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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
3 S; \8 z. ^ |7 M1. predict_fun.m为主程序;
1 r2 U. @) W1 X$ P" r' Y( r9 b2. timeseries.m和 serie**pan.m为调用的子程序
# z' ?$ J, z: g4 B0 @
7 ^( f$ J i3 |- x- l. ffunction ima_pre=predict_fun(b,step)! i% c6 Z" d! P
% main program invokes timeseries.m and serie**pan.m6 y5 {' X! T% V/ c4 g B2 l
% input parameters:1 ]( n: B( L: Z- ` f4 T
% b-------the training data (vector);
/ u, C& X' r' T( K, \% step----number of prediction data;3 M5 Z$ d+ F2 y& X- }) y" n
% output parameters:: u% P5 e8 G. x$ \- S* t
% ima_pre---the prediction data(vector);+ H# n5 g+ u$ v: t
old_b=b;
- Z/ X2 p$ [, k! |- s0 m/ k! Qmean_b=sum(old_b)/length(old_b);
2 \" N& A: J1 Z+ l+ v' |4 mstd_b=std(old_b);4 K" [! L* Q6 ^' b" s' J
old_b=(old_b-mean_b)/std_b;( N# P. d2 ?2 `9 A! N' h+ P7 S
[f,x]=timeseries(old_b);
" F q4 ]1 H( ~/ X. z' Z) D8 Mold_f2=serie**pan(old_b,step);9 F5 j# G( Z0 S0 T
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;
, u8 Q. n+ s- S* s8 n# t9 PR=corrcoef(f);
6 X4 k) q- ~% o+ t- Y8 L; F[eigvector eigroot]=eig(R);
3 G/ q+ L) ?) X/ N* r; q: o3 meigroot=diag(eigroot);
8 p' U) J: F! Y" P0 d$ Ha=eigroot(end:-1:1);
1 W: h; I: Y: G2 A9 Dvector=eigvector(:,end:-1:1);
0 x; C* \7 F. q: F' Y! NDevote=a./sum(a);+ E% P m8 H+ r( n8 D( ` ?
Devotem=cumsum(Devote);
+ Z" m# t2 P; j9 ]3 H, nm=find(Devotem>=0.995);# n! ^- J- u/ y# I6 j3 t3 b
m=m(1);' F2 z6 k" H* d+ C: c; N( e
V1=f*eigvector';
2 Q+ d5 X$ S' r/ f5 }0 ^V=V1(:,1:m);4 S* o& ~' b+ Q' \
% old_b=old_b;
4 N0 t, _$ r/ l3 G$ g/ Hold_fai=inv(V'*V)*V'*old_b;7 ]" a6 u$ O, `2 ]0 j$ r( b
eigvector=eigvector(1:m,1:m);
9 ~, d$ E- d( i5 [' I+ d# pfai=eigvector*old_fai;
0 z& a* Y9 W" p! S. Of2=old_f2(:,1:m);3 Z+ x& |2 D, s# Q. q
predictvalue=f2*fai;
" _) d* a4 H- C8 S7 w7 j( Vima_pre=std_b*predictvalue+mean_b;6 G8 W& K4 q5 W! L( N; Q- d( \! L
) B3 B1 d8 W# b5 c4 }1 T4 C1.子函数: timeseries.m 2 g1 ^8 G7 S; W+ n$ u
% timeseries program%
) q8 Z! z& U% q; z8 n& o- @% this program is used to generate mean value matrix f;
7 d( i, [) v& o8 V( ~5 {+ @$ q" zfunction [f,x]=timeseries(data) " P: b: e& ?0 l: {' k6 N
% data--------the input sequence (vector);
+ M; y! {% u5 d) k! h% _/ l% f------mean value matrix f;
( \7 G- u: |1 v/ Z7 p3 Nn=length(data);! ^+ p' Z# u1 J
for L=1:n/2# x5 Y8 V* c# m, [# H& ]& W
nL=floor(n/L);4 c2 i- j5 ?( Y# S
for i=1:L2 J, U* B9 Q( \# ~, l) t. _6 m/ a
sum=0;3 l5 x& E0 B7 l9 W( E
for j=1:nL
' ~+ g8 U2 S5 `# Y% h; U- d sum=sum+data(i+(j-1)*L);, f! [4 y5 J4 V M; y
