一 基于均值生成函数时间序列预测算法程序 % H) i, h/ X3 V) a2 l! ?4 ?% s/ a1. predict_fun.m为主程序; # Y8 Y# X5 f/ U, w6 ]8 G+ y* T9 `( R: f2. timeseries.m和 serie**pan.m为调用的子程序' W0 g% I/ R. b, \0 W3 ~& l3 R1 e* [( v
# Q0 }# J. f8 S/ m9 T6 W
function ima_pre=predict_fun(b,step) 0 l% H) O: D: z0 a9 J0 v' l, y4 Q) d% main program invokes timeseries.m and serie**pan.m1 a8 W5 G6 I S' w& S7 A
% input parameters: ; K/ ^# d! N9 m8 q5 a% b-------the training data (vector);% R; P% b& ^" C- S2 y, h4 p
% step----number of prediction data; 4 r' D$ N* d- u! |: k- I% output parameters: 3 [, ]+ n. S. C1 {* s: U: [% ima_pre---the prediction data(vector); * ?6 I) k; ]- c# X- Z* ~old_b=b; 5 x% `- C) c- @0 M" x0 o1 lmean_b=sum(old_b)/length(old_b);' E s* i6 Q- }, B# R/ T6 A3 F6 N: K
std_b=std(old_b); ) T* D' z1 V2 h% }5 oold_b=(old_b-mean_b)/std_b; 5 N! x# w- x4 r( f/ e[f,x]=timeseries(old_b); * f+ E E& l2 z r. ^9 N3 aold_f2=serie**pan(old_b,step);$ j+ j' ]/ C5 A8 O& Z
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps; . f) [/ D5 f! h& x( |/ V: x0 oR=corrcoef(f); + m! ?& }; ?/ [[eigvector eigroot]=eig(R);' Q5 C( X9 o7 \5 I8 m; X
eigroot=diag(eigroot); : z+ |# D( {" h: Ta=eigroot(end:-1:1);' M2 \; D" h& s( c
vector=eigvector(:,end:-1:1);; _! A" G5 j# ?6 U
Devote=a./sum(a); % U1 c5 o0 _ t% u" CDevotem=cumsum(Devote);1 q0 t# P5 b5 q8 V2 r# M
m=find(Devotem>=0.995); 4 ^9 ?& K# {% K# Lm=m(1); + O* q4 t' K) `) a( K5 C8 z; xV1=f*eigvector';7 z4 L# M; x+ h8 A/ K% G
V=V1(:,1:m);* s* a8 s; p& X9 n
% old_b=old_b;* G( B7 c! v+ w# g
old_fai=inv(V'*V)*V'*old_b; 8 C$ Y1 R, H5 O! W+ xeigvector=eigvector(1:m,1:m);, ]$ [: X) E; c3 {/ _
fai=eigvector*old_fai; , b, \7 T) P9 w* w3 d5 F% Wf2=old_f2(:,1:m); ! B" q, V' @. l# {5 \$ ?, z% Mpredictvalue=f2*fai; & J$ U7 E; J* y3 f, M( ]8 Nima_pre=std_b*predictvalue+mean_b; 6 {2 k ~4 ^* R* E 1 y' _0 F/ `5 b. e- f1.子函数: timeseries.m $ c, `+ |( P M$ X4 g" N# O$ L% timeseries program% & E4 N+ ]. k1 x% this program is used to generate mean value matrix f;) v, I7 W; a2 X8 B. {7 ^
function [f,x]=timeseries(data) $ i) ^; _! E9 M5 Q% data--------the input sequence (vector); 8 p4 p( c9 S5 n$ }% f------mean value matrix f;7 B& x% r- ?7 h2 |
n=length(data); % }! A/ a# k* m3 e# ifor L=1:n/2 0 d: I! V# R* t: m' V' ?5 Z nL=floor(n/L);9 q& c/ m1 P% E" f
for i=1:L H( t' g8 [, B. ?3 o sum=0;* U2 O$ I9 z8 \" ]3 A
for j=1:nL : x8 |% M z' C( S5 \8 n* s: t3 `" o sum=sum+data(i+(j-1)*L); 6 h, \. G/ h0 ^( X7 y% l# K0 e, Z end * o- d1 q+ S8 t( v+ u! ~1 y9 h x{L,i}=sum/nL;; p5 |1 A- U2 ~ w. |. r v
end: R* z" R6 M* f4 `
end ; O# r* x& l. F. NL=n/2; $ h$ U9 q" D) |/ jf=zeros(n,L);: A9 E; b2 ~/ \& x
for i=1:L 2 |' W0 k1 c' V3 N rep=floor(n/i); / N# l! |6 \& F7 S res=mod(n,i); * N1 s9 Z( I2 O6 S/ C; x- g$ Q/ y b=[x{i,1:i}];b=b'; " h, u& x+ ^7 I' A5 e8 Z; ?4 l f(1:rep*i,i)=repmat(b,rep,1); # Y4 L0 {3 k5 D: W if res~=0+ k) ?' L! h; D9 w: e. M3 V
c=rep*i+1:n; ( Y* g3 }2 `% C, I! M1 S' ] f(rep*i+1:end,i)=b(1:length(c));) o$ H( p( R2 L. S# a/ U$ Y
end" S7 N$ W: A* d3 K; U
end 6 `0 n v& V! s' P2 H& c7 j% p, ^( ], {
% serie**pan.m 0 R6 q" c- t7 G& m, K4 Q/ F% the program is used to generate the prediction matrix f; 2 Z8 c6 q1 ?; k' Y$ w
function f=serie**pan(data,step); % |" |* v& b m: l7 g6 W%data---- the input sequence (vector) ! [; w. n# o8 n! }% setp---- the prediction number;+ H" H. e C3 O
n=length(data);; U6 Q5 ~( W6 r. S
for L=1:n/27 q, \" n" x! ]% d
nL=floor(n/L);5 D* o, m9 J; ~& Q- W
for i=1:L l- S% M* G- l" Y O! R sum=0; ^$ i/ o0 r) ~1 g7 a for j=1:nL 4 ^ `6 W3 j- E; q- B# C, x sum=sum+data(i+(j-1)*L);5 h1 t9 G3 T& Q9 O$ I/ Z% [4 G
end8 F( M. [$ f, M) P
x{L,i}=sum/nL; 3 B% n& s% B$ G0 @" k, n end - s5 f: a; B" G, Uend' ?0 f3 v- U7 Z+ i; t; f) v8 {0 e
L=n/2;. H3 n/ G0 W# S& L, g! v
f=zeros(n+step,L);9 E# y: J* z4 W4 l
for i=1:L 5 x4 i! ~: ]+ @: F/ R" ^ p6 f rep=floor((n+step)/i); & m6 W, }5 @3 U res=mod(n+step,i); ( n' ?# F8 y% R, _ n b=[x{i,1:i}];b=b'; I9 R' P/ T7 f0 [0 ~( s2 c: H# o f(1:rep*i,i)=repmat(b,rep,1);4 f) S) f& e9 A8 N
if res~=0# c3 A: L7 `- A7 \
c=rep*i+1:n+step; ) @- _! P) p- I9 N$ s. @ f(rep*i+1:end,i)=b(1:length(c));' @1 P$ Y( q3 ^( g
end ' v+ ^; {- z0 Q! e8 eend & c m! \0 Y; a" g+ Y7 ` + B( p( k2 |( \2 [; }二 最短路Dijkstra算法 8 E1 p. ?8 T. _- I% dijkstra algorithm code program%( d. ?# v9 Y$ |4 C
% the shortest path length algorithm * x) Y) n8 s: x- Afunction [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint) 0 H$ t7 }3 y0 ]" y5 v% |# @% Input parameters: 4 w, ~1 O- {6 \, S! z- O% Input_weight-------the input node weight!3 P4 h, p' |" z
% start--------the start node number; # ?/ k$ ]& p, I, r9 C" ]% endpoint------the end node number;; u/ Y4 K! O7 z' `( b5 V3 m+ }& B) ?
