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

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    2013-2-4 10:49
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    发表于 2012-9-1 15:26 |只看该作者 |倒序浏览
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    %TSP_GA Traveling Salesman Problem (TSP) Genetic Algorithm (GA). g6 c9 `- M0 s. M7 c% ~3 J
    %   Finds a (near) optimal solution to the TSP by setting up a GA to search$ f# C, a+ ]% b# Y! d
    %   for the shortest route (least distance for the salesman to travel to
    9 w, Q: t$ ^0 w%   each city exactly once and return to the starting city)
    * a8 R. D3 o0 b/ o- G6 `6 w%9 q+ [+ Q3 V/ Z4 m2 n, ^) M
    % Summary:7 g* k, t, o! C& m1 X3 y( y9 n, z
    %     1. A single salesman travels to each of the cities and completes the
    " k" V. a5 ?$ Z. z%        route by returning to the city he started from
    . G8 J4 X" M0 Z. I; r- U+ z%     2. Each city is visited by the salesman exactly once$ \$ |2 a) H, |0 x$ u
    %
    4 M; p/ Z/ a, w0 H$ L' d% Input:/ y( z2 U# @. c& i+ j* G  d9 t' U, E
    %     XY (float) is an Nx2 matrix of city locations, where N is the number of cities
      ]7 e5 U3 f4 {1 G7 Z8 g; C$ m%     DMAT (float) is an NxN matrix of point to point distances/costs# x  P# V" D* c' g, ]4 {  e
    %     POPSIZE (scalar integer) is the size of the population (should be divisible by 4)- o. o* @: h4 {% i: H8 h9 P
    %     NUMITER (scalar integer) is the number of desired iterations for the algorithm to run- g. L; Y$ q2 H( a1 t* F" \
    %     SHOWPROG (scalar logical) shows the GA progress if true- j, Z* ?8 r# O2 z+ K8 ?8 k
    %     SHOWRESULT (scalar logical) shows the GA results if true5 S- K3 N6 _/ b
    %
    - C! x, s5 l! R$ O% Output:1 i- N. m( I, x7 \/ B
    %     OPTROUTE (integer array) is the best route found by the algorithm
    * ?1 b; @+ {. H3 k%     MINDIST (scalar float) is the cost of the best route
    9 ?: c- U( H" R2 q* ~3 @4 |%
    7 @' b' h9 A: j  b/ J" F! Y2 u& c% Example:3 J: a# q" J2 L& \' D
    %     n = 50;
    % X- h& o% _5 W9 h4 n%     xy = 10*rand(n,2);9 s: X9 |% k' J% J- m
    %     popSize = 60;
    ( q# _3 R' ?8 N* G, ~%     numIter = 1e4;1 G2 `' u. B. G) }
    %     showProg = 1;4 r$ m' g0 z% Q* r4 _$ L3 c
    %     showResult = 1;! l$ u. P) E) ?. G/ }: F) G
    %     a = meshgrid(1:n);
    % r! |* c0 t# w" d6 q%     dmat = reshape(sqrt(sum((xy(a,-xy(a',).^2,2)),n,n);/ h* y( f" ]5 A
    %     [optRoute,minDist] = tsp_ga(xy,dmat,popSize,numIter,showProg,showResult);* |6 }- m, T+ \
    %( U: v6 f5 ~( q% }3 R9 j
    % Example:
    * U# f+ D' E% O%     n = 100;( U" @: Q% x5 Q4 s8 o1 }, e1 Y
    %     phi = (sqrt(5)-1)/2;
    2 V9 `; i* P9 P2 E. ]%     theta = 2*pi*phi*(0:n-1);
    / {' w% A& x( I%     rho = (1:n).^phi;2 \! e( B' ^' B
