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TA的每日心情 开心 2016-11-7 00:15
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[LV.3]偶尔看看II
一 基于均值生成函数时间序列预测算法程序# l6 ]8 n% t$ y* G
1. predict_fun.m为主程序;
. _0 E) h! l6 E( J$ L 2. timeseries.m和 serie**pan.m为调用的子程序
! r0 ?' T* N6 U. J7 b9 U* \) u
8 [7 _# H1 _0 h* c; P+ _# } function ima_pre=predict_fun(b,step)
$ N9 e) ?7 o0 C0 ~9 j; z % main program invokes timeseries.m and serie**pan.m4 Q6 I6 r6 P& q, T6 }; E
% input parameters:6 q$ K [7 \ V8 x& s
% b-------the training data (vector);) Z4 Q' z! x+ o
% step----number of prediction data;/ x/ a+ Z5 [2 {7 k2 ]+ L u
% output parameters:
+ T, ^! `3 R, v! z0 [+ K$ P: a6 G% c % ima_pre---the prediction data(vector);3 v9 }1 N% ^8 `
old_b=b;* f9 z8 _/ t2 j5 Y1 G
mean_b=sum(old_b)/length(old_b);
- P, o9 Q/ [8 l; l' A std_b=std(old_b);
9 d2 P: C" |' [/ x# _. f old_b=(old_b-mean_b)/std_b;
3 ?1 ~1 }5 s3 b( q* p [f,x]=timeseries(old_b);
; }; F# v s( a @! a+ Y old_f2=serie**pan(old_b,step);
, ^$ K) I! Q: O6 l( i: E6 { % f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;7 |+ c! N: H" k; U+ B
R=corrcoef(f);
0 n2 x+ P5 M1 ~3 I7 y) }2 q [eigvector eigroot]=eig(R);6 ~) o* I* C) X( u9 G" v) _- P. L
eigroot=diag(eigroot);; {/ t5 [4 `6 ~8 z. h3 T9 {
a=eigroot(end:-1:1);
0 i8 I' W+ \ @! L2 Z6 v vector=eigvector(:,end:-1:1);0 Y8 H+ q- `( z3 E
Devote=a./sum(a);
" b; z; \6 S5 _% t- p' \ Devotem=cumsum(Devote);
% O1 d' \5 v0 Y- |( ?5 {: a m=find(Devotem>=0.995);
$ ~0 N1 e1 @+ Y7 | m=m(1);
" h" C, z4 Q( c# O" m2 S V1=f*eigvector';9 ]1 X0 Q; Q0 F& N J( S' b4 `
V=V1(:,1:m);
! Q! E; N) v3 a3 w# c6 ] % old_b=old_b;0 j& j! A) A9 b6 n# R: i L- |
old_fai=inv(V'*V)*V'*old_b;
- U2 V! X- h, P/ Y+ o eigvector=eigvector(1:m,1:m);
6 h" b& R: y+ z fai=eigvector*old_fai;% {+ `. N- n* t
f2=old_f2(:,1:m);+ D' j' R& T0 c
predictvalue=f2*fai;
H: ~; u/ `" D' e; k ima_pre=std_b*predictvalue+mean_b;
' n! w. Q- `6 _" I; U% V( q0 f! `1 Z 1 Y( G2 f# N3 _) D" @
1.子函数: timeseries.m 8 X9 S+ r4 s4 l7 W" d# Q
% timeseries program%
e& Q$ ?! Q; m % this program is used to generate mean value matrix f;
# v' a# |2 E4 l" o& _# o function [f,x]=timeseries(data)
( I% [) v1 }3 c0 C% H % data--------the input sequence (vector);
1 K5 K, C4 H7 P! f % f------mean value matrix f;" w" Q0 n8 y. V+ ]4 n
n=length(data);, T3 k8 b6 {! H' Z, P" H9 A
for L=1:n/2
* p4 X0 _6 U, l1 a2 K( F9 A nL=floor(n/L);, Z7 m/ r: @7 O& Y, i& V7 D
for i=1:L
2 y8 M1 h5 H8 S# m1 b% G sum=0;1 |! h8 T, _4 ?1 z) V% c/ J' ~. e" F
for j=1:nL3 s: c2 C' |( m3 |
sum=sum+data(i+(j-1)*L);
5 b9 y1 ]! }6 i: U$ I% V end
# b( H: \0 x8 @8 j x{L,i}=sum/nL;
3 ]& a1 C3 _. Z" y5 p end" f- K$ [6 r# G u; u
end+ \0 J" Q! v* C. a L0 N( S( U
L=n/2;
3 A* y" ?, p$ J; o f=zeros(n,L);
* I7 ^! z! e8 X5 C: f+ o for i=1:L0 g0 ]/ A" O, p2 j
rep=floor(n/i);
% K5 C* {! p. k! l& M% T res=mod(n,i);- ], j1 E. s8 d9 _% }( \
b=[x{i,1:i}];b=b';! K! y$ a& h6 w/ {0 l1 [. L
f(1:rep*i,i)=repmat(b,rep,1);! n$ {- H0 {% A
if res~=0
% w; n9 h) M; n% W) Z! i( b# I% g c=rep*i+1:n;
& L$ |6 s& ?: n: W% M: W' C/ b$ g f(rep*i+1:end,i)=b(1:length(c));
P, k) h- e: I v end
8 l i" t( K% ]; ^. w end/ a, r' p! v& N
0 s# C: v$ o6 {! W, H2 Q' J
% serie**pan.m( n% i8 j) T7 ~1 u1 P
% the program is used to generate the prediction matrix f;
+ F% a' j7 N! Q2 e" R; p6 { function f=serie**pan(data,step);& @" f1 m! k: g3 g3 B) N
%data---- the input sequence (vector); a3 d, r. T/ ?6 |6 U3 N
% setp---- the prediction number;
`; N, g7 p- `* i3 M/ }& j) { n=length(data);
! i+ O! t$ i5 O l$ x for L=1:n/2( r/ a4 l# k2 B; R, ^" h/ ]* E
nL=floor(n/L);
* Z3 Y! s- O0 o) A1 g for i=1:L
' o- P0 ~( H0 O sum=0;& b) R2 t/ T& Q) u; e
for j=1:nL& N) C# R) M( Y' O
sum=sum+data(i+(j-1)*L);
3 N6 q5 {/ c: q/ z end& K% t4 \7 D" y; r: R
x{L,i}=sum/nL;
* d' Z: h4 ^% L5 Z( c end3 E; ]7 g5 `' G0 K7 t% u
end; x# {# p: @9 ~' l( `, w
L=n/2;
1 n" [, w' _8 t) J/ B f=zeros(n+step,L);3 C0 ]# ^+ L* L% z/ T
for i=1:L$ A) J4 N! U/ H# a6 J
rep=floor((n+step)/i);9 T: {3 `$ Q* p2 ?$ z
res=mod(n+step,i);
! N. I7 w+ Y1 Q- ~6 S3 v" y b=[x{i,1:i}];b=b';. F& C) l/ [0 f
f(1:rep*i,i)=repmat(b,rep,1);4 O) z! u! w3 j. ^/ D7 o3 f
if res~=0
0 A0 S* {: @) n8 ~: E+ x- x c=rep*i+1:n+step;
: m* u2 ? @' [* N, T: N f(rep*i+1:end,i)=b(1:length(c));% A M) }) T0 k, L; D, [& V1 w
end
' r2 W) J5 B! g$ C( T V end
9 b( c$ Z0 X V ; ~2 C! S m1 ~ o9 r
二 最短路Dijkstra算法) q( s1 i& x& y O; T v
% dijkstra algorithm code program%
7 I/ K) U6 Q8 q % the shortest path length algorithm
4 e& F2 Y2 B( D3 z# Q( J2 p function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)3 f/ M$ ^% W6 \6 u! z) F' H
% Input parameters:; j. ] n- r! i( S
% Input_weight-------the input node weight!
