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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* b3 r! j: c4 T& d- Q
1. predict_fun.m为主程序;
# M( b! W# J7 ?' I( A7 s2. timeseries.m和 serie**pan.m为调用的子程序
2 j: U# p* e! n% w* m4 @6 y& Y& \7 A- Q6 Q% `- v4 K' P6 u2 W
function ima_pre=predict_fun(b,step)
* m3 Q7 I# q) E% main program invokes timeseries.m and serie**pan.m9 w1 z. d, v/ w
% input parameters:
& r& g& ]5 h& S# R$ ^% r: V% b-------the training data (vector);) B4 O2 v: `% O: o* B
% step----number of prediction data;/ g; O. O6 M t( A
% output parameters:. M$ j/ ~( O2 Y: `' P1 q
% ima_pre---the prediction data(vector); m5 l8 m' M4 b& Q9 M
old_b=b;
/ l" v. r' R( x: imean_b=sum(old_b)/length(old_b);
2 @7 _# x* O( S/ Mstd_b=std(old_b);
) k% c3 t& W! ~' D' `old_b=(old_b-mean_b)/std_b;
6 O" _7 u6 S. @6 p, c7 l% e4 B3 T[f,x]=timeseries(old_b);! ] u$ h' J# _+ M c; n. Y
old_f2=serie**pan(old_b,step);
! {: s& @$ x+ p$ e' }/ k% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;; @, Z, g, a0 k
R=corrcoef(f);
; X. ^3 u( a, x% [1 }1 q5 P[eigvector eigroot]=eig(R);* _- c Q8 `1 j/ F& r3 P
eigroot=diag(eigroot);
/ h/ W6 X! R( k. O) ja=eigroot(end:-1:1);; P* |/ p5 A& q% Y6 A6 Q( }4 w7 @
vector=eigvector(:,end:-1:1);" q! l2 x+ G. W- C# T+ @6 O# s4 \4 G
Devote=a./sum(a);# _( d6 ^/ o, q& j
Devotem=cumsum(Devote);
# E& V: S0 n+ lm=find(Devotem>=0.995);$ S e; D! }" y/ G' q2 s
m=m(1);* S$ m* J3 A# t5 m
V1=f*eigvector';( ]) i) e% z% N& V+ j1 Z* G# f1 H1 r
V=V1(:,1:m);
- I' r7 |& s! w7 d! Q/ J% old_b=old_b;% }" ?5 n' @' m. u
old_fai=inv(V'*V)*V'*old_b;/ b7 [/ p/ ~$ f: @! X* X! A
eigvector=eigvector(1:m,1:m);
" B7 o5 F+ t4 a" `1 F; Efai=eigvector*old_fai;
' P1 B X0 Z. i! m' ff2=old_f2(:,1:m);
* }; i( z+ W5 l+ G4 W# G Kpredictvalue=f2*fai;: |6 [5 v& T( c2 j5 I" N( @% J
ima_pre=std_b*predictvalue+mean_b;
$ p1 {/ N, D j6 ?5 X
+ r; K( N& Y4 E2 z1.子函数: timeseries.m % N! b1 h1 n3 G5 ^
% timeseries program%( X+ Y6 n7 Q) k/ d
% this program is used to generate mean value matrix f;
8 h* [7 L9 M6 n& V: m$ t6 g4 d1 ifunction [f,x]=timeseries(data) ! [* U3 s0 w1 r% s5 y, |/ s3 {
% data--------the input sequence (vector);
% `2 T. {5 ?5 k0 @- I: [: f( L% f------mean value matrix f;5 M+ T8 l' M' ] w0 C" Y# T
n=length(data);
5 X; g& e3 d+ M; U" @for L=1:n/2
1 N7 r2 M: Y) P5 y4 N5 h' v1 b4 X nL=floor(n/L);& x$ R3 }1 y' b ^2 u4 ?
for i=1:L% c% W/ ] \1 A6 l# U
sum=0;. y/ s, ~% U2 h$ N: D& E/ u
for j=1:nL) H8 x" K1 [" Z, E8 R3 ^% q. Z
sum=sum+data(i+(j-1)*L);
+ U2 L% G# N& y% O* O end7 k$ Z$ _0 I! k4 W+ z# |1 g5 t- f! C
x{L,i}=sum/nL; I0 M& R1 t5 ^# X4 Q/ w6 J, X; w
end
* L u1 b' I. g! R) W& [5 h: e {4 Qend# H/ r1 w0 I5 b o) L% `! B: }
L=n/2;
+ v; m g& [: b9 u# Y" M8 ?f=zeros(n,L);) B, G- d7 f1 C f1 z f2 w. p
for i=1:L
" I8 L* l! w0 r( u5 K7 U rep=floor(n/i);
* u9 b+ O, R1 f9 f2 V$ _# r res=mod(n,i);
" W# }, X, W2 a: p3 @4 d b=[x{i,1:i}];b=b';- C X; k( u+ t! ]. l
f(1:rep*i,i)=repmat(b,rep,1);
% p" Q2 i4 `, D if res~=0
& p- k% M2 Q% E E; B c=rep*i+1:n;
- l1 L$ C2 y( S3 U2 V9 w f(rep*i+1:end,i)=b(1:length(c));3 ~4 O0 J# t, h" }* N
end
: M7 w: {6 `" [end% S7 r8 R/ c5 b( o# `
; h3 l. n. y/ m- b* l0 j
% serie**pan.m8 G4 D5 e( V. ~# R* g/ n3 z
% the program is used to generate the prediction matrix f;
$ E H; C$ K% a! Y# kfunction f=serie**pan(data,step);) g! f1 H% S9 \; k& [
%data---- the input sequence (vector)
7 H: G% V) l3 w f+ i- z- `, B8 P7 Q% setp---- the prediction number;. s7 V: e7 Z. }+ o) L4 a, O; [) z
n=length(data);
2 R! w8 t3 J* `0 M6 [for L=1:n/26 Z6 A& `7 N. l" F
nL=floor(n/L);$ \- R* Q: C- P; ~7 `: S* G; N
for i=1:L
]- | h3 t& P. L& Q) g sum=0;
2 ] d) r3 c# u for j=1:nL! c% d+ J7 M4 q4 p4 K( F' l; a& o; j
sum=sum+data(i+(j-1)*L);
- t4 R: m7 [# j% B' r2 [ end( R' p" ?- x$ a0 ^0 E+ w
x{L,i}=sum/nL;, G1 O) C" E) d; V
end) J9 O# o8 h3 _& u7 C9 T7 t# e
end
, |/ m- B1 e! m( fL=n/2;
! y2 e7 O+ j+ I6 bf=zeros(n+step,L);( p/ ~& ?) z% l% ]4 k' P* D8 _6 r- L
for i=1:L
' l: e# I0 V$ E X7 | rep=floor((n+step)/i);
0 z8 J, U& K! g/ @ E res=mod(n+step,i);
0 \* D$ n; u' y+ }# M; u# C9 J- h b=[x{i,1:i}];b=b';! d- y# i: X' U2 n4 }6 b) f5 b
f(1:rep*i,i)=repmat(b,rep,1);
- W+ U% @- I, b if res~=0! ~% a2 q3 B; @3 j
c=rep*i+1:n+step;
5 `+ Z9 `/ q! s9 ] f(rep*i+1:end,i)=b(1:length(c));+ y/ g0 k8 I4 Y* _9 r6 h
end
, z3 ]( D) x% ^% a8 Iend
# ~. S+ q$ {( `9 P/ r( Z
6 ^' I" K3 n* I4 t J+ W1 k8 G二 最短路Dijkstra算法- `$ K+ ]1 b( Q
% dijkstra algorithm code program%
( V4 h# z! q, n; R% the shortest path length algorithm
; F; Q0 Z0 @: A! @7 hfunction [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)
* T" ~4 C1 m7 | _# P/ J% Input parameters:
' m. U U" D# U- Z+ ]; O( P; u t0 m! w% Input_weight-------the input node weight!
