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升级   48.42% TA的每日心情 | 开心 2016-11-7 00:15 |
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签到天数: 7 天 [LV.3]偶尔看看II
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一 基于均值生成函数时间序列预测算法程序2 Y/ d. V- q2 z) d; Z3 ]# y
1. predict_fun.m为主程序;' j) y# l" z; q1 u7 b
2. timeseries.m和 serie**pan.m为调用的子程序
S7 G. W( z2 {6 T4 ^0 I
4 }$ v, m/ \0 }function ima_pre=predict_fun(b,step)/ t. L0 q, u9 a, I
% main program invokes timeseries.m and serie**pan.m
8 m0 B0 B6 v. E/ M% input parameters:+ |: s4 l e) G5 d
% b-------the training data (vector);1 {4 O& n# ~+ y# e+ k8 {3 s
% step----number of prediction data;
) y' r% Q5 D/ R9 n# }% output parameters:
) _# F5 k6 P# u( w% ima_pre---the prediction data(vector);
+ @9 p/ x6 a, \( Z& W1 Kold_b=b;
- H) z: P& B% umean_b=sum(old_b)/length(old_b);6 @: j2 J, b: x( {3 Y* Q. t* [
std_b=std(old_b);$ S" h* h3 }% v6 i
old_b=(old_b-mean_b)/std_b;( |3 Q: F1 m' I: K
[f,x]=timeseries(old_b);! }4 N; k) ]% I+ K
old_f2=serie**pan(old_b,step);
$ J h$ v4 s) Y: I' n' e% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;# i! C! M+ N, P
R=corrcoef(f);
/ ]( o. K" u' ^9 x[eigvector eigroot]=eig(R);
) L- u# q' o9 Z; a! {5 d* `+ N8 a B9 ]eigroot=diag(eigroot);
5 D/ \: a) F, K$ m- @: ba=eigroot(end:-1:1);
7 T6 C. J+ x/ ]5 m' p, g$ r0 @vector=eigvector(:,end:-1:1);; C1 i/ w @, v* g, E" j0 \
Devote=a./sum(a);
& c! K4 H8 j5 S5 U: d4 L1 |Devotem=cumsum(Devote);
. x4 I- s3 z) U# _. b! d& Am=find(Devotem>=0.995);8 a+ U" e: s* O' l8 S y' q# `
m=m(1);
4 [" D# b" q$ H6 r2 L% k4 LV1=f*eigvector';. P1 H2 e6 [. W/ r3 t! m; i
V=V1(:,1:m);3 N- Q; L) a+ B' G5 i9 z; ^8 Y
% old_b=old_b;9 ~/ a1 S l+ g! |. N+ U
old_fai=inv(V'*V)*V'*old_b;) P3 P% U' Q8 ?6 d. L( \# ]
eigvector=eigvector(1:m,1:m);
) v# u3 {: B+ S" R2 l# l8 Lfai=eigvector*old_fai;
2 {0 b1 D( C' l* S! T+ I9 F$ ]5 Tf2=old_f2(:,1:m); y, E8 l6 n+ b6 u6 Q* g
predictvalue=f2*fai;# R8 W8 o% D) }& d+ }
ima_pre=std_b*predictvalue+mean_b;
" n6 Z% T% `. m. l$ b) M
- j% o6 w/ d- R$ S1 n5 c$ a1.子函数: timeseries.m
4 V2 M+ S: e* o( I" C5 y2 {% timeseries program%
* h3 ^2 v$ Q9 z% this program is used to generate mean value matrix f;
@4 |6 t& M5 X2 V9 j! `5 a* f( H" C' vfunction [f,x]=timeseries(data) ! y6 S6 i; _4 G" |8 Z5 P
% data--------the input sequence (vector);; d% X. o3 W( i7 V' P. f4 ~
% f------mean value matrix f;2 f" i7 \9 b' B, l* v' y
n=length(data);" k0 O+ d2 H& t: s$ N4 S3 ?
for L=1:n/2
; {& L/ G) Z* K1 \% S nL=floor(n/L);
* D5 n) m" Q; t# a( T8 p' O: F. t for i=1:L' V1 R% Y: Y X' ^) ^
sum=0;" @1 _6 Y5 u: V& Z# I
for j=1:nL
* I! m: S2 K# F sum=sum+data(i+(j-1)*L);
w# J0 J4 {2 V! ` end' c$ Y- h2 O: i; x. ^, \
x{L,i}=sum/nL;
" g4 t3 f, ]+ I& i7 p# Y end
6 t1 p; h$ r0 Z8 ], Nend) K# g, z! q. ?$ G5 }
L=n/2;# a9 u9 @+ i+ I7 L p$ d; F z
f=zeros(n,L);4 l, c' W" b8 z$ B: f
for i=1:L& i* \- d1 r5 y( u) s
rep=floor(n/i);* _& [) V# n. H7 c2 G/ [7 n
res=mod(n,i);2 u @. ~# O; g1 H
b=[x{i,1:i}];b=b';
& T( B; z1 o" O0 b: V& J5 I/ P; i f(1:rep*i,i)=repmat(b,rep,1);
$ C" m4 y k- E2 a% Z0 S2 f0 ^ if res~=0' s" Q+ l2 o. V) I% |
c=rep*i+1:n;0 y2 H, O( I+ Z: A C6 d8 I/ { `
f(rep*i+1:end,i)=b(1:length(c));7 f# y e: J, V
end8 ?/ q5 ?8 G$ Z0 Z( z
end2 Q; _% T# D& d% P
# i3 m+ j: ~; L' T
% serie**pan.m/ O9 ?9 u( E# D3 l0 h$ R8 M
% the program is used to generate the prediction matrix f;
. n' x4 N$ V" \8 m% ifunction f=serie**pan(data,step);. J. Q) F' i; M
%data---- the input sequence (vector)
6 l! [, a4 v9 e% setp---- the prediction number;
4 \2 I7 q4 E$ @. D; L2 an=length(data);
: p8 M* P% f( F9 e5 B* Q* {for L=1:n/2