9 I- T' s1 u( w( y2 d, K % start--------the start node number;/ m9 R( F2 s5 _6 v
% endpoint------the end node number;+ h5 Z! ~9 E: j* d# [! Z8 t
% Output parameters:
7 `4 Y! P C, D0 Z% t8 w: m % path-----the shortest lenght path from the start node to end node;
. v# t, X6 W* B( c % short_distance------the distance of the shortest lenght path from the
8 M3 w4 _6 F8 L4 w/ A d7 J) U % start node to end node.
* C2 V# q( a1 Y& t+ k. N2 f [row,col]=size(Input_weight);
8 I" O/ M/ o! j- k1 Z6 k d
& S! S( C2 P+ O+ k %input detection( |- c6 ~8 u4 N3 y. ?2 U
if row~=col/ X! v5 S r- G! y9 y4 j+ A
error('input matrix is not a square matrix,input error ' );" O& J4 D8 H$ o* |7 }/ ~
end6 |+ ~( ~; Q/ t2 s& i
if endpoint>row* }4 J2 e. i3 G4 e8 ~. W/ B
error('input parameter endpoint exceed the maximal point number');3 [( v7 C6 r. n3 O K
end6 L4 C8 s2 K C
3 ^! f) Q- y+ Z% g5 g0 A
%initialization
1 T6 G5 N- Q+ U* Z# e s_path=[start];3 S; K j# o- n) J) W1 H' [
distance=inf*ones(1,row);distance(start)=0;& S' T- i, z2 w6 ?1 s/ Y
flag(start)=start;temp=start;; p6 m0 d2 q1 X0 E: y
5 r! ]! K) M( o z3 J) h- j0 {, r, q( _
while length(s_path)<row
N0 F8 Z3 Z# w' H8 ?; A' f pos=find(Input_weight(temp, : )~=inf);
. Y8 l; X% ?4 @' @; a# m for i=1:length(pos)/ E- a0 A% c4 ^' n' d
if (length(find(s_path==pos(i)))==0)&" a( _; B( `& M* r) M6 \ K
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
6 a7 A6 o( O3 Y' ] distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
1 [3 E9 C# D) _( X flag(pos(i))=temp;
1 c+ G ^2 k J4 f' I% }7 R9 ~4 y end8 B* J+ h8 n" N- D1 r. x
end
8 \6 [* S6 H/ d/ H0 B+ ?0 x k=inf;
! f( Y4 L; Y* e7 x7 h for i=1:row7 q8 E5 ?3 `$ t" S( b/ @
if (length(find(s_path==i))==0)&(k>distance(i))
- v! l9 B, V' X+ R! a: W9 f k=distance(i);# l5 j* T5 c" q f. T$ p
temp_2=i;
0 _1 `8 ^+ w: G8 f3 i; N; ] end/ z9 @! h$ g, U4 z
end0 s, F, p' O0 Q/ ?: B$ P
s_path=[s_path,temp_2];/ C5 T* k0 b% k; X! w( }
temp=temp_2;
! v5 q: T) s$ }. J; v% i; J end
9 D; F. a: @2 z6 x% Z 9 Q) W% o1 u/ S
%output the result2 I: U: B# @( `: P! t: T
path(1)=endpoint;- v% ~9 l2 @+ g* V
i=1;" q) B# r/ ~/ Y8 k1 V3 r7 L
while path(i)~=start
. k* P) w+ F" W1 z7 x% ^ path(i+1)=flag(path(i));
0 z, x0 b* @. G! u' N6 P8 r2 T i=i+1;
7 S" a" H2 y0 \! O4 m, X end8 K U# D! r6 A5 \9 _
path(i)=start;* O& E, b+ K' ?8 a9 Q
path=path(end:-1:1);
( _1 F' ~* f) c: m+ j N& ^ short_distance=distance(endpoint);1 ~9 x5 a) d3 ^
三 绘制差分方程的映射分叉图
1 _( i3 B" b( R% X6 b * c9 q5 s2 i$ q4 B/ t l6 A: q' L- n
function fork1(a);
7 C: O5 C% O p o 0 h5 e" Q* |2 o1 w& S: V- F
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
! _$ H. Y0 f+ t- ?: q: C1 o % Example:
: Y' f E% e" X P0 v+ P % fork1([0,2]); ! o# W$ D g l7 {* c: H+ J+ C
N=300; % 取样点数 . L' @6 X7 |! P$ k( E r' [# h
A=linspace(a(1),a(2),N);
2 X* b# A. E3 ]& D! V starx=0.9; % n9 M/ z9 ?$ x, x5 ^
Z=[];& A" E/ c0 k. k
h=waitbar(0,'please wait');m=1;
6 F, l: g/ w$ S. ? for ap=A; " n4 N" L1 w5 Y. V6 n, y) p) V- I: `
x=starx;
7 U4 U. O7 @3 q7 M' A! @ s9 S for k=1:50;
1 O" U( D2 g6 S: u( I* I x=1-ap*x^2; 5 b7 u O ^5 t( t* _' u0 t. I& f
end 8 G1 }, _' k: }5 ^( f" U/ E9 T% d
for k=1:201; / D2 O5 g7 V9 K# M
x=1-ap*x^2;
- M2 Q, N# Z( `4 e. \& e Z=[Z,ap-x*i];
4 k# S! a) m5 q, d, j7 o end
; ~/ v1 {# Y' Z waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
2 x! c' O( X. J- A7 y4 ` m=m+1;
/ J* J' l& P) W/ u+ V8 g end 8 p+ i1 x0 v0 Q( T+ U
delete(h);
1 n5 x( L8 W+ K: K plot(Z,'.','markersize',2)
* J u8 U0 Q7 X+ s& M7 R3 |/ u1 C+ Q xlim(a);# \, _, f9 E [5 I5 k& t