end7 u, Y2 I" R8 a2 q& g1 B
x{L,i}=sum/nL;
& j" C. ^' {$ t. q5 @0 {7 { end& G. a1 a7 z: {9 q
end
) t/ t2 K" a3 WL=n/2;
" ^ c' h. T5 V8 xf=zeros(n,L);) d& O* r0 ^2 k, |1 D( a9 A
for i=1:L
! V5 _$ J0 k* }) S rep=floor(n/i);
2 Y/ {$ n8 ^$ P# Y res=mod(n,i);/ `- K& x! ?/ x8 @: i
b=[x{i,1:i}];b=b';
% m8 a' A5 w' e; R) @2 E$ Q5 m6 ] f(1:rep*i,i)=repmat(b,rep,1);
# X, E b: J9 G' X) a" N+ D if res~=0
. N5 y' n6 G7 @ c=rep*i+1:n;- [8 D l+ F% s! R
f(rep*i+1:end,i)=b(1:length(c));
% ?* H% S5 J0 ] end
0 ~+ C+ o/ A! {' J: g) ?1 Hend) @* L: _' ?- {* I2 f& L
# ?* _% @- J7 w: J3 X1 g% serie**pan.m
; ^" Z7 l5 j% F' v" y4 P! b4 g% the program is used to generate the prediction matrix f;
( U4 X8 y# C1 J5 `0 Mfunction f=serie**pan(data,step);' c+ ?. C& n$ D' g5 }% q
%data---- the input sequence (vector)
7 ?# y* `! t D/ R- K% setp---- the prediction number;
; G8 W; ?8 ~# I6 _! F- F5 Ln=length(data);
2 n, m/ x- ^% o7 a" u; F* e: Ffor L=1:n/2
% y, n R' I6 _2 T9 M/ f/ | nL=floor(n/L);
# F( q# \3 |( G' O9 A! x for i=1:L2 C' p' }! n. S" X
sum=0;. o; @+ J; a! t2 o9 r9 n# V
for j=1:nL( `4 g( i$ ?" r' z* @" O c
sum=sum+data(i+(j-1)*L);3 G+ a3 `: u/ h7 v+ M( ]
end
1 a( e7 j6 t8 m! @% H x{L,i}=sum/nL;) A0 B e, ?, F# }3 i
end/ X8 m1 A' u' k7 c. a7 i
end
! I& S( Y1 K" H6 Y# I6 W; NL=n/2;
* }1 U0 s" [+ m# P) H+ Q- lf=zeros(n+step,L);1 i* d7 Y- x0 f7 K* ]
for i=1:L
. x! p* T( ^+ n0 `' [# p7 e, \ rep=floor((n+step)/i);2 u( K- r$ ~. ?' v: q* x% i; L
res=mod(n+step,i);0 b$ u2 u: l+ T
b=[x{i,1:i}];b=b';2 c1 |' e1 Y4 A& g. e% z6 f2 }4 r
f(1:rep*i,i)=repmat(b,rep,1);
1 j( S# A* @$ D9 L if res~=0
3 h6 f- F; p% c* j" _ c=rep*i+1:n+step;# h0 s/ |- G1 Z6 H( `" K
f(rep*i+1:end,i)=b(1:length(c));
0 x( Q7 R, y4 S+ B6 F end* D( o1 T/ X0 Y7 ^! X# p& p
end* v( g8 h8 a3 D7 l% ~2 K, Q z
! q( Z3 ?$ t% }$ c; X6 d! K
二 最短路Dijkstra算法( J5 {% d O, m0 I: C; f
% dijkstra algorithm code program%1 {3 \$ r# o/ N8 l: G
% the shortest path length algorithm
( Z I8 O2 H9 Afunction [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint). U+ E" p. _1 r
% Input parameters:
1 r8 ]1 @3 e1 H0 k! D* o) n$ ^% ?% Input_weight-------the input node weight!6 C- q$ x0 Q9 c7 e! A. O; ?& Y0 X
% start--------the start node number;1 B3 {4 s2 {# y1 l; \& f! o
% endpoint------the end node number;
8 R# S% ?% b8 q% _% Output parameters:
% c. Y8 t4 k% ]5 |2 c s7 U% path-----the shortest lenght path from the start node to end node;
7 K2 u! F- O+ o& f% short_distance------the distance of the shortest lenght path from the7 E* u/ W- [- f" i: {6 y
% start node to end node.