h" o( U( m& i6 @% start--------the start node number;( `# A! V% N" z
% endpoint------the end node number;
m8 A2 b8 m, X& A8 v9 B- o$ q% Output parameters:
5 Y/ C! b9 M2 S% path-----the shortest lenght path from the start node to end node;4 ?, Z q W' L. b5 A/ L* t$ f4 J" S
% short_distance------the distance of the shortest lenght path from the
5 F3 _1 @( l) t/ {# k7 p( ~% start node to end node.
" r4 f& C5 k/ \* f[row,col]=size(Input_weight);0 P+ R2 R. u4 J/ Y
2 u$ ~' Z' h" }8 q/ o5 W%input detection
& C) m, N! Q4 yif row~=col; S- ?; G4 m! I, P: `
error('input matrix is not a square matrix,input error ' );4 c" {6 n: ]$ p8 H
end: [( C- _ t- W, ]) N: z4 }
if endpoint>row
A5 U: b- k2 B' L# _. ]9 H. j- i) N. h error('input parameter endpoint exceed the maximal point number');) n3 d: i' y) S, y# @9 r& U
end, t3 G% `5 A# c; l* d5 o) G( h# e* ^
: d2 D [8 N6 @% V5 ~%initialization( @7 E* h9 T6 b8 L) ~
s_path=[start];- O( E y& J) S v- A
distance=inf*ones(1,row);distance(start)=0;$ t `6 t- R2 @ t
flag(start)=start;temp=start;, h( P5 D5 t+ C& }1 M& g5 A$ _. l
- E- ^( u+ {9 Q0 Y( \while length(s_path)<row
# J$ }; k) V$ \+ U4 l pos=find(Input_weight(temp, : )~=inf);
. c: i9 S8 e, L# R: X for i=1:length(pos)' c2 W3 m0 {2 s6 K* ~; N
if (length(find(s_path==pos(i)))==0)&
( C# B$ ~2 n$ e(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))0 o m& c2 r+ i! w- L% H8 {
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
& }. ?3 L" z* h0 E. ]6 n flag(pos(i))=temp;2 [% C2 W$ Q9 K1 H% e, s" l
end& \6 m6 r/ R* d6 n" j3 C E- n6 A2 h
end
% T" K2 \; p% r' b* Z k=inf;
6 _- ^: m+ ~3 H" @& u( m; Y4 r# t for i=1:row0 V7 f6 E- @, ^- ?6 |$ m
if (length(find(s_path==i))==0)&(k>distance(i))
$ u( O. X) L5 L k=distance(i);) H2 _+ l" S$ t. |
temp_2=i;1 _& D, y) [9 R" y% }
end
- g+ L4 K) G* s8 } p" D6 Q end
. O1 r% X5 e4 c3 x7 Y% C s_path=[s_path,temp_2];
" D, P8 u* {2 F# z temp=temp_2;' |5 b; w& B; D5 w3 x" i4 t. K6 g
end$ o% U; e$ X; u/ u; b) I' L
. T$ l8 H1 Y3 [1 e9 `%output the result( c: a( J5 ?( p8 j, c
path(1)=endpoint;* v- h ~% [+ s2 u
i=1;
* k7 R' Q, K/ K+ F9 L6 ]+ E {while path(i)~=start; o& [9 B* ~, W! B. a5 h8 k+ L! r+ b
path(i+1)=flag(path(i));, ~, z( q: ?1 f8 @ M( h9 h( ]
i=i+1;
% `% F! T" {! F8 nend7 X7 S# J/ a: o4 G' `& k/ e2 M
path(i)=start;
) L8 V, \" `3 a* n/ v3 K0 j' `path=path(end:-1:1); C: _" P' A3 D6 r5 J! Y
short_distance=distance(endpoint);
0 w2 X1 I' k" t6 j. z三 绘制差分方程的映射分叉图
1 h' ?1 h# j1 x# M# C) v- E9 l+ l; N$ {$ n& _4 j( H
function fork1(a);
& d# q% J: v0 o
0 @& W }/ b+ m. n% 绘制x_(n+1)=1-a*x^2_n映射的分叉图0 {( Y7 @9 p5 s) |" |$ r3 u
% Example:
. e# c" J! h/ i% fork1([0,2]); - H3 J& V' t9 u: y- r7 ?( v
N=300; % 取样点数 0 @, F, j, I& F+ X, n8 h: o! A: R1 a
A=linspace(a(1),a(2),N);
: D3 g8 N) P# m( I( h; g6 ?3 ]starx=0.9; - |! A0 u- g _! h4 R4 Z: J: `
Z=[];7 j& X' i+ l' z( s
h=waitbar(0,'please wait');m=1;1 ^4 b. O3 y3 r6 N
for ap=A;
8 U8 }# C ~* a x=starx;
9 q& g; o% W" F2 m/ Z7 [9 R! E: P for k=1:50;
" J; b) o+ R6 | x=1-ap*x^2; 5 h6 I8 \% h' {1 D+ {$ ]
end 4 m# s1 B3 F8 W& v2 I/ O2 S5 o' Q$ g
for k=1:201; 7 S8 v3 ^5 u& {$ N/ G% ~' H
x=1-ap*x^2; . c) @' G/ r& d/ \5 _
Z=[Z,ap-x*i]; 1 {1 Y- ~+ I6 M8 F% @1 s
end ( I( I, `, e+ x* L
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
# y: h$ D h `0 A( | m=m+1;2 s; C k6 [1 b/ M1 O/ B3 _( \
end
7 |" g( Q+ M2 T- e+ Vdelete(h);
7 y' I- C! j6 oplot(Z,'.','markersize',2) 9 L6 b1 u( D1 G/ Y5 |" |! U# N
xlim(a);# z2 G2 Z) H* Z [4 Y9 Q
0 f/ U. n6 O' J& D0 N! X四 最短路算法------floyd算法/ m9 e& h) O1 a, W. n: p6 E/ t
function ShortPath_floyd(w,start,terminal) 4 \' _9 a* @; Z& P+ Y8 i8 \