$ P- Y8 @/ Z9 y, U0 Y; R nL=floor(n/L);2 K4 i! m% L+ m, v! L
for i=1:L( f% N7 w5 j" V5 [9 i
sum=0;3 R( Q6 O% j5 j' q8 f4 y
for j=1:nL- S4 a+ u' i1 \) n! D$ S8 s J. H
sum=sum+data(i+(j-1)*L);
( u2 P9 Y3 W2 l C end9 D; Z) R2 y5 o, r
x{L,i}=sum/nL;) Y! S% B. @6 V' _( _# s
end
) P I0 [/ F& z2 a5 K, G6 c+ M. Eend5 k! P& _6 n9 d; _& |! M
L=n/2;* ]3 a; S v! y, F5 ~
f=zeros(n+step,L);+ s) u, z4 e" l5 C$ N8 n+ U
for i=1:L: [7 L5 f9 ~" z3 s# b0 z
rep=floor((n+step)/i);
4 t* x/ S1 v7 l6 w) l res=mod(n+step,i);
- v# t2 t3 ^2 f6 c b=[x{i,1:i}];b=b';
1 c# }8 q) c$ _0 [6 J1 y f(1:rep*i,i)=repmat(b,rep,1); G% u4 L) l5 m% G
if res~=0
+ i9 S# P" u+ J5 a5 O( ^4 B) u! [$ S c=rep*i+1:n+step;
0 d# q A. S1 y: P1 i( B: p f(rep*i+1:end,i)=b(1:length(c));2 q' {) x+ C9 s2 N2 q! m
end9 X i8 g _; z1 _
end+ D# _ N6 F% w& V% Q8 L. X, ^1 p {
( p/ I+ l" ? p+ Y& M/ [6 E/ \6 c二 最短路Dijkstra算法" p3 U7 y: P; i( u2 q( q
% dijkstra algorithm code program%1 J( D/ z3 R/ C+ S* ?2 M
% the shortest path length algorithm, d9 Z1 I: w7 T+ H7 d; G" ]9 D
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)! x5 o! P6 Z) t
% Input parameters:
( `# C# x" ]9 _% Input_weight-------the input node weight!
/ y( I( w: Q: n& h- D% start--------the start node number;
4 f4 H$ L0 k7 [) i! F% endpoint------the end node number;- v( N8 J2 H# F3 ^; N
% Output parameters:
1 w( y' _$ E! o( `! R( m1 y/ X% path-----the shortest lenght path from the start node to end node;
7 ?$ x6 Y F& ?% j7 H% `% short_distance------the distance of the shortest lenght path from the
9 V" D* b( J# u6 P; C b% start node to end node.
0 i$ G. C+ ?: K0 p0 n[row,col]=size(Input_weight);7 i& p- r* f2 n4 h, v: f7 ?, H
1 M) V- ?, @ a; Y: W
%input detection
2 t1 }* G1 t4 E( iif row~=col" B7 C% y1 [3 n
error('input matrix is not a square matrix,input error ' );8 H. j/ O" e( ^) |) }( _
end
* D& v' Q8 a+ ?" S6 v" l( wif endpoint>row
6 y; r! {; n0 m* ]$ o- }, ` error('input parameter endpoint exceed the maximal point number');. C, A6 z. y# R+ t7 `
end
! T. E3 a9 F' I3 @5 |; c9 N1 F1 `, p) w9 _: O; p
%initialization' N+ {" U$ @2 l5 R% @
s_path=[start];3 E3 b+ Q3 B G. j
distance=inf*ones(1,row);distance(start)=0;$ a; s+ `) B- r
flag(start)=start;temp=start;3 ]6 Z8 F/ j$ k
6 A% E1 i, y- x! z
while length(s_path)<row; e0 p. J3 o a2 M0 \, p
pos=find(Input_weight(temp, : )~=inf);
) Q) M& |1 U' b2 j" } for i=1:length(pos)
5 ^- Q9 w4 G6 O: i' w. y( C if (length(find(s_path==pos(i)))==0)&
0 |& l* R, n! X: s: x3 l(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
z% s" ]+ B, f9 f distance(pos(i))=distance(temp)+Input_weight(temp,pos(i)); l* Y. E8 ?1 Y. T
flag(pos(i))=temp;- ^. D6 T3 s' N3 Z$ J) b
end
2 S V8 ]+ w& u1 M end. `/ ^# V- j6 z6 l; U1 g
k=inf;" g# @& @' w4 r0 c. [% I# c
for i=1:row
6 J# T+ D) m( i# ~ if (length(find(s_path==i))==0)&(k>distance(i))1 y& g0 s+ A) Q- U1 {% d
k=distance(i);
" Q0 M2 T! A# f! O$ [# G temp_2=i;$ q$ {' w5 G& v+ y. S2 s/ j a
end9 c7 s7 n* W5 y4 e: Q/ O: Q7 q
end
" ~/ U- N) M# Y& Z4 d- r s_path=[s_path,temp_2];8 A0 j& Z2 u5 `/ ?* @/ B
temp=temp_2;8 I% v" @. f# S. m7 Y# r/ b
end& W0 l7 U4 d! j) {
$ i2 K& @/ {9 I. W& z6 v5 L& W%output the result) `( F# K I4 U; L
path(1)=endpoint;
4 Z O5 o4 ^: y5 ~1 ?- s6 e4 Oi=1;' k- d: ~' K+ f1 P
while path(i)~=start+ }4 E' T5 V7 e- p- D
path(i+1)=flag(path(i));0 y6 T9 _8 Q# N% C4 k+ a1 a' V6 t
i=i+1;: @( J9 m$ F% B. x
end
$ R) j) C) Y; p vpath(i)=start;7 y" _8 h5 h4 V2 _( ]& i
path=path(end:-1:1);
2 g: `1 Z0 z' [2 q% k1 Sshort_distance=distance(endpoint);, G, U6 W4 x+ c% t/ { ]* X! [
三 绘制差分方程的映射分叉图8 p) M/ {! A' p5 Y" ?
