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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)
    # m" l' o- I$ q9 U%   Finds a (near) optimal solution to the TSP by setting up a GA to search
    0 \8 i  e7 }0 g5 Y$ c- ]%   for the shortest route (least distance for the salesman to travel to; k' u7 e& |/ V2 m# z& E- h  o
    %   each city exactly once and return to the starting city)
    ( ]2 g% S, k% |) O9 E& n%" e" o9 |/ ^0 D$ q$ D! |7 t+ e$ G  f
    % Summary:: }: {- U! J" |3 _3 q2 F- ?
    %     1. A single salesman travels to each of the cities and completes the
    ! v# Q4 f6 f& Q, ?%        route by returning to the city he started from
    & ~: E% Z! k$ S7 @) T! W2 r9 r%     2. Each city is visited by the salesman exactly once
    ( D+ s  Z% j. H# r$ L0 D% ^% N%
    4 _' t; R- v# r% Input:
    % e- J# \; o7 j6 o%     XY (float) is an Nx2 matrix of city locations, where N is the number of cities
    + P$ m( n) \, z' d# d$ H%     DMAT (float) is an NxN matrix of point to point distances/costs) j  A! T8 A# R# r% V7 z4 A8 F2 ^+ J
    %     POPSIZE (scalar integer) is the size of the population (should be divisible by 4)$ D5 d! u5 `- q  D2 ]2 c8 m
    %     NUMITER (scalar integer) is the number of desired iterations for the algorithm to run+ C1 M# j5 o# v# t1 g* B: {
    %     SHOWPROG (scalar logical) shows the GA progress if true
    . Z0 g, W2 R  r" r# u9 d2 q, r5 {%     SHOWRESULT (scalar logical) shows the GA results if true$ B3 N2 ]0 g# E5 h
    %2 H  X8 W7 `* r9 F6 k- h$ i; C
    % Output:
    8 g' U+ b3 Y) O. J%     OPTROUTE (integer array) is the best route found by the algorithm  j5 C$ H% @" X8 q/ w( T, H. J9 d
    %     MINDIST (scalar float) is the cost of the best route
    ) Y" V( ~8 f; o- b6 K) ]% U" q8 i; W%. W5 _' y6 g  |6 c# s6 k! @
    % Example:+ N  Q5 m1 q3 s! i! l
    %     n = 50;
    . C1 P3 T' }7 z3 l5 T%     xy = 10*rand(n,2);
    # W, U& T' t) u' p# N) d; n3 c6 T%     popSize = 60;; p0 j; ~# S, ~1 p: G& y7 U* |7 r
    %     numIter = 1e4;. v4 e0 c6 l4 \
    %     showProg = 1;' s( U! C, W+ O
    %     showResult = 1;, I. s& X9 `9 F0 ^+ S4 F9 O! T
    %     a = meshgrid(1:n);- c8 d# Y# P: B
    %     dmat = reshape(sqrt(sum((xy(a,-xy(a',).^2,2)),n,n);
    3 t6 R) m4 ]+ ~+ i% ]%     [optRoute,minDist] = tsp_ga(xy,dmat,popSize,numIter,showProg,showResult);
    2 [- K/ F, M+ u%5 a5 l, @8 \: q2 [
    % Example:/ k( r  P( U, C7 J% N+ r9 f
    %     n = 100;2 z$ y6 _' _# Q3 ]8 P
    %     phi = (sqrt(5)-1)/2;  N$ I$ F' v2 M
    %     theta = 2*pi*phi*(0:n-1);
    / \8 ~+ N! V# T0 `* X%     rho = (1:n).^phi;
    2 c. K* A7 j& x  A% j4 V%     [x,y] = pol2cart(theta(,rho();
    9 T4 |. B  c& o& Q9 @# `%     xy = 10*([x y]-min([x;y]))/(max([x;y])-min([x;y]));! x( t+ `" p& d) g# {