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;) K# Q( O9 G( k
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
, Z# x6 _! c0 |%start-----the start node;
' A5 O9 A$ {1 A%terminal--------the end node; + l3 c. f% S: d$ _
n=size(w,1);3 B2 N( D( j/ r
[D,path]=floyd1(w);%调用floyd算法程序/ j. u/ ?. p0 A2 ~6 M
% I# N, J* u& G" k4 L" K6 s% B
%找出任意两点之间的最短路径,并输出' o+ I' n( \1 u/ o
for i=1:n8 X. E; f5 @5 a
for j=1:n! J# J. u# b; M* b- Y" t6 h7 J. M
Min_path(i,j).distance=D(i,j);4 ~' _5 b- S! ?) @- S) _/ ?. ^& J% `
%将i到j的最短路程赋值 Min_path(i,j).distance: |' ~+ o" K$ ]1 J# W8 G$ z7 z& ^
%将i到j所经路径赋给Min_path(i,j).path" n$ V1 ^2 d2 c" N
Min_path(i,j).path(1)=i;& g, A! K0 b/ O/ x& H. K- n
k=1;
/ i2 G- [" c4 t# e* S while Min_path(i,j).path(k)~=j
3 a8 f/ V5 z2 Q9 n( k$ R' ~ k=k+1;
' h, g% v2 n* w! z Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);- H: Y1 j7 A( b8 E& h) f
end
, f8 t0 B } j3 e& d! r end
+ w2 k& B6 \' Dend
. |' m6 }) P- \& u* N _s=sprintf('任意两点之间的最短路径如下:');
, ?* g1 G1 V" u! l6 udisp(s);
8 u9 t6 P8 M4 ], ]" |! Ifor i=1:n' W3 i0 K0 q0 g/ N
for j=1:n0 Q( x6 v9 J( p L$ ]
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
" ?! Y* W- g) N ,i,j,Min_path(i,j).distance);- F* h- p5 K3 m, s! A
disp(s);
; k% r1 [ E; H disp(Min_path(i,j).path);
$ }7 Y! K( k. Y$ K7 u8 y# W3 j( \* z end+ b, |7 x# B: S' L( Z7 y
end
7 Q& H5 @ y* ~- o3 Z& ~
* @2 B5 |/ X: E) Q1 n# z- \1 }%找出在指定从start点到terminal点的最短路径,并输出
7 v- V' a5 O, q( q) `str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...7 T* Y1 Z8 R4 L: J
start,terminal,Min_path(start,terminal).distance);
. B0 ~7 Z0 g; `1 k1 s6 Mdisp(str1);$ }# f. W+ w2 e* R9 @' f2 C
disp(Min_path(start,terminal).path);4 Y# e* O a/ N1 x% D
- E5 h0 c2 {8 s" Z. e( {# T- d
%Foldy's Algorithm 算法程序
4 v& Y2 {7 I) c6 f* \! N* c f5 [( X1 ?function [D,path]=floyd1(a)
5 `; V E0 W' A& F" F0 F% Un=size(a,1);! R0 b9 I. t4 o9 C. u8 y
D=a;path=zeros(n,n);%设置D和path的初值1 i- _' @: l# A* [) J v+ k& ^
for i=1:n
8 j# q, {' G$ g/ {* [% q& A% ? for j=1:n: J. [8 W4 y z
if D(i,j)~=inf
1 k @4 Q6 ` l. k# s X path(i,j)=j;%j是i的后点
5 h: |2 A) R6 b& R( b) \2 s end( l5 q6 o5 y% `( |. Q9 w
end$ D& ]4 A" q) G% ]0 |' u: r0 D
end
- g( B4 o9 y3 v! E%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
& L3 I. |- E% O8 ]( u- G, a& _for k=1:n5 \, A8 e1 h1 W5 d* O+ u% f. c
for i=1:n
8 M6 u7 x0 F& {. ` O for j=1:n
& Z- L! t# i9 h. B if D(i,k)+D(k,j)<D(i,j)
/ o; r; f5 |# e! c% | D(i,j)=D(i,k)+D(k,j);%修改长度
' ~7 p: U/ }' _# `3 r path(i,j)=path(i,k);%修改路径2 R( h! Y* E: M% A$ Z+ ~
end
+ R1 N% w5 @ J7 |" b i* Z end
; u7 \/ P6 m/ c2 J3 U end
: K4 x$ b5 S6 Z, o) c W7 Tend; \' R2 r1 v. ~, T3 g8 ^
! P6 x/ i' y! V0 E% R# p五 模拟退火算法源程序
8 S m* E4 f0 Z1 M8 k- A3 \: ~function [MinD,BestPath]=MainAneal(CityPosition,pn) x! ^. ^7 E9 ?/ W
function [MinD,BestPath]=MainAneal2(CityPosition,pn)
( W4 ]' ^/ ~7 P6 W3 R%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) [4 b; s9 v6 E( Z1 b
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
- ~( o! E( E) P/ H7 o+ a% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...- h* V+ d; |5 a7 d9 B1 F
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...9 ?9 m9 w2 P- ?" A
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
" r& z& k4 [# A2 f- y$ e% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];! c5 x( e4 v9 L) @6 z% L
9 O$ P* s$ E4 X+ {2 D
%T0=clock
( m% B# H. }1 m0 p* p* [5 o$ f% p6 ?global path p2 D;
. q w$ F1 Q# Y: F% Y[m,n]=size(CityPosition);
( Z7 j/ [. K. i4 [3 l%生成初始解空间,这样可以比逐步分配空间运行快一些
5 N, S" S% _: Y9 O+ rTracePath=zeros(1e3,m);
' l3 P1 U+ F0 W/ ?; jDistance=inf*zeros(1,1e3);