% Output parameters:1 L6 ~& N7 T Q& R7 m. F. ^' _* B
% path-----the shortest lenght path from the start node to end node; 2 O" z$ c$ s# U' X% short_distance------the distance of the shortest lenght path from the- ~& L3 i$ ~' T( Z4 b7 Q# _4 `
% start node to end node. . S0 y% n' h) p/ F" j[row,col]=size(Input_weight); 0 W* i4 E K- V+ g+ @% H 7 t7 h# _* l1 @$ l" o) a%input detection - e& E% V4 x$ g6 jif row~=col 9 |5 x; o% D4 { B, D error('input matrix is not a square matrix,input error ' );) j' d/ `' x. H. y7 f% z
end 2 E/ Q; ^6 X+ q0 I4 m$ m: o( hif endpoint>row& I( h4 O- x# s
error('input parameter endpoint exceed the maximal point number');1 l! J% D; R; `# F8 a
end! A, a: L& n5 c' J$ P
. j7 A V7 e3 q! r%initialization; G* H1 D# L8 [% a( ]. O
s_path=[start];; N5 R" C8 H5 Q9 d# I5 t
distance=inf*ones(1,row);distance(start)=0; , \: ^! c7 `# f) t: p2 _- Xflag(start)=start;temp=start; + C% W8 J. s# @# s( X" k6 Y* ~* h% t, T1 B; A5 r3 X" N. X5 }
while length(s_path)<row) J& P3 Q, X7 T! U# V; U
pos=find(Input_weight(temp, : )~=inf); , S2 z$ J, Z. {. o* G9 F for i=1:length(pos) * I1 B% B1 f1 v if (length(find(s_path==pos(i)))==0)& , n: L. j8 x7 _% J4 i: V) h(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))' T0 m9 B9 i) ]* k5 f( C9 o
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i)); 9 r0 ^1 S# ]+ T, ]5 {1 a( E) g flag(pos(i))=temp; 0 @! }' q1 K# f$ m end; D- v/ A' B* t& n) z# |
end; Z& {3 }" P( @4 s. {$ Q/ b
k=inf; 7 H4 i( y, X% k8 [ for i=1:row# q8 o. R* ~6 S
if (length(find(s_path==i))==0)&(k>distance(i))5 w0 w4 P2 q/ ~1 M
k=distance(i);' P7 F* Z4 ^0 k+ A3 N+ C" J
temp_2=i; ! t) X2 R, ?% d& e; r% [7 r! K$ _ end- ^) {& a. R6 S
end # R: n/ M" \3 c0 w1 a8 P s_path=[s_path,temp_2];0 B Y* y8 }6 z' C
temp=temp_2; ) o2 g# d/ _: Yend , s7 K' D" H5 `: Q* [( R& |/ @. G& p5 @+ Q
%output the result $ @( P3 a' T& o' p, _' x$ npath(1)=endpoint; # A! r4 f. a- f$ \+ yi=1;) `" y0 t- I$ W( [
while path(i)~=start 8 t0 |6 p# f. w path(i+1)=flag(path(i)); + h2 R) C6 y: ~7 h3 X) D7 j8 y i=i+1;1 d; I& b4 d$ \8 X* |3 e1 c
end " k+ o2 U4 z" ?path(i)=start;( }2 a6 d! m* k5 F
path=path(end:-1:1); - h0 V* N# s: Lshort_distance=distance(endpoint); , o4 b# V$ Y8 s三 绘制差分方程的映射分叉图 5 f0 l% N9 c _$ {0 { W$ C: q, ~ J/ B4 I$ Z4 ?1 k( W* h
function fork1(a); , u) D1 o0 g8 r7 P x* l' k
8 O# O/ F M5 P: c3 P; N! x4 g% 绘制x_(n+1)=1-a*x^2_n映射的分叉图 9 M! X6 k* |& k% Example: $ g+ {% L* y* z# B' o# k& h- F% fork1([0,2]); ; S1 Q1 O5 f1 f) A$ u! sN=300; % 取样点数 v4 P6 o$ z. g8 d! XA=linspace(a(1),a(2),N); / E/ u9 R- m& t- D0 \$ i% Mstarx=0.9; 8 ^* ]6 y7 k$ d% g
Z=[];7 p5 o6 I l; Q! e6 ~" n) H
h=waitbar(0,'please wait');m=1;1 m7 ~! C& }) P( _: u. ?1 i( y7 s
for ap=A; - ^& P; K4 A4 @+ S' `) y# o
x=starx; ' C! R0 s. y9 Q% h3 Z
for k=1:50; 3 J% w2 T% j/ N# ?$ q, ^ x=1-ap*x^2; $ E5 Z! N0 {) U, O! y
end % y; W1 p* w8 z8 B( ~2 S6 v for k=1:201; , ^2 B p8 L M0 Q9 e% |9 C x=1-ap*x^2; 1 }6 u2 h3 q" B; U: X8 m Z=[Z,ap-x*i]; % p4 o" A: C7 U& D! V
end * e: o0 D' a! J% B( ]5 _/ \ waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);+ ~! J. v0 o, x) S' y: g- n0 A
m=m+1;; E+ L3 Z) T: z3 |% r0 p. D$ Y ~
end ) A" e5 u; r8 b* D- X
delete(h); 3 o: l& w4 X1 T) C9 `( Cplot(Z,'.','markersize',2) " z% z+ d& }4 E# m3 X/ s4 uxlim(a); % g. \: L9 N6 L0 q) y4 ^ 2 d: l5 K: n. I8 r4 i' f四 最短路算法------floyd算法8 i- D$ a# Q1 a# ]* X0 G: r
function ShortPath_floyd(w,start,terminal) 4 S, v! G8 [+ U8 k. l5 C& H- t
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80; - c1 z: m, @" t- ?6 K; q%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0]; z+ ]# _) X! a9 U; H" K1 \; V }%start-----the start node;# j2 Y3 F6 p1 B+ G& R
%terminal--------the end node; 6 C2 {% g, b* O; R' K/ Y2 x) J6 L! a, Wn=size(w,1);. i% h4 s4 I* e
[D,path]=floyd1(w);%调用floyd算法程序 6 i4 v, z/ ?. j( H 4 M% p8 r. ~3 V5 O. H0 r! ?8 u* N%找出任意两点之间的最短路径,并输出" G+ N/ d; F- r3 R& b2 |% e
for i=1:n8 r- r+ v4 J3 e( \; O