    %     popSize = 60;" M" v5 `/ O. e
    %     numIter = 2e4;- U8 ]- p8 a3 R3 o
    %     a = meshgrid(1:n);
    ' C/ c! B1 a$ o" |# r: q( g%     dmat = reshape(sqrt(sum((xy(a,-xy(a',).^2,2)),n,n);
    2 d  H- z" A. H: z; A4 r%     [optRoute,minDist] = tsp_ga(xy,dmat,popSize,numIter,1,1);
    : m1 `' ?# T6 B  ^+ \%
    ' }! B+ j5 G+ ?" M, I0 ~5 k9 s; p% Example:: L" @7 |# _/ a, N
    %     n = 50;; f" Q5 @) B) j2 ^% J/ a
    %     xyz = 10*rand(n,3);1 a1 R0 H" j$ C# ^; j
    %     popSize = 60;4 \* F6 o; C( U
    %     numIter = 1e4;
      y# H* Y( F+ O- a2 f) X, [. w%     showProg = 1;
    & ~* f* B% v* Y1 k9 J* {%     showResult = 1;
    ( Q3 E  @/ d! W5 B- j* {9 ^9 i) K. E%     a = meshgrid(1:n);
    9 ^; q9 w# r6 `  L% U%     dmat = reshape(sqrt(sum((xyz(a,-xyz(a',).^2,2)),n,n);/ S% q7 K. J3 a3 S
    %     [optRoute,minDist] = tsp_ga(xyz,dmat,popSize,numIter,showProg,showResult);
    : J0 J; D% _# n" ?+ B" d+ d# I%
    0 ~& w/ k; ]* b9 T& H* _) O2 h% See also: mtsp_ga, tsp_nn, tspo_ga, tspof_ga, tspofs_ga, distmat- p& v6 d9 S7 b4 c6 Q
    %: R! P5 f9 }3 A; z; q  }" Y* M
    % Author: Joseph Kirk
    : P+ C. B( R8 b7 h. e0 q% Email: jdkirk630@gmail.com
      ?$ Q+ Y9 U" Q: D6 C( X6 s: }; m% Release: 2.3+ T. f) `. U8 `: x
    % Release Date: 11/07/11
    & b, _* q0 R7 x- B7 q- A; y3 bfunction varargout = tsp_ga(xy,dmat,popSize,numIter,showProg,showResult)9 O$ S$ w+ e' U8 X
    ) r# Y1 F1 ?" V8 b8 K: ?
    % Process Inputs and Initialize Defaults, Y% q4 t2 M. _) _
    nargs = 6;
    7 V. w  @) W- y! F5 \' xfor k = nargin:nargs-1
    : U: R2 O/ V, H( t- J, {/ H% q    switch k0 a: v5 O6 \% L# I2 Z5 `; G
            case 0
    $ Q, R) p  z0 ?# S            xy = 10*rand(50,2);7 z: a  x* ~$ D6 j6 s
            case 1
    ) I# p8 U; l9 J- k2 Z. ~            N = size(xy,1);
    $ @' C3 s8 e+ ?/ S) G( {4 t0 Q            a = meshgrid(1:N);" c: P6 Z5 |0 M& P2 L9 u2 b2 Q
                dmat = reshape(sqrt(sum((xy(a,-xy(a',).^2,2)),N,N);+ a, w* W4 t5 G- a, p% S3 [: N
            case 2
      n( ?5 |- u0 c$ n$ }            popSize = 100;  F- H1 ]9 \! U2 F1 A
            case 3
    ! k& G" P) ?7 G) v& o            numIter = 1e4;
    ) r! S$ z3 B4 f7 x        case 4
    , r0 j7 m5 m2 I* J! z6 f            showProg = 1;( [0 ]* s- L" n% Z* |
            case 55 s1 t4 d$ G( S5 ]
                showResult = 1;. d# Y; ~0 D2 r+ K5 D& g
            otherwise* x7 @# W8 A" r
        end$ }2 N1 l! V+ C; p' Y
    end3 t+ F* k6 c) L3 g! h, C# |- R

    6 C/ @# C# @/ j2 g$ c9 G5 @% Verify Inputs
    4 y. b7 f, r) X( w+ l$ q[N,dims] = size(xy);7 O" f5 J8 x/ E7 K0 W1 D' ~
    [nr,nc] = size(dmat);
    9 K+ i; H3 ^& V- ^if N ~= nr || N ~= nc
    4 e. Z. K2 n0 o- K' k- _    error('Invalid XY or DMAT inputs!')