, `/ f3 K6 M( G( _* v 四 最短路算法------floyd算法
% H) F ~' m9 Y! } function ShortPath_floyd(w,start,terminal)
. w2 r! B* N9 p/ v, e+ T %w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
) ^9 t( J/ p9 V %inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];, r, n- ] a, c
%start-----the start node;
r5 K) j1 j2 ]1 S! k %terminal--------the end node; - Y+ h, q; f0 Z
n=size(w,1);
" a/ @) w) Y4 }/ W [D,path]=floyd1(w);%调用floyd算法程序
6 v* g" A! F- h. b0 T ( ]( v6 P+ S3 @$ N: b
%找出任意两点之间的最短路径,并输出; S6 [3 X& p7 K; k
for i=1:n* ^% k' h% X, K9 `" M* |! N$ [" f
for j=1:n1 U! r; M4 V1 g: h( Z
Min_path(i,j).distance=D(i,j);
- y: m, Q3 k& a1 D8 v6 Y %将i到j的最短路程赋值 Min_path(i,j).distance. g- j. P& \5 V
%将i到j所经路径赋给Min_path(i,j).path6 a) v1 t" [* W/ l" E$ D, S8 z/ m
Min_path(i,j).path(1)=i;! j: q9 J: p* b2 W/ L
k=1;2 m7 K" w5 D& h
while Min_path(i,j).path(k)~=j
@+ K' p C" [/ N/ V/ H- R# V k=k+1;
# y* A8 t1 E! Q& F Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
) c4 i3 g/ I& }9 | end
Q5 T% i7 m. D end E, t, u: L j% @" f- l
end; u8 J1 j1 L: b H. y8 |4 E
s=sprintf('任意两点之间的最短路径如下:');
3 Y: ^( g9 G/ [; m+ B' a- s9 r disp(s);
4 K! Y: O0 n: I; Z for i=1:n
7 {* n4 j; I! W! S/ [! I0 | for j=1:n
1 n* c9 a3 ?' i" o" M* L7 e s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'.... x9 u# x8 ^8 P G0 [
,i,j,Min_path(i,j).distance);! u/ _7 U5 d! u9 a
disp(s);
) n: |/ F p2 D! c/ e; C# F1 n$ v" K disp(Min_path(i,j).path);" G7 S* ~; f' E
end! r# U1 `6 n+ ]0 ?+ y
end! j& P" M' O h+ L& b9 l" ? m
4 ?) D C* G8 I! d2 T %找出在指定从start点到terminal点的最短路径,并输出
, `" B8 p% _, T, b str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...+ y, w$ w8 f; B t/ A
start,terminal,Min_path(start,terminal).distance);$ x1 z7 t/ {' A! M5 ?
disp(str1);
3 v# g$ ?# _; ~, {6 k disp(Min_path(start,terminal).path);
; L- m# K' p! \. s: F - l! r! }0 N. T" |
%Foldy's Algorithm 算法程序# t) N1 w6 n7 [: U! Q Y
function [D,path]=floyd1(a)8 b( B* K0 m* {6 L; \4 ]" K
n=size(a,1); {. M- ?1 y1 i* `/ m7 ]
D=a;path=zeros(n,n);%设置D和path的初值/ Q" c2 L8 v3 [9 c0 y7 q" ]
for i=1:n
6 \# O- C% [- h: @# L$ u6 S for j=1:n( K9 w- m- C$ j' a3 G
if D(i,j)~=inf
+ L- F( @ K: x& g6 q2 K path(i,j)=j;%j是i的后点
0 e2 U; X1 Y/ v0 _4 l: l end
k- b" d+ j& j. E8 _! {% n7 \ end- l" c4 R3 A( a8 O
end3 H( G* N$ E I, b& }
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
) [0 t O8 i, \ for k=1:n
: ]( T7 `" M) Y; @# Z3 D" M for i=1:n
3 E3 [ Z! l, A' K for j=1:n
; a4 a6 \ f$ Y1 k: w) H, z, e if D(i,k)+D(k,j)<D(i,j) `( o$ \$ B" K0 ^: B# G* F V' f5 M
D(i,j)=D(i,k)+D(k,j);%修改长度2 P$ L6 Y8 O1 [' {+ d2 Z
path(i,j)=path(i,k);%修改路径
& A7 m1 V6 v, J4 B5 { end
& L( A. J2 k6 m4 j: i! U# @ end
5 q1 |. ?% N: G% ^7 |7 m% l end
: V9 p3 E! j+ e/ _% E* C) v end& \" Q) E J/ T& m% N+ c
, _$ S5 \- B& W, ?+ H2 P' F
五 模拟退火算法源程序9 g, |. V5 T& |( A* Z9 i0 l* V
function [MinD,BestPath]=MainAneal(CityPosition,pn)
( _2 ~5 \2 w& N$ s, ]8 i. q8 M. l4 i) x function [MinD,BestPath]=MainAneal2(CityPosition,pn)2 q2 f7 u( N' N! D! x
%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
0 R1 _/ W: S. l3 i6 B' h, Z3 f %CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...' o, R W0 H5 {+ _
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
) ^- d: F2 W3 D % 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
2 ` a4 z. I6 L5 E/ y % 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...& p3 B5 I1 E% z1 N6 d9 L( q4 I. B
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
9 y0 X1 u" w) d$ T3 V1 ]2 P4 n9 x 7 K) |; v$ z( ?