for j=1:n) Z; l4 j p$ i) k
Min_path(i,j).distance=D(i,j); - p. q( w. z2 n1 G5 p* n# W& w %将i到j的最短路程赋值 Min_path(i,j).distance8 D/ x' U1 e% S
%将i到j所经路径赋给Min_path(i,j).path G8 k* u8 I O
Min_path(i,j).path(1)=i;, d0 P. v$ X& Z5 V" \2 p1 H
k=1; : ^' h' M1 n0 m. {3 t: ~$ E- r while Min_path(i,j).path(k)~=j 4 x, [# x+ x* Y5 C k=k+1;+ _- ` |" n/ N# Y! I; S
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j); . N2 T- c3 a e3 a end" c1 Q! M2 D: M
end9 X/ b9 H8 z0 p5 h8 Q! N8 o
end 2 f @* p. y7 O5 zs=sprintf('任意两点之间的最短路径如下:'); 3 s6 C4 l/ s: w2 n, y# A( k; ^8 }disp(s); - C! z+ M- K# t9 q3 L) ?for i=1:n , V1 d8 F# _6 \' l* z7 R for j=1:n % F4 Y8 ]: A% g s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'... 0 C7 J2 t, G" Q* v ,i,j,Min_path(i,j).distance); ! M$ N. p8 M. G! q disp(s); }; Z9 \ k' ] E* h7 z' R9 Z' I disp(Min_path(i,j).path); 2 t1 s: o- p( ]1 @; l. O5 C3 T end P: z& ~ T: k7 r% Q* ?end( J$ k# T+ B3 h$ V1 q* ~
0 ^2 v3 x- _( n; K( U$ U& {%找出在指定从start点到terminal点的最短路径,并输出, G. d8 w. [/ x( h" G0 K9 r
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...$ U$ Y+ q! [: t5 f1 ?( H
start,terminal,Min_path(start,terminal).distance); 4 ?$ R# B1 o+ o# [1 v1 U: ?( Ddisp(str1);6 L, v, h2 j& b P
disp(Min_path(start,terminal).path);; Z" ^) X$ g+ ^ Z9 H6 J* P6 O7 f
6 K4 h. i$ Q, e
%Foldy's Algorithm 算法程序& I) F; G" C& ` S& q
function [D,path]=floyd1(a) 0 @- o0 Q# g2 y" l4 E, f/ Z2 wn=size(a,1);8 m0 t, p' C( X4 r7 c# J, C; B
D=a;path=zeros(n,n);%设置D和path的初值( V1 P+ l: C" `( o! R; o
for i=1:n 8 `# i2 u- `" z( c+ ? for j=1:n 1 z/ U# S( j$ } if D(i,j)~=inf( B9 c) F1 Q2 M, ?" {4 [
path(i,j)=j;%j是i的后点; [: ?" u, H' S
end: {# u( l, O, z
end , o" i4 d& K- u. v* J; n+ `9 r0 Bend 5 f `9 Q. ^9 I& |) c1 t%做n次迭代,每次迭代都更新D(i,j)和path(i,j) - i8 Z; E0 g3 Pfor k=1:n0 L' D- K; }) W$ Y3 }5 A0 o
for i=1:n' y' F& i& q# ~5 @4 D& y5 R
for j=1:n 0 `) K' I9 @5 X4 k3 q+ `) O if D(i,k)+D(k,j)<D(i,j) . Q/ l+ ]( ]- d. f! g! Y, I D(i,j)=D(i,k)+D(k,j);%修改长度 ( R) K; ~; w2 H path(i,j)=path(i,k);%修改路径 ; O3 _+ T" g( B) t! c9 S3 l/ s" S end 2 r# I" M1 l! I6 j; R end* b0 B9 K7 Y3 [5 [
end 1 r0 k- {; F8 \6 s' n% a0 Send ) o. Y# P5 L# t" T4 `# W4 x6 z* H+ t8 e+ O Y
五 模拟退火算法源程序" J) \* G. z: J6 l( \% k) e
function [MinD,BestPath]=MainAneal(CityPosition,pn)! |! x, V1 f. W# `$ V2 }
function [MinD,BestPath]=MainAneal2(CityPosition,pn)5 y& U! `! L: z Y- k
%此题以中国31省会城市的最短旅行路径为例,给出TSP问题的模拟退火程序6 D, b* I5 |3 e/ @' h
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;.... Z( t0 O& U2 c
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...* }4 S, K1 X0 @! Y
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;... 0 N9 P" o: F3 o) n% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;... ! |# }, u# l/ I% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975]; [+ t/ z& B4 F: T/ p/ M
) ] @- {: \2 ?" j& V v%T0=clock; m% Y. p% r* P) \8 F
global path p2 D;# X: r) {* P* f+ j& I" F2 Z
[m,n]=size(CityPosition); % { C) j( G0 {! J( n%生成初始解空间,这样可以比逐步分配空间运行快一些$ e$ n& V/ @& d& M
TracePath=zeros(1e3,m); K2 m( A+ ~* Y( XDistance=inf*zeros(1,1e3);6 v# J- v {5 F! J& P5 b1 D
! V: p2 ]0 K0 _2 _; w1 vD = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +... ' ?* b) ~- Z( K: f8 ? (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );9 V3 I/ S8 g# ?3 R3 B2 e# ^
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵) 1 O" N# Y0 ?" y4 ~% gfor i=1:pn x0 n" ^0 v( L' T1 F2 C: e6 R( c
path(i,:)=randperm(m);%构造一个初始可行解 ; L+ P7 r# B! N0 G. [end' M1 G2 a6 V9 y
t=zeros(1,pn);; h% G4 V K: w! Q( Y) d
p2=zeros(1,m); + k- N; v( e8 D [3 w. y' o a# A+ w3 |
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' ); ) d* g( o; H2 M) t- `' om_max=5;%input('请输入固定温度下目标函数值允许的最大连续未改进次数m_nax=' ) ; 1 F1 u J3 S. M3 b+ P6 P8 h) l%如果考虑到降温初期新解被吸收概率较大,容易陷入局部最优 1 i8 M. r. B# f6 I%而随着降温的进行新解被吸收的概率逐渐减少,又难以跳出局限 . X+ `% E) I8 C) c' q9 Y# v%人为的使初期 iter_max,m_max 较小,然后使之随温度降低而逐步增大,可能* B8 w! B2 C% H3 l3 g9 ?