" G1 b8 l% o1 r7 I V" O' f \/ h3 P5 i/ D
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
+ z- O' q$ W" b! @$ t0 ` (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );2 L+ [' ^2 v1 k$ d6 \1 o: J
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
8 F# r. Z( D @+ o: s. Jfor i=1:pn$ l x8 r* c+ ~+ d. k" w. {
path(i,:)=randperm(m);%构造一个初始可行解
r5 T4 D R3 N- ] l2 v8 Z# ~end
4 |% `0 I7 g- A6 K! g4 f. U; v2 lt=zeros(1,pn);: D) _( H! c( A& v
p2=zeros(1,m);: U6 O" b4 K+ W1 v
4 M- f7 z+ X2 R) o
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
0 [! z. {8 t# {$ hm_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=' ) ;* r2 ^- R9 @' G6 t& S% ^4 y" x# ]4 Y
%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( e: ]/ N. w6 t9 @
%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
R& c, G+ N* m- O%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
7 I( P# m, j3 J& b' }%会收到到比较好的效果. ]9 ]/ z( E A1 }, [+ m& S
8 X8 U5 j# w! O) |. k
T=1e5;
+ Y' e- K0 U8 T$ MN=1;
+ q) J D' q: ?3 a9 \8 h+ Gtau=1e-5;%input('请输入最低温度tau=' );
1 w5 h! C/ p" R: {1 F j" y%nn=ceil(log10(tau/T)/log10(0.9));8 ? a# n+ n+ y" P) }0 J
while T>=tau%&m_num<m_max
4 y) T/ R- u' N- T& r4 _ iter_num=1;%某固定温度下迭代计数器6 j Y& Q7 t: W/ T% h4 ?: r3 l& J
m_num=1;%某固定温度下目标函数值连续未改进次数计算器. H8 B8 W: j* @" ?
%iter_max=100;
2 q0 G0 u6 a; m: y# `: c/ a0 h% i7 ` %m_max=10;%ceil(10+0.5*nn-0.3*N);
4 Z, h* [* ^; D+ T; Q7 M, K- G while m_num<m_max&iter_num<iter_max
, Q8 T( ^$ L% ]7 X %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
$ w, A6 c' r# N3 ` %用任意启发式算法在path的领域N(path)中找出新的更优解
4 x; {' _) ~: S for i=1:pn6 o0 ~; H1 F0 F% l; R' ^, c
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
0 e y8 I0 S- g, a' s0 o- _%计算一次行遍所有城市的总路程 9 H9 B2 E& e* I; \
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线4 t6 g" e* v4 _
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);6 m# s) p2 x+ o* W1 j
end
; ]: D' Y9 r' Q% L, u %Len1
8 ~7 }! | Z" P6 N6 Z( _ %Len2
4 H; e- O' u! B %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand" z7 L3 F9 Z8 U' E4 J
R=rand(1,pn);
3 \; D6 Z& K+ E$ k) l. M4 ` %Len2-Len1<t|exp((Len1-Len2)/(T))>R
* _% k6 V7 B$ w" V* j& q if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
7 ~+ Q9 E5 u& J T. m$ Q, _ path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
4 v& q0 V( D1 M$ l- E Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
3 ^& w- C6 v& g; C& H* p2 F [TempMinD,TempIndex]=min(Len1);
$ i5 s3 U: `$ ?+ Y( v %TempMinD
0 [$ Y8 ~* B# q( C$ r! ?( x TracePath(N,: )=path(TempIndex,: );
7 n- m. Q) X7 N+ t* H& R Distance(N,: )=TempMinD;" `6 A& K, v7 P# S. M
N=N+1;( T: w2 }# }7 J! P: E% T
%T=T*0.9
8 a; ^9 m' h6 s* h, u m_num=0;
/ ~8 [" l! k# ~6 e S; \$ C% w( y else
$ b _! Q2 I7 d* P0 A m_num=m_num+1;
( s( ]1 o, T" X+ U& z end" Z% ]' s% C5 Y5 P
iter_num=iter_num+1;& n. S Q- F6 Y
end
& {) X0 \8 O0 k5 I {* s6 l/ @ T=T*0.9$ O0 e* |3 S4 `& J& ~
%m_num,iter_num,N
( z, O2 x O/ K: X; kend " I2 g% ?1 J3 p
[MinD,Index]=min(Distance);
1 [) w5 L; y* p: z" o/ wBestPath=TracePath(Index,: );
" d( |2 B: C" Q6 O- ]; ydisp(MinD)
: H4 H0 v# n8 b# {# w%T1=clock$ k( j$ ~2 p% Y2 H' f
' ]% o) V1 i9 |% S/ V; z/ | # r% A$ ^ C+ g; ~' n9 y
%更新路线子程序 A; W- W1 Y9 X
function [p2]=ChangePath2(p1,CityNum)
4 U2 d0 r# r0 d) p. {( Vglobal p2;
" u: i+ N3 n& \ f: g Jwhile(1)
( j+ B, n5 j/ ]' H, O& ^; ^" y R=unidrnd(CityNum,1,2);
0 E5 Q6 O0 Z y) G if abs(R(1)-R(2))>1
' E7 w( u0 L4 w5 r5 o break;
( N2 `& h+ U6 C- k end$ B, P! |3 t+ e% m9 V. s# Y, c2 `7 ^
end- ]$ O6 e3 ]+ Z0 M
R=unidrnd(CityNum,1,2);; M, n" i. S/ N
I=R(1);J=R(2);, Y I8 |* a- j& H* l+ A, ?