9 K$ V0 q8 S& ]1 N. ]3 F* pfunction fork1(a); 5 H) C1 d1 l. L* A
& T1 @, j/ i; I% Q
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
+ {' `$ Q: P' W" u9 j% ?% Example: ! U( q+ _8 s, n: g9 m
% fork1([0,2]); 8 n$ i" m2 @8 a, Z* [
N=300; % 取样点数 5 c5 k$ m) R4 V
A=linspace(a(1),a(2),N); 2 \6 z; B1 l/ u- v2 o4 Q
starx=0.9;
7 l7 }0 u( c/ q3 q. Z% ~Z=[];
: s: G: k( f7 J$ V! ^' _- Lh=waitbar(0,'please wait');m=1;
* r2 W+ N( _# T. _for ap=A; 5 ~8 L9 y3 v3 I% M& V. O
x=starx;
1 P& R, u! r: V& G: t; ? for k=1:50; . k! j5 {. x0 q. P
x=1-ap*x^2;
/ T9 `$ h6 p. C/ f! p9 P- @ end % S0 @- L: h6 Y' o9 n0 K [0 f. {
for k=1:201; 6 l Y! T% n1 x1 G
x=1-ap*x^2; * h# w: G- x2 D' E) P
Z=[Z,ap-x*i];
: V& m( a4 P, B0 q1 p end " h: X6 B4 A5 h7 u/ v+ X
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
+ y5 M' l# Q6 g1 v" X5 x. O m=m+1;& c; E# H a9 Y, V9 D3 W" J. P
end 1 @/ w9 W8 @9 v- S \2 p
delete(h);/ t$ F- x& U: z e) ` E! E
plot(Z,'.','markersize',2)
1 g; _' b1 x. t, nxlim(a);# |0 _* |; Y$ N
% Q6 s) k9 U7 h1 [4 H5 r, Y四 最短路算法------floyd算法
2 _ {8 e+ K0 P. |- Ifunction ShortPath_floyd(w,start,terminal) % z* t) O8 N, ^, q
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
' V) v& s' `8 b" U0 D, G# g) Y9 D1 r%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
' E/ E: \# n0 e3 N: @%start-----the start node;
& B/ R+ Z! |& e7 {# k: v- {( n%terminal--------the end node; 9 G" |" O, Z: j8 f0 b5 a5 o7 n7 k
n=size(w,1);5 h) B0 f( i7 N$ i4 l2 F+ ]4 ^
[D,path]=floyd1(w);%调用floyd算法程序8 \" X. j% A. x# f
# t, O K7 F X" L& p%找出任意两点之间的最短路径,并输出+ s0 r6 h. H) Y0 ^. L$ A: d3 z
for i=1:n9 h6 S% Z5 s. u' `; n0 z
for j=1:n
$ X9 E& _% `) O" B) `% G Min_path(i,j).distance=D(i,j);6 G; W% U& k/ G# M2 O; x) Z1 S
%将i到j的最短路程赋值 Min_path(i,j).distance
9 F+ ?) Z% s) s! W %将i到j所经路径赋给Min_path(i,j).path A# v l2 c5 |/ L# n8 |: ?5 {
Min_path(i,j).path(1)=i;/ g# @7 P3 N. W6 y1 y) a$ d
k=1;3 W, F: i/ }) x& S3 }
while Min_path(i,j).path(k)~=j
! z! H* q/ Z* r k=k+1;' I/ F8 W$ k/ p# c- X5 z8 [ i
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
5 i+ H/ }3 i% l4 |! E end9 b6 e" j* A6 L$ K
end
! c C, k6 Z$ X8 gend# m! a5 b4 o W2 e
s=sprintf('任意两点之间的最短路径如下:');2 y& i- s& n% O% X6 C
disp(s);
/ W: p b( p( qfor i=1:n
6 ^! D8 L' h- J3 h* Q3 f/ S( ? for j=1:n
8 k+ D6 w. b1 w4 T9 |7 l: p s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'..., D) {0 b8 e; t1 l2 \% [
,i,j,Min_path(i,j).distance);
! v' g, @8 ]; X" q8 `8 [' L. } disp(s);; q1 _# i6 Z. X
disp(Min_path(i,j).path);
1 t6 s. T. h3 {5 V& W8 R7 [ end a5 x+ Y% x" P5 g' m
end
; [9 E, t1 O- x% g0 o: O7 {' a
1 H( P. }/ d" j/ F/ f* N%找出在指定从start点到terminal点的最短路径,并输出" O& \& B5 v8 w. Y3 n
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
$ S% X' g6 |6 [* A- Q1 O start,terminal,Min_path(start,terminal).distance);; U' b9 i- \1 e# D. O
disp(str1);, T! W+ H+ p6 _ t5 M/ D
disp(Min_path(start,terminal).path);
# ~$ A5 N+ a6 C) D0 J/ \( W$ H' {' ?( ]' O
%Foldy's Algorithm 算法程序
$ r' j9 ~# ~6 m: }; H8 `0 pfunction [D,path]=floyd1(a)
2 O2 Z# n" [; P' T6 Y8 |- P" @n=size(a,1);
6 G# G0 ?6 Y8 q1 ID=a;path=zeros(n,n);%设置D和path的初值
% O2 q, C8 v, i# }# R9 m6 D' xfor i=1:n2 F2 V$ @) r, X4 |
for j=1:n
/ \8 _" K; A1 |% _2 M if D(i,j)~=inf- Z* s" z0 K& Q( S% R+ J
path(i,j)=j;%j是i的后点2 c! D6 ?4 T! L e7 N
end, k, o- j5 v8 [2 Y
end
0 H7 w' I; i. z/ gend
* Y# i* o3 w$ I3 j$ J' ]5 [%做n次迭代,每次迭代都更新D(i,j)和path(i,j)) Q, f j: O9 _3 F8 m; R I
for k=1:n# Z0 }2 V) b7 W( F- H" W. s9 @$ a
for i=1:n
% p, r4 j u7 t; u8 Y+ H for j=1:n
- F U; z' v$ x% d if D(i,k)+D(k,j)<D(i,j)% W: U, b" @, q) t7 J& B
D(i,j)=D(i,k)+D(k,j);%修改长度. `/ c% Y$ V+ t9 n
path(i,j)=path(i,k);%修改路径
: [' X$ @; f5 G6 q2 c* e) [ end
; _9 w' O" C& T! a* f! [8 ~' ? end
" ]2 b- S- d5 p- O$ v, r" V end o& S3 u, W9 r a' r
end
; q p7 _0 E+ \' t) c5 n) T, h: r# r3 A
五 模拟退火算法源程序% u) S/ ^$ Q! u# Y+ `
function [MinD,BestPath]=MainAneal(CityPosition,pn)9 t5 n! x* y5 w1 E" H3 v
function [MinD,BestPath]=MainAneal2(CityPosition,pn)5 h) l6 r) e( q0 p; t9 s" e1 Z! u
%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