%会收到到比较好的效果4 j: L3 P' @9 K( J' { g* P
8 ?% h3 r( ?& e# ^+ b
T=1e5;9 ]. i7 P: R: _7 ^5 }0 [
N=1; 5 X3 y; M W: C$ g6 L% ytau=1e-5;%input('请输入最低温度tau=' ); 9 s- |" x ? e* s3 U5 s%nn=ceil(log10(tau/T)/log10(0.9));9 r/ \4 ^( B0 D# K
while T>=tau%&m_num<m_max ' p& V. Q, L0 g$ a3 b9 ^
iter_num=1;%某固定温度下迭代计数器" n8 V) o& g( @
m_num=1;%某固定温度下目标函数值连续未改进次数计算器 + ^3 `. s) X5 N2 N %iter_max=100;/ O% }, C, \$ ~8 S( f6 _6 ^
%m_max=10;%ceil(10+0.5*nn-0.3*N); 8 [) {9 j3 v% J! T7 D. y- `8 T while m_num<m_max&iter_num<iter_max 4 ^8 s0 v% A8 o1 l* X( t" k+ O %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:5 @, q; B( R: O+ R. m
%用任意启发式算法在path的领域N(path)中找出新的更优解 & q% ~3 ]8 c6 B$ q/ L7 n9 C for i=1:pn # d9 N* L' e8 @$ t4 ^: O Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);4 `/ l3 H/ H. h4 T
%计算一次行遍所有城市的总路程 : l4 I& O* \+ `" e- e; y( ^" B
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线! b" x1 c% ]- |" s* G- W. E
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]); ; C, I; k( H' H2 k2 J1 B end. L. O" f7 A9 q Y
%Len1 , g, F- B6 e' } %Len2 0 `) M$ K& ]9 t$ b6 C0 ?# l+ { %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand1 a- f' ]2 ^, L/ r
R=rand(1,pn); ( G8 ^6 F# T) k/ D %Len2-Len1<t|exp((Len1-Len2)/(T))>R : I i. Y0 H4 u0 {. b' p( m; J if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0) 8 C) {9 T* T" x. N x path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );) x- N( G2 Q+ M; u
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));5 ~/ H4 H4 G0 Y# ?
[TempMinD,TempIndex]=min(Len1); # U3 [6 y- `+ k* M5 t %TempMinD ! @, p8 D' g w% l9 r TracePath(N,: )=path(TempIndex,: );( P2 j' T/ s4 z8 V4 V% D: }
Distance(N,: )=TempMinD; # i6 ]& ]* e$ U9 c5 |9 s: H" z5 u N=N+1; K6 e# j5 l( S %T=T*0.9/ \1 K* _/ a2 J+ a& v
m_num=0;: T& |& C- l7 s e
else + c# q4 Y% \6 _, _ m_num=m_num+1;# K" q9 V5 M1 f! T# u) |9 Q1 Y: ~
end$ ~3 ]4 N' x) P! B7 H" L* e' e9 z& G
iter_num=iter_num+1; : b# c' T2 v$ t6 h* y3 [ end( K7 ~+ H1 l1 A$ @7 {
T=T*0.9 ) m3 q$ i+ X, P%m_num,iter_num,N 5 g5 Q. _( }- y( x8 [ c. W2 ^end & k! a, m+ `9 D% {: _( X[MinD,Index]=min(Distance); 5 W$ H' E; T0 a1 ?3 P- eBestPath=TracePath(Index,: ); ) n1 J6 y! E$ d3 g& Wdisp(MinD) 6 _% ^1 X: C% D9 ~+ ]%T1=clock) c* _8 d. k, J* K2 R3 r0 ]2 G3 G: a
8 _: _6 q/ P5 E
% l0 K, d# |" ]" O$ }
%更新路线子程序 ' Y# Y7 U2 s) \4 cfunction [p2]=ChangePath2(p1,CityNum)' p: u+ L4 v a
global p2; 2 Y$ F2 ]1 ~1 a* y7 I3 rwhile(1)& q5 k; o: Y$ V3 A+ e
R=unidrnd(CityNum,1,2); 2 S+ w/ p; G& e2 }# @1 {& T6 f2 R if abs(R(1)-R(2))>1 ' d6 h& Z) q. G" f5 P9 N1 i8 } break; / N5 U* i4 t: A0 Q7 p! _ end2 k, Y7 U9 x X. e
end% N0 ~$ o8 _7 ~* X2 x7 N, `
R=unidrnd(CityNum,1,2);+ |0 D0 J6 _( \! h, k' S- u
I=R(1);J=R(2); ) F3 |! l' a7 U& A9 a" E%len1=D(p(I),p(J))+D(p(I+1),p(J+1));$ \; _7 z0 J: F2 k2 \3 G5 v6 w
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));5 U! O2 m Q; K/ y' K
if I<J # \ E; h* A Q1 g, G+ T, u2 g+ v p2(1:I)=p1(1:I);6 e) @5 a, i; d: p
p2(I+1:J)=p1(J:-1:I+1); 6 q$ F0 O$ V: I& V5 e, q+ e1 X( | p2(J+1:CityNum)=p1(J+1:CityNum);2 Q2 l/ _* f, ]4 F$ S
else$ _. m1 q2 h) H6 g8 p
p2(1:J)=p1(1:J);; a% P% C) |! n* o1 ?