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));5 Q( \! x D7 x. J
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));, `, {; M$ S0 E5 D) D7 F
if I<J
5 h, O( D/ r" ?1 n p2(1:I)=p1(1:I);
; g& p8 [2 ] }& a8 z p2(I+1:J)=p1(J:-1:I+1);' b" R/ Y6 T' W) b* N' b
p2(J+1:CityNum)=p1(J+1:CityNum);7 M4 y; ^+ a, g0 }" o8 _, X; I
else, i8 w5 ^+ }7 Z
p2(1:J)=p1(1:J);" j4 x3 i* F& R$ e/ p: v
p2(J+1:I)=p1(I:-1:J+1);
0 I; L0 ^' i) N5 ~- l; L p2(I+1:CityNum)=p1(I+1:CityNum); r$ E8 y( J1 M/ Y$ z% f
end& _2 w7 b8 U& Q2 t
" p; y$ Z& t Q! S8 o六 遗传 算 法程序:: l$ H0 Z! H3 l) M1 z
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!* P H5 g9 h4 n" }0 I' E
4 l0 q: N% {; \$ k7 r6 H3 d
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options), _( e& n% p x! \9 i# W& B2 F
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) 2 T1 I' W7 @' t3 k2 C
% Finds a maximum of a function of several variables.
" b% r2 w+ z" v. l* [% fmaxga solves problems of the form:
) k8 [ \ i& k# \. o% max F(X) subject to: LB <= X <= UB
& L4 _3 ~/ ]: [2 w+ S% BestPop - 最优的群体即为最优的染色体群' K) } `) y6 {& ?3 K' c
% Trace - 最佳染色体所对应的目标函数值 o4 M0 x2 W5 d9 d4 H" h8 T
% FUN - 目标函数
+ E f4 f/ P& h( I2 E8 n% LB - 自变量下限
5 Q0 `# l; d# ^% UB - 自变量上限 ]: M1 S5 D1 B9 V( k2 s7 c0 q e
% eranum - 种群的代数,取100--1000(默认200)' e9 O3 _7 {+ l L
% popsize - 每一代种群的规模;此可取50--200(默认100)4 s4 s4 o8 @: Q8 w2 | `- G- n6 F
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)) u) Z! ~: F# T$ e; Z# h9 K2 z& F1 B
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)+ N; U) g4 x4 H1 \6 G2 H
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
& {! A1 D$ q% z& ?; S5 y% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编+ ]: \# @& H3 @$ T9 j
%码,option(2)设定求解精度(默认1e-4)0 b7 L; f% @* Y
%) M( Y$ Y: u% ?7 l0 x+ ^' e' @ F
% ------------------------------------------------------------------------
/ r! f5 e5 n* K# K" F% Z6 `' [ W" o( S
T1=clock;
z$ ~" S' r, R( Z) M$ {if nargin<3, error('FMAXGA requires at least three input arguments'); end
" q X% x: e/ ^if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
3 E M, f1 v: t% ^ Q7 L; c- z- V) j6 Rif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
7 V* G1 r1 w0 ~if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end. o! B" f4 j) q u
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end4 V6 P: p$ Z+ b, {
if nargin==7, pInversion=0.15;options=[0 1e-4];end4 \6 P) y' }9 s+ t; ~* \! W
if find((LB-UB)>0)
' s+ V7 e; A2 ~8 V! r error('数据输入错误,请重新输入(LB<UB):');$ _0 P e; p- {( F; k/ H
end7 w. ]" c; B+ G) B. j* e/ r( F
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
$ w' m: }2 q( sdisp(s);* Y$ S! V3 f& Y: l5 g
0 s6 m4 B, V. i6 ?$ M5 v
global m n NewPop children1 children2 VarNum; z6 C8 s% q3 R
. B3 k3 u7 P3 j# \, _bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);: b1 h2 X( Y0 }4 _
precision=options(2);%由求解精度确定二进制编码长度
2 n& p! a0 Y1 Y) zbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
- r3 c3 O# o* I9 B; _[Pop]=InitPopGray(popsize,bits);%初始化种群
- q( d7 v8 q5 v0 K1 {[m,n]=size(Pop);
6 W3 ]6 U1 t; z8 {! wNewPop=zeros(m,n);
4 B) z% d( e( A1 L1 l2 jchildren1=zeros(1,n);* r3 E$ X. |$ j5 f
children2=zeros(1,n);/ J' f: w6 y) B
pm0=pMutation;
; p- S* l$ T* J- K/ m7 `) u) V! PBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
# s7 @5 a5 g6 cTrace=zeros(eranum,length(bits)+1);4 u' I' Z4 ^- U' R" B4 O
i=1;/ h; P# z. A# k8 ?9 |, X# y+ D) X% ]$ f
while i<=eranum
0 q8 f$ J r$ }& g* p" | for j=1:m
+ a6 X# I" z# m3 m" a/ u% i% n7 @7 V value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度) j! d- k: \/ }8 y' m6 i: g
end
* F/ R4 @" m- {7 P [MaxValue,Index]=max(value);
# D" w! Z0 v& M5 B) m6 f/ z/ C BestPop(i,:)=Pop(Index,:);
! V6 u# j6 I9 `+ d0 G# E1 O Trace(i,1)=MaxValue;) O" |0 S7 ?) B, F; U7 }. y8 @
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