; i }7 o/ i$ h( Y2 I# e' M' u/ b%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
2 h3 B# B# t% C" R* L9 n) S/ j% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...7 `4 p( J; O/ U9 |& J2 x w
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...6 O1 k9 U1 n% z8 E1 ^3 r! q
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
& ~9 P8 b$ b1 F% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];3 v% P% J# } Z7 ~5 D
, B5 Q2 t, U% O# b: r/ v
%T0=clock5 W- e0 z9 W7 t6 Y
global path p2 D;* y4 k: J+ {' ?9 {3 H3 F- n- @6 l. j
[m,n]=size(CityPosition);
; R2 y9 e7 G1 a1 K! Z8 R9 d g# [% {%生成初始解空间,这样可以比逐步分配空间运行快一些
* g1 s6 c0 f: rTracePath=zeros(1e3,m);
2 ?0 x% h! N/ T+ J! _$ _Distance=inf*zeros(1,1e3);
5 O) c' V$ C* B6 |) g' B* O9 @' C! M) [3 c; c! } s2 ?( P
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
! Z" `. R/ v* J* o5 _1 r (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
9 x! D% |; L: b%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)9 s6 v! G0 s# I6 E& s3 |/ A
for i=1:pn
7 d. c2 J7 P) P" S7 d path(i,:)=randperm(m);%构造一个初始可行解
& y) _4 @, i, p9 w* send
, i$ r- G4 i; m; Y6 et=zeros(1,pn);
: Q+ l6 G3 V6 \) r% B5 o! r' [& H) qp2=zeros(1,m);
5 w% T, h+ I# b0 w7 q( ?. ^8 ~ p4 t# i
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
7 }, s+ Q8 O" T) z h0 Zm_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=' ) ;
: i+ b" z0 C# s$ W! W; y# {% H%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
( W# X! i1 t6 D6 @- O+ F%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3 O$ l, y v& r! U5 J7 D
%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- q3 J9 b, ?! H( E6 ]
%会收到到比较好的效果" i: u' d, f+ O7 a! T
% N% b# Y! @7 R1 ?* m0 P( HT=1e5;8 V8 U% V, ?4 L/ q1 {
N=1;
% J/ [" m/ Y7 b3 R) ftau=1e-5;%input('请输入最低温度tau=' );+ y( z" e+ L! ]8 {6 k9 W+ x
%nn=ceil(log10(tau/T)/log10(0.9));
Z5 V; ?: i2 Y0 v. r6 v ?while T>=tau%&m_num<m_max
% ~$ U# g- k p' J iter_num=1;%某固定温度下迭代计数器
. p# p; j& s- d: S4 @5 ~4 z4 f/ s- K m_num=1;%某固定温度下目标函数值连续未改进次数计算器: s5 Q, @; N) U, L6 L% T
%iter_max=100;8 s8 L6 {( n. H& i% U+ A9 h7 r
%m_max=10;%ceil(10+0.5*nn-0.3*N);
/ H. x: j: z4 r# ~& A0 N& ?3 C while m_num<m_max&iter_num<iter_max& K$ g' i& @2 E$ @# n/ Y, R- E$ G
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
6 j6 Y" I; U) D; A %用任意启发式算法在path的领域N(path)中找出新的更优解& y0 w6 G* H/ e
for i=1:pn$ `: G2 R- Y2 ]5 R9 |3 C) g3 d8 x
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
/ P ~8 L1 ]) w5 {2 v4 I) _6 h1 E; X%计算一次行遍所有城市的总路程 2 P( l. W8 c9 H& ]
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线, k* U4 H* ^4 @" f) @1 d% Q/ w A
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);: R% H- `9 K. s8 v5 N% A
end, `5 M; J$ g$ Y$ k* c. {8 A# d! \# k
%Len1( X2 d( P h+ z( m4 A# M+ `, {
%Len2: } [% \; s3 h* d) t
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
7 |8 k" m) \! N& d2 u* l R=rand(1,pn);
0 M/ b+ W1 {& v1 w7 I) q! O %Len2-Len1<t|exp((Len1-Len2)/(T))>R
2 O$ U( p( H/ _' v if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
* E! s; b1 Z/ G/ W/ }. ^ path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : ); J& z: R" G! W; ?- t6 ~
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
3 l* U6 D5 l9 I# N [TempMinD,TempIndex]=min(Len1);
. Y, e0 O$ B8 l6 y3 D %TempMinD" q$ t: O) H! v3 [2 X! M) Z# Z
TracePath(N,: )=path(TempIndex,: );
* j7 S- e* I& }. H8 w, h Distance(N,: )=TempMinD;! m8 n5 T4 Y- j" u# G: \( C
N=N+1;
$ ]# ], s# t6 U! J %T=T*0.9/ P Q" R7 T- G6 q" \
m_num=0;
+ Z9 ^7 E* f3 }2 L else
/ y# ^# {! K7 Z m_num=m_num+1;
. @6 P. _7 p" T$ L end
/ x! B0 A- J1 H* V6 Z b iter_num=iter_num+1;/ L% p3 I {" v- l
end
- H" Z* b; E# \ X8 e; n+ h: G T=T*0.9
& V! O% ~. V* D%m_num,iter_num,N3 w6 W v4 I% e. |/ @4 c1 g
end
$ S: p7 u$ g* Y9 x1 u[MinD,Index]=min(Distance);
$ T5 L) A' m j* IBestPath=TracePath(Index,: );1 X# z g: N0 O1 X/ o+ t; v
disp(MinD)7 c1 P% G- r1 V8 V+ T" g0 Y
%T1=clock
. {# p; @3 A- Q! e% i
% A* l$ s1 O+ y3 [9 Z
) I' U" C% x5 M/ [$ X" n u/ S%更新路线子程序
2 G8 {' X. t7 g( C& Q4 s" C! s2 zfunction [p2]=ChangePath2(p1,CityNum)
4 P% K% s- E1 Dglobal p2;