p2(J+1:I)=p1(I:-1:J+1);5 p( ?5 L* d5 l- |6 V1 v
p2(I+1:CityNum)=p1(I+1:CityNum); W; ?0 R8 x) b7 G- @* u1 v' i
end 7 V' L1 I* M i- [3 u& }( _7 W1 x1 Z! ?- i0 i- a, |
六 遗传 算 法程序: 4 G0 W# B( M9 o/ V$ [; p 说明: 为遗传算法的主程序; 采用二进制Gray编码,采用基于轮盘赌法的非线性排名选择, 均匀交叉,变异操作,而且还引入了倒位操作!0 K s1 ]5 ^: [5 P( K( B
! F; O$ L) G4 F! R4 P: B1 q3 Y
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options) 2 O( s: e( E# [ `$ b$ O% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) / w5 H: [9 O$ e. `% Finds a maximum of a function of several variables. 1 }9 i' B7 }: n/ w5 U: @% fmaxga solves problems of the form: % c }+ d* l1 c, H* o& P, V% max F(X) subject to: LB <= X <= UB 2 I$ n0 n9 [+ _: n% BestPop - 最优的群体即为最优的染色体群 0 Q6 A" s+ y% Z/ E8 N% Trace - 最佳染色体所对应的目标函数值 7 S0 Q Z8 i/ D( J5 C% FUN - 目标函数7 ~5 R4 ^- w( e; t0 P' h
% LB - 自变量下限 0 B2 r( z/ v- v% UB - 自变量上限, E8 w" \; l3 i" K* I
% eranum - 种群的代数,取100--1000(默认200) ) G i2 d, h. S$ E% popsize - 每一代种群的规模;此可取50--200(默认100) ' T' m* y; U% X2 V% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)4 Y* D" V; Y a; p" g
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1) ) a- u8 O- v0 T% s! A% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)2 M6 u _% v" R g: L7 K; \/ j: N
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编 3 d2 i0 O+ _- Q! q$ I+ L%码,option(2)设定求解精度(默认1e-4) 0 |! G' @: d8 ?" v, P6 D5 h) b% # g0 y9 U* o9 Y7 ]! c8 [% ------------------------------------------------------------------------! m' l* u8 u0 F- x) z
( W, x& I$ e* P- u: f$ z7 kT1=clock;- W) T9 w4 r0 Z" M$ [! I
if nargin<3, error('FMAXGA requires at least three input arguments'); end3 c* j/ c0 y) @; \3 y6 x. B
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end i, z* G9 B1 B6 x& s ? [if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end , z, P2 @6 H6 {2 h$ w; J1 Rif nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end6 Q0 K2 C+ o# d; D; u4 {; b
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end* t6 s. [3 r4 v1 e4 v
if nargin==7, pInversion=0.15;options=[0 1e-4];end) e( a+ `+ y: @ U! y
if find((LB-UB)>0) 3 T) K2 o6 ]' q/ f- | error('数据输入错误,请重新输入(LB<UB):'); 6 q! p( s! {' xend& M+ i: z8 n" F. c* N" h9 B& q
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000)); 2 B' S: y) s' _( s# @disp(s); 5 m( x% m2 P# G + G/ c; [2 c5 a" d z/ zglobal m n NewPop children1 children2 VarNum + y& H$ n' u! m% f, ? 4 @9 r( T" Z2 V* lbounds=[LB;UB]';bits=[];VarNum=size(bounds,1); 4 x% B2 |. }# jprecision=options(2);%由求解精度确定二进制编码长度 5 C" r/ \5 ^' |+ `3 i2 ~$ xbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间7 Y8 C- L3 P- i5 y, u- W
[Pop]=InitPopGray(popsize,bits);%初始化种群) U% g; ^ o4 K; |# U( M! u
[m,n]=size(Pop); / A' P7 D) x( k8 I& ENewPop=zeros(m,n); 3 F5 j2 x T$ D: k1 Y& E5 Echildren1=zeros(1,n); ; E# Z C* a# K0 I2 A3 ichildren2=zeros(1,n);+ e9 V4 S5 q; L9 V
pm0=pMutation;# ~% |5 R' Z( s2 Y K
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace ; X% R. Y# z7 C3 @% dTrace=zeros(eranum,length(bits)+1); 2 w5 o# ~/ }( r( b# K# Q% F) Di=1; " _* N" n' m' l) P* b# t7 V2 G/ Iwhile i<=eranum 2 O1 y0 \. h) g0 Q; P for j=1:m2 @. b- k. K4 B# q- P8 c
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度 3 q: y" S$ ~) ~& T! F7 K end7 \% E1 ~" A( z' f- D' ^; }$ V
[MaxValue,Index]=max(value);0 a) v B9 `! E+ w9 H' \
BestPop(i,:)=Pop(Index,:);8 O9 @8 [6 d/ |" B
Trace(i,1)=MaxValue;) ^1 a' e! p5 T6 K& W% H
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits); 0 k9 c! r5 n1 a1 Z6 p [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择' {! U h( ~' m4 w
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));' s5 i& ~8 g O8 z* N" F
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率 & y/ {3 e$ B1 v0 f! t) y %round(unidrnd(eranum-i)/eranum)6 B& R7 o: p. E% Z" f* T! J
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异. U. R5 l. `4 R* ]& d! C5 V
[InversionPop]=Inversion(MutationPop,pInversion);%倒位 8 a" D2 I) {9 g( R! B9 F Pop=InversionPop;%更新8 y7 h$ ]6 d# q/ o6 y+ m3 M
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); i4 M$ w S }; k9 U2 X
%随着种群向前进化,逐步增大变异率至1/2交叉率! p2 O( _! e$ `; }' L
p(i)=pMutation;4 b$ |5 \: n! u# j, h
i=i+1; 5 b! i1 G/ Q5 Xend F) Y2 g D J8 O1 o+ w% H
t=1:eranum;& c: z! \5 o" \" e# i
plot(t,Trace(:,1)');7 G' e1 {3 E3 X
title('函数优化的遗传算法');xlabel('进化世代数(eranum)');ylabel('每一代最优适应度(maxfitness)'); 7 c! k! y2 [, h) K( D5 H( s1 t[MaxFval,I]=max(Trace(:,1));5 ^2 c3 Z3 A) ?9 F