    %     [x,y] = pol2cart(theta(,rho();
    ; y! J: I+ ]$ q%     xy = 10*([x y]-min([x;y]))/(max([x;y])-min([x;y]));
    8 d6 i$ T2 @8 q7 ]7 U. p7 P%     popSize = 60;0 U6 }, Z; Y+ K5 R7 T8 a9 N
    %     numIter = 2e4;+ y! ?; k/ P. D2 i* n
    %     a = meshgrid(1:n);
    " z2 d/ }& v& `8 j%     dmat = reshape(sqrt(sum((xy(a,-xy(a',).^2,2)),n,n);
    7 D- A5 G- f# E  c  p2 D% H%     [optRoute,minDist] = tsp_ga(xy,dmat,popSize,numIter,1,1);
    . L  h0 m7 a' j7 H- ?+ ]' i$ M2 _%
    7 I6 [4 a7 l1 |' q$ f% Example:
    7 N- w, ~- a# u: c( [%     n = 50;1 t2 C+ m6 l8 S  g! v2 Y
    %     xyz = 10*rand(n,3);& M' J, h, u3 C4 C7 @! ?6 c  A
    %     popSize = 60;: J) n1 U7 U) d# q6 M8 {
    %     numIter = 1e4;
    1 s4 @/ a* F# y7 Y%     showProg = 1;
    4 @) N+ A/ w; L3 I; o/ t2 P%     showResult = 1;
    + L- ^3 G) T3 a%     a = meshgrid(1:n);- ^, E2 G! P$ E9 v; N5 e
    %     dmat = reshape(sqrt(sum((xyz(a,-xyz(a',).^2,2)),n,n);
    $ t$ x. }' M$ G* B) Y%     [optRoute,minDist] = tsp_ga(xyz,dmat,popSize,numIter,showProg,showResult);6 s0 n) \& A: J
    %1 |* e, G- n- S) F$ o+ m
    % See also: mtsp_ga, tsp_nn, tspo_ga, tspof_ga, tspofs_ga, distmat
    3 D9 \2 f. E. o9 |% R/ i! p; I%( ]7 X" `) h& ^6 G
    % Author: Joseph Kirk
    ' |9 ^: C% O% e: }0 A% Email: jdkirk630@gmail.com
    + o* M% o, ~( _  d" H  {! J% Release: 2.3
    9 {  H: n7 t; g7 [, G- M% Release Date: 11/07/117 ~. z: f  L9 X
    function varargout = tsp_ga(xy,dmat,popSize,numIter,showProg,showResult)
    % x$ n% B; |1 m+ W- \" R
    1 e4 \3 d+ K1 J& x" ^% Process Inputs and Initialize Defaults
    8 b- P- X9 }4 ?  \nargs = 6;
    2 Z8 y& Y6 |% [3 Zfor k = nargin:nargs-1" z5 d# K8 s, l  l9 r
        switch k
    & ]* q+ n: Y- m! v9 S3 x4 f& m        case 0
    & m/ @5 u! _7 _: f. |" l2 A            xy = 10*rand(50,2);
    3 N1 m; \# ]2 G+ O# A4 V% D% D        case 1' q6 L! n0 w5 D. E- X9 e
                N = size(xy,1);$ b8 S$ [! l7 I% B4 g" f
                a = meshgrid(1:N);
    5 |5 S* k* h9 c9 y" k  j: ]& l            dmat = reshape(sqrt(sum((xy(a,-xy(a',).^2,2)),N,N);
    + w( ]: d$ P5 J* \: c: K+ P        case 2( L/ I4 W* F" ?1 W+ }3 q! [
                popSize = 100;
    ( r  \2 F6 c6 d/ D        case 30 g8 c" @2 z: w  v+ X0 t# ~
                numIter = 1e4;
    ; E: \0 `9 l  H; v' f+ ?        case 42 p8 @6 Y2 D$ z
                showProg = 1;
    ' O  |: w  `2 A+ i        case 5
    * X5 A5 t! o4 [6 _7 m            showResult = 1;" j& l% D6 C, X2 ]2 Y: V0 O% j
            otherwise
    6 t5 ~: I, _0 ^& I: n    end! ]0 X% X5 O- D7 s6 ?9 I
    end
    * i# i3 o/ `! v, _% R  b
    1 Z" }( M8 @# }6 g7 ^% Verify Inputs
    2 U+ E: z# Q& U! y2 |[N,dims] = size(xy);
    ( m$ y: }% ?+ l# t, A0 i: ?[nr,nc] = size(dmat);/ X0 b" D; t* H
