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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)7 [6 f4 ?" {' ]0 F# {
    %   Finds a (near) optimal solution to the TSP by setting up a GA to search7 d8 i) w. g9 Q- v8 S% ^
    %   for the shortest route (least distance for the salesman to travel to
    ) g& }, U9 I& Y; }1 D5 _2 m%   each city exactly once and return to the starting city)
    , _% V) _, H% x3 u8 o/ k, y. Z%
    1 w/ x8 b$ X- z2 h3 U% Summary:
    - y* r& R* j, S1 D%     1. A single salesman travels to each of the cities and completes the: o* H& {* Q: h$ |% }0 U6 u
    %        route by returning to the city he started from
    # d2 x" V" x, ?7 h. z%     2. Each city is visited by the salesman exactly once! {0 H7 ]0 T3 y4 ]
    %
    1 D0 G! i. \* M/ r: T8 w% Input:
    6 l+ n5 M7 n9 p: o2 h( X) S( t2 {- e%     XY (float) is an Nx2 matrix of city locations, where N is the number of cities- [3 R0 }3 c/ ~( }! i
    %     DMAT (float) is an NxN matrix of point to point distances/costs
    # S5 e: d1 t6 B- B* c) ^%     POPSIZE (scalar integer) is the size of the population (should be divisible by 4)
    1 e$ t- E; U3 g%     NUMITER (scalar integer) is the number of desired iterations for the algorithm to run
    2 i" T" v: w; ]%     SHOWPROG (scalar logical) shows the GA progress if true6 ?1 J$ O9 a) x0 _  ]
    %     SHOWRESULT (scalar logical) shows the GA results if true0 M& n; L/ i6 ?
    %& A4 ^# Z" K/ J
    % Output:& P# m# Y' Z& f
    %     OPTROUTE (integer array) is the best route found by the algorithm" g  g0 R1 O  j: S! v2 `" A! x
    %     MINDIST (scalar float) is the cost of the best route
    0 c+ S  O; |6 C# `. }0 T%
    + _3 D' l/ _) e6 J% Example:5 T( w4 p( l/ n. s1 O6 P
    %     n = 50;+ L( r' E3 R! A0 p7 n
    %     xy = 10*rand(n,2);
    4 ~3 y9 j) W7 U%     popSize = 60;
    ; U) y0 \9 P4 `" C%     numIter = 1e4;
    + N3 [0 o# H7 s+ F& P8 x  G3 c%     showProg = 1;! p( e- B6 e8 Q( h# ]1 N( C  k- O
    %     showResult = 1;4 a$ ?5 j6 n( l' \7 y8 r
    %     a = meshgrid(1:n);
    $ D3 m! D! U1 y6 K. v%     dmat = reshape(sqrt(sum((xy(a,-xy(a',).^2,2)),n,n);9 l0 e* P% g# n% a% z( m! l3 F6 Q
    %     [optRoute,minDist] = tsp_ga(xy,dmat,popSize,numIter,showProg,showResult);0 C/ a2 h' V- k0 V6 S: _
    %
    ! f1 p2 z$ T. ?! D7 P/ k$ s& K  h% Example:
      p8 n" ]- Z; S( z9 M: P%     n = 100;1 J4 j( p4 b! T3 I" X+ d
    %     phi = (sqrt(5)-1)/2;3 }/ f! t6 J% B5 R1 x
    %     theta = 2*pi*phi*(0:n-1);5 ]: N8 m$ u5 C3 r* U
    %     rho = (1:n).^phi;
    % W+ Q* e. V2 [1 A%     [x,y] = pol2cart(theta(,rho();
    $ I6 P( d" O5 A) I%     xy = 10*([x y]-min([x;y]))/(max([x;y])-min([x;y]));$ J: u( G/ h2 ]4 M" q/ [3 n
    %     popSize = 60;7 }6 G2 ^& ]4 S
    %     numIter = 2e4;
    3 K% j9 d, _# S& i%     a = meshgrid(1:n);
    . ^, V7 f6 S/ ]3 d" ?%     dmat = reshape(sqrt(sum((xy(a,-xy(a',).^2,2)),n,n);