# i, j6 @( N* k( |while(1)
" ?* J1 O5 F( C# ~& k5 g* X R=unidrnd(CityNum,1,2);1 s$ n3 i7 ?5 \- R
if abs(R(1)-R(2))>1( Y7 f' Z$ Y0 g6 Y9 P% ^
break;0 u) [, H3 n# ~. b
end* V F! \) d% j& E
end; {) ?0 g9 O6 N/ @2 h# b* h
R=unidrnd(CityNum,1,2);3 |4 X( A6 N8 p8 {2 i! l! v
I=R(1);J=R(2);7 `1 c0 b" v! O
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
) J) X4 D: G2 E2 f4 K%len2=D(p(I),p(I+1))+D(p(J),p(J+1)); b7 w# e3 J; g1 d% d% ~% E5 n
if I<J/ I2 w; N, }, I, }6 l6 H
p2(1:I)=p1(1:I);
2 e- F: _, M) k p2(I+1:J)=p1(J:-1:I+1);
3 I. a4 a G5 ?& X, _! Z) o- u p2(J+1:CityNum)=p1(J+1:CityNum);$ k" V% m8 D, a8 I: n
else
7 z, v4 k7 P5 p N0 b p2(1:J)=p1(1:J);
7 p. b. S$ F' B& c' I' s8 ?6 w) | p2(J+1:I)=p1(I:-1:J+1);
7 L7 l }7 b. v' Y p2(I+1:CityNum)=p1(I+1:CityNum);
( l6 Z( q" ], y3 ^end
( N) b: C8 W1 u5 A1 n* |6 h7 r# I
六 遗传 算 法程序:5 h3 t: Y1 }5 |' a/ V1 M
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!+ y6 T0 a& u- K- S9 X
, y2 C/ W& J* }) M$ ~function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options): E- s) E# U; n- O/ t C7 N
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) $ }, t) t; W3 }. X" }5 V9 x
% Finds a maximum of a function of several variables. V3 P, Q6 a) O5 L3 H9 W4 X
% fmaxga solves problems of the form:
4 s( A+ q/ [8 Z* U% max F(X) subject to: LB <= X <= UB
6 E. P9 f# q1 q( l- J" s% BestPop - 最优的群体即为最优的染色体群, G' R# E$ y8 A0 }- }& t6 J+ r
% Trace - 最佳染色体所对应的目标函数值
8 a6 ~% x* l3 z4 F+ _+ f8 C6 C% FUN - 目标函数2 A! O. f) ?9 e3 t" B9 k
% LB - 自变量下限
4 l6 H( k: E0 k+ P- g6 w% UB - 自变量上限
2 S/ I( c" _. `2 a9 [* s4 W+ B4 U+ F; F% eranum - 种群的代数,取100--1000(默认200)
' K l h0 m+ x7 y% T% popsize - 每一代种群的规模;此可取50--200(默认100), c9 y3 y% \5 @5 A) b
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
, ~7 L4 _0 S' U, d0 T, j% O ?, y6 ~% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)! _0 x6 j/ S4 z
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
1 F4 l% r) I$ a9 s% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编" r9 C1 r1 V5 T7 I
%码,option(2)设定求解精度(默认1e-4). e3 C3 S% k7 _. t, Y6 N& C+ `
%
2 }7 t( ~) |2 i8 @% ------------------------------------------------------------------------8 w, p% n4 G% I7 Z
T. h7 f) Y: s+ t5 e! BT1=clock;* L; J1 c* z: s
if nargin<3, error('FMAXGA requires at least three input arguments'); end6 J+ W$ W4 a2 x" W
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
. E. b8 p- O8 H: P6 I6 r7 g1 Dif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end3 w e0 }% l6 o5 E' s4 n
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end# w/ `$ j/ u: h
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end2 F8 ?( f0 J0 @+ F' J) d; {
if nargin==7, pInversion=0.15;options=[0 1e-4];end
! r6 v T8 P* d; P6 A4 a8 Dif find((LB-UB)>0)' u i) y% x. w0 g5 M
error('数据输入错误,请重新输入(LB<UB):');
6 m/ A0 `8 e+ q+ U/ H) V! q. [end$ U: J% v: e$ q" u0 m3 B+ g
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
' f; D5 h; ]( y4 R2 y7 O! e4 sdisp(s);+ p; k8 Q# K8 V" K2 K4 E
% e/ P8 P& B, ]# G0 ~( J; Cglobal m n NewPop children1 children2 VarNum: r4 G* i* X) C) o
- q$ u! y% ?1 V! n6 nbounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
. J1 l$ M, F# {# H! H" fprecision=options(2);%由求解精度确定二进制编码长度
) b/ u+ o4 f. Y4 ?bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
8 S& l. B0 s$ X: U[Pop]=InitPopGray(popsize,bits);%初始化种群/ Q. X% y% [) v- N$ ~& P% j* m2 M
[m,n]=size(Pop);
" M8 C1 c9 K1 zNewPop=zeros(m,n);
! ?# R6 W) t& S' vchildren1=zeros(1,n);
- J' u+ b5 Y4 q9 pchildren2=zeros(1,n);
+ Y" } Y' l) }pm0=pMutation;, Y! O* [. S& @: T g- H; I
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
; u" {# }/ z2 n) Y9 GTrace=zeros(eranum,length(bits)+1);
8 K; k5 X8 k( e3 n' \5 r1 fi=1;
. T, x/ ]% g7 d& nwhile i<=eranum; z9 Y* k. v) [0 v2 D
for j=1:m9 U% \2 c# M5 a0 _
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度% A9 p* H- Y* A. s( L
end
: z& ~: }; m% j9 D [MaxValue,Index]=max(value);
9 K2 `0 V# x2 s2 e [/ d/ e, W4 N6 Z BestPop(i,:)=Pop(Index,:);# Q% s, A( Y0 k
Trace(i,1)=MaxValue;
% F& D. N6 ^, Y M8 B Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