    5 q7 W1 r; n4 h" u, p; Pend
    8 O2 J6 U4 }6 @$ @. {n = N;, b) s- y) y; P2 L/ G, U

    ! t  t8 R6 T! j% Sanity Checks
    3 ]/ O$ b) i. r6 MpopSize = 4*ceil(popSize/4);
    % ]8 W2 o$ k6 X( ^* N0 |) KnumIter = max(1,round(real(numIter(1))));
    4 n; D# x  x8 B7 F- ushowProg = logical(showProg(1));
    2 a; L8 |+ B) `$ xshowResult = logical(showResult(1));6 k, H6 D0 P! h3 U1 J2 Y$ e% ~
    1 J0 ~3 u; t/ }2 ]
    % Initialize the Population
    ; Y" V0 R) ~7 Y% Ipop = zeros(popSize,n);
    ; P- `* _. R/ p1 @pop(1, = (1:n);
    7 P5 F8 U/ X: g0 ~: n7 Xfor k = 2:popSize
    % y: Y1 e+ J/ P/ c: L    pop(k, = randperm(n);% n; A: `2 J1 y
    end
    " X8 C7 e* T7 j3 q6 m6 C! V: i: C( W% n; q
    % Run the GA
    ( s, ?- n* w, l" ]globalMin = Inf;  ^0 y( n% G- N. E3 M9 z
    totalDist = zeros(1,popSize);( y# \; W$ e8 ~7 z1 A' J
    distHistory = zeros(1,numIter);7 V; ?0 r, S; t/ J% l
    tmpPop = zeros(4,n);
    # R. d$ Q9 n9 Y+ enewPop = zeros(popSize,n);
    % U6 ]+ d1 f2 ?2 |$ y# d& Gif showProg, E4 d* a; j4 r% q) ~4 O3 k
        pfig = figure('Name','TSP_GA | Current Best Solution','Numbertitle','off');
    1 M7 p+ ^. r6 dend, {% {" J. A; e% P$ L- i; D* B- ^& ^$ O
    for iter = 1:numIter: }& E: V7 v2 l+ t
        % Evaluate Each Population Member (Calculate Total Distance)
    5 b' i$ L! ^7 ~  z. x    for p = 1:popSize
    6 \- a: e+ f3 w/ e; Q& s        d = dmat(pop(p,n),pop(p,1)); % Closed Path
    ! k. w" u4 s) _3 Q- Y        for k = 2:n
    ; a8 c' q' f2 d            d = d + dmat(pop(p,k-1),pop(p,k));
    - Z+ H2 I  j& s- s8 w. Q' U6 b        end; `* ^) [$ h) }) e) t8 `
            totalDist(p) = d;+ K+ ]0 S; V  y! v/ I7 w$ u, W
        end9 ?$ y5 t# U$ t
    8 \6 E* `4 l: \# E
        % Find the Best Route in the Population, y- x- L! d; d6 B. M
        [minDist,index] = min(totalDist);% ]. h0 a) C0 S( ^& l
        distHistory(iter) = minDist;8 Y8 ^+ u( y, L- p& U+ C
        if minDist < globalMin
    8 p# U+ s. W9 C' g4 _2 t' L0 J        globalMin = minDist;
    ; g- {3 a9 g0 d& r5 ?) I        optRoute = pop(index,;0 H: d  l' G" H# c
            if showProg
    - h% T. |! S7 n6 w            % Plot the Best Route& l$ P  L/ h9 f) I& Q" O; l
                figure(pfig);( d7 g1 [3 c. ~! k8 l! F
                rte = optRoute([1:n 1]);2 D. S. L) D* u/ L* R
                if dims > 2, plot3(xy(rte,1),xy(rte,2),xy(rte,3),'r.-');& A6 u' c  \9 {2 E
                else plot(xy(rte,1),xy(rte,2),'r.-'); end! y- _, g" T1 ]* F
                title(sprintf('Total Distance = %1.4f, Iteration = %d',minDist,iter));6 {. I8 Q* Q  d, f$ _3 p
            end
    6 x7 s! {2 L. U& T% R    end/ V2 E, m, I5 S5 z! u: M  {* l

    $ `; t& D% I& ^2 f  X/ D" A% W    % Genetic Algorithm Operators
    / X1 j. A# D( c# l7 L. s    randomOrder = randperm(popSize);' K- }8 ^) R% b/ J% u. ^3 q
        for p = 4:4:popSize
    * q$ D7 B% ^5 E$ N5 V* D; O        rtes = pop(randomOrder(p-3:p),;
    7 `% Z4 K+ F4 S: B# q6 Q. S        dists = totalDist(randomOrder(p-3:p));
    # i7 @. S9 y, z" A" x) _        [ignore,idx] = min(dists); %#ok& C, {. v$ H- v) `4 L2 z& s
            bestOf4Route = rtes(idx,;  O! y' a( {$ l- p9 ~/ T
            routeInsertionPoints = sort(ceil(n*rand(1,2)));
      q" E, D$ T, ], h) b) h, o        I = routeInsertionPoints(1);
    6 l8 ~0 J# r7 p8 @1 ?, X4 W# H        J = routeInsertionPoints(2);
    # a! g) ?2 @4 c  y        for k = 1:4 % Mutate the Best to get Three New Routes
    4 B* \. L/ Q$ `0 v            tmpPop(k, = bestOf4Route;; s4 _/ h* S+ O0 L$ Q/ }; \7 g& a
                switch k
    7 U: R" Q+ ^+ q                case 2 % Flip; L! Y$ I$ A0 G
                        tmpPop(k,I:J) = tmpPop(k,J:-1:I);/ a# u  ]+ z& w* c  F5 J' I
                    case 3 % Swap1 r" d7 l9 M- q  ?