    if N ~= nr || N ~= nc% i) S/ f" z9 A& \& F
        error('Invalid XY or DMAT inputs!')) R/ r: G: D' I" b, j5 Y
    end4 N0 M- \  _5 r: }! u. ~$ }
    n = N;
    3 m7 N2 [4 p5 p6 P5 ~
    3 w3 Q* b3 s8 W# P6 v: P% Sanity Checks
    0 M3 G9 I$ V- {  b0 @+ @popSize = 4*ceil(popSize/4);: q7 T7 M4 f  R! R. D
    numIter = max(1,round(real(numIter(1))));
    8 Z7 z1 d9 U3 Z7 PshowProg = logical(showProg(1));: J+ f' M# W# J6 }
    showResult = logical(showResult(1));
    6 O2 y, t2 s3 a# \0 Z* [( C5 r) Y, p5 N  J9 F. Q, p6 l
    % Initialize the Population
    6 C1 [) j3 A* Q" q5 }pop = zeros(popSize,n);
    6 t  G% K. O! Z' [  }pop(1, = (1:n);9 I2 J# y7 u, D1 _
    for k = 2:popSize
    . g; y! \. B8 n* K! \  C' ^    pop(k, = randperm(n);8 p6 `7 T+ B+ ^" Q
    end( r9 B& K; i, H+ e6 l; g
    5 H4 }2 w8 T% d, x0 j% X7 m
    % Run the GA
    7 m* F& x5 p4 J+ k2 z; i. |globalMin = Inf;
    : X# y' L& p6 X! S% |( v* rtotalDist = zeros(1,popSize);
    ; A$ U3 W+ i+ o0 G% G% t% x7 odistHistory = zeros(1,numIter);
    3 z, {$ K% a3 g. I' D  ctmpPop = zeros(4,n);: a# }! Z: @3 l# Z
    newPop = zeros(popSize,n);3 K4 k  h( R. K7 ~: K1 l/ d2 s# s
    if showProg3 o% [+ Y% e8 I" x% u3 R. p* Q  a
        pfig = figure('Name','TSP_GA | Current Best Solution','Numbertitle','off');9 P7 C  Z1 g/ q- i
    end
    4 J6 u! ?* ^8 k9 G+ ffor iter = 1:numIter
    ; F3 D; l& K- \1 @# A9 q+ d    % Evaluate Each Population Member (Calculate Total Distance)
    ! z6 p. _* n% M: h2 `8 Z    for p = 1:popSize
    3 J1 w# q7 o7 h" o        d = dmat(pop(p,n),pop(p,1)); % Closed Path7 x; t* w  O( @/ J) L( ^
            for k = 2:n
    , J4 M8 ^+ S7 q5 X$ `+ y            d = d + dmat(pop(p,k-1),pop(p,k));" [" [) `5 ^$ b# ^& _
            end
    : _* ?7 I2 x) Q        totalDist(p) = d;
    : d' u. T) c! u& n0 e+ \- d0 N% F/ z    end1 `0 X" q" J6 Z6 a4 Q  e' O
    # _9 X' l  F" ]- i' g
        % Find the Best Route in the Population! Z! r+ \6 _4 M7 E* s. ^& R( q
        [minDist,index] = min(totalDist);* H# Y6 E5 V, W" M* d
        distHistory(iter) = minDist;
    ' j. ~3 r& C% K* F- ~    if minDist < globalMin/ v4 k! ^. w2 N* e1 S/ f' y  k. C
            globalMin = minDist;
    0 x+ E% B9 n1 \! C  A        optRoute = pop(index,;( O* e4 d: J8 @" E  o# l1 f5 e
            if showProg
    2 F: M' Q# S1 h$ c  q/ ?4 C            % Plot the Best Route+ m. X% I; z  c7 v9 ]# o* k* }" Y
                figure(pfig);* b  F( n% c  Q8 ^% Q! ?9 X
                rte = optRoute([1:n 1]);' @$ n) w- G! U) j" K! y
                if dims > 2, plot3(xy(rte,1),xy(rte,2),xy(rte,3),'r.-');4 {0 ^. {! I5 F0 A1 c2 N+ _
                else plot(xy(rte,1),xy(rte,2),'r.-'); end% a! u/ t( \2 S8 |! }0 X! F
                title(sprintf('Total Distance = %1.4f, Iteration = %d',minDist,iter));& [( ?* O: Y6 v
