by 4)
%    NUMITER (scalar integer) is the number of desired iterations for the algorithm to run
%    SHOWPROG (scalar logical) shows the GA progress if true
%    SHOWRESULT (scalar logical) shows the GA results if true
%
% Output:
%    OPTROUTE (integer array) is the best route found by the algorithm
%    MINDIST (scalar float) is the cost of the best route
%
% Example:
%    n = 50;
%    xy = 10*rand(n,2);
%    popSize = 60;
%    numIter = 1e4;
%    showProg = 1;
%    showResult = 1;
%    a = meshgrid(1:n);
%    dmat = reshape(sqrt(sum((xy(a,

-xy(a',

).^2,2)),n,n);
%    [optRoute,minDist] = tsp_ga(xy,dmat,popSize,numIter,showProg,showResult);
%
% Example:
%    n = 100;
%    phi = (sqrt(5)-1)/2;
%    theta = 2*pi*phi*(0:n-1);
%    rho = (1:n).^phi;
%    [x,y] = pol2cart(theta(

,rho(

);
%    xy = 10*([x y]-min([x;y]))/(max([x;y])-min([x;y]));
%    popSize = 60;
%    numIter = 2e4;
%    a = meshgrid(1:n);
%    dmat = reshape(sqrt(sum((xy(a,

-xy(a',

).^2,2)),n,n);
%    [optRoute,minDist] = tsp_ga(xy,dmat,popSize,numIter,1,1);
%
% Example:
%    n = 50;
%    xyz = 10*rand(n,3);
%    popSize = 60;
%    numIter = 1e4;
%    showProg = 1;
%    showResult = 1;
%    a = meshgrid(1:n);
%    dmat = reshape(sqrt(sum((xyz(a,

-xyz(a',

).^2,2)),n,n);
%    [optRoute,minDist] = tsp_ga(xyz,dmat,popSize,numIter,showProg,showResult);
%
% See also: mtsp_ga, tsp_nn, tspo_ga, tspof_ga, tspofs_ga, distmat
%
% Author: Joseph Kirk
% Email: jdkirk630@gmail.com
% Release: 2.3
% Release Date: 11/07/11
function varargout = tsp_ga(xy,dmat,popSize,numIter,showProg,showResult)

% Process Inputs and Initialize Defaults
nargs = 6;
for k = nargin:nargs-1
switch k
      case 0
         xy = 10*rand(50,2);
      case 1
         N = size(xy,1);
         a = meshgrid(1:N);
         dmat = reshape(sqrt(sum((xy(a,

-xy(a',

).^2,2)),N,N);
      case 2
         popSize = 100;
      case 3
         numIter = 1e4;
      case 4
         showProg = 1;
      case 5
         showResult = 1;
      otherwise
end
end

% Verify Inputs
[N,dims] = size(xy);
[nr,nc] = size(dmat);
if N ~= nr || N ~= nc
error('Invalid XY or DMAT inputs!')
end
n = N;

% Sanity Checks
popSize = 4*ceil(popSize/4);
numIter = max(1,round(real(numIter(1))));
showProg = logical(showProg(1));
showResult = logical(showResult(1));

% Initialize the Population
pop = zeros(popSize,n);
pop(1,

= (1:n);
for k = 2:popSize
pop(k,

= randperm(n);
end

% Run the GA
globalMin = Inf;
totalDist = zeros(1,popSize);
distHistory = zeros(1,numIter);
tmpPop = zeros(4,n);
newPop = zeros(popSize,n);
if showProg
pfig = figure('Name','TSP_GA | Current Best Solution','Numbertitle','off');
end
for iter = 1:numIter
% Evaluate Each Population Member (Calculate Total Distance)
for p = 1:popSize
      d = dmat(pop(p,n),pop(p,1)); % Closed Path
      for k = 2:n
         d = d + dmat(pop(p,k-1),pop(p,k));
      end
      totalDist(p) = d;
end

% Find the Best Route in the Population
[minDist,index] = min(totalDist);
distHistory(iter) = minDist;
if minDist < globalMin
      globalMin = minDist;
      optRoute = pop(index,

;
      if showProg
         % Plot the Best Route
         figure(pfig);
         rte = optRoute([1:n 1]);
         if dims > 2, plot3(xy(rte,1),xy(rte,2),xy(rte,3),'r.-');
         else plot(xy(rte,1),xy(rte,2),'r.-'); end
         title(sprintf('Total Distance = %1.4f, Iteration = %d',minDist,iter));
      end
end

% Genetic Algorithm Operators
randomOrder = randperm(popSize);
for p = 4:4:popSize
      rtes = pop(randomOrder(p-3:p),

;
      dists = totalDist(randomOrder(p-3:p));
      [ignore,idx] = min(dists); %#ok
      bestOf4Route = rtes(idx,

;
      routeInsertionPoints = sort(ceil(n*rand(1,2)));
      I = routeInsertionPoints(1);
      J = routeInsertionPoints(2);
      for k = 1:4 % Mutate the Best to get Three New Routes
         tmpPop(k,

= bestOf4Route;
         switch k
            case 2 % Flip
                  tmpPop(k,I:J) = tmpPop(k,J:-1:I);
            case 3 % Swap
                  tmpPop(k,[I J]) = tmpPop(k,[J I]);
            case 4 % Slide
                  tmpPop(k,I:J) = tmpPop(k,[I+1:J I]);
            otherwise % Do Nothing
         end
      end
      newPop(p-3:p,

= tmpPop;
end
pop = newPop;
end

if showResult
% Plots the GA Results
figure('Name','TSP_GA | Results','Numbertitle','off');
subplot(2,2,1);
pclr = ~get(0,'DefaultAxesColor');
if dims > 2, plot3(xy(:,1),xy(:,2),xy(:,3),'.','Color',pclr);
else plot(xy(:,1),xy(:,2),'.','Color',pclr); end
title('City Locations');
subplot(2,2,2);
imagesc(dmat(optRoute,optRoute));
title('Distance Matrix');
subplot(2,2,3);
rte = optRoute([1:n 1]);
if dims > 2, plot3(xy(rte,1),xy(rte,2),xy(rte,3),'r.-');
else plot(xy(rte,1),xy(rte,2),'r.-'); end
title(sprintf('Total Distance = %1.4f',minDist));
subplot(2,2,4);
plot(distHistory,'b','LineWidth',2);
title('Best Solution History');
set(gca,'XLim',[0 numIter+1],'YLim',[0 1.1*max([1 distHistory])]);
end

% Return Outputs
if nargout
varargout{1} = optRoute;
varargout{2} = minDist;
end