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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8 @) X# x: F) W) j' _7 }
1. predict_fun.m为主程序;
" W' X8 f2 O+ ?8 _6 T7 P! z8 m; n) P2. timeseries.m和 serie**pan.m为调用的子程序* m% L: G$ e7 Y+ E, `- E* j7 y
& t9 A+ ~+ k/ rfunction ima_pre=predict_fun(b,step)9 w1 ~/ m3 j/ k& i I% }
% main program invokes timeseries.m and serie**pan.m
9 y# R/ o, z# [. H. @ v% input parameters:
" R) i) l3 l: B; A% b-------the training data (vector);" U6 X& y. d2 L% p
% step----number of prediction data;
6 I+ c$ z" ~' D" e& N, ?3 }% output parameters:& U. U+ u" d& Q4 R' Q' ~1 y' c
% ima_pre---the prediction data(vector);
* ~7 G3 c: z2 A% d% }8 mold_b=b;
4 Y1 a y. H/ m, ?: Umean_b=sum(old_b)/length(old_b);# X! u" s& r" W# m% ~3 b
std_b=std(old_b);
% `5 g# z! r+ K6 d5 ~old_b=(old_b-mean_b)/std_b;
7 C2 G z# Y6 V6 D[f,x]=timeseries(old_b);7 z. A' ?* R5 O6 |4 C. X0 Q$ ?
old_f2=serie**pan(old_b,step);2 ^% Y3 O1 ]3 g8 Z
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;" M) Y I6 O; D
R=corrcoef(f); e- |* R8 Y7 E4 Z5 I6 S
[eigvector eigroot]=eig(R);+ M7 V! h! P' P4 q) Y, K
eigroot=diag(eigroot);
; x5 p" E! D3 L$ e# p# }+ ]6 A& qa=eigroot(end:-1:1);
! [! @9 v8 h$ I" k+ q8 g! dvector=eigvector(:,end:-1:1);
1 w% `' b( {8 w/ R' jDevote=a./sum(a);* y2 z7 s' s# V1 {- L# k
Devotem=cumsum(Devote);0 o% W v- \6 m$ C; a& l# y
m=find(Devotem>=0.995);/ g/ L3 l: D) [
m=m(1);* m! M3 G9 P. ^4 x+ D; }
V1=f*eigvector';
7 Q- x+ i5 r4 d z, V" v& gV=V1(:,1:m);
* ^1 S+ m1 r4 Q. k% old_b=old_b;
7 Y, g0 A) U' G9 z' l( w7 dold_fai=inv(V'*V)*V'*old_b;
5 \( x( H0 Q6 A6 y7 c6 |# i. Veigvector=eigvector(1:m,1:m);% m1 r% e$ ? s5 B9 w. [ _+ Y
fai=eigvector*old_fai;
; e; l* M6 S: _) W4 W) kf2=old_f2(:,1:m);
, D) a* t, b* ?predictvalue=f2*fai;% }1 S0 W6 g W$ k% z/ x
ima_pre=std_b*predictvalue+mean_b;( Q5 G) y7 c5 `; h$ K
m+ D# h) z0 E2 ?1 L1.子函数: timeseries.m a/ b8 P. @: G/ @
% timeseries program%( W; |- G0 j0 l# H t8 c
% this program is used to generate mean value matrix f;$ K( w" {( O$ p5 R. @5 I8 B8 {
function [f,x]=timeseries(data)
- z1 G& i, U3 d6 n) F* @- e( J% data--------the input sequence (vector);7 J( @3 z! t8 v7 L1 s1 Z
% f------mean value matrix f;
, N8 v b; ^4 }n=length(data);0 f. b' ~, [3 d* J- Q5 M7 B
for L=1:n/2
! w4 K+ |! ?1 L0 A" Q! H nL=floor(n/L);
$ a. b7 R* Q3 i for i=1:L4 B# Z( d5 }4 \; `# ]4 ?& N
sum=0;2 }" K P4 u5 S9 n
for j=1:nL# h; ]+ F2 {; t0 |$ A L
sum=sum+data(i+(j-1)*L);
@5 y) h& w! ]9 T% I0 t+ g2 ? end1 I4 b# V! V( I, [
x{L,i}=sum/nL;
9 M+ m- a5 p: C7 s1 c3 j( H& k end
) q' }! o$ X* {* o- @) e, Lend7 e0 R; P4 }% h* r; l
L=n/2;
8 r, O* \1 t* k2 d- tf=zeros(n,L);
; F( t; `! ?& ?9 V' b4 qfor i=1:L
3 i# L; ]) G3 i9 y- N rep=floor(n/i);
& V2 b1 ]) j0 e2 \ res=mod(n,i);
( i2 H% r# |$ `1 I& U% Q* i! s b=[x{i,1:i}];b=b';" x2 r. z9 Z+ j
f(1:rep*i,i)=repmat(b,rep,1);# I2 [7 v, ^/ a1 b/ r" W/ f" a5 G0 z
if res~=0
1 k" Q; d) \' ~% z c=rep*i+1:n;% n8 g, v+ G( N& O4 M
f(rep*i+1:end,i)=b(1:length(c));. D6 d2 \5 g) D- e5 e2 k7 r
end
4 h) Q2 t; o0 H* M" k/ G0 _1 l0 eend
8 B4 t8 {" ]) z
, W: A$ A6 B! B) n, i. I, `2 u% serie**pan.m/ X$ a( S! e$ H- \) k& h6 o) M5 ~$ \
% the program is used to generate the prediction matrix f; ! P' H( v& a( D# X; T6 H
function f=serie**pan(data,step);8 l& R! K8 g6 W& T; k# J8 ~ X
%data---- the input sequence (vector)
" ?( e8 ~9 J) k5 m# |% setp---- the prediction number;
8 Q! \4 ~: A7 Z& Hn=length(data);
+ R+ g" A) ^7 `; pfor L=1:n/2
" J i' d# Y$ S* |3 h4 X- |- p nL=floor(n/L);7 P0 x3 P: B$ n, t4 A4 x
for i=1:L
8 s# D4 \7 G) v9 O sum=0;
% J8 q/ ?% U8 A' Y+ G for j=1:nL0 w' r) H4 `/ ^! @7 s( ?, K8 L6 S
sum=sum+data(i+(j-1)*L);! w; ^$ f$ ]3 ^7 e k5 A% b
end$ ]$ s. i7 A9 k: i# t
x{L,i}=sum/nL;
6 G0 A; T" K2 f" W/ `8 z6 p end$ j* L+ c, N) S. ]( \+ b
end
. z* \0 @- M! _ Z1 D2 qL=n/2;$ i, z( t' p. H
f=zeros(n+step,L);. m7 I" }$ n0 `' [6 m
for i=1:L
4 A4 \9 |+ S, f rep=floor((n+step)/i);; J& {& U# |+ [
res=mod(n+step,i);8 n+ @. o( Y; M2 x% I, g