            end
    + u6 J* ], b1 C+ ~' S$ j    end
    9 B* y: w9 X7 ]1 S4 C0 E) L4 L; x5 N+ J1 q- N! ?
        % Genetic Algorithm Operators5 G' v8 H. h9 W
        randomOrder = randperm(popSize);
    # T1 G' I, }( C# J' t4 b  P    for p = 4:4:popSize8 ~4 r( H, }3 i! D1 o; A
            rtes = pop(randomOrder(p-3:p),;% t0 i% M, x) X
            dists = totalDist(randomOrder(p-3:p));" V8 i' m# u% H1 t
            [ignore,idx] = min(dists); %#ok
    0 C5 P1 @. M- R$ U0 j# L        bestOf4Route = rtes(idx,;8 ^/ T3 f! E5 O2 y6 X1 }  v+ V
            routeInsertionPoints = sort(ceil(n*rand(1,2)));( Z9 L6 I5 r$ R( Q# z
            I = routeInsertionPoints(1);
    1 r) D3 K# v0 P* R4 G5 G/ T        J = routeInsertionPoints(2);
    ) {' e4 s" m- e$ ^        for k = 1:4 % Mutate the Best to get Three New Routes
    4 H! r1 \0 `3 S# O. d2 D            tmpPop(k, = bestOf4Route;4 K% @  F: f( C) \& G: M
                switch k
    3 K5 n+ ]: W$ b4 u, p                case 2 % Flip
    * A2 H) B* G8 |6 `) T) m                    tmpPop(k,I:J) = tmpPop(k,J:-1:I);4 V# K$ P) c5 w, `5 e
                    case 3 % Swap
    2 X: ?$ l% ?# ~2 S. i                    tmpPop(k,[I J]) = tmpPop(k,[J I]);
    - o$ ^3 \7 o3 e$ y% c; @) c                case 4 % Slide
    # k/ M- w4 o6 x/ }; @& B$ z# W                    tmpPop(k,I:J) = tmpPop(k,[I+1:J I]);
    3 j$ B- A% x% a4 |& W                otherwise % Do Nothing
    % A$ f" w7 E' S" R( M- e6 Y            end$ ]/ {9 C* E3 i$ T
            end* G3 I* d5 C5 W
            newPop(p-3:p, = tmpPop;
    % e  x2 _7 R. V/ X5 [    end
    4 k; w' K3 x+ \. a3 E  @4 y    pop = newPop;  f8 e% j$ x/ ?7 F
    end
    2 o) o2 U# n! u; g
    ; X, W/ F% j" F- N% \9 l  T5 H$ {if showResult7 u! @- I" t% U0 |9 n: n; u
        % Plots the GA Results( F! Y8 p3 _! X% G
        figure('Name','TSP_GA | Results','Numbertitle','off');1 Z. y6 {7 g( q" g( r7 T
        subplot(2,2,1);
    ' |. c+ p# x/ n8 e! T  U    pclr = ~get(0,'DefaultAxesColor');! o  O6 [3 b" V, l& D
        if dims > 2, plot3(xy(:,1),xy(:,2),xy(:,3),'.','Color',pclr);. Q0 @% o$ s. w+ I: _5 m
        else plot(xy(:,1),xy(:,2),'.','Color',pclr); end0 T( W1 H+ q" }$ C- O1 B
        title('City Locations');9 W. t; n/ f  x+ s9 B( Q& t+ M
        subplot(2,2,2);
    , X; x) D' H8 k4 l7 g* R    imagesc(dmat(optRoute,optRoute));% s8 B- |4 y1 O* |& M
        title('Distance Matrix');
    3 f' U+ m7 p; ]8 |  w$ x: l/ t2 p, ~    subplot(2,2,3);
    # i* o2 }* D5 m; T" U    rte = optRoute([1:n 1]);% ~3 e- v6 `* V
        if dims > 2, plot3(xy(rte,1),xy(rte,2),xy(rte,3),'r.-');
    % N1 ^# M5 z/ B, i# e" _, Z2 i# F3 Q    else plot(xy(rte,1),xy(rte,2),'r.-'); end8 I1 {0 X/ X0 G" V# U6 X, w
        title(sprintf('Total Distance = %1.4f',minDist));5 E# [  B- ~8 n) m9 Y# u: I
        subplot(2,2,4);
      ?8 u) s. u* L+ r2 _& K    plot(distHistory,'b','LineWidth',2);
    + b. R; G* s# s5 n    title('Best Solution History');; f9 c# f  _. Q* u5 ?
        set(gca,'XLim',[0 numIter+1],'YLim',[0 1.1*max([1 distHistory])]);6 C5 D1 i% O8 |' X$ O" R$ M( R6 k
    end' @  y2 l; K, a3 H1 R) k7 d

    ' H* h2 S" i3 d6 g+ e6 l% Return Outputs& n5 q6 P' E& j; y7 a
    if nargout
    8 I$ s' L. |. R$ Y" C    varargout{1} = optRoute;
    4 N8 B1 G. d7 q+ n8 V( b    varargout{2} = minDist;
    # O" }+ M- G% [' C, c4 Dend
    $ @4 B: c2 O( P' z- j( i4 Z

    旅行销售员Traveling Salesman Problem .zip

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