1 H) P( W3 W' w$ }, Z- u[row,col]=size(Input_weight);
- P) D0 w$ S9 q ~
3 k( c' y) u+ \' Q4 c) w%input detection
$ g$ X% [( @6 @8 y4 H) Tif row~=col! n$ V7 L" H2 H- n
error('input matrix is not a square matrix,input error ' );
: a$ H, r2 y5 H, n. T9 send# q' V, M: {! H l( V) o
if endpoint>row
( R& p1 p& H* w; l0 m% U$ H error('input parameter endpoint exceed the maximal point number');' d& E! m& S- ^. y; _
end1 F1 E% g( y+ M. K
/ u H7 A; g$ U6 f; p2 G" D%initialization
7 m' f, U6 s; T$ i# n1 is_path=[start];- H) s! O. a& S: h" s
distance=inf*ones(1,row);distance(start)=0;! w5 D; j. G9 U; v
flag(start)=start;temp=start;0 V& d* v3 |# A8 f) @' |7 P( b: G
3 }5 g) t; ^2 k- `while length(s_path)<row
% a2 v' O' H2 V: ?. @ pos=find(Input_weight(temp, : )~=inf);
9 j7 l. v+ F* [% s for i=1:length(pos)1 A' y, z! _9 [9 E8 A# O, M0 E
if (length(find(s_path==pos(i)))==0)&
3 ]2 u3 r) V7 w( J' c(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))( u% O& J7 m' ` A {
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
. B9 l3 X, [ F& S flag(pos(i))=temp;
% S5 ` \+ s* E( [5 k* D" {% n end n4 R O5 e3 ^
end
; j' }& j( |, y" B$ r5 e k=inf;2 l- k8 W! d# d! L& H0 D+ q
for i=1:row6 x6 k3 N0 F, y# h
if (length(find(s_path==i))==0)&(k>distance(i))3 e! ?0 D3 ^- k \
k=distance(i);
/ K4 V8 O9 Z% ?( E temp_2=i; y2 R4 ~; O" r: e$ O
end. v4 A( y: t0 s
end
+ D* n1 ]: ^+ S: h& s5 c0 V s_path=[s_path,temp_2];! v) |* g1 m; _, h/ Q
temp=temp_2;) k1 G! O1 ]- F/ {; w! R
end f. U3 S; O! t7 w6 n1 t3 x+ t
! I0 P& y( y Y& b8 l! z%output the result( S0 q) u% `; T }/ V: p: a
path(1)=endpoint;6 z; j9 K% V8 j( r! i- ?
i=1;$ |2 X- R6 I( \
while path(i)~=start
2 a! O* n4 m) [6 ]* ^ path(i+1)=flag(path(i));
& E4 {: s; ~5 [2 x- ` i=i+1;6 j: g5 N* o# ?/ q6 w! F! @/ I
end
9 J y0 U8 f Ipath(i)=start;
2 Y% [% a3 {" Xpath=path(end:-1:1);
# Z: u1 s" d( }% x- L/ n' A( `short_distance=distance(endpoint);3 G" d+ p f8 D! \3 B, W
三 绘制差分方程的映射分叉图& O W/ ^4 o" f% v
H& M/ C9 p/ r, ?function fork1(a);
; F a* f$ j* `- m0 \/ V( p/ }+ {/ ]5 C5 i) D+ w9 {' w9 Z
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图% P* i# r- @: ]7 [4 x( {
% Example: 9 n: Q0 N, T- e. S
% fork1([0,2]); ' P M# y1 i5 w
N=300; % 取样点数
( ^& W/ o) \8 l! h$ d ~A=linspace(a(1),a(2),N);
' c5 D \- m9 f& Y# ]. astarx=0.9; + ~6 m r: D1 j( l! v
Z=[];
$ F3 m; F+ ]4 c; m8 h. w7 t3 Nh=waitbar(0,'please wait');m=1;+ V5 G% Y% U/ B) Q$ H, k. L% }" p
for ap=A; 1 {6 I, j# `! f; Y
x=starx;
! }$ w1 D. |4 I, }2 s for k=1:50;
2 G; U6 c5 f+ n- Y u7 e7 m% x x=1-ap*x^2;
9 o' O4 n9 @! Z& Z) X5 O end & j( C( x# d3 Z/ H6 r: _5 N
for k=1:201;
/ B+ L0 K: j: Z" Y x=1-ap*x^2; ' @" P( k% ]- g$ L- j; L
Z=[Z,ap-x*i];
$ f k/ S3 o" D1 P end * q. d) D }6 c7 U: I( [- P