b=[x{i,1:i}];b=b';$ f/ H+ e1 ~# Y9 b3 @* J
f(1:rep*i,i)=repmat(b,rep,1);
, b8 S3 ~ T6 s) w( }: u4 | if res~=0* l( B1 ^1 L- \6 n1 x( V$ t I$ U
c=rep*i+1:n+step;
% q! z; n% u- f f(rep*i+1:end,i)=b(1:length(c));+ B( |, n a% t% H
end* z' X: L2 Q7 J" G D# t) h
end1 b E% d# G. q, x2 Q) T! a. P
0 N2 y4 D/ r9 F
二 最短路Dijkstra算法4 r7 O% X6 I$ Z) E, X6 y, [& X
% dijkstra algorithm code program%8 r5 u6 v# d3 O( o1 f
% the shortest path length algorithm
* X# x( l F* q) x: bfunction [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)5 x; z; o/ f/ l# t3 w& }
% Input parameters:7 Y2 l7 S0 Q, v- C9 }
% Input_weight-------the input node weight!1 L% q2 Y% P1 }
% start--------the start node number;5 y" J* e$ E8 h' e/ }0 G
% endpoint------the end node number;
3 V% m$ Z! h& \% Output parameters:
- ~# v% I# H! \0 Y+ g m; n' }% path-----the shortest lenght path from the start node to end node;9 d1 q# R: c6 \4 H {8 j! f
% short_distance------the distance of the shortest lenght path from the
6 P6 L( M) |9 A4 \2 v y9 f% start node to end node.
; F* T# @0 Z7 N. q5 p4 s[row,col]=size(Input_weight);% t) V- p' ?" {
, {( v& f1 u5 J! X1 i2 V! o. K
%input detection
& k; x' Y8 `+ M0 d& xif row~=col
3 A* l" U5 ^- U% {# C error('input matrix is not a square matrix,input error ' );6 `) I6 a0 B( [$ f' k* m. ? U# {* ]
end |; W) W+ d" L# |/ b
if endpoint>row. A7 r# b2 z( U; v
error('input parameter endpoint exceed the maximal point number');
5 L8 P, ] L6 M0 Pend' G- i3 Q! R, _2 ? q
$ |, e8 N7 N1 I6 V%initialization0 P& I$ A8 H, F5 ^9 y
s_path=[start];9 O: r3 @& X% C' W) ^8 ?2 F
distance=inf*ones(1,row);distance(start)=0;6 d* [2 U" ]" z
flag(start)=start;temp=start;7 P/ `' F! p3 b( n P$ O8 @
& V" r" U: M% X X4 a1 _+ }while length(s_path)<row& J. n/ K6 c& R2 @. A1 g
pos=find(Input_weight(temp, : )~=inf);( }2 f$ H3 b9 e( z# ~7 w0 o
for i=1:length(pos)6 ]2 N% B e1 n9 Q1 Z
if (length(find(s_path==pos(i)))==0)&! b! j0 i+ W6 ~; L4 ~
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))+ @" o6 w! O8 s* @
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));5 k% j, F- Q, a9 l( M
flag(pos(i))=temp;
' l9 h7 K1 _! s4 B end- Y8 Q9 u1 v7 U8 j
end
! P, n8 d6 d+ Q6 e$ p2 N, x k=inf;6 W) h% R, p' e: P9 r; u
for i=1:row
, U4 F3 c! k5 q- t if (length(find(s_path==i))==0)&(k>distance(i))
Z) F! d2 Z% @ k=distance(i);
' }5 ]/ I& n- @) M temp_2=i;! }9 V; F* y, M0 d1 k; w% V' Z3 S" N0 x
end
3 l! l$ | M- X4 P! ? end& j! L% O" x, n. c$ S
s_path=[s_path,temp_2];
- Q+ T8 M4 g3 r temp=temp_2;
. z* T; Q9 r" aend
6 T& {" _& `7 _, H( z) D8 c7 x3 \/ }: {/ C
%output the result
9 W: {# A5 m( O: J. a2 ^path(1)=endpoint;0 x" N" {; V% J0 z
i=1;, ], C) g9 b- X( I' C( k( \2 t
while path(i)~=start& f8 F1 k5 K9 w: o e, L
path(i+1)=flag(path(i));0 H* U9 V+ |- I! q6 z3 J' M
i=i+1;
, l' ]0 ?1 i/ [0 n4 rend4 K* H7 f7 r! V/ J6 J- d( R. e
path(i)=start;$ k1 P" D- p) H! J. S
path=path(end:-1:1);; k P% Y# k" C
short_distance=distance(endpoint);
' o0 @/ M" z. k, }" ~5 ~2 N7 j2 p' o9 ^三 绘制差分方程的映射分叉图
& ]$ ^9 Y% ` Z
' o w6 P/ p/ A! q9 r- z+ {function fork1(a);
" [5 r4 C; t: B- p0 s/ _3 X& Q- T3 P. `3 S( e: k
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
Z( t6 n9 a$ R% Example:
! k6 ^/ k# \& L% fork1([0,2]);
- a8 E+ c( e" h' l3 P# E: AN=300; % 取样点数 1 Y. m/ v5 D5 z- m+ M9 ~4 i2 B
A=linspace(a(1),a(2),N); 4 b4 C2 T A8 z! I5 o8 i3 d
starx=0.9; 9 [. o$ C8 W2 ~
Z=[]; C4 i1 L5 U0 n+ c7 G' H0 Q+ \
h=waitbar(0,'please wait');m=1;* a; I: P6 a9 s4 M) h5 G
for ap=A; " l- o7 M5 o( U, w$ }
x=starx;
( o; m8 ^5 D, J" g o7 p# @( p for k=1:50;
" C" i8 s7 a; L' b/ ^% k x=1-ap*x^2; 4 c4 s9 ]9 u3 W0 r n) P8 l
end
4 d! J/ d+ q9 ~) n for k=1:201;
5 _' Z$ m |% S5 c8 U! b x=1-ap*x^2; ! p7 A) q7 w1 M" ]- ]' E0 K
Z=[Z,ap-x*i];
o1 ~; v+ s* L% L end
% d6 U# Q$ Q$ f6 ?& W* ^6 s0 m& M) y waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);1 _) Z+ c6 ~) T' j' d( G/ W$ H
m=m+1;, {( w/ a4 K" e6 G% ^. U
end : E3 }% |1 i- K" x& i$ |3 p
delete(h);6 a P# V0 C* _. p& L
plot(Z,'.','markersize',2) ) \8 r2 q$ S- Y8 J. e- ?