    0 T* H6 C9 _; D%     [optRoute,minDist] = tsp_ga(xy,dmat,popSize,numIter,1,1);, B6 ]- ^& e4 {5 ]  [9 _& i
    %
    # ~, p( S& U. ]$ h  n% Example:  x! c2 Q( z- {
    %     n = 50;* R6 r' q4 U/ b: Y
    %     xyz = 10*rand(n,3);
    6 C9 X/ s1 Z1 f0 X; c( |! H%     popSize = 60;: Q, D7 {8 Z6 h& t+ v/ d$ [& g
    %     numIter = 1e4;
    / w2 r: P: k/ h- S* [' G0 v%     showProg = 1;
    / ~& _& V1 w& \( C0 @6 T%     showResult = 1;
    2 e7 b1 ~0 L" M4 ~%     a = meshgrid(1:n);: v! t) `3 _1 F9 q. W
    %     dmat = reshape(sqrt(sum((xyz(a,-xyz(a',).^2,2)),n,n);' \* |: N. V% L
    %     [optRoute,minDist] = tsp_ga(xyz,dmat,popSize,numIter,showProg,showResult);
    + q. ^. ?* ^0 k; y%
      B2 b7 p* C. a, m$ {- \% See also: mtsp_ga, tsp_nn, tspo_ga, tspof_ga, tspofs_ga, distmat
    : s8 {1 k% R8 o# ]# |0 e%) o: n( s+ n7 H* I/ K0 v& S, o
    % Author: Joseph Kirk7 E# O: C; F0 x9 Y" I6 E8 j
    % Email: jdkirk630@gmail.com' k2 f4 O1 g4 G6 _
    % Release: 2.3+ e5 m# m4 I  [* b  h
    % Release Date: 11/07/11) Y7 y% }- W8 b) {+ t! ^0 b
    function varargout = tsp_ga(xy,dmat,popSize,numIter,showProg,showResult): s# m6 W  l" k: s' J  Q7 S9 {

    9 ~  u. q/ q$ Q( J6 O# V% Process Inputs and Initialize Defaults
    & E, V% c& d& n! y4 V. Rnargs = 6;
    9 r1 S3 o8 _2 d& e: Y7 p2 yfor k = nargin:nargs-1
    8 U/ G- O9 E4 t3 b    switch k
      s0 R4 n* e* O5 z        case 0
    . h; |/ O. r' w  l            xy = 10*rand(50,2);) g6 `  j: ?" G2 o" @
            case 19 J: ?4 L7 E! V0 ?5 T" U1 H
                N = size(xy,1);0 I% ]/ D0 R: m
                a = meshgrid(1:N);
    1 v& {3 f# V9 |8 m9 d9 O/ w( t( a9 d            dmat = reshape(sqrt(sum((xy(a,-xy(a',).^2,2)),N,N);1 N) @* H* m$ y) s4 p0 d# d3 ~* R
            case 2
    4 W2 V9 ?, v% Q8 g/ e: z* C            popSize = 100;
    9 M, Y8 y! x; m2 O" I/ V# [        case 32 x6 P: n1 r/ f' i; R
                numIter = 1e4;2 K/ k# C, z1 g2 t. X7 Z
            case 4
    0 Y( b3 _* w5 Y  w  o8 r9 Q            showProg = 1;
    % M! Q& S6 U9 {- \0 s' h        case 5* a; k1 N6 G/ O% ]
                showResult = 1;# R8 m  m8 p/ B( N5 a  T) m& N
            otherwise
    8 l0 e- k7 J: T1 }3 |& B4 r% F    end# I9 _6 M- }! p, x& b5 `
    end
    2 s9 Z7 Z# K2 `0 Z* [8 D3 N+ g/ B% E& S' E9 A( x6 z* M) [/ X
    % Verify Inputs
    1 R, M: S/ T4 `# u& B[N,dims] = size(xy);
    , z( \2 D2 E* F2 j0 l/ k$ v; J[nr,nc] = size(dmat);0 i1 d- T$ Z1 Y
    if N ~= nr || N ~= nc+ }# A, N1 o" w  a6 N) w
        error('Invalid XY or DMAT inputs!')1 d& V1 [$ G/ m
    end( n8 g0 J# P# J4 T7 b- C0 G
    n = N;
    0 k% h' U; E1 m1 Y9 z3 t; C2 \! p) o! Y- q5 i/ R. [1 x* D+ e
    % Sanity Checks+ u5 |% J0 T: g% A, N/ l% ]+ N
    popSize = 4*ceil(popSize/4);
    . Z4 k; @4 i. C+ e3 N  ^* Z5 T9 X/ vnumIter = max(1,round(real(numIter(1))));) T5 `, a9 S* |& i, r
    showProg = logical(showProg(1));: N+ A. Y4 F* @' e
    showResult = logical(showResult(1));; W# Q- [" \  d7 n& X- g# ?' i
    ; j  Z; R- M- ^& P  R+ c0 ^% ?