%T0=clock! @) P) q* ?& a8 y- a
global path p2 D;0 B1 z7 L3 J$ p! O0 ?
[m,n]=size(CityPosition);
r/ G7 D) @% Z/ W/ } %生成初始解空间,这样可以比逐步分配空间运行快一些
$ b4 P- u# L8 K' p9 n1 @- A/ E TracePath=zeros(1e3,m);
" [& c# v; o2 q o Distance=inf*zeros(1,1e3);
9 S1 X! q0 b; a4 \* A , U& X% I& |; B% `: Q! ?
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
: s4 I; n8 H' U: m( z (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );, \0 m# A# Z5 q/ e# C
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
0 E5 Z/ i5 j0 Y7 k, _+ i; s5 x for i=1:pn
4 H1 {) D8 H4 h1 K4 j$ \/ i9 v& H/ q0 y path(i,:)=randperm(m);%构造一个初始可行解1 Q7 Q5 @: C" f* q( f$ j' \
end$ Y. P9 d% o4 a; j0 U
t=zeros(1,pn);3 ]% `- o+ Q3 t, f, A" q
p2=zeros(1,m);) n1 V& }/ h" ^+ ^: d
j& z9 n% k- f6 C& x- k
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
" j# ] f$ O9 W4 ? M8 i m_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=' ) ;
& O/ f8 D+ _; V- T6 \4 H5 r %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
/ {" u+ A X$ G7 A3 F$ O %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5 O. ]6 c) t! r3 H+ x" T
%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- u4 E3 ]. A" g9 r
%会收到到比较好的效果& J% R6 k. S6 A' s) }' X# W
/ |6 s9 a3 R' |' l
T=1e5;8 h" i5 X& \0 I$ X) A; ?3 y
N=1;6 {% E \! J% a2 I. T
tau=1e-5;%input('请输入最低温度tau=' );: J+ F# \# `! N5 u; W2 P
%nn=ceil(log10(tau/T)/log10(0.9));* o' R2 C3 y$ @% k Q
while T>=tau%&m_num<m_max
0 B, M# ^/ l/ y# a1 N iter_num=1;%某固定温度下迭代计数器4 F7 M; @7 r, N- C
m_num=1;%某固定温度下目标函数值连续未改进次数计算器
& s7 I7 M$ E" L0 W$ m+ P: m %iter_max=100;
1 r6 Q, f' k9 i0 C0 c %m_max=10;%ceil(10+0.5*nn-0.3*N);# Y$ t7 d4 Q. r2 F2 M/ m
while m_num<m_max&iter_num<iter_max
% O5 N5 c+ q6 l1 {) I2 O. u %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:+ F% W5 @, I' a5 \/ b+ f
%用任意启发式算法在path的领域N(path)中找出新的更优解
: `; d4 e- ~% G" ] for i=1:pn
# ~. N2 ~: O, n% Y Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);* t* \2 ~3 } n
%计算一次行遍所有城市的总路程
' D7 W9 C3 ~' r0 t( [$ g9 j$ D [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
$ l! I; d: o2 E( 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))]);
1 H1 {) ?3 i8 k end4 Y; Z$ v3 U4 ]3 [ z6 G
%Len1
+ P% P1 A& j4 E0 p %Len2
: X$ G& H, S! X& W1 i9 K %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand! R+ k& p/ f; ]( U1 [$ I- e& L
R=rand(1,pn);
1 @0 v- J4 ^- |& N %Len2-Len1<t|exp((Len1-Len2)/(T))>R1 w2 W% s5 @, A$ r( L' |* Z. P3 Y
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
* c* ]/ c- q. b path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
3 `4 Z7 o9 Q4 O, q Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
" }/ k7 b: M6 |3 L [TempMinD,TempIndex]=min(Len1);( v$ `( @/ I( W% N
%TempMinD$ i3 V7 T5 \* j$ P- n: n @
TracePath(N,: )=path(TempIndex,: );
& {4 N0 |& N/ S; ] Distance(N,: )=TempMinD;4 l8 s" T5 K# |9 b2 D3 F% q0 M
N=N+1;0 M! E& J# e" b% N$ z: |& [: k
%T=T*0.9
$ I) l: a0 y8 o m_num=0;
# C' d9 }" j7 C3 z- C& L6 c& R else$ ?6 h" _' h/ Z, o6 V
m_num=m_num+1;' A+ y# Q9 u" w T! @# ]- P( Z
end; `& J# e' T# m
iter_num=iter_num+1;
3 T3 ^, W# n% I$ ]' Z% ~' Z end2 r( |3 u' u* P* l P
T=T*0.9" x0 r3 C' I. d
%m_num,iter_num,N
8 \5 K9 ^: {- I! ~1 m1 j& W; D end
! Z Q+ v E/ F1 z! }3 m% E [MinD,Index]=min(Distance);! F1 B0 m" D f
BestPath=TracePath(Index,: );
2 L* O" K3 W' l2 Z5 M disp(MinD)
3 R$ Y1 v1 A6 }* ?: q. U %T1=clock$ t3 w6 s; G0 ?' W
; K+ ?7 v1 t! w" `& F, B# X# H
9 j5 _2 h( t& \; K% A- { %更新路线子程序 % y! k i2 }* O6 ?5 e* w3 R# I
function [p2]=ChangePath2(p1,CityNum)
2 l8 D, G6 ]5 H) T' J* N* m/ b global p2;
+ q) v: n8 _! ~$ L' l: Z' O7 ^ while(1)
: W' `( t+ ]$ o$ @ R=unidrnd(CityNum,1,2);: U; d+ D" u s$ N/ V' y; y
if abs(R(1)-R(2))>1
! L h0 ~) A! F7 O) o break;
- S2 \/ I" ^- D" s end' {% l( X) h5 m' h
end$ a$ m7 V; L+ l; z2 N' ?: N5 X$ y
R=unidrnd(CityNum,1,2);$ k2 I. R; C9 p O6 _& n* y
I=R(1);J=R(2);
4 _5 r6 t" y" R& P6 o %len1=D(p(I),p(J))+D(p(I+1),p(J+1));" x- {, A2 m, O
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