xlim(a);2 u/ h; w% g5 T3 `
, k- p e0 A/ ]5 M! ]
四 最短路算法------floyd算法2 E; ^: g4 F- V& u
function ShortPath_floyd(w,start,terminal) ) b# N; G: ~* z. I8 g
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;3 o$ `" W7 M. B+ B* G5 G
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];8 H( L2 m7 K3 s C, B( x4 g* Q
%start-----the start node;
# a7 D; e! i' ^/ r0 w- _%terminal--------the end node;
6 o. ~- J3 j2 _6 Q' L$ e; ]n=size(w,1);
0 q/ d0 c* g1 L7 o1 D[D,path]=floyd1(w);%调用floyd算法程序' t) ?" O7 y3 Q, B& g- k; M Z1 J
* i G8 Q1 o' T5 v) d: |" F; f& Y# R%找出任意两点之间的最短路径,并输出
+ D' b. \6 V" }3 ~8 ~for i=1:n8 ^) W2 ~* f6 M; o9 J5 q+ O1 @* ~. M! o
for j=1:n6 o# Z4 J3 i7 i, o
Min_path(i,j).distance=D(i,j);
) I/ c6 y- [6 _: o %将i到j的最短路程赋值 Min_path(i,j).distance: c/ _7 |; R7 R7 s$ M/ q
%将i到j所经路径赋给Min_path(i,j).path) K( |- X( e% |: E8 t; X6 B+ r4 k
Min_path(i,j).path(1)=i;
$ z C/ P& P( J' a k=1;
' I% X! Z" O1 S while Min_path(i,j).path(k)~=j9 R# V9 L, ~' f5 o$ I; `6 D7 ]
k=k+1;
$ g O V3 f& t) y Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);" O( N( B/ Z0 @$ p7 `
end+ E& c, ^3 s9 {' y2 G4 d, _
end2 N- g E* R& o q& h9 \, s. X
end
2 \3 F6 @* q8 R2 i! u/ o5 Es=sprintf('任意两点之间的最短路径如下:');9 k' j, a$ t4 R, j
disp(s);6 W2 g8 `, X+ E* \0 b0 a( _2 }
for i=1:n
) h* v7 q1 T: Z$ c7 {0 c for j=1:n
9 G1 C7 s) ?# {/ c: @ s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
& w6 N9 Y9 U3 Y0 f5 d$ ?& P5 d ,i,j,Min_path(i,j).distance);
4 m5 |2 b$ v) C- ]& B disp(s);8 k: Q) W& @5 k1 W9 a2 a! Q5 c
disp(Min_path(i,j).path);2 H. @$ @4 c# m+ U% C- b
end; F0 @/ @6 W: C& Q9 c% a2 G
end
. D& r( z1 Q) {. W$ [$ e6 u* _! v( m0 q, l
%找出在指定从start点到terminal点的最短路径,并输出
8 h4 |; U5 k2 t" {( e2 istr1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
6 d# ?0 n' u2 k' K: F start,terminal,Min_path(start,terminal).distance);
+ c+ g$ C- e' B4 M1 C9 Jdisp(str1);6 V$ ~5 K& }" q+ C$ U
disp(Min_path(start,terminal).path);/ v* |% E3 U F* o# t& w( X6 Y
& ^# T& u Q* M) ?9 T$ t" b; m%Foldy's Algorithm 算法程序
% m9 O7 q9 y- H; h! Z8 z B/ V; Cfunction [D,path]=floyd1(a)
2 F8 I! f. t' ~2 @; x5 bn=size(a,1);
9 ~5 ?; L. K# a" o5 DD=a;path=zeros(n,n);%设置D和path的初值
6 [1 @0 D# M# Z; Xfor i=1:n
4 r% y3 i& C. H( O. K. `/ j$ t+ e for j=1:n, n; V9 \6 V9 o) p
if D(i,j)~=inf
2 c! u1 m9 @ d$ n7 y path(i,j)=j;%j是i的后点 d _" m* E, T- x" ^. R
end; p/ C3 f( @, Q B! b8 S
end6 I% R0 i6 ^6 r7 w
end5 m$ `6 E2 C: l, J+ K& }
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)3 h& w" d' w$ }; D" R" s# i
for k=1:n
) h$ N @, L0 B. k for i=1:n
+ N; }3 ? p4 X7 `" L for j=1:n
+ e! U q$ R1 {, M& q4 Z x if D(i,k)+D(k,j)<D(i,j)
& @$ c \6 w8 t D(i,j)=D(i,k)+D(k,j);%修改长度
. [7 t* {" B6 Y path(i,j)=path(i,k);%修改路径: b: _) P$ f/ G+ n$ I% [( b( ?