# |; u+ r7 ~, ~* L [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择" S/ L1 }( |1 ?' G8 E1 p
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));, |: ]; K8 M0 \) D) G7 z
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
0 x, w6 L+ ]% S) p1 N) N %round(unidrnd(eranum-i)/eranum)
4 s( J0 ^" ]0 `8 h0 D, s7 e [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
2 h; ~- G2 Y* Y5 P [InversionPop]=Inversion(MutationPop,pInversion);%倒位
/ ?8 e, n. A9 C y8 a Pop=InversionPop;%更新
( ?5 w; H" l6 V; b9 wpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
3 P9 F: n5 }$ { p5 P%随着种群向前进化,逐步增大变异率至1/2交叉率4 I" C# R5 Q0 }$ Q, b
p(i)=pMutation;! s6 `* z! v% i( V/ {
i=i+1;& s" B# _! v* a7 U0 H8 a
end5 \! h# u( f( A& }% T
t=1:eranum;0 V% E* [2 y Q& Q9 u
plot(t,Trace(:,1)');
7 `: |) W; b) ctitle('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)');! l9 T0 @' a! }5 a" F
[MaxFval,I]=max(Trace(:,1));
7 Q0 S+ b4 n1 T5 E. ^; UX=Trace(I,(2:length(bits)+1));
* X+ z4 _0 {5 hhold on; plot(I,MaxFval,'*');. S& z8 I. N) m/ Z! M
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
% H# B G" A* B8 z& b6 Wstr1=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,:)));9 |" f6 p9 b% z9 V( K
disp(str1);! l0 o0 w, T7 f! j
%figure(2);plot(t,p);%绘制变异值增大过程
" S# J/ H7 g/ K0 a3 P7 L' F' o% OT2=clock;
( L, X- {7 E' L5 pelapsed_time=T2-T1;
( ]* t2 G0 Y* I9 ]( r- H" @0 A. V4 g' N4 \if elapsed_time(6)<0
: x/ D9 u0 h: w1 I1 A; m elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
. w7 f9 Q( i- A3 r4 i2 _" kend3 I* q' a0 u$ F6 V7 U5 A5 E
if elapsed_time(5)<0* |* l4 ?; R- |' S
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
, I; D5 w7 f1 ?4 i! nend %像这种程序当然不考虑运行上小时啦
4 R! u! O1 f0 I1 n. c! Ystr2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));1 S! m1 ~. |: `& H
disp(str2);) N/ T9 q$ `, X; c' c e5 n: }5 M8 P `
. A+ R, y4 Q" }0 o8 Z( i7 F# o% [( m8 X% M
%初始化种群
% h& S t$ b( H$ j. [3 Q1 O/ Y* b%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
! n! d* N a, m! Efunction [initpop]=InitPopGray(popsize,bits)
3 F u N# u: V0 glen=sum(bits);4 H* X7 v Y# u- E1 d) P' Q
initpop=zeros(popsize,len);%The whole zero encoding individual
. I( P7 E3 |5 ~: Z8 f C2 cfor i=2:popsize-18 h6 [1 C$ D- M- z7 Y5 b$ b! V7 l
pop=round(rand(1,len));
$ D! N$ |* g' T9 G pop=mod(([0 pop]+[pop 0]),2);8 B$ t9 P; Y$ |% n, C& [- p
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
" S' h1 ^4 @ \4 @/ T Q9 s( b0 t" V %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
" j" o4 E6 ]% i initpop(i,:)=pop(1:end-1);
- Q9 o% \; }, S0 kend
% y4 n2 u) B* A9 U; Zinitpop(popsize,:)=ones(1,len);%The whole one encoding individual
) w7 J! I5 ?1 ^/ | j) e: ]; b%解码! t' A" k5 ]& }! X
4 `! q1 q0 I8 ?4 R
function [fval] = b2f(bval,bounds,bits)
e" z$ I! n4 J6 b& y% fval - 表征各变量的十进制数
2 f* c, A% q1 p9 C7 g& G0 K" y% bval - 表征各变量的二进制编码串( q+ }) d+ O5 ]. C% Q" W; ?% m
% bounds - 各变量的取值范围7 d L5 `7 m2 X0 y' a
% bits - 各变量的二进制编码长度" {1 ~8 q& ~7 Y" ]# k; a0 k
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
5 U3 j) d; |! Z9 g/ u4 i2 fnumV=size(bounds,1);
& q2 a$ k0 d N$ R/ f, scs=[0 cumsum(bits)]; 8 |7 B) _ J3 h/ d z
for i=1:numV$ P5 u2 U7 `& k: r* p" K& s
a=bval((cs(i)+1):cs(i+1));7 s& t4 t X8 Y3 R: Q4 `
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1); p% W3 j! ]9 e3 D$ c8 P/ t
end
: F( r0 @: S3 y2 q%选择操作
{' n7 y" b. c4 q%采用基于轮盘赌法的非线性排名选择9 {: a9 h5 E/ @' a3 e2 |2 o7 P
%各个体成员按适应值从大到小分配选择概率:
" I( O+ I# c+ Q# K- N( i' {%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=12 h; S5 B, a6 h, d
/ P0 ^( ^/ R4 e h" j" e+ dfunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)$ P+ H3 [5 B5 q/ W9 f3 f# d Y) }
global m n/ l7 q$ D( e f o1 O0 X
selectpop=zeros(m,n);
0 V3 m r6 A, ]9 M1 K* Vfit=zeros(m,1);
6 q$ {3 a3 A# \" ]* |for i=1:m
* y2 M3 P9 b: N$ s fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据5 Q8 W9 F8 d2 {$ k( l
end+ O" }5 f. G, I9 z) H4 l3 W" |0 d
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)- q |2 ^# z* x, ]
q=max(selectprob);%选择最优的概率
- o0 K0 H& o' w/ s( h, vx=zeros(m,2);3 L8 D' E# T- _5 r' [3 e9 c