1 h f3 F5 |" A if I<J; K9 A& n6 E+ V7 c2 I" w
p2(1:I)=p1(1:I);& a/ x* u" A) m6 a$ S
p2(I+1:J)=p1(J:-1:I+1);
/ P h+ r1 ]6 Z p2(J+1:CityNum)=p1(J+1:CityNum);
) l' @; g P- Q2 B else9 D! V7 o" `1 I# F; Q( P1 B8 H
p2(1:J)=p1(1:J);( Z# V. s, \* I( ?1 F8 m
p2(J+1:I)=p1(I:-1:J+1);
, d( f9 C4 ^- c0 i! a p2(I+1:CityNum)=p1(I+1:CityNum);
9 ]2 I$ \5 t0 ~: }( U. U7 [ end
6 u. U6 Y$ |5 P Z - d @. Y0 l* j% D, w
六 遗传 算 法程序:
% t. c! J8 F c% K, E 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!% S/ c0 f# j3 J
" U& n+ S A" D5 M( |
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
6 g8 ~7 z. O# r3 C$ B % [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
6 J: T9 q7 q; H' u) U% r % Finds a maximum of a function of several variables.7 D# i; }* w- E( n
% fmaxga solves problems of the form:
2 ^6 |3 n4 W4 w % max F(X) subject to: LB <= X <= UB ) U& F/ X( z1 T; z, M7 G4 v i
% BestPop - 最优的群体即为最优的染色体群. b5 k8 p4 m1 B# ]+ h- ^9 ?
% Trace - 最佳染色体所对应的目标函数值
+ A9 c' u& p; e% x2 x- a1 S % FUN - 目标函数) Y T* L2 K, n4 a& |4 j
% LB - 自变量下限/ T' Z8 R3 a+ X7 f j, w$ G! V
% UB - 自变量上限% W( B6 H' G& {, y, N; ]
% eranum - 种群的代数,取100--1000(默认200)) C5 J+ \7 c7 H" P5 @) {. ^
% popsize - 每一代种群的规模;此可取50--200(默认100)
5 Z, p r! R, k4 P1 ]. X0 k % pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8): P' w: ]9 ^( f' A, w7 }
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
+ o- V& h( @0 ?$ ~. j % pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)7 Z9 ?8 n) i8 a5 i5 l
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
7 ?8 j7 C* _9 d" C %码,option(2)设定求解精度(默认1e-4)
2 `5 R8 w- }! ~ ?$ b- E %
$ ~" A5 ^, m" k: ]% v % ------------------------------------------------------------------------0 |: s% h" z+ C2 f1 q& _) n
) L; O- c& A4 N" O0 r. l" M) A T1=clock;
/ P5 q' @1 d) \ if nargin<3, error('FMAXGA requires at least three input arguments'); end6 ]7 x' |1 ?# J! n! ^
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
5 R: D0 ^% p) x if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end4 W5 \4 \8 X+ o9 a+ }6 {
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end% L! I+ p% I8 l$ b) W* k
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end# g) o+ d) M8 M
if nargin==7, pInversion=0.15;options=[0 1e-4];end% u- i) a! B& @ \( L
if find((LB-UB)>0)4 f# x2 _ `% h+ r3 I" J$ }% b
error('数据输入错误,请重新输入(LB<UB):');. }% G5 H% Q% j! Z/ i
end c& W6 x4 U9 X. G" @& b- l- r
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));9 j7 ^) c% \& c3 ^' { h1 j
disp(s);4 G/ K! @# {" X* c/ y0 m
% Y& ]2 C" W- t9 M6 ~' r4 W
global m n NewPop children1 children2 VarNum; J" B% Y5 |! d( ~. S8 I) \
4 v2 L, ~# b7 L* |. |6 V# D
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
7 d }1 x- _" q! _ precision=options(2);%由求解精度确定二进制编码长度
9 S$ h& X' m4 ` bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
* O* s7 }/ |! \& v+ n- P3 { [Pop]=InitPopGray(popsize,bits);%初始化种群
2 u! L6 i% X. |- _# K/ ]' G [m,n]=size(Pop);9 H% J {" t9 W8 a
NewPop=zeros(m,n);
( w* H L- t, I2 p" G1 T) L children1=zeros(1,n);$ z% x$ {( j' i/ Q% I4 b9 j' A
children2=zeros(1,n);4 I O( X4 p/ s# i
pm0=pMutation;
* a0 L5 J2 s% h! L ~ BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace/ K6 A. ^; U! h. i. U( @
Trace=zeros(eranum,length(bits)+1);
1 q/ K' v U8 I, h i=1;
7 e3 }* C9 G) X L3 B! ^ while i<=eranum/ K1 C, c0 a. p- f" V& j# [
for j=1:m( I# q0 E' I4 j" k" Z6 S8 n0 F, K
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度# ` e5 U( I4 l; U
end
; C# w% {$ _. A. e; `6 y [MaxValue,Index]=max(value);$ j& c' j1 ^" O: F
BestPop(i,:)=Pop(Index,:);8 e9 a6 ]6 j# R& [- d+ x
Trace(i,1)=MaxValue;
, {% i( D) a6 U+ J0 a Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
7 P5 `7 a" O4 B. E2 t: { [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
! A! ~7 D! s/ B [CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));4 T3 |( n) d( v2 o; K! m
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率( `/ l( ?3 ?; o. i! _; Y8 i- ~