end+ [9 M& v# m @5 f) v
end
2 ?, ]- r4 s" f0 E7 k end4 k& y: |8 Q& q0 \- z" l
end
+ C0 F/ }1 B3 N7 F) ?* p1 R7 b- E z) j5 m: m2 W% g9 u A5 O0 O
五 模拟退火算法源程序
& f7 _, V/ a& G: Mfunction [MinD,BestPath]=MainAneal(CityPosition,pn)6 [9 j2 n. W4 n. ~, j# M& H6 o5 P5 H& a
function [MinD,BestPath]=MainAneal2(CityPosition,pn)
6 G0 V6 G2 N% [1 ?3 z3 m, @%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
1 Y8 q5 P: l; t- s1 c%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...4 g" [2 \* }- |# G9 O. F6 N1 ^) C
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
0 N4 I; W; W. ^! f% [% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...+ t' A' E, T" D5 Q4 h* X+ V
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
( r3 G. I, P& H+ b7 v% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
. Z2 |1 N- M# I8 A$ l% X: m0 V/ s2 S& g. b6 F+ e: Y
%T0=clock
: h U! p- f% ^" z+ p( I6 Dglobal path p2 D;) O5 w# e# P+ b5 H5 S. O' d
[m,n]=size(CityPosition);0 O* `: p8 W% B0 L. f
%生成初始解空间,这样可以比逐步分配空间运行快一些
; b8 `- ~; R, B# eTracePath=zeros(1e3,m);
6 y, I4 y) X$ R- {* m6 RDistance=inf*zeros(1,1e3);( h& \8 b- A G
& O8 ]' k' a6 ]" X# ?
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...) n+ j/ T( D7 Y' r% ]- B5 Q# ?
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
: ]; Q& |- w4 j0 ]# g \%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵); E9 c/ M# O9 r6 ^/ ~/ V
for i=1:pn. \( i4 w) o. _' O$ q
path(i,:)=randperm(m);%构造一个初始可行解2 ~( B- P# x7 @6 Z) u5 @
end
+ y, I" h2 M* M+ it=zeros(1,pn);: ^: W2 i7 a0 v
p2=zeros(1,m);7 v/ {# w9 g; i% w- h
0 B/ U! A2 e Y3 g5 c! _; J
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );8 Y) ?, o( I/ _+ q' k4 ~! y
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=' ) ;* v1 L, |9 k3 s2 g1 \
%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* ~7 T u; W9 x
%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
: b( u- l5 w# f+ c+ }%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$ \5 I0 ~4 W- n
%会收到到比较好的效果' v6 ]/ _" I: z
1 o# c1 x" d& _' n+ [. IT=1e5;( m& Q" q$ r" L
N=1;
* Q: S; f1 V u! C% P( l+ \tau=1e-5;%input('请输入最低温度tau=' );
" O. L, h5 q4 L+ e* R) G8 Y1 X%nn=ceil(log10(tau/T)/log10(0.9));
7 z1 C {9 r5 f u0 vwhile T>=tau%&m_num<m_max ( f# M6 \: ?" Q5 x0 ~
iter_num=1;%某固定温度下迭代计数器
! L' u3 |9 A8 w8 _8 f9 O$ I m_num=1;%某固定温度下目标函数值连续未改进次数计算器& r: Q7 J0 _+ b9 \4 G% W; x
%iter_max=100;. z; b% p1 U2 l5 _# [ V
%m_max=10;%ceil(10+0.5*nn-0.3*N);
) A g- K, d& r" A; \6 | while m_num<m_max&iter_num<iter_max5 ]6 j% l3 @, n3 c1 G! l( ]
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:- i& p* }, s: G
%用任意启发式算法在path的领域N(path)中找出新的更优解
; a* `# |* P0 Z for i=1:pn
" S. v0 W$ u1 p m6 H5 @ 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# O1 [' |3 q& a$ O- k w6 L
%计算一次行遍所有城市的总路程
+ O. T) ]9 ]* Q6 E [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
0 h$ ?. V4 r; P9 ^% o Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
& f T3 l2 d7 [: Q+ R- X8 j' r end
- j9 ~2 }+ D0 k. [ %Len1
& \. w+ l2 P: B %Len2
" A/ v4 r3 ~* x8 i' ?9 l %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand6 `: P# R3 b' o G2 N2 U. d' m
R=rand(1,pn);
) U0 K* D* h7 Q. h %Len2-Len1<t|exp((Len1-Len2)/(T))>R
% i& A+ N2 t J: b if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
, K0 y0 ]* e8 ~$ E: b5 } path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );$ F" M" t& T+ G
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));1 p$ S7 h8 `+ S4 J0 \; ~
[TempMinD,TempIndex]=min(Len1);/ @2 W7 z1 l3 B0 |4 a6 g
%TempMinD/ p& T; ?) T+ N4 s
TracePath(N,: )=path(TempIndex,: );
4 [+ L! A( i6 c' S' ?& d Distance(N,: )=TempMinD;! O# l4 v8 M6 {( R# E3 a
N=N+1;0 u6 o! J' T4 x- s) W/ s# ]0 R( T# b
%T=T*0.9
; V _) I5 @; w) e1 p$ I3 l8 A m_num=0;4 }. s$ u) j( h. P, r
else$ j, S+ |/ n8 p# x& b/ S
m_num=m_num+1;
8 u$ p% i9 A" G end
5 g5 M* t2 r8 j) A& h iter_num=iter_num+1;
$ k. T: |+ x6 X# R, I- w end
* X; Y0 h- a8 e T=T*0.9* {7 T# u7 x* a8 ~8 u
%m_num,iter_num,N
/ Z, M1 @; j, |( M4 M- ]) O4 Mend 4 Q7 N1 [6 X/ R6 h! [
[MinD,Index]=min(Distance);
3 F5 ] w7 l- J% J$ G. G* ZBestPath=TracePath(Index,: ); K- V4 e7 Q7 y7 M* {6 J