x(:,1)=[m:-1:1]';3 ^1 R, S7 ~7 [# @0 r" K; s
[y x(:,2)]=sort(selectprob);
& |* O' u. M% O1 @$ i) ?4 x, ar=q/(1-(1-q)^m);%标准分布基值
7 `/ f D% u; F6 ^) R& v6 t Vnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
6 {# y) ?/ _! e% fnewfit=cumsum(newfit);%计算各选择概率之和% e! [9 l9 ]9 G& V( @
rNums=sort(rand(m,1));6 j0 Z! r+ F( G- v% D
fitIn=1;newIn=1;
1 C( P8 C5 _& F# v. @* _4 mwhile newIn<=m
. X# a7 B2 W5 c: A8 l9 \8 i if rNums(newIn)<newfit(fitIn)
$ ?3 o8 Q0 H9 t4 q8 n% f selectpop(newIn,:)=pop(fitIn,:);6 u H# p! ?9 q! }! N. Q3 L' v
newIn=newIn+1;$ g' l5 Z8 C4 X0 A! Q. |8 D
else3 U0 t. n6 e- j k. h% t1 T$ w
fitIn=fitIn+1;4 P/ W0 i# l7 V! m& l5 Z6 p
end) _1 K% U0 ]0 K; u4 y* ^ G
end
7 q5 Y9 ^/ `1 T/ x%交叉操作
# W- l9 e0 Y* A- L9 K2 k* a* Mfunction [NewPop]=CrossOver(OldPop,pCross,opts)
: g. g! d8 z4 @%OldPop为父代种群,pcross为交叉概率
5 [# w8 h" o0 w6 V( \, _global m n NewPop
. b) G |( Q1 q5 X. c6 or=rand(1,m);
4 F3 _0 C7 k1 ?$ Y9 ^: fy1=find(r<pCross);! c5 m4 `( |# X" g( k4 Q
y2=find(r>=pCross);- B( ]( t' R" k# N# Z" x
len=length(y1);3 ?4 g: S2 G- J8 n1 r
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' [6 j: i0 S, X6 @) ^) g
y2(length(y2)+1)=y1(len);: _% j% l0 U+ t( y3 D. g6 [
y1(len)=[];1 q; p$ s6 X9 K" j
end
. o9 w P6 j+ I; P8 Lif length(y1)>=2
# \2 O+ m, F) Q5 h for i=0:2:length(y1)-27 L4 X- r# o1 p2 B9 L
if opts==0. H0 \, ?$ [* L5 _( r9 n$ Z( f& X
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
8 D" E7 R( V+ W5 a1 c else7 o6 d. k3 m* W4 I
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));% G9 O) E% K7 v+ |5 u
end5 J2 F7 n, J* }
end
' m5 a# P( `$ yend
v" u0 d+ @: M# E+ Y1 vNewPop(y2,:)=OldPop(y2,:);9 ]- Y, } C/ `$ s$ i! T
) q1 t, I% J1 ~( U" Y5 f/ O
%采用均匀交叉
3 ~" ]8 q+ T! l7 q! y- wfunction [children1,children2]=EqualCrossOver(parent1,parent2)9 V( T; C( V* i* U* P
( G8 m x! m& c( T2 a6 A5 \
global n children1 children2 5 U" s6 y) P2 m& Z* O" w
hidecode=round(rand(1,n));%随机生成掩码 u9 u+ R" ]( V4 l" Z
crossposition=find(hidecode==1);
+ {4 x& j* n$ d# Dholdposition=find(hidecode==0);
! Z" ]/ } H7 ^" F2 W; Pchildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
6 W$ U: T. W9 i2 x9 r q4 Kchildren1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因5 P" y; S3 g/ a- J( j. R- G& H, P
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因, r5 K P0 `6 ^3 Y7 P" [2 L" h
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
& L- E9 A6 w( G; V$ L& V+ y5 h% _1 M8 l4 n
%采用多点交叉,交叉点数由变量数决定4 Q% ]+ n- f6 y* k& h: `. U
) \$ u& R& z+ f* H+ N4 L1 g, jfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2). R j+ J+ ^- ]
. s: z3 O$ S$ D
global n Children1 Children2 VarNum$ W* X2 E6 r* n+ T# B
Children1=Parent1;
# e5 N& H3 C7 h/ z& CChildren2=Parent2;+ H. w( ~# F7 Y8 P5 K& ^
Points=sort(unidrnd(n,1,2*VarNum));5 S! `6 }; Q2 i c+ w" _
for i=1:VarNum2 Q( x7 t, w$ ]; A. ~( E
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
/ [5 D3 n% r: B Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
' t4 o [& S Jend/ L% i; v) e8 B' w, P4 o2 Y
$ A2 N" d f& _2 V5 O" t0 C%变异操作
5 v; e% z( q: _; e4 Nfunction [NewPop]=Mutation(OldPop,pMutation,VarNum)
9 y+ T+ ?7 T; Y) E8 l- |
% K, [" i* U* |+ u8 l8 z: tglobal m n NewPop' e! p ^7 W# m& A* E
r=rand(1,m);
1 r8 q, D P- b J0 H; N, i9 c9 I" Y3 Uposition=find(r<=pMutation);9 f6 R" a# g, i; V, S4 y, E
len=length(position);
- D" n9 z5 e6 Y+ c9 J! rif len>=1
- M# Q U; G: h7 \* n+ N0 W/ v for i=1:len; d4 f/ t/ E; \( Z, `
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
c( @3 ^/ { _ T; E8 c for j=1:length(k)
4 E' M$ O( J4 W9 B if OldPop(position(i),k(j))==1
0 U# g# u' n0 r# Y1 C4 Z4 g OldPop(position(i),k(j))=0;
?* w, m4 r4 N: \; O9 ?- T else
+ }; P; J+ @* c, l3 v+ P/ o OldPop(position(i),k(j))=1;6 w. \# i+ O+ a) N. w
end
7 t4 }, s% O7 N# `6 }1 {* e end }8 C% V, s2 f- N; ^! W8 |" W m
end
6 o" h3 ~; R& E8 M0 D% u& f: G8 xend
+ H& d' b5 w: ~3 x0 j0 TNewPop=OldPop;
$ I' G# M. n- A( l a
5 A6 v8 L* R; a4 Q%倒位操作! H3 s: t- K s: T1 Z/ \) [
* `3 s& b0 I" dfunction [NewPop]=Inversion(OldPop,pInversion)
8 H7 m$ a' | t E: x2 D* J0 f* i4 X' \
global m n NewPop* |: @! W4 x2 P1 g4 \