X=Trace(I,(2:length(bits)+1)); 3 x" H0 I D4 m) f! c2 Whold on; plot(I,MaxFval,'*'); 9 G! m/ T% } m- F: w) O- z" Gtext(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);/ u' g# H$ I- G r s
str1=sprintf('进化到 %d 代 ,自变量为 %s 时,得本次求解的最优值 %f\n对应染色体是:%s',I,num2str(X),MaxFval,num2str(BestPop(I,:))); 0 L' w, T" ?9 H/ D2 X) |disp(str1);# p1 Q, q. C/ q `6 E1 {
%figure(2);plot(t,p);%绘制变异值增大过程 Q4 @ W' t. P
T2=clock; 7 s' W2 I3 O, ?4 velapsed_time=T2-T1;* z' b& o3 ?' v! Z/ x% n) Q5 \) y
if elapsed_time(6)<08 X' _8 `5 c- i/ W0 C L2 J
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;" K* F1 y+ u- F4 S* V
end : M% r7 o" I* l& r! m7 B- Zif elapsed_time(5)<0 ; x3 U) \1 }8 n# M( Y O& h elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1; ' p+ m) z& a- q7 R+ eend %像这种程序当然不考虑运行上小时啦5 l' }% j, M- c
str2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6)); 5 n0 \' Q; m$ p+ q/ S3 T7 jdisp(str2); 6 N6 `1 @5 x; `" i$ @) s* v7 p 5 o" _- k' q, d$ A% i4 i1 T6 `( I6 h' ?$ L" F/ Z
%初始化种群 8 Z7 n' H0 G3 }& i' N%采用二进制Gray编码,其目的是为了克服二进制编码的Hamming悬崖缺点. @: {' O: P# O2 [, s1 R- d/ L' o
function [initpop]=InitPopGray(popsize,bits) ; ^0 y# |/ X3 r) U2 W* ]len=sum(bits);) L& \, ?) ~. ^; x" Y
initpop=zeros(popsize,len);%The whole zero encoding individual % h+ U0 p4 j+ X& kfor i=2:popsize-1+ t0 c( l+ }5 N
pop=round(rand(1,len));; u" E3 o V" b* Y' B
pop=mod(([0 pop]+[pop 0]),2); + h2 B. O' Y& K% k %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)$ G- I1 a% o& _; k
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n) 7 x7 m6 h U* F; L1 t initpop(i,:)=pop(1:end-1);: ?* p( V3 b+ u# _$ w% [. f; x _
end' O/ \. H4 _5 i2 k- Z. j* G
initpop(popsize,:)=ones(1,len);%The whole one encoding individual+ C L4 `! r/ Q( d: y
%解码 ( m* N/ m$ \$ \5 @8 R9 | " y" w6 C( E! l$ ^* J! D7 _function [fval] = b2f(bval,bounds,bits)( u' E5 R; M4 W# T: H0 Q
% fval - 表征各变量的十进制数 1 }* U2 p& f1 k+ x. s) N: p% bval - 表征各变量的二进制编码串 & O2 p0 ]! p# r% bounds - 各变量的取值范围" x( ^( @3 ~0 Y
% bits - 各变量的二进制编码长度 1 I& H) G; L# r- Oscale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables6 } v' n5 r. x8 d, V, G# P
numV=size(bounds,1); , v' x& f8 u8 F( O2 f0 Q! mcs=[0 cumsum(bits)]; : n$ l. \0 p& J2 Ffor i=1:numV + a; {2 v" t/ v; G- t- m; U a=bval((cs(i)+1):cs(i+1));2 i* i6 X" M5 Z) G# F) r0 K
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1); 7 V% e# [& A6 p- _end # J2 K' n. C: T3 _- ?%选择操作 2 E1 g8 W0 R) W% o* A%采用基于轮盘赌法的非线性排名选择6 X3 E; |: d! ?6 x+ t/ v
%各个体成员按适应值从大到小分配选择概率:4 j% S4 V9 O6 }" p1 P, K" j
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1 * w" F# \8 m/ Z5 p, {# N 9 o( v8 M b7 |2 b# Gfunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)2 s/ P5 W% y% o0 J% i. [
global m n ) m Z6 t+ [7 |* _selectpop=zeros(m,n); - A) |( y; V5 B; x$ C% J6 bfit=zeros(m,1);) ?& U* Y% n. L0 o; [
for i=1:m- @) ^% r9 Y9 r& J) Z/ i7 I
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据 D0 V* x+ e! A- F2 Yend ; o3 B$ M" Y, Rselectprob=fit/sum(fit);%计算各个体相对适应度(0,1)/ {! c6 T' q5 `! m
q=max(selectprob);%选择最优的概率& l+ W3 v& x, R/ q- k- j6 M0 F( l. O8 T
x=zeros(m,2);* P& g* O6 F u
x(:,1)=[m:-1:1]';+ ~6 l0 J0 H! p2 N% k! Y
[y x(:,2)]=sort(selectprob); $ g/ _+ l0 _7 \0 l/ @( v& Tr=q/(1-(1-q)^m);%标准分布基值4 A$ u" x8 q2 K) J' B* P% n. B
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率2 ^% e! g" L- @+ Z. B) I
newfit=cumsum(newfit);%计算各选择概率之和% ~1 S: v+ \( P9 `' Z. p9 z; Y
rNums=sort(rand(m,1)); % N, x) h; F/ r' T' c9 @fitIn=1;newIn=1; 7 Q( q+ m7 |5 G3 Y% O0 _0 Vwhile newIn<=m& G& ~( K2 r7 y' i8 V6 T7 W1 c
if rNums(newIn)<newfit(fitIn)$ g1 W6 g1 x; U
selectpop(newIn,:)=pop(fitIn,:);& _) F' X( `5 F& }& B# \
newIn=newIn+1; 2 i3 P8 ^+ Z7 b& U+ n else, Z7 S9 K7 o: z3 e- G% S
fitIn=fitIn+1; ! ~" E2 O% t0 M end ; f3 Q2 @) a$ W4 u, [end 0 F1 m2 E7 @3 d0 ^%交叉操作- ]1 N7 j) B, U1 @6 D$ v
function [NewPop]=CrossOver(OldPop,pCross,opts). }3 r& n1 w2 ~4 G
%OldPop为父代种群,pcross为交叉概率% d. D0 ?" s J) O6 ~( D d' {& _
global m n NewPop 5 f' e7 u- E) H! R
r=rand(1,m); : n, B) Y9 s4 V( w" N4 k6 B- X, \y1=find(r<pCross); ; i& e: g A7 h7 U( G$ Ly2=find(r>=pCross); % t. V) {) H+ l5 Blen=length(y1); 4 r7 _2 ?; k) M6 p; ]if len>2&mod(len,2)==1%如果用来进行交叉的染色体的条数为奇数,将其调整为偶数& O& J- ?( y. Q9 W& k9 q4 B8 ]- @
y2(length(y2)+1)=y1(len); 6 V- Z- h. ^4 y3 t3 K: f+ E1 B5 M y1(len)=[];1 Q7 X8 |, _+ s1 v
end. e. D7 Z/ _7 S7 k4 L( G
if length(y1)>=2 2 h9 F2 E% D9 U2 G for i=0:2:length(y1)-2# }/ d! ?7 L* R
if opts==03 P0 |4 ]4 D" B$ _3 `6 J4 \8 f0 ?