disp(MinD)( ?, }& }8 x j8 v% Z) P; M
%T1=clock
0 \& K# b6 S# i4 Q& ]
& N# M* w( B% Y+ I9 |, E : F' A+ ^9 j+ c& D# k4 k
%更新路线子程序 ) O& j: N' v3 q d( P: U$ A
function [p2]=ChangePath2(p1,CityNum); {; O8 [ d4 h, Z8 N
global p2;. w6 E* M& l( x' N% A9 |/ a* P
while(1)6 t* c$ B6 h q1 l/ J5 {( N
R=unidrnd(CityNum,1,2);9 m) X& g& `- O E
if abs(R(1)-R(2))>1
! d8 _/ l# ]+ x0 m+ W break;
: o' u0 Y6 Q+ ?2 @9 [) X& z end0 T T, W1 k6 ]* _, x* I# U
end
* o# A% w3 t: DR=unidrnd(CityNum,1,2);; S4 v5 Q( D3 x( u7 C
I=R(1);J=R(2);
- b) k/ @$ l o5 p. x) [* C%len1=D(p(I),p(J))+D(p(I+1),p(J+1));; p0 ~& f3 m/ e0 f$ k3 B7 o4 |
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
# T' u X D9 y' aif I<J2 r' D' F8 A! W' P
p2(1:I)=p1(1:I);
4 T1 U% \& v a* v" D( K; ?* ` p2(I+1:J)=p1(J:-1:I+1);
$ W3 d7 \2 k( t) O, N p2(J+1:CityNum)=p1(J+1:CityNum);
. A6 \! |* X5 e$ Delse
) z8 |8 {: r; R! x. i; \ p2(1:J)=p1(1:J);
$ A! q9 r1 N/ N' f p2(J+1:I)=p1(I:-1:J+1);' m) A9 W W% m& k" r, j# s
p2(I+1:CityNum)=p1(I+1:CityNum);
' a8 s' Q3 |+ N( F. X+ J: Eend) Q1 o5 t7 `+ L1 ?! s1 C
4 h/ x' ~# Y1 S- A六 遗传 算 法程序:8 i* \+ g1 J( L4 p' R
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!& d' n& E1 @; R- x2 L4 Q0 l
8 K# p0 j- o. h7 f* p3 t6 @
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)% q- p( F# f) l0 @% m
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
$ K( T) ?+ A, h* ^0 s+ l4 J5 Q% Finds a maximum of a function of several variables.8 F3 _. f7 _+ h" m2 Q: Q
% fmaxga solves problems of the form: 5 z4 X( k9 s1 S% U& L& @! M, u
% max F(X) subject to: LB <= X <= UB + l/ ~% G' ^6 j7 L ^- q
% BestPop - 最优的群体即为最优的染色体群
0 q' Z/ L; Q7 S' |/ h% Trace - 最佳染色体所对应的目标函数值
1 g# c3 q, O& X' q% FUN - 目标函数
) f4 P# s5 [; u7 s! Q l% LB - 自变量下限
# ?0 ]" u. s" F c- l/ E% UB - 自变量上限
' i/ \& t6 K) @6 I% `; \3 l* B' q% eranum - 种群的代数,取100--1000(默认200)
0 |4 w6 w, ]( M, k! x' z$ [9 }+ n5 f% popsize - 每一代种群的规模;此可取50--200(默认100)
: u+ ?( I3 x+ L3 c! M, j. m1 D. e% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
A0 \- |2 W6 y$ t% L/ `5 D% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
2 `& S) ]7 S$ V7 I. `/ \; v, \% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2) X7 S* ^1 r- t# a3 v$ ]$ B
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
* t/ N* j+ C0 X* a3 S7 [: O5 p3 e%码,option(2)设定求解精度(默认1e-4)9 m, ]1 v' ]$ @) c- ]
%5 o" [: t5 n! j5 s2 t/ y$ B
% ------------------------------------------------------------------------
U- ?% T9 }& ^8 P# r
m, R! D/ Q' kT1=clock;
6 n' z" g# H& L- fif nargin<3, error('FMAXGA requires at least three input arguments'); end4 i, C" |: ~% ^2 q R! u. `- q
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
' `. r6 ~) u! w+ f; q. i3 Yif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end0 J7 y( }+ T" L. z
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end. H. L3 P4 o4 H% R& X5 G
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
2 g2 V9 ?; C" h# O/ ~3 P6 Jif nargin==7, pInversion=0.15;options=[0 1e-4];end
! e1 z, `7 m& O! R% I- e. }- N! F3 Pif find((LB-UB)>0); I7 `: a5 r# l# Y
error('数据输入错误,请重新输入(LB<UB):');
/ p& i: @0 F6 m3 X3 i% Eend% u1 E( p2 F' U) T' W: p
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));2 F" S, k. {: [1 g* E
disp(s);3 c ]/ b8 L" v% t
# k& x# P$ B' r% c: Z% q
global m n NewPop children1 children2 VarNum
' U2 }# H" C2 e+ e' ^8 X, N" z* ]. s& H
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);: |: d$ V" p% w( h
precision=options(2);%由求解精度确定二进制编码长度' U" q7 ]% i' o; M
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间9 E+ Z% i& d" i$ P ~
[Pop]=InitPopGray(popsize,bits);%初始化种群1 ^4 z8 @0 k# l% }, [+ i$ Y
[m,n]=size(Pop);
. Q3 b/ Y% o8 p0 S; INewPop=zeros(m,n);& U6 f# V+ i* x6 o8 [- t' A
children1=zeros(1,n);
# x( I; G6 n; Xchildren2=zeros(1,n);
+ d0 L* ]3 Y( L3 d% K& _4 q( ?pm0=pMutation;' @) _' o9 ?! z# Z2 _
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
2 |0 A# R: Q1 L4 J7 zTrace=zeros(eranum,length(bits)+1);
' B( u9 l( _2 }i=1;
) M2 I. h& ~7 w+ qwhile i<=eranum
! w; M, {4 W& ]/ O- A for j=1:m
; G+ o) ]6 T: w) d: b value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