%round(unidrnd(eranum-i)/eranum)
) c; {; M: y2 Z1 g0 E2 h/ j [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异4 @: p: f. p. R* N% n* s& ]
[InversionPop]=Inversion(MutationPop,pInversion);%倒位
4 k1 \& a3 v1 ]+ v) T: T Pop=InversionPop;%更新' x- b+ b! l V6 ]; X: w
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); # R& g$ x& I5 M
%随着种群向前进化,逐步增大变异率至1/2交叉率
, R8 }$ {: v4 {# q1 O& x8 V p(i)=pMutation; ]- _; D U! X2 H3 J8 h$ M6 h
i=i+1;
! t& n x* V! z5 ?3 j. P end# N+ [7 x, m+ s: Q" F, k- d# Z8 _
t=1:eranum;
; V9 _+ ]( h" t# T. N3 o plot(t,Trace(:,1)');
# ^& G% u* e4 _& ?' T 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)');
" [& k$ O; E0 a. i0 I& N) l [MaxFval,I]=max(Trace(:,1)); _7 o I2 F+ A3 h. V
X=Trace(I,(2:length(bits)+1));' x$ n# D4 Z" }7 \9 C1 q7 _
hold on; plot(I,MaxFval,'*');% e4 c Y4 D; u/ H# u" R0 n& ^
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);5 |* g& \, Z8 F( V! ^
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,:)));
5 e) K2 S2 @. I2 g! q- f disp(str1);
/ y3 ]1 ?: q* l M+ y8 N %figure(2);plot(t,p);%绘制变异值增大过程5 E* W- L9 _6 V: c2 Y! r
T2=clock;
: |& L0 H1 [- ?5 |- i elapsed_time=T2-T1;
# o3 X5 u, a0 y7 q- w" j if elapsed_time(6)<0% W+ l$ u; W% [7 P
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
& ~ M; _4 C$ @1 ~$ @! k end6 \/ Q1 D+ \+ q. u6 M* H1 Q
if elapsed_time(5)<0
" {5 D7 c# g( x' E elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
; ~' [6 K. s1 A. Q7 e2 |, P% |" d end %像这种程序当然不考虑运行上小时啦
7 R9 W9 K0 s3 h1 I 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));- Y! `; K1 `) v( B+ v* F
disp(str2);' e7 B% Q* _, W8 v) {0 D6 C
2 x) P7 K- `' A& o& W
! o3 m. B5 T t$ ~8 k6 @: f
%初始化种群
% r& F$ j8 {2 _( {1 g. y %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
) Y+ G7 P3 T5 E; u. @! P function [initpop]=InitPopGray(popsize,bits)+ g: ], Q }( I9 U
len=sum(bits);
% Z3 @4 x, \2 j1 b# A- l' a5 t' h initpop=zeros(popsize,len);%The whole zero encoding individual; v8 {7 l$ D' C; @
for i=2:popsize-1
; ^9 V2 t' A; s G pop=round(rand(1,len));
% ]1 l) J4 q' |8 ^. I& e; J+ s pop=mod(([0 pop]+[pop 0]),2);- H' ?6 L' |+ G
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2); E9 n. z8 i0 }% H; k
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)3 n: R& Z" T9 H9 p0 W/ i
initpop(i,:)=pop(1:end-1);" } n7 @% }8 L/ p
end
8 a6 e) F: i5 }: w k+ \ J initpop(popsize,:)=ones(1,len);%The whole one encoding individual
+ c+ I% q- @8 z+ u& t1 k %解码" a R9 E- {3 f' f
! v! q( T) h1 Q
function [fval] = b2f(bval,bounds,bits)% O: D4 Y0 l" z4 p/ t
% fval - 表征各变量的十进制数
' q e- B8 U: F, k6 p ` % bval - 表征各变量的二进制编码串
$ {7 D, }# r/ l) c( E % bounds - 各变量的取值范围1 V6 I9 n0 s7 q! O
% bits - 各变量的二进制编码长度9 u1 r6 w" J" [8 {' u
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables2 Q5 l+ X" X$ q' ]$ C5 B
numV=size(bounds,1);# W+ m$ [9 {% w7 Q4 r/ d
cs=[0 cumsum(bits)];
! U% n' n5 v# S/ z for i=1:numV
$ A8 g! {' o7 }$ @ a=bval((cs(i)+1):cs(i+1));4 l' i8 s7 ^) V5 c
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
) q' `# B1 a/ i |( i end
: ~- F; U8 t- z8 G# U %选择操作" I1 Y$ C8 e. O! ~7 I
%采用基于轮盘赌法的非线性排名选择1 N$ F/ K5 y- J% h U
%各个体成员按适应值从大到小分配选择概率:# { \2 Q4 V$ e: g$ g/ |; p: A
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1
" Z; p' I0 ~, w8 Z$ K) Y , L, \1 X8 j. H+ v* z
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)& Q& J% q8 w* z( u' V8 c
global m n: a9 J# U* |$ ?" f- q
selectpop=zeros(m,n);
1 e; |7 T2 L% G- C: i# q8 r/ i fit=zeros(m,1);8 U7 F4 ?$ S$ n& G
for i=1:m
( W4 s M7 F" Y( V' B" y fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据! o5 X' |3 p& @& J) |) Q" c2 `( @
end! k* o5 K7 e L; q. k
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)% B$ y8 q) `! J0 X, f
q=max(selectprob);%选择最优的概率# F0 r. A# ~' v7 d9 Y' D" a; S
x=zeros(m,2);/ Q4 r/ k2 l* Q! z
x(:,1)=[m:-1:1]';
+ Z4 k6 C- r9 w [y x(:,2)]=sort(selectprob);$ X2 v6 n4 ?& ?# ^1 y8 ]
r=q/(1-(1-q)^m);%标准分布基值
) Q) f+ i' h" ^3 Q; P newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