/ G \3 ~( b% }+ F7 { @& D0 m [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择. j l4 A1 X0 i0 l
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
- M% ?5 k7 l; B: `% _%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率: u8 i4 m6 ]6 m# z3 u/ x
%round(unidrnd(eranum-i)/eranum)5 x+ H |: ^/ b$ |) Z- t: a& b
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
" I, [/ |3 P0 X% K- n& c [InversionPop]=Inversion(MutationPop,pInversion);%倒位; ~7 \7 f- _8 z1 `
Pop=InversionPop;%更新
* u% g7 m$ J2 U% d; M4 upMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); ) _, i, J) V& B# m. k2 t
%随着种群向前进化,逐步增大变异率至1/2交叉率7 f2 U, Q1 p9 {7 X2 S' p$ k7 a0 K
p(i)=pMutation;. N0 V" [& z; ?) l" d- v
i=i+1;
9 w2 ?+ N, N% n ?- Z$ Cend/ f0 l5 K1 K l2 g
t=1:eranum;
8 U) |2 W) B+ Uplot(t,Trace(:,1)');: D6 q1 o8 X3 S: ^; Z; 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)');
0 N9 a! I8 I- n# v[MaxFval,I]=max(Trace(:,1));2 S# H3 {. r9 j
X=Trace(I,(2:length(bits)+1));8 n& A8 ~, }* X6 F1 m
hold on; plot(I,MaxFval,'*');% X- g1 z- L# o
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);0 Y8 z' Q6 o8 C" {4 h
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,:)));
7 k) x( X5 J0 r, d0 | d: e. k7 ^disp(str1);' U$ c1 C% |& V; ?, K
%figure(2);plot(t,p);%绘制变异值增大过程- p& j8 T8 M5 x& o7 g/ f/ }9 n1 T
T2=clock;/ Z& T4 O9 [3 p
elapsed_time=T2-T1;
) O# [* D7 P( a) Z6 R) c) [if elapsed_time(6)<0' }. \- P2 k" F" B8 d
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
9 U8 i* z x, w! G/ A. r1 f) v* ^9 Yend
6 x( o0 |' l6 T4 d* [( Oif elapsed_time(5)<0
# l% [3 {6 b. L; \ elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
6 f5 h, \9 _, q- `: X4 V: Z1 dend %像这种程序当然不考虑运行上小时啦" t6 K: K' w2 ], p" k# S' S
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));* w1 j/ y' |+ K, Y B- M- I
disp(str2);* g; f3 H4 j9 A% C: o2 k
* d* Y/ c( {. l7 ^, s/ t# C
* R+ h! y, ?" T, s2 z/ ^) \3 h# w
%初始化种群
u8 a- o2 e P%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
% S' {- {7 E; r9 _' c- Ffunction [initpop]=InitPopGray(popsize,bits)
8 f( n2 {# z- n2 f% X4 [, rlen=sum(bits);
: {$ [0 {' ]( T: ?' I8 R/ cinitpop=zeros(popsize,len);%The whole zero encoding individual4 i1 d+ n1 I; r+ Q$ M3 f
for i=2:popsize-1
6 c1 s0 j7 u" Q' H pop=round(rand(1,len));( Z. E7 {- u9 Q% w0 G. e9 E8 u3 k3 j6 V
pop=mod(([0 pop]+[pop 0]),2);# x* b8 |+ I) G& I! a
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)( D* G( l6 O+ h5 A, M! [
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)& c" y) q6 n n( j# r. F
initpop(i,:)=pop(1:end-1);) ?( Z, a$ {+ w
end
! B: I* b: p$ q' b- F! Vinitpop(popsize,:)=ones(1,len);%The whole one encoding individual/ N" V* x4 l% ?$ P2 s7 u
%解码
+ F* L% {6 `5 I i
/ J; }2 E) u$ X4 u _function [fval] = b2f(bval,bounds,bits)
4 A2 x1 Z" t2 y6 l% fval - 表征各变量的十进制数
- e, N% B; E4 z) r. S% bval - 表征各变量的二进制编码串
9 f% m0 l1 q# l' z2 |% bounds - 各变量的取值范围; _- g$ U* A' o4 ?; L2 r/ `
% bits - 各变量的二进制编码长度% ^! i. p- d5 G) t
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables6 O( \- X1 u1 V1 k5 z5 y9 ~$ E6 ~
numV=size(bounds,1); U ^8 K$ S+ v; c# i, s k
cs=[0 cumsum(bits)]; " d. k. v; n x
for i=1:numV
8 \4 m* [8 q t4 Y/ `- l. o" d a=bval((cs(i)+1):cs(i+1));
2 f7 k6 x$ f8 P/ ` fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
1 U! ?. N' P& J* U4 K0 tend1 x5 `- G7 i0 R* X( d' V* j- v6 z
%选择操作- v4 Y# _! X8 u/ f- p! A! B9 Y' m
%采用基于轮盘赌法的非线性排名选择1 t5 z* O; ~, K2 ]( u! \
%各个体成员按适应值从大到小分配选择概率:
' S' y3 P+ U2 p9 |/ z6 J0 [# g%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1* D$ S2 o% g; F/ w% ^8 m" v& }
+ C2 h) X0 C9 @5 Q1 ^7 E- d. t
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
+ b1 G/ s6 ~- S. mglobal m n! Z P! H4 D* V7 f3 b5 s2 r S6 B
selectpop=zeros(m,n);% p% V, R0 T* _4 U: l) R
fit=zeros(m,1);" [. ~& P# z+ t! |! \. p& X' f
for i=1:m3 x: {8 h+ W4 `# }
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据7 Y5 |/ G; e; }% o! N1 `
end- Y5 T* i3 u% ~1 u/ ?