                        tmpPop(k,[I J]) = tmpPop(k,[J I]);/ u: E/ O9 Z( e% ?. ?
                    case 4 % Slide
    ( c, n4 Q  w( ^% ?                    tmpPop(k,I:J) = tmpPop(k,[I+1:J I]);
    0 r' ^7 s& t- W/ G6 L9 W                otherwise % Do Nothing3 m1 G* X( B  T3 B& P
                end
    3 }7 J0 m" V! ?! J% e& y        end! q8 u. P0 P+ x8 X* ?* J
            newPop(p-3:p, = tmpPop;8 Z& T5 O- c& M
        end% {2 k; v3 l* s4 a, O
        pop = newPop;
    / D* x9 e4 E5 K9 Hend
    8 e. w, X$ w. t2 S8 m. t9 ^( o& H
    if showResult
    - a! F- G8 E4 S/ ]7 u8 p    % Plots the GA Results
    1 s+ y9 m0 t1 ?2 y. T1 o% X    figure('Name','TSP_GA | Results','Numbertitle','off');
    3 G! J; I7 I" }* o9 t# `    subplot(2,2,1);
    & `' P! s" j( O, V- v- ]) y+ |    pclr = ~get(0,'DefaultAxesColor');) c. v, W8 ]  n& P
        if dims > 2, plot3(xy(:,1),xy(:,2),xy(:,3),'.','Color',pclr);
    . g0 `  t$ Q0 x: h5 J    else plot(xy(:,1),xy(:,2),'.','Color',pclr); end7 w+ O( t. g: Q4 P( u
        title('City Locations');
    6 i/ j4 m2 w; e2 ^, w& j! z    subplot(2,2,2);
    $ o& |4 F* H; n/ d" X" a    imagesc(dmat(optRoute,optRoute));, X7 ~8 N( h8 G
        title('Distance Matrix');1 v2 w, K$ O; ?  e6 I2 L6 X
        subplot(2,2,3);1 M0 W- p( b0 [/ z
        rte = optRoute([1:n 1]);% y5 ~% A6 |/ r; v0 g
        if dims > 2, plot3(xy(rte,1),xy(rte,2),xy(rte,3),'r.-');
    1 Z9 m/ R6 f% t' [    else plot(xy(rte,1),xy(rte,2),'r.-'); end
    & |& D  t9 U% K* Q" E    title(sprintf('Total Distance = %1.4f',minDist));
    ( T! F* d( O8 t    subplot(2,2,4);
    , k. E, n8 M. ?& T: H/ w+ h    plot(distHistory,'b','LineWidth',2);
    ) ~. ]3 l4 Z2 U* \( c9 ^    title('Best Solution History');5 P  Q  V5 C( i( t: D
        set(gca,'XLim',[0 numIter+1],'YLim',[0 1.1*max([1 distHistory])]);
      j% c9 \9 x! k* R) q! gend- \/ b" T+ X8 a; n
    / x% W/ N8 e& X& b4 z
    % Return Outputs
    & }1 I2 z; `; Y+ z- |1 Sif nargout' T2 L5 e5 e6 F3 K$ P7 M: V
        varargout{1} = optRoute;* E! L# }3 @  A5 x& ^
        varargout{2} = minDist;3 q! y6 i9 D; V; Y
    end( z: d8 v4 _2 _6 }0 m5 H$ R1 K/ n4 V

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