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:)); ! `" X8 K4 \. D else ( v' }+ Q" Y8 y5 p( r: T [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:)); % x7 B3 ?$ U \ end 0 z* n5 t! n$ E/ k E( ^* ]7 D, W9 y end 5 z$ h# S. ?$ T0 I. T' Z. q
end ' @- e3 N8 O9 c! Y3 P9 nNewPop(y2,:)=OldPop(y2,:);- c- k/ C- v$ y" Z7 l8 }% W
3 n9 I. \6 d' h2 y! E( `' B* R%采用均匀交叉 . e' i, J# u+ L6 m6 p' Y
function [children1,children2]=EqualCrossOver(parent1,parent2)7 s& ~: V6 Q2 s+ t7 n6 O0 v s @
( _. W$ [# L9 C& ?. \ sglobal n children1 children2 5 D) s( x- V* Y* K7 \( b
hidecode=round(rand(1,n));%随机生成掩码# J6 W# M u, V3 [1 F3 O3 K
crossposition=find(hidecode==1); # p0 o$ c+ a( Q+ Pholdposition=find(hidecode==0); 8 u& @1 o! V7 }* ^9 uchildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因% `4 O& k' D* X4 m( z' ~# a
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因0 G: n7 }: z% Y9 a5 s
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因 7 ^; O& }' V; Y$ m) `5 x# ochildren2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因$ E1 p, w, w6 R0 y$ z
$ g; g, {( o; v0 [, R$ Q. ^
%采用多点交叉,交叉点数由变量数决定 i# I, J0 B2 M% P( t
8 q/ ?: p- H) d
function [Children1,Children2]=MultiPointCross(Parent1,Parent2) 1 U1 a: u$ d1 l2 P9 k- J. B / d9 Y" K! s' h& Y! P8 [- ^1 Rglobal n Children1 Children2 VarNum R' j7 Y" j1 i+ g
Children1=Parent1;9 b) P4 s7 S6 I4 B" _
Children2=Parent2; 5 U, J; Q) d& h2 R f, K1 ]- bPoints=sort(unidrnd(n,1,2*VarNum)); + ~2 [5 h( C5 g% l9 q! o* qfor i=1:VarNum ; u Z& C( a/ E! ~8 ], P$ ~0 ] Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));( X/ o3 N3 y2 l0 ^9 d' _# o* S
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i)); a) o* L6 w' t0 V2 t
end# N4 d. k: x/ ?
- `8 q& Q* @3 |% d9 @: |* {%变异操作 q3 H' N( Y" L# Y# H6 ~$ O J, ?2 c
function [NewPop]=Mutation(OldPop,pMutation,VarNum)+ L1 G; E% E' c4 J/ ], |6 B
/ @- _; j( g1 {* P$ t$ ?6 p7 ]
global m n NewPop3 ~7 a+ I2 |; h+ z6 H* X/ |& a
r=rand(1,m); : P9 ^8 B9 z/ F8 N3 N1 qposition=find(r<=pMutation); # S( z. Q0 R" K4 ^( flen=length(position); ' E0 V ~0 }2 A. i6 B- l) s Aif len>=1 6 l( I! v2 l6 B2 q for i=1:len$ r! t9 R& L+ T2 l& x
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点8 B) i7 M) J: a& P: j5 O0 l
for j=1:length(k) 2 m1 p7 N, c% [& t1 U if OldPop(position(i),k(j))==1 . \' U7 s( O1 K' o OldPop(position(i),k(j))=0; $ B W( T1 v( `3 v, Z$ ^ else9 k, k7 b, q1 S; l
OldPop(position(i),k(j))=1; K& O9 f" h# i' w
end . d J1 d+ ~ t/ O; m) @ end ; t$ [7 r9 x5 I7 q* t5 |& ^ end # U0 ^ b5 g4 j# I: Rend# {$ O1 j' c0 z6 E, V
NewPop=OldPop;/ g7 e2 p6 U9 Q9 S8 F# A
2 \& U5 f/ _# M$ D; @* v
%倒位操作9 q$ _6 g1 B3 N
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function [NewPop]=Inversion(OldPop,pInversion)2 k7 C6 m, C, m9 o7 A. Q
, f" m7 g, T2 bglobal m n NewPop( V/ V1 p9 L1 t; a# x
NewPop=OldPop; * r( [8 z8 \0 w0 Y6 {- R% f1 Cr=rand(1,m); % g* G% N+ V' aPopIn=find(r<=pInversion); 6 L0 m ]1 W9 R2 l- `$ Z ?- ^len=length(PopIn);' z0 V) P9 g2 g
if len>=1 " W; u5 I: J; e7 S9 [/ P/ ` for i=1:len 4 R% V) l/ o) J3 ^/ j) B, T0 c d=sort(unidrnd(n,1,2)); 2 h/ S3 e3 Q1 R' o/ ~ if d(1)~=1&d(2)~=n. R: K8 e# u- H& C$ V) o: l+ [2 [
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1); 4 t# A* f* U; { NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1)); / k* p# O9 r8 t( h NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n); & [ r1 x3 w! [* I# _6 W end; E, z0 |! ~, Z3 t- B9 i6 P
end # I6 B/ O: s- y% ~( n" |1 k2 Xend - [9 U. w9 [ p* r! Z7 e' ], q5 Y* e5 o6 j
七 径向基神经网络训练程序 % N# n4 P; }) V4 {5 M/ j$ F$ u0 s * ]; i. B7 ?# _ L1 Qclear all; 5 M7 Q0 ~" w* T6 Y+ p1 hclc; ^& R& ^# c* x q1 Y( a% t
%newrb 建立一个径向基函数神经网络' q! Y3 I& s3 g3 O% {3 K7 f3 w
p=0:0.1:1; %输入矢量 1 n, V$ w/ v) ^, j; {8 U: Qt=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量 0 b- ^9 p M' W2 Y* d2 {; R5 {goal=0.01; %误差; b U4 L0 d, n" y" ]1 ?