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
* O- d. u; E+ `( ^, ]2 C- Kq=max(selectprob);%选择最优的概率
) e9 i5 Z0 @) b- {6 P% px=zeros(m,2);6 _% s7 B7 J' l; b
x(:,1)=[m:-1:1]';
4 V& T" t) h( ^% ^7 n[y x(:,2)]=sort(selectprob);
5 q. \* e2 A8 D. W# _r=q/(1-(1-q)^m);%标准分布基值
6 |8 B- E3 g7 ?1 |" l# ~6 ~newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率9 Y& O1 p5 g3 o% a. r
newfit=cumsum(newfit);%计算各选择概率之和; s& M2 T3 [3 M: O5 d/ o9 v
rNums=sort(rand(m,1));
+ k+ I3 m6 K9 [9 y7 kfitIn=1;newIn=1;. u0 ?2 M9 c) l( D* q0 }3 Z
while newIn<=m& d. T/ n' L b# T5 E- O; g, X/ H* u6 |
if rNums(newIn)<newfit(fitIn)( w/ u8 D/ I7 @; a' ~; b2 k
selectpop(newIn,:)=pop(fitIn,:);
( g. F2 Z' O, q8 U! R* s5 z' ]% s newIn=newIn+1;
' F7 @2 u8 A7 o) ?9 s9 n# } else8 o2 i0 U3 K$ A0 L
fitIn=fitIn+1;& D# v. ]( A! m: b* _6 R$ b. h
end
3 P: ~" c( e& u& r% {2 W" yend0 m7 x3 e, |0 m) D% A
%交叉操作
" n4 u8 t# s; }1 ]function [NewPop]=CrossOver(OldPop,pCross,opts)3 z( w) e I1 E8 _
%OldPop为父代种群,pcross为交叉概率/ U. r6 o4 r# \1 k6 P0 m' n: X
global m n NewPop
4 }8 T& J* y/ H" M* k# @r=rand(1,m);
7 f* L; o7 }& ny1=find(r<pCross);
. C2 R0 X& F; i0 `( x: }# ~y2=find(r>=pCross);
1 d, k0 e2 _# ]8 ~* y) clen=length(y1);1 I0 K! _7 ]( i4 j: Z2 x
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
% G8 Z: n8 S+ e7 X& G y2(length(y2)+1)=y1(len);& ?6 X. S8 |/ m, C
y1(len)=[];
) T/ {) x9 v$ Q) Dend
& B8 ]3 Q5 [; S0 `if length(y1)>=2% N5 h; C0 {9 i0 P6 j$ u
for i=0:2:length(y1)-2
' `0 `2 T) y0 Z if opts==0
8 Z- f& W. K) R& |7 D A4 u [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));8 Q1 t" M* Y' t E
else! ~4 h2 F# H( Y4 _% ]- D
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
# a) p9 f8 O% O O ~! x end5 ^# ]+ }" T/ Q, [4 u
end
: t) B2 u6 x% a( p2 E8 Vend
% r/ u+ V9 g- g) \. [NewPop(y2,:)=OldPop(y2,:);9 |# [) K) \7 `- C% o- _" j. `
8 l9 v! @4 n# }4 u6 h3 u%采用均匀交叉 ( H& Z8 I$ _, |" w9 Q2 C9 E. p. O( H
function [children1,children2]=EqualCrossOver(parent1,parent2)
% k' j2 D# q( f2 D1 v/ c+ H1 o4 v4 |; j" x* i, r) Q
global n children1 children2
: N. S' `( K- t5 ]8 phidecode=round(rand(1,n));%随机生成掩码% C! e7 {4 ]9 v7 _/ K( Q: _- f
crossposition=find(hidecode==1);( k# v( s! V/ C i) E; k
holdposition=find(hidecode==0);9 |) c8 I+ r' R5 f: J
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因1 w# H: m7 D1 P: m$ b! H$ h- l, y4 g
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因5 ~, G3 f: y' W" f
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
! R. q) b! A6 y& C' L# W* Q# I1 Hchildren2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因7 c' o2 K8 t% ~1 \
$ c4 v6 e' h7 m/ Z) u%采用多点交叉,交叉点数由变量数决定6 E8 f. n7 {% s! s. |' p
/ E0 H6 d- f9 T8 N, o0 o# S# l
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)
5 J$ i3 u. {; n+ ?% g$ K
2 I9 R! S8 ]+ Sglobal n Children1 Children2 VarNum
: T" _& o8 r! L3 x" S |Children1=Parent1;0 C3 ^9 ^* K2 Y7 H" H
Children2=Parent2;
# n2 Q$ S# b; t+ OPoints=sort(unidrnd(n,1,2*VarNum));
" p- i6 G' `# h: h, F- Jfor i=1:VarNum
! x$ ^% @( C# O* z' ~& [& ~ Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));8 W0 ?! l4 Q5 D; F: s1 y/ u: T
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
7 d* Y5 G3 |% a' J. a3 t3 Vend
" j/ l# Q! }7 U% x R1 F6 \" C( s. S+ R4 z0 P1 u+ q! s% m
%变异操作( u/ S7 C; q% G' \
function [NewPop]=Mutation(OldPop,pMutation,VarNum)
4 v) |4 `5 _, x* Q& B' u) ]9 A, S* ~
- J, j- t2 z- n4 n* l0 ?8 D* {" Fglobal m n NewPop( j& t; H. I9 C
r=rand(1,m);
1 W6 U* R0 T9 _$ ]3 B9 {6 Z7 rposition=find(r<=pMutation);
8 G2 Y4 X3 d4 n% ]# N; Dlen=length(position);0 {# d0 R' a$ @8 v
if len>=1, h0 |4 u0 U Z$ ?# k' x3 R" S
for i=1:len
9 R% e+ R' @* T( t Q' h. U5 Z8 d k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
+ C( m& R1 R) j z% I* o for j=1:length(k)6 F6 g3 w& {! u
if OldPop(position(i),k(j))==1 \3 @' x2 r; ^
OldPop(position(i),k(j))=0;
" \3 P0 [- J, b else
2 r- F" j" A6 o( b' f/ M OldPop(position(i),k(j))=1;- E4 j- a5 i% i
end; u: T3 p, d" R$ A* q( h$ `
end
/ N7 m! b% x' u6 [& y% b end+ m" \. l! |+ A7 S' T- ^
end8 c& b+ A5 Z, e4 @
NewPop=OldPop;
+ I- |0 m! J' s$ Q
- ?# W4 x( e% X$ o: |%倒位操作$ y& Q. V) V' u: y f7 x5 R% h
6 H( u1 t4 D# t2 j% X! cfunction [NewPop]=Inversion(OldPop,pInversion)! f2 {5 i. i( Y+ Z4 S6 D' w
2 B$ Z& F. y$ ?$ r
global m n NewPop
( e5 R& `! Q- WNewPop=OldPop;
8 ^( v/ V$ R6 {6 Q: Z% r$ u% Or=rand(1,m);
% Z! Q. v6 Z/ W+ D% [% m$ ^- KPopIn=find(r<=pInversion);1 }1 Z4 m7 A1 d( M$ w
len=length(PopIn);. r; p6 ?/ P; i: b8 l
if len>=1: ]( ?5 L( V$ `) I
for i=1:len
! k/ G9 b/ c) a d=sort(unidrnd(n,1,2));0 d8 v+ _$ Q8 v0 b
if d(1)~=1&d(2)~=n, f5 H- r Z4 ~* l/ f# _
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);/ G* S# \) |2 h
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));# \1 j+ V. M; W' A4 p# k
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);% ]3 v$ j$ `) h' N/ y
end
, w+ f( A4 u9 W. j) { end! S8 m' a5 i# E5 q( |) ?7 \9 ]( D! r- T
end: ]" {; M: h1 K6 Y: q, N q4 ~
& S* w4 @- V4 c+ u2 Z; V6 h
七 径向基神经网络训练程序
2 I9 F' F0 M5 w# r2 K" N
1 `. t& f" G( W% ^! e" yclear all;( k) M( R, c) I; d0 `, O9 _
clc;2 M" C/ w$ C' Q( o6 O4 J; ~0 m
%newrb 建立一个径向基函数神经网络: v0 E) ~! n1 P' d5 K
p=0:0.1:1; %输入矢量
" Y3 T3 V; e' e8 S! L/ {t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量2 w! z# |+ |' P+ ]0 k* ?