NewPop=OldPop;
* X- H# b5 n8 V+ K/ jr=rand(1,m);
) @1 i% O3 d j7 j" a# S+ `PopIn=find(r<=pInversion);
, y& C' `! T' }0 R& blen=length(PopIn);
- s u9 D k1 G* pif len>=1" j: K& d. _ k9 x4 V0 }7 [. B- T6 O
for i=1:len
: Q0 y/ v* r: q d=sort(unidrnd(n,1,2));
% p) ~* n. u# p8 b! l6 | if d(1)~=1&d(2)~=n* l# |# X0 _: r/ z3 W$ q
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);, a5 g, C0 U# ^% t
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
2 C5 J- r& z5 o- a: ^# N NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);$ z6 d5 e5 J) f. e0 [
end# M2 n6 ]: T6 ?. t
end
; A% K, \ @5 V; x: ]0 eend
& o, K* x2 P5 T& T$ |6 W" q k' E4 ]8 g( E# y- e+ @
七 径向基神经网络训练程序
7 t: K" J) x' U; ?, B1 p
( x* a- v. }( \' yclear all;" [5 x1 J" Q F7 m# ]
clc;
$ D* q/ ]7 b% R9 M8 L; Y6 S%newrb 建立一个径向基函数神经网络
# n. T m- A7 `3 `+ ep=0:0.1:1; %输入矢量
! l7 c- X, x% \; s) Z( st=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量: v" g0 h7 P" U+ o {. f
goal=0.01; %误差
% b: F8 ?- T) ^8 T2 u% f5 Lsp=1; %扩展常数1 F. H1 D+ i0 U3 q0 }% m6 t
mn=100;%神经元的最多个数 b7 `" j$ ~$ F }9 X9 M2 _ A- ]6 |
df=1; %训练过程的显示频率
! e/ j- X* q4 g0 I, u( o/ ]. d[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
0 t4 y, K& `( j' t/ K% [net,tr]=train(net,p); %调用traingdm算法训练网络
% q6 U9 w+ }, X' \& W%对网络进行仿真,并绘制样本数据和网络输出图形
2 ~# J) r: q# KA=sim(net,p);- F& \# o! k" S/ J; x
E=t-A;2 ]+ J! v- M" D; H8 o& W1 _
sse=sse(E);* c* m& \, J4 F( V% c9 l# V/ }
figure; ( V1 g8 a" G( D# r% H. y* o
plot(p,t,'r-+',p,A,'b-*');- L y$ W H8 U6 k5 M' x
legend('输入数据曲线','训练输出曲线');& s7 Z/ c2 b5 W5 w! i3 |
echo off
6 ~/ o. `6 V- `5 Q
0 K' j h7 ]: w; K; b) w说明:newrb函数本来 在创建新的网络的时候就进行了训练!1 B5 s' V) H1 E7 t( E* R7 T
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,: b& W7 \: n, _* a( z+ R4 [
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!4 n7 V% }- M' n3 ^) N
: ~% ]% g. v& g3 Y# X
" {3 v$ }+ R$ @4 Y4 X训练结果显示:) s4 e1 Q( g" N5 Q9 u0 w0 l! P
NEWRB, neurons = 0, SSE = 5.09734 ^! q( s* Z, H1 R+ U
NEWRB, neurons = 2, SSE = 4.87139
' C6 h& B+ p* a P1 eNEWRB, neurons = 3, SSE = 3.61176/ O" v, R4 `$ s6 d1 l" d
NEWRB, neurons = 4, SSE = 3.4875
) ?8 s( ]# f8 Z7 a- @$ Z: SNEWRB, neurons = 5, SSE = 0.534217" g6 z1 D2 O3 z+ X$ ?7 w4 ~7 w
NEWRB, neurons = 6, SSE = 0.51785
: n* O. G0 n% wNEWRB, neurons = 7, SSE = 0.434259
6 X# Y3 c9 b5 T# {$ KNEWRB, neurons = 8, SSE = 0.341518
9 {, u% _7 ?0 H3 h( s! Z( `NEWRB, neurons = 9, SSE = 0.341519
! w2 L' n, l( {( a1 R! INEWRB, neurons = 10, SSE = 0.00257832
V2 [/ I+ V5 T" T" ]* k( y$ F) N6 I, o8 t- `
八 删除当前路径下所有的带后缀.asv的文件; V, k& F6 [' d0 G: h
说明:该程序具有很好的移植性,用户可以根据自己地/ |, g k) u- o3 o6 Y& F
要求修改程序,删除不同后缀类型的文件! 7 h7 J4 x4 g. ]: O7 Q5 |0 b
function delete_asv(bpath)
X2 E( y. g+ `%If bpath is not specified,it lists all the asv files in the current! w7 j: v9 Z& V6 x9 L) ~
%directory and will delete all the file with asv
( L, b4 _) o& L, D; L/ _: L% Example:
5 X3 ]% m' x/ G# U/ p0 I r! |4 `4 M6 k% delete_asv('*.asv') will delete the file with name *.asv;! T0 j' k3 }! R( @7 u
% delete_asv will delete all the file with .asv.
9 s# x/ Q5 |8 T( t7 I
; M7 x! s- L0 O7 N* ^if nargin < 1
5 e- K" o5 u- |& y* x4 @7 c%list all the asv file in the current directory
. h/ \2 ^( h% w# T' P files=dir('*.asv');' M. P/ A* }! S& D( p
else. N8 |1 `/ I9 m: A$ _) g4 U
% find the exact file in the path of bpath; M0 t5 J7 ?, _: S
[pathstr,name] = fileparts(bpath);! k. u* o8 m: B5 }3 b( _/ n
if exist(bpath,'dir')
4 h; D: I) q8 ^2 e( K5 c8 U- W name = [name '\*'];
3 p% U% ?: W8 `( F- } end
7 L; n" l. l+ M% ^ o% w6 x ext = '.asv';
# x5 f5 V, e; W$ q$ Z* p' O, S" p: c files=dir(fullfile(pathstr,[name ext]));* e& B9 A; m# X& |$ T- n4 x- G: d
end
; g0 Z" x c1 u5 S; s- O3 A1 Z, v, [- L- K, U2 B
if ~isempty(files)
9 ]9 C# c; F' @5 ? for i=1:size(files,1)- |9 o! s3 e* P- @
title=files(i).name;5 C; ^( k; B3 S4 K9 }3 {
delete(title);' s- g5 o& {: I4 `; M
end# {( m8 ^) X/ g
end {1 C% N, H1 F2 l
$ a; \" H7 }, s! v& H
' u) l0 f l' F1 v) ]8 Y同样也可以在Matlab的窗口设置中取消保存.asv文件!$ O9 U+ v% @5 x
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