- ]8 N* m7 e0 |4 k end
, B# T/ [, g% s [MaxValue,Index]=max(value);
: p4 P& \ D8 Q2 [' t" A BestPop(i,:)=Pop(Index,:);
) h! [( d+ l. k2 [7 _ Trace(i,1)=MaxValue;
( Q2 n5 Z' A) ?1 ]6 A# G8 A Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
, w7 I$ L4 x7 I. @7 l* @1 J [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择" F' }' {. @. v* y- u M% J
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));: d/ }3 |/ _; z
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
, C `, N4 Y! M! A+ Y! a5 G %round(unidrnd(eranum-i)/eranum)
?# e% ^4 `8 S. x5 ` [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
. l, }2 [! U* f) w2 b [InversionPop]=Inversion(MutationPop,pInversion);%倒位% T4 F+ E; A. W1 r- d
Pop=InversionPop;%更新# |9 K7 B' T# q/ o T
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
6 n4 k" k+ H# Y9 J%随着种群向前进化,逐步增大变异率至1/2交叉率' ?4 L2 L" N: _! c' Q
p(i)=pMutation;9 \8 S. W, O" M1 z0 k+ {
i=i+1;' }+ s1 `! i% x& q4 O5 O1 p
end
& \+ F8 n( I+ `. j( U* Yt=1:eranum;
7 H4 O6 K7 P1 ?* }3 v( `, R! eplot(t,Trace(:,1)');6 \- b5 W: F% Y/ k$ h
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)');
1 O4 N' G2 A M2 ^[MaxFval,I]=max(Trace(:,1));2 H- W: ~, v8 y& c7 O1 P- V4 n
X=Trace(I,(2:length(bits)+1));
& `6 s7 X6 G4 P3 E% ?hold on; plot(I,MaxFval,'*');
0 J' X9 L: W3 p2 G$ X) ytext(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);8 P( }% s- [% N1 R# J2 ]5 R
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,:)));
8 c! t. G; ^) X- U7 `8 E0 Wdisp(str1);7 Z2 i% Z' x2 Y' k
%figure(2);plot(t,p);%绘制变异值增大过程' N8 R$ N/ Q: Q' [. |
T2=clock;- R7 J3 w: P1 C- X Z
elapsed_time=T2-T1;
; j: U% u' a) c/ {9 F8 o j) mif elapsed_time(6)<0$ @8 {6 K) y+ L( h# i6 \+ V. R
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1; h" d' {( c& ^9 d2 n
end
+ D; c. D6 Z6 ?6 ? Oif elapsed_time(5)<0
! r3 q& v+ @7 z% G elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;7 R# J$ W+ t& D3 w$ h
end %像这种程序当然不考虑运行上小时啦# i( n% f. a/ F
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));
3 D9 {1 F6 F3 ]8 wdisp(str2);
- m" Q' ~* @6 t6 p( R; \$ P# a/ `+ w+ A5 e' R9 D- i2 Q
2 a, c& }( H0 t2 s%初始化种群
: L% D, J" \4 \ l4 k0 _- `! h: {%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
8 `7 P, x, y+ t% t2 K+ o' yfunction [initpop]=InitPopGray(popsize,bits)3 i2 y, {1 L* k+ s2 m! d3 V! c% `6 N
len=sum(bits);3 U: e/ y* {; i% {+ P! T8 P
initpop=zeros(popsize,len);%The whole zero encoding individual
- ?5 c" q7 S6 w, R8 i+ yfor i=2:popsize-1+ |; \% p% `, s$ B" i; a2 L
pop=round(rand(1,len));2 Y3 Z2 _! t3 o# a( k' J9 V2 t: E) |
pop=mod(([0 pop]+[pop 0]),2);; v" u; G+ A6 c }5 A: W
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
+ ?1 O" d) G; L4 a %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
/ r" P! l8 R- A4 M' g initpop(i,:)=pop(1:end-1);: Q0 r: w% H& y# X8 u2 X# I& f$ ^0 u
end4 H. U# X$ Y. Z; ~5 A
initpop(popsize,:)=ones(1,len);%The whole one encoding individual
; u4 P5 {, I; j% w V%解码
! G# }( d; M4 i: K1 T2 `
: I/ B7 N% W' Z+ V- Afunction [fval] = b2f(bval,bounds,bits)
, |, l+ H/ y8 H% fval - 表征各变量的十进制数
% R: H! X3 l; G% bval - 表征各变量的二进制编码串) \3 Z" {7 S% E1 N$ M- t* l
% bounds - 各变量的取值范围: P6 _" v9 k$ d( ]9 [0 Q
% bits - 各变量的二进制编码长度. m- e' h; U7 k6 u. ~8 n
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
% B5 Y. X: h, [8 }numV=size(bounds,1);
2 g, [8 `; p: j4 E5 S8 tcs=[0 cumsum(bits)]; + v& [ Z" Z) w' v1 }5 i, z: ~
for i=1:numV/ U& g8 R+ t4 P- H0 x
a=bval((cs(i)+1):cs(i+1));
" g* z- }% k" @1 n2 }+ h" ~ fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);$ Q1 y$ A0 c( q; X
end
L' h: v# _! O7 i* _ E4 q3 k9 s% H: ^%选择操作
$ t( G4 K: B n: S8 @3 B8 Y/ I%采用基于轮盘赌法的非线性排名选择. b6 J6 R4 H! Q& n, p5 o
%各个体成员按适应值从大到小分配选择概率:
0 l8 u. u# a* @0 ?# [%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1
. j9 O5 B- d7 F- P
$ }, Q& p f- a- g6 L6 A5 Cfunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
* O; A0 U6 Z1 V8 zglobal m n+ Q0 P( X$ ^ L' V
selectpop=zeros(m,n);
- c2 t2 |. L& N' c5 k2 Tfit=zeros(m,1);7 o5 j6 q. B9 n8 p. O" l
for i=1:m
. {* Q. H6 a" }* ^6 n fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