goal=0.01; %误差% p& { ?4 B3 ~, U) ?
sp=1; %扩展常数" f5 P7 L7 H# l5 a( ]
mn=100;%神经元的最多个数
; O2 p2 \- ^ A1 a( D5 u( Fdf=1; %训练过程的显示频率
- C4 r9 l N& J8 B+ O" T7 g# F[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络/ a9 L2 v. M2 I- K* H5 ^
% [net,tr]=train(net,p); %调用traingdm算法训练网络
" _7 n, V3 \4 u%对网络进行仿真,并绘制样本数据和网络输出图形* a. u* {: ]# B7 b7 v2 s3 A' ]
A=sim(net,p);' f) L% ?- Z9 E9 a3 t3 C% ` T
E=t-A;
0 k5 x& q7 t, e- H, q3 Z5 Gsse=sse(E);" E8 M8 `& Z Y2 m4 s
figure; ! R" c( {6 M% V+ k9 g! a' v. @ N
plot(p,t,'r-+',p,A,'b-*');6 [% O8 Z: P. m& @5 _. p4 d
legend('输入数据曲线','训练输出曲线');
: X" _3 A1 n, M! I/ f% _echo off
0 R4 [$ \' Y- f0 ]
; k; M( n/ l; ^: s/ c( a说明:newrb函数本来 在创建新的网络的时候就进行了训练!
\ q' K/ Y" `' \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,( \2 [- R8 G% }: L' Z2 G
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 e* [" M% @
6 A, X& U( o+ \
3 k1 C( y, B' |' V: F7 n训练结果显示:2 a: Z5 y- q7 u8 @+ P8 ^9 H$ B& p
NEWRB, neurons = 0, SSE = 5.09737 \8 l: V3 G. Z" L0 q
NEWRB, neurons = 2, SSE = 4.87139$ b: p$ s7 h3 g
NEWRB, neurons = 3, SSE = 3.61176& ?" k: l: t7 E# k5 w2 j0 B
NEWRB, neurons = 4, SSE = 3.4875
+ J" ?# P3 Z1 a3 o7 F! C( |4 JNEWRB, neurons = 5, SSE = 0.5342171 h. ?! p2 a8 x0 o
NEWRB, neurons = 6, SSE = 0.51785
) q2 `7 I- R1 CNEWRB, neurons = 7, SSE = 0.434259 h) ]6 `" p$ P, N' d' p+ I
NEWRB, neurons = 8, SSE = 0.3415180 o+ y7 e0 p4 l6 Z8 d G3 m7 ~
NEWRB, neurons = 9, SSE = 0.341519/ p, h' W% ~6 r# L& r. l
NEWRB, neurons = 10, SSE = 0.00257832
7 V! s. R, z2 U" g% k7 O( D/ ~- Y S4 _1 b( D
八 删除当前路径下所有的带后缀.asv的文件; v" k4 ?9 N* I+ s" \
说明:该程序具有很好的移植性,用户可以根据自己地
. F/ ~# C' q- `2 C, Z4 i9 d要求修改程序,删除不同后缀类型的文件!
8 m8 W4 b! [0 n- T+ t. p% Mfunction delete_asv(bpath)
/ I6 G. ?$ [+ c8 z6 B1 j# J; P2 ~%If bpath is not specified,it lists all the asv files in the current
" F `; w0 k* t2 a9 | Y- z" i9 D%directory and will delete all the file with asv # e5 w& k$ K# I) O0 i1 J8 h9 y6 {
% Example:" H. Z& m0 F7 k7 C) q
% delete_asv('*.asv') will delete the file with name *.asv;/ [: K! Z! k0 ?* L7 Z
% delete_asv will delete all the file with .asv.
# y1 P& w7 o' ^% y! v
& v$ N: t3 z9 `8 [/ }if nargin < 13 F6 M% l* c0 I0 B$ Y/ L, T: D. E
%list all the asv file in the current directory
5 o. ^2 }- E/ a0 Q# N) j! S files=dir('*.asv');! T0 k2 `4 T4 h
else, F0 u- M4 D1 Z* E
% find the exact file in the path of bpath+ C3 \( H% _8 m2 U8 N, ^
[pathstr,name] = fileparts(bpath);
) c& v9 u% N/ I3 T3 T* o: c if exist(bpath,'dir')9 e9 Y& a4 q2 x ]
name = [name '\*'];
" `" d; @( v2 R6 P0 M" K end* y) I H3 R9 w5 e: S( ]) s
ext = '.asv';
4 ?' H! J! n. V6 p1 D6 i files=dir(fullfile(pathstr,[name ext]));) x) ?5 z: y8 |' U% w
end' [) E! U+ ^6 N) ~, w" K
; M' M- ~' R* ~; r
if ~isempty(files)
) }. T- M& I0 _# o; r for i=1:size(files,1)1 u" Z' e. }! i9 a$ y, m
title=files(i).name;
2 f2 @2 e% z% N* Y! j delete(title);( G/ Y! u7 N/ i4 f6 A
end
$ ^3 F1 O! ^- Zend
/ K u6 w' w/ S" P! H2 L
7 n& O0 f# W5 O: C8 M" W% f2 A) ~$ j P( a1 M: s. V) x
同样也可以在Matlab的窗口设置中取消保存.asv文件!3 f4 U8 z9 z6 r* x4 j G
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