& ~- ~# E# z( G# }" }+ N) y newfit=cumsum(newfit);%计算各选择概率之和) t$ R/ c' i! L. w
rNums=sort(rand(m,1));9 ]) }3 W4 i9 a$ n. N
fitIn=1;newIn=1;7 i. r5 E# W& z
while newIn<=m* R9 b. L- H) ?" ?* G% k
if rNums(newIn)<newfit(fitIn): r( g% b# S1 ]
selectpop(newIn,:)=pop(fitIn,:);
$ C8 k( ] A$ p) h newIn=newIn+1;: e+ Y1 V( Q0 B) }
else
5 Z1 K, {. Y0 u fitIn=fitIn+1;' ]; }" R) e2 X4 r* Y8 H+ Y# P) H
end3 ?/ w8 D7 N! L3 {! x2 n
end
' `. {. Y% {4 ]% C %交叉操作
. ^, b+ L7 j$ C function [NewPop]=CrossOver(OldPop,pCross,opts)
# \4 @: v. D0 U# Q! [7 M m2 L %OldPop为父代种群,pcross为交叉概率$ }( M! L8 }6 \( I: q4 O8 ^
global m n NewPop
/ e r3 e3 n' N6 d* N1 x3 \0 H1 _, h r=rand(1,m);
- z% F, j2 Y! C8 i7 Q; C y1=find(r<pCross);. V* X1 F& P* `5 }/ N, C
y2=find(r>=pCross);
: T- c9 ]0 j' T9 z. A1 p len=length(y1);; F/ e' c- x0 {: |$ U! o
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
/ @; a. T* T( t1 }0 |0 R) v y2(length(y2)+1)=y1(len);
' V; ]+ E1 t- P* @6 U* G- E7 T5 i, s y1(len)=[];; j1 s$ U1 X9 W9 n3 z
end
6 B2 x5 t: g6 e if length(y1)>=2
! m0 V( Q7 C+ \! H; @! g4 t for i=0:2:length(y1)-2
" j5 K8 c1 s" S6 Q: p if opts==0
# x3 |) e4 C" ~% a& @: D( o9 @ [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
3 M& p$ N3 \; W else
% j0 C! {$ H4 j5 u) i* y [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
. q2 _6 w M A( _( y$ ]+ a end
; G. V2 C! E& k end
_/ V! S2 F3 U4 q end
9 N4 l7 d5 q# ]) A& B7 x NewPop(y2,:)=OldPop(y2,:);
" m4 U8 M& f- _+ z5 j3 t- r5 k4 q8 A
8 T' X. s" q7 A1 F. Y) |" u %采用均匀交叉
# M4 m# o! Y3 U5 W D$ W function [children1,children2]=EqualCrossOver(parent1,parent2)
% V" M- \2 z- r! G( L & u/ h4 r( |5 ?. a' k
global n children1 children2 ) w9 L& s# O$ l
hidecode=round(rand(1,n));%随机生成掩码
* _) k# {3 H! m% ~ crossposition=find(hidecode==1);
6 O+ W+ D! W' W( l2 F7 G p8 D( T holdposition=find(hidecode==0);6 j$ X+ d( x n" D
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因8 b5 X0 E! o# I" G
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
) g, c: H8 e( r) R& A( _4 \ children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因8 s; z6 A6 T" `5 s# q s
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
) d# m' o5 N) R9 [5 X7 u8 ` , F) F# D8 F7 `4 T
%采用多点交叉,交叉点数由变量数决定+ a6 \2 d& j! y6 A* g
# ^. ]0 X3 C; Z( S. w: ]
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)
. l0 w2 Z( R: i0 \ g
" J' q. N6 w: C* L( T global n Children1 Children2 VarNum
$ e+ s% |' [$ _3 C: C+ t# ], U3 m. D Children1=Parent1;
( h/ n& M) B, ?$ \: O Children2=Parent2;
! m+ X3 M6 q2 H6 D. v Points=sort(unidrnd(n,1,2*VarNum));4 f" h" }: u7 P m. ^; u
for i=1:VarNum! p8 k4 k9 m: U; o$ K
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
3 k; ?: |& M( I6 [6 k" {1 H Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));2 _* u6 C, Z% J4 `& n5 c2 ?% u9 F
end
# f: E- G3 Q2 e0 f & o9 T2 A i1 q: \
%变异操作) B9 [1 m6 }1 i; @ U+ j
function [NewPop]=Mutation(OldPop,pMutation,VarNum)
" y9 n* C# q# b; @( \
" B2 ~* k: c. ~: C& N2 _" ^% K: S4 x global m n NewPop
6 P9 W+ d p) d5 Q$ _ r=rand(1,m);
0 X: U5 Y$ D! z8 R' J- f position=find(r<=pMutation);
& A- i; N! @2 C4 d" J( \0 C len=length(position);
6 E+ B N4 r3 F3 i8 \ if len>=1
* m* {! T6 J2 r8 f4 @. E6 k$ C for i=1:len9 t( J; e Z' r5 k" E
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
: W7 u8 m1 t" C; F7 a/ j: d for j=1:length(k), H* c$ I: P* R a" s1 o& _% o3 _1 `
if OldPop(position(i),k(j))==1
( b# {, [ P4 a; F OldPop(position(i),k(j))=0;
. t& j. d3 A5 A# c1 ~# h% F else5 V" I! y8 u) f) _
OldPop(position(i),k(j))=1;
; j" w$ f4 ?' W1 Y end- J7 ~5 B+ m& x/ q
end4 x' u; i: t" N+ A
end
7 N8 R2 ~; D8 k: \8 p4 J; c) V- k end
' r2 A) I9 v8 C3 U NewPop=OldPop;& m# J1 V& O, q/ ]
) g* }& D. F8 K %倒位操作. n6 R: j j) \$ m, f
R6 k1 ~6 M8 |8 f function [NewPop]=Inversion(OldPop,pInversion)
1 p. [2 n. p7 o& u& A" L% o : |- w/ z! w* s
global m n NewPop$ u" g B' e0 D4 ]+ m+ D4 ~: a
NewPop=OldPop;
7 W6 s F% O+ c; e r=rand(1,m);