8 k9 A3 g# j% x5 R) u* S0 O' i& jend# y) V. J; Q9 D2 y; L8 v3 ?' I
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
) E l0 V- w1 N6 q$ uq=max(selectprob);%选择最优的概率: @7 @7 D0 e/ d6 @" Q: ]! U
x=zeros(m,2);
; w- T- @9 O! C# c1 fx(:,1)=[m:-1:1]';
$ m/ q: j8 V' _4 M/ L[y x(:,2)]=sort(selectprob);
' M8 \6 O! @& p( H" B. q; M$ _) tr=q/(1-(1-q)^m);%标准分布基值, ~* |: i7 b/ y9 Q, W
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率7 ?1 m# X+ v8 T( F: o0 n& D* i
newfit=cumsum(newfit);%计算各选择概率之和
1 d2 @ L/ `2 @6 l$ X9 UrNums=sort(rand(m,1));" ` }; n4 j3 m% f
fitIn=1;newIn=1; V* r, k# B0 C9 {, c2 B3 h7 M' ^
while newIn<=m4 I/ e% V0 g! K* X
if rNums(newIn)<newfit(fitIn)5 ]1 O: X+ q6 u% G) G4 I% N
selectpop(newIn,:)=pop(fitIn,:);
, [/ _- e% n z# E newIn=newIn+1;
$ D( F* D+ O6 j Q+ ^* g else7 f' w( `( {. r8 c2 S n0 V. {
fitIn=fitIn+1;) a& e" M% Z+ S# @7 T7 H
end
: H6 P/ ~0 _5 v" p4 z& w7 aend
+ h' n( g* B, a: S0 I%交叉操作
! }$ Q( A5 }" L* [$ `5 |( Jfunction [NewPop]=CrossOver(OldPop,pCross,opts)
& B8 t0 X8 K) l3 g5 H2 @%OldPop为父代种群,pcross为交叉概率9 B* d3 u& O9 M) F% _ u
global m n NewPop
8 Z/ w- X) v+ Z! Q5 a6 G" Vr=rand(1,m);
. B9 `0 `2 ~% C- c0 p* Uy1=find(r<pCross);+ ]$ w+ G# N+ G; O: Y
y2=find(r>=pCross);
6 X% _% O: u- O9 Xlen=length(y1);, ~# P) _3 U) G/ ~! L0 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
( x6 d1 N6 Z% g0 ] y2(length(y2)+1)=y1(len);8 H, G8 P2 ]% I% s. w' H3 c% @7 s
y1(len)=[];
1 O9 }4 [! @9 p2 h; b) Vend; o n9 b: N. a+ D
if length(y1)>=2$ `% Z. u7 f& T% f' p0 \
for i=0:2:length(y1)-2- U8 t+ q( ~+ {1 ~6 H& z6 N
if opts==0
8 V9 Z) C$ d, m [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));2 J0 Q8 ]2 Z, s9 J- R6 T
else% Z, N4 C, |, _# V3 f% a
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
! N4 n1 S! O3 b3 ]) e' @) Z# U end
# R' y6 g; l# E0 L end
& G" y, l1 @* f" P8 N# ?end
* ^& ]4 Q/ T/ `. C# M3 l/ fNewPop(y2,:)=OldPop(y2,:);, x" h" k' F; @! a3 W5 [9 y* J
" \3 S2 z. D! {, {% X%采用均匀交叉
0 F" P+ | g9 O' K: Y. y. ]9 M. qfunction [children1,children2]=EqualCrossOver(parent1,parent2); y. X8 ], P4 m; [4 h
1 Q0 U! E4 G* vglobal n children1 children2 9 k% ?8 E+ M1 i; k3 a$ K
hidecode=round(rand(1,n));%随机生成掩码 I" R c" N& A) _
crossposition=find(hidecode==1);3 M+ N7 J2 [" Q+ r( J
holdposition=find(hidecode==0);
9 l( H- L+ @1 L, Y6 echildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因; j) R2 d9 j2 C2 z
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
5 k8 ~, u/ P4 S, G7 e) P/ pchildren2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
( @" i3 c. p* D$ _children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因) d& Y/ Z2 @9 x; J% N4 x
/ O9 |2 f2 d0 X- m0 a%采用多点交叉,交叉点数由变量数决定
! o4 ?# ~* E8 E' C
/ W1 u) A) M! Nfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)
}$ y* i7 J$ L" ~4 ~' J* {" {* _& A7 O
global n Children1 Children2 VarNum; ^7 e8 u0 `3 z2 V
Children1=Parent1;5 c' S0 W3 ]) ^4 L. [9 f
Children2=Parent2;2 T: d X, y% W- ~4 n& f
Points=sort(unidrnd(n,1,2*VarNum));+ R8 {* Y2 v% x
for i=1:VarNum
; t2 {2 K% H3 ? w Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));" |- q+ J- R3 H/ v
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
# O, B- @9 X8 U# R+ Gend
6 j2 e3 W( ~( `" g* w
% a; {( i" S6 A2 r# a; t, K6 w%变异操作1 e# k0 p! D$ {' h3 E1 C A
function [NewPop]=Mutation(OldPop,pMutation,VarNum); z2 w; K9 @% e& x
# ]. o6 A4 @9 O2 a* `% J
global m n NewPop5 r4 T S2 i- d% ~$ e! d
r=rand(1,m);$ W3 ]5 C1 i5 g$ J/ R
position=find(r<=pMutation);
! r3 ]! |$ E7 {0 d( b* p- Alen=length(position);
: X" W# s! U2 lif len>=1 H- Z- n: ~$ k1 F9 f: Q1 Y6 b6 n
for i=1:len
`+ k5 ?. q3 ^7 r# p k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
( h; f" I4 C2 U- u, q3 o3 i) D2 K5 C for j=1:length(k)) T2 [) j( a- D M/ w. x J
if OldPop(position(i),k(j))==1
+ \/ z' M/ _8 e( j5 f. |; i7 \) m OldPop(position(i),k(j))=0;
6 i k! q4 S2 k4 `5 N* N else
- e9 c9 H# b, n+ f7 I+ y9 y* v OldPop(position(i),k(j))=1;
7 h6 U6 ~% Y4 f7 s$ y end
3 f& _( U3 v, \9 P. f* o0 o7 K9 ] end
0 D9 t f" Z |# q4 | t end
! Q3 c7 t% x) S+ Q9 H" y# ^end
. G3 M0 \5 P( WNewPop=OldPop;
+ i" j! r1 y1 h2 A! A+ S$ s" A* {7 W* P" s+ {* j' Y
%倒位操作