    % Initialize the Population
    3 Y1 Z4 A" a" P" p1 j2 {* N5 {pop = zeros(popSize,n);* _; @) ]6 T9 {" l* T: A$ s" R
    pop(1, = (1:n);
      V/ `% N- ?# N. |for k = 2:popSize" g+ b/ j& g4 f5 q! [2 ]* l
        pop(k, = randperm(n);
    ) }8 }0 e( N0 A5 {( C8 @end8 D! d8 n  I( l& @6 `
    0 {' n3 f- v- s$ F7 }+ {$ s
    % Run the GA
    ! Z0 T6 v1 C4 y; lglobalMin = Inf;
    4 y( }) l5 J  T7 A; u& e9 M9 ltotalDist = zeros(1,popSize);
    & g! x; s0 t! Q3 b' YdistHistory = zeros(1,numIter);
    ' m+ C* V! Y# ]tmpPop = zeros(4,n);
    * p  w. u4 T( P0 G- Q. Q; InewPop = zeros(popSize,n);+ n/ ^4 N% C' W
    if showProg
    ) S" `3 W  y+ L: y8 n    pfig = figure('Name','TSP_GA | Current Best Solution','Numbertitle','off');0 r/ x1 ?5 `3 P  ?* q- B
    end
    4 v5 v; o' G& y3 ]' v& `$ _( nfor iter = 1:numIter8 P- U0 J  Y% A
        % Evaluate Each Population Member (Calculate Total Distance)
      b1 I0 Z2 A2 l5 j    for p = 1:popSize
    " b' ^+ E, \% N. u4 a        d = dmat(pop(p,n),pop(p,1)); % Closed Path
    8 [) R4 g7 s( H. S6 E+ h        for k = 2:n! v0 M5 i" {! {% Y4 r/ [4 h0 R
                d = d + dmat(pop(p,k-1),pop(p,k));0 F% f: {; x: g' F
            end
    3 p0 {( w  ^0 r/ }$ k1 l! t        totalDist(p) = d;- p+ q3 C% h& f' z2 V7 j5 b0 n
        end
    1 u* i: A' f, w" ]) B6 ]/ E5 I9 l: H
        % Find the Best Route in the Population
    2 u6 G% ^, K% h4 Z: p    [minDist,index] = min(totalDist);
    ; L0 X7 s: e) V5 ~, ]- M    distHistory(iter) = minDist;8 [" ?) N$ k$ c7 [
        if minDist < globalMin. f/ }2 y. v) i) M3 N( K
            globalMin = minDist;
    ! s3 r6 {4 Y& N: r        optRoute = pop(index,;- [6 P+ I* q) Q
            if showProg
    % F  {$ D4 M, u5 g: Q9 w            % Plot the Best Route7 f5 `+ d7 v4 Y
                figure(pfig);. k) k& F4 I& y7 t5 f: z
                rte = optRoute([1:n 1]);
    % D, h( C, _  V' O0 ]1 n            if dims > 2, plot3(xy(rte,1),xy(rte,2),xy(rte,3),'r.-');
    ! g: v( S1 V% g/ _/ }/ D  i# y            else plot(xy(rte,1),xy(rte,2),'r.-'); end* k3 D4 W3 w9 A/ A
                title(sprintf('Total Distance = %1.4f, Iteration = %d',minDist,iter));
    - Y& c/ X# n3 e        end, M8 r0 @8 c6 V
        end
    ! F* X) g; U" h- r4 E+ @
    $ x" E0 e; m3 B9 }    % Genetic Algorithm Operators3 s9 Z8 ?" a) D6 k& ?