sp=1; %扩展常数1 B; |6 L: w" W! ^: L
mn=100;%神经元的最多个数 6 N/ m- ?* Z' Udf=1; %训练过程的显示频率8 O$ Y% [! U! C) S m- ^ D
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络 : T! R) J+ G# O% [net,tr]=train(net,p); %调用traingdm算法训练网络 . ?& ], ^8 G& r' [: c" T%对网络进行仿真,并绘制样本数据和网络输出图形. z" k4 f1 M; l( }# m3 [' w+ Y
A=sim(net,p); 0 P+ N' G( W9 Y* @# ?- ME=t-A;$ u" d, x( U$ F2 k' F: U2 ^
sse=sse(E);+ O. D+ L' u% U. ~' v! M
figure; 2 W8 p u) J3 A4 J7 [$ dplot(p,t,'r-+',p,A,'b-*');+ s7 s- Z4 @6 H! C# x
legend('输入数据曲线','训练输出曲线');" @: Y" p/ ]1 c9 k. M* e- x
echo off / D) N/ ^5 W5 N1 a, [( C. _2 N+ n* t0 V7 O
说明:newrb函数本来 在创建新的网络的时候就进行了训练! & ]4 y3 H0 g" g! M/ F/ r每次训练都增加一个神经元,都能最大程度得降低误差,如果未达到精度要求, ' {1 w! y. {. R3 q/ t/ x. I0 P那么继续增加神经元,程序终止条件是满足精度要求或者达到最大神经元的数目.关键的一个常数是spread(即散布常数的设置,扩展常数的设置).不能对创建的net调用train函数进行训练!5 h% k' n) ~9 ?7 u. Q- g4 U
! Y0 B4 [1 ]" d0 C3 v" Q$ x X
) J. m, u% q7 J+ P1 t" d训练结果显示: . d9 s8 U# T+ ONEWRB, neurons = 0, SSE = 5.0973 6 ]# A1 K2 A G4 JNEWRB, neurons = 2, SSE = 4.87139" N3 m2 f) ]' ]9 i% j9 |# i
NEWRB, neurons = 3, SSE = 3.61176 ' p( U$ T+ C+ C( k- _' QNEWRB, neurons = 4, SSE = 3.4875* V: k) @5 @# s
NEWRB, neurons = 5, SSE = 0.534217+ B8 n( v! g: ^# N. f) O* K S
NEWRB, neurons = 6, SSE = 0.51785 : ~. A- K6 D) nNEWRB, neurons = 7, SSE = 0.434259 2 q: S: l* ?* `0 fNEWRB, neurons = 8, SSE = 0.3415181 n% j! c- ~2 X5 y6 E" ]" ?2 J
NEWRB, neurons = 9, SSE = 0.3415191 P2 b& _( J- \1 O! P
NEWRB, neurons = 10, SSE = 0.002578327 v& \! h0 S: S
2 @/ I& Q* P- b8 |6 ]
八 删除当前路径下所有的带后缀.asv的文件 c9 A8 S5 B, V6 A, X' \) A说明:该程序具有很好的移植性,用户可以根据自己地) ]9 u/ {3 P+ `
要求修改程序,删除不同后缀类型的文件! ' M- d: h% n; {
function delete_asv(bpath) & B) q5 ?/ A, F! `
%If bpath is not specified,it lists all the asv files in the current: a. x! l8 N4 Q2 {
%directory and will delete all the file with asv 0 L4 [4 U, i6 V# p/ n/ A
% Example: % z D# m6 p8 B. L% delete_asv('*.asv') will delete the file with name *.asv;0 M! }7 H9 t$ a$ ~) T! J. _
% delete_asv will delete all the file with .asv. 3 E4 G1 j0 x+ G# I& X {, u/ r4 G& E" _$ s7 D7 D4 d
if nargin < 1 ' I9 [) Y) v# Q% Q%list all the asv file in the current directory) \2 p8 o8 b9 {' m* g9 B
files=dir('*.asv');/ g3 w+ q3 n! _6 x2 J6 T
else : e( b6 v; `2 q L0 {/ \% find the exact file in the path of bpath# i' @' T. x7 C) o: F; s
[pathstr,name] = fileparts(bpath);! v: R) ~! e4 E5 [8 Y
if exist(bpath,'dir') 9 E! {. N: k6 V, Y: t M# |9 w. o) M1 A name = [name '\*'];0 O1 t5 o i) N
end % H3 @3 T! E- I5 x ext = '.asv';0 E, P& i* u4 G# L! y" z2 F0 b
files=dir(fullfile(pathstr,[name ext]));2 w: ]9 ^0 ~# x& w5 _# K
end4 I# [" n7 O6 d$ ~+ z; d4 g
6 D" G" e5 g5 a5 p# _) Y tif ~isempty(files) # L# X7 F) t3 }3 W6 l for i=1:size(files,1)! d* ~& E4 c0 g4 S# I
title=files(i).name;# ]" ~* ?/ d6 a
delete(title);' z$ Q4 j) w* C
end 0 @" Z" D1 ? X- F+ yend . H/ c6 \$ M; x% q " {$ X T3 Z3 [) E4 y4 ^ 0 X" N( G+ U; V# e' B" u) @同样也可以在Matlab的窗口设置中取消保存.asv文件! ' t$ ^' ~7 I! P! @" s; o5 U