% A9 i8 G8 z, S$ ?9 t0 J% {+ P w! ^' k ]9 T
function [NewPop]=Inversion(OldPop,pInversion)
2 Y7 i: ]7 P- H7 u+ `- h* t; m6 d% {
global m n NewPop
9 p- L0 Y8 \4 ^* f, n. zNewPop=OldPop;
. ]5 C. f! J( a% rr=rand(1,m);+ R/ `& T5 P8 E0 V1 I0 j5 X
PopIn=find(r<=pInversion);1 N' S: H! H) r5 R. r2 q) m
len=length(PopIn);
. n% D8 |; V0 ?) U0 Cif len>=1
7 ]& o) ^+ T/ F& X6 v for i=1:len8 p6 U% |; `! r
d=sort(unidrnd(n,1,2));
# `/ l1 T4 C) I" H; a if d(1)~=1&d(2)~=n9 L+ b+ \& Y+ g" s
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);$ a$ M+ G# b: i$ [" e3 F) v# D
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));1 c) X, \2 Z! \5 W: J
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
! \" z8 T& U& k$ o/ F end
4 @ r, j- A# q2 @6 E& p end
% G6 [9 }0 o+ A! ^$ _: gend% k- f$ E% V" X' b0 h, b' U
) b9 `; u2 ^* i: z# I+ E' |9 b# p
七 径向基神经网络训练程序
5 X4 _2 l- E( \6 \" f" e) Y, k6 P0 H
clear all;
1 {8 ~6 T* P0 lclc;) Z* m; H1 S( \% E/ Y
%newrb 建立一个径向基函数神经网络% l# k+ m6 s/ G
p=0:0.1:1; %输入矢量
( p: m$ a* J- i8 D) W& R6 S0 It=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
6 |8 y% R6 d3 W' m' I& A& x2 Kgoal=0.01; %误差' {8 o) P* I4 b4 S g; |
sp=1; %扩展常数
" E; L# c, k+ `: g: A2 n& Smn=100;%神经元的最多个数4 K6 `7 Y( T$ G% ]: g
df=1; %训练过程的显示频率
: F$ H; Z- s) l9 }! N1 D" l[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络+ ]: D, \5 m4 j% C! G0 U
% [net,tr]=train(net,p); %调用traingdm算法训练网络. p- S5 g! w' [, v1 ^* Y
%对网络进行仿真,并绘制样本数据和网络输出图形4 o" g7 ^5 a O6 B9 D( s5 y$ ]
A=sim(net,p);& {$ H7 T1 R6 n4 u2 R# S
E=t-A;
) D0 Y3 C/ U+ F+ a) n, v# gsse=sse(E);! v6 ?( }: w1 y, g
figure; 3 l9 N+ V# V: N$ O, d8 K% r# }
plot(p,t,'r-+',p,A,'b-*');
+ l; Y. A6 A3 F7 W! o6 @6 ?legend('输入数据曲线','训练输出曲线');
! G: u7 G3 f5 J9 A, N3 uecho off
' S; M2 T- d% S1 ]4 w5 a G* D) r0 u
说明:newrb函数本来 在创建新的网络的时候就进行了训练!2 k( N8 s) S! C3 F/ Z6 I
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 g" |, V3 Q/ G6 ^, M9 q5 V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!
0 [+ n% z/ t$ D A. S5 h/ e: G+ O* X2 `7 X
( ?4 r) d1 o) ^% N: A训练结果显示:
4 C3 X0 I' x" F U0 T( uNEWRB, neurons = 0, SSE = 5.09734 a: z# L, ~1 a$ V0 x
NEWRB, neurons = 2, SSE = 4.87139. u0 Q" k# i. T( }! i, C
NEWRB, neurons = 3, SSE = 3.61176
/ {+ C; Q, ?/ e% uNEWRB, neurons = 4, SSE = 3.48751 w1 e- d/ B$ Z9 L! u
NEWRB, neurons = 5, SSE = 0.534217
* G( p" O) t9 j" ~NEWRB, neurons = 6, SSE = 0.51785 e$ _9 G8 H& E
NEWRB, neurons = 7, SSE = 0.434259
. ]" l b" R0 L6 _9 KNEWRB, neurons = 8, SSE = 0.341518, Y0 E" ~$ k0 x
NEWRB, neurons = 9, SSE = 0.341519
: \* t* ?7 _ `0 i9 aNEWRB, neurons = 10, SSE = 0.00257832" m) c& o. q0 o4 g+ G
# d- ]0 V2 ?/ f: J9 b4 |
八 删除当前路径下所有的带后缀.asv的文件! h2 w! g9 T* \+ f5 z
说明:该程序具有很好的移植性,用户可以根据自己地4 f1 u; G7 m) W
要求修改程序,删除不同后缀类型的文件!
. ~, L( u$ R; k! mfunction delete_asv(bpath)
0 I9 h4 ?5 @, H- O8 G1 {, U0 h%If bpath is not specified,it lists all the asv files in the current4 E! L6 y) r+ I% u
%directory and will delete all the file with asv
- w2 E8 e" K, L8 m5 p$ i$ P% Example:
3 l; V( t' R' h o4 L1 {+ u0 u% delete_asv('*.asv') will delete the file with name *.asv;! _. ]# q2 K, S8 v6 f
% delete_asv will delete all the file with .asv.
# Q7 A& `# y3 K: r1 K# y1 Y: z5 Z6 a, b$ V; |9 C
if nargin < 16 H1 W% R: z1 e3 |
%list all the asv file in the current directory
; l$ M9 G/ `2 j2 ~! F; } files=dir('*.asv');1 K' u& H Q; A" a" Z m) W9 M, C7 i
else4 L& H3 U9 s2 f) g% E
% find the exact file in the path of bpath+ I8 b* x) a F2 w" f. q: K
[pathstr,name] = fileparts(bpath);
. @; B) H6 V+ z o4 A. r4 c if exist(bpath,'dir')
- C6 |$ [6 a5 S! M, ~( q3 m name = [name '\*'];6 f8 Z; c- x+ i
end5 ^; |4 }( [8 K6 F
ext = '.asv';
6 ^. o$ s. f$ Q# Q files=dir(fullfile(pathstr,[name ext]));0 U8 c1 ]5 I, Y" n
end
1 Z1 q' D! F0 T7 N& _1 u1 P8 c3 N6 ` @! `0 o
if ~isempty(files)$ t' @1 {* P1 \1 y: X
for i=1:size(files,1)
) O3 u% V: D* X2 P& d3 T title=files(i).name;
2 v& k' r' c4 S6 S delete(title);
1 x3 m7 w3 A. H& d end
( h% ~, h! A# y, B( ~ L, Zend
1 S4 f3 x" A' M# o9 }1 S9 F( k1 e% R4 [) W2 o. |/ ^+ T
! b4 @5 @3 a# O, D. p6 `
同样也可以在Matlab的窗口设置中取消保存.asv文件!7 _7 ^+ Z4 t$ K
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