8 u; v4 N+ x# V$ ^ PopIn=find(r<=pInversion);
& r, y8 k( V6 H$ v6 r6 ?3 p' u/ X len=length(PopIn);
5 q3 P& n2 I0 Q! L( y1 { if len>=1" }" t' _7 K! ?! N
for i=1:len
7 u" P6 F7 K8 J1 Z) D& u, m d=sort(unidrnd(n,1,2));
' ?( r( w2 ?/ w/ V if d(1)~=1&d(2)~=n( a5 o) U) @% k% o5 _
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);4 V( e& o4 J2 d' H2 b* V# k
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
* k+ f1 R. I% J NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
/ I8 z5 A$ _" @, A. E' J end' e2 Z6 n& p9 g( A
end/ o0 p9 x+ n( X ~4 n; t- l
end
3 v! w5 `( ], P; q9 U3 I, |- P
/ D7 c1 N" Q8 ?2 R8 M 七 径向基神经网络训练程序0 t; y/ u( K3 O, [8 V, l
" Q7 }7 N2 \% l0 Y, v# C3 J clear all;
: [3 B7 v% ^6 U; t0 O2 V! n7 L5 ^ clc;' w5 w$ P! c# S' Y% Y! q
%newrb 建立一个径向基函数神经网络
) }& s0 P& f+ E& o# _. F: u4 Z p=0:0.1:1; %输入矢量
; Z9 d2 j; t& v- f# x! i D- n9 f t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量9 P, ~: I; Q+ X" A! `( v
goal=0.01; %误差
2 E- Q0 h* l5 W& f sp=1; %扩展常数
2 P7 J( v8 S+ _: f4 T+ y mn=100;%神经元的最多个数
- H! e( V$ ?3 v5 X) t7 y } df=1; %训练过程的显示频率
: R. H5 r0 s8 o, N% w% U [net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
% Z, r0 e" G" M" I* f % [net,tr]=train(net,p); %调用traingdm算法训练网络
8 t% A: D: j( x, f+ q7 D %对网络进行仿真,并绘制样本数据和网络输出图形- ~$ S) Z7 E/ r+ k
A=sim(net,p);
% R& ?# y( \+ T7 q% N* z. h E=t-A;% A( V$ q0 e) |' G& ?0 y
sse=sse(E);
' X+ h* e/ I/ x9 M9 u figure; 8 j+ u `* k9 L& p3 t
plot(p,t,'r-+',p,A,'b-*');
6 P$ D/ r& G& | legend('输入数据曲线','训练输出曲线');1 ^6 c N" n; u4 w7 u; x
echo off
7 s1 q+ r3 @" `7 e/ C 0 t/ v0 _) M+ U2 h8 M- F
说明:newrb函数本来 在创建新的网络的时候就进行了训练!
# }0 [8 Z; }7 n* ^1 p$ e 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,
5 `5 W8 Z0 ?+ @- B ~ 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!
" r$ w3 t: Y- V3 C7 ^6 {# T! ` ( x9 ~7 k1 x( ~% r6 \ P4 Y
1 P+ G6 V: D/ t# c/ r* P 训练结果显示:
/ N1 a8 L" s& m ]' i NEWRB, neurons = 0, SSE = 5.0973
7 Q. Q. @2 e* e4 U9 ~3 m NEWRB, neurons = 2, SSE = 4.87139& ~/ P4 c7 D. w% D+ F7 n7 y
NEWRB, neurons = 3, SSE = 3.61176) ~, ~- j/ O. a% y1 N# t
NEWRB, neurons = 4, SSE = 3.4875
, A1 c2 u# M h) w7 _4 R! k* B NEWRB, neurons = 5, SSE = 0.534217
6 n2 K$ y$ j3 }5 j( z7 v- Z0 D NEWRB, neurons = 6, SSE = 0.51785
1 q) s& |* }1 [3 F7 k- m NEWRB, neurons = 7, SSE = 0.434259/ ~9 n. o+ T" _ r: U
NEWRB, neurons = 8, SSE = 0.3415180 t# v' |) Y. D( i
NEWRB, neurons = 9, SSE = 0.3415196 L' ~# t7 {% Q2 ?
NEWRB, neurons = 10, SSE = 0.002578328 X! D% A1 \ D
+ B5 s& x0 d0 P 八 删除当前路径下所有的带后缀.asv的文件
) n+ d7 M$ L% y# h" h4 P% ^( v 说明:该程序具有很好的移植性,用户可以根据自己地
# b. a/ U T+ c' O 要求修改程序,删除不同后缀类型的文件!
, b4 n4 d" \: ] function delete_asv(bpath)
, V" B1 c; T! o2 |& G %If bpath is not specified,it lists all the asv files in the current
1 q$ Y2 o. T8 u %directory and will delete all the file with asv 2 Y; [" ~8 @% z! ^
% Example:+ u; x/ m' Z2 ?7 T+ r' i. w: c
% delete_asv('*.asv') will delete the file with name *.asv;
% [9 k; S$ E+ k+ S G5 Y % delete_asv will delete all the file with .asv.
( v' |5 s' F5 M( J) d0 |0 Y * b E8 _" I" x; D% X# k# ]
if nargin < 1. Z1 t' S" q3 r8 v. p
%list all the asv file in the current directory
2 e7 X- ^3 s1 o. }. ~ files=dir('*.asv');
6 N9 a4 x# \- @7 f/ } else8 I& G- O( U4 y0 l/ O h2 ]
% find the exact file in the path of bpath* p# | C. ~) {0 s
[pathstr,name] = fileparts(bpath);7 c% _( |$ n% D; C- b8 N
if exist(bpath,'dir')' f/ j4 K' T' e; K$ d
name = [name '\*'];) S$ }5 N7 p! b- p4 L- j
end/ g3 H; G9 m3 H
ext = '.asv';
3 f$ U% e, u4 k files=dir(fullfile(pathstr,[name ext]));
. C0 j0 l* J u end# w4 p( Z6 \; k5 @; }
* j P2 ^5 M) L" i' \ if ~isempty(files)$ x. R- Y% } z
for i=1:size(files,1)
" I+ Q7 p3 ~& O0 _3 r1 o% k title=files(i).name;
; s+ K8 R0 F5 O- j delete(title);- Y8 t/ N' g5 u* X5 I
end
! p! d- |$ g+ O end
) R- T6 n, _0 X. _& B- E$ C: Z4 w# c+ r
1 A; x6 u9 f, d
8 u8 h8 c4 L) Q6 x" T' A 同样也可以在Matlab的窗口设置中取消保存.asv文件!2 x* z( n/ W6 ~! s8 T
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