        randomOrder = randperm(popSize);( y% `1 Y! h7 `7 M( R- y* I. Z
        for p = 4:4:popSize% E; X1 `( Q! I" I
            rtes = pop(randomOrder(p-3:p),;9 N. b9 j* z4 {
            dists = totalDist(randomOrder(p-3:p));
    - E3 L& \$ {! y3 D5 d        [ignore,idx] = min(dists); %#ok
    0 M) q5 {- D4 v8 }* i. v8 M        bestOf4Route = rtes(idx,;
    0 f( P/ @8 {' _) P5 P* G1 D% ]        routeInsertionPoints = sort(ceil(n*rand(1,2)));
    7 P  j4 D1 f+ o+ Q/ J7 `        I = routeInsertionPoints(1);, t- s6 l+ d7 V. ]
            J = routeInsertionPoints(2);
    ' d8 M; v/ d" ]        for k = 1:4 % Mutate the Best to get Three New Routes
    9 |7 g1 Y6 m. C* r( z& s6 ?2 w- x7 P1 e            tmpPop(k, = bestOf4Route;
    $ h1 r0 _% v& H8 Y            switch k
    # `$ w. N+ [% N: C  p9 Y5 B( u                case 2 % Flip
    4 Z) u8 D# Z4 i- m                    tmpPop(k,I:J) = tmpPop(k,J:-1:I);
    9 O2 C9 M: O' {% N' U8 u3 H* v; b) V  n                case 3 % Swap! k2 C8 ~! J6 A* ]. }$ |, Q6 [7 c
                        tmpPop(k,[I J]) = tmpPop(k,[J I]);1 \2 c' K) N* m: i3 B, X' k
                    case 4 % Slide
    : h' @( i" C6 ^& K, T2 t6 \                    tmpPop(k,I:J) = tmpPop(k,[I+1:J I]);
    & d5 a/ T; m- \# t                otherwise % Do Nothing8 `* Z0 f9 K; e; V- t" \6 v/ d
                end
    ; d6 M; D9 d0 U. Y9 x        end6 V9 R8 m' n- f8 l. J* s5 w2 ~- C
            newPop(p-3:p, = tmpPop;
    : f5 q" X+ r5 B: b- ~0 r; k    end
    5 Y( T0 q1 y; ?7 w$ i    pop = newPop;
    # f8 Q9 F) D# L" {8 R* gend
    ! h# T2 ], l9 g' v4 J  G# U8 Y: L# z4 p
    if showResult4 _9 n* o* ]  Y1 I' H3 {( q6 e; K
        % Plots the GA Results- `9 G& `! l' q0 ~$ ^7 H
        figure('Name','TSP_GA | Results','Numbertitle','off');$ ?7 M; o  D$ X4 \
        subplot(2,2,1);. u/ F* a* a! p, V
        pclr = ~get(0,'DefaultAxesColor');5 A- A% A) i+ f! S8 `0 l
        if dims > 2, plot3(xy(:,1),xy(:,2),xy(:,3),'.','Color',pclr);
      a$ d- g- A6 f0 V. V' C    else plot(xy(:,1),xy(:,2),'.','Color',pclr); end9 d# I7 o2 D( j1 x
        title('City Locations');
    6 ~+ U/ }# K* H. w3 F. ~+ z) c    subplot(2,2,2);1 M. o0 }" e0 T* T; v
        imagesc(dmat(optRoute,optRoute));
    1 ~; Q# _2 b' |    title('Distance Matrix');# P. s0 a! o7 o
        subplot(2,2,3);
    . w$ j% f% W4 L, h    rte = optRoute([1:n 1]);
    1 B. o+ q) u3 v- M2 |4 V- f) T    if dims > 2, plot3(xy(rte,1),xy(rte,2),xy(rte,3),'r.-');/ M! b/ h2 y) r# I' g5 f9 }2 q3 K
        else plot(xy(rte,1),xy(rte,2),'r.-'); end2 }4 Z+ B0 p: R% f; d" T) A
        title(sprintf('Total Distance = %1.4f',minDist));- ~' _; H6 r- `: P
        subplot(2,2,4);
    $ y+ I$ e! K. R' `+ y    plot(distHistory,'b','LineWidth',2);" ?$ @' Z& g: o, n
        title('Best Solution History');
    2 h# d; ?) B# s3 w    set(gca,'XLim',[0 numIter+1],'YLim',[0 1.1*max([1 distHistory])]);/ z- {! M. k4 T& z2 _) t$ d
    end; E( h# b; h2 K8 D0 x. k" g5 {
    9 A% ~. y6 H4 Y: B
    % Return Outputs
    0 z3 U- E, e% \+ N7 k, eif nargout
    " l8 q9 C7 }) h/ U  B) M4 i    varargout{1} = optRoute;  W/ N* s) d2 g# \1 o( O- j8 \  ~
        varargout{2} = minDist;
    2 n. E; w- A# O' x" Fend7 ?/ G2 f: _; k  W6 k4 C

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