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);( d2 w( R. b5 _! E. a
m=m+1;" E+ N( g% w1 y5 v6 {
end 0 s. q: D( U, X( b) r4 f4 F
delete(h);- C/ T) Z' f5 A! R) K" f
plot(Z,'.','markersize',2) 3 L/ w2 P+ ^9 [- Z- f" \- B: T
xlim(a);
6 \4 k$ O8 h4 J, u9 |" p. B
0 n) n3 a" L7 [: a四 最短路算法------floyd算法
( A: y3 ?- r# r4 pfunction ShortPath_floyd(w,start,terminal) : P8 }/ O& Q6 O5 i( p" A
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;& x% _5 a+ v5 m/ b6 }" y
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];- w5 H* r+ M" y5 ]4 O' z$ O
%start-----the start node;# e7 l. f# W% `/ s
%terminal--------the end node;
. N; H. h6 C$ z# c' S3 t4 k& j+ Tn=size(w,1);( W$ L- C! l$ z# q4 e
[D,path]=floyd1(w);%调用floyd算法程序
8 Z7 ?" K* M6 P0 N% y5 ?! [8 ]' |! ?( ?1 p% a
%找出任意两点之间的最短路径,并输出6 P! Z. d5 i$ o' ~1 D
for i=1:n, R/ D/ e2 f- D% o- V l8 B
for j=1:n
: d9 o+ O& Y+ X Min_path(i,j).distance=D(i,j);+ O) ^0 @& C: S& A$ w3 v8 Q
%将i到j的最短路程赋值 Min_path(i,j).distance) D1 o' c; c' k- o$ P, W
%将i到j所经路径赋给Min_path(i,j).path
( h0 \, R7 g* B2 m1 D. _ Min_path(i,j).path(1)=i;& H8 ] S. q- o7 n
k=1;/ F0 v! f" h/ u5 ~. b; N. X0 K+ _, C
while Min_path(i,j).path(k)~=j
7 z' C7 V# I' h& F, h- R; ` k=k+1;
' Y% V- D* X/ B: p Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
6 ~5 a o4 M3 }1 m end# N8 m0 E' C8 [
end
, k! \ F, c* Y1 U' g1 Yend. `2 C, c; K5 T" n7 T- f7 ^6 r
s=sprintf('任意两点之间的最短路径如下:');4 \9 G" r% A% V7 Y
disp(s);
* |! v2 O& C( w' Pfor i=1:n
' y* d. O4 j0 Z% {& g for j=1:n" `% m3 L! S) Z I
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
' s( u5 H( L6 H# b5 Y ,i,j,Min_path(i,j).distance);
9 N. _2 A" r( g, B disp(s);
) ^1 t5 j! d5 G1 t* n+ b/ u disp(Min_path(i,j).path);
) I; ] {7 |8 S5 L end# T- ^. l/ h1 F( d" y- `# B
end" H- H8 | V) a* H& E
4 Q, Z9 ]3 Z+ u0 Q6 x
%找出在指定从start点到terminal点的最短路径,并输出6 m$ s A/ g9 c1 \) Q
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...0 n% V* c! z+ {0 F
start,terminal,Min_path(start,terminal).distance);# N* K0 ^$ i2 x: v' ?0 e9 }* l
disp(str1);
7 s9 `8 v7 I" ~' G8 U1 |+ i! k7 gdisp(Min_path(start,terminal).path);7 o, t3 p; g6 U9 B( e+ |6 x
6 m7 j! x& I/ w1 S7 M& H7 s" A
%Foldy's Algorithm 算法程序% \) y1 u0 w9 g
function [D,path]=floyd1(a) M ?# ^+ c, J- Z# o! r+ h
n=size(a,1);
" L* J3 y+ H* G/ o* MD=a;path=zeros(n,n);%设置D和path的初值4 K t, t# Y7 [( {
for i=1:n8 _! ]2 h: }" c6 ]4 k
for j=1:n& _# i3 M% a0 l9 Z B% ^# C; j
if D(i,j)~=inf6 Q9 L4 s) p- h7 Z
path(i,j)=j;%j是i的后点
C5 K9 P/ r7 A y& B end: n7 q, X0 y6 h% C& D1 ?# `8 V8 B5 W1 S
end$ B: K" B, v7 @* e6 x
end
- i7 V) h! }. M, S%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
8 U4 }3 r$ ^4 gfor k=1:n7 i; \, ^" ~) b" [: Z
for i=1:n
0 T! [) v1 J4 k# M* B6 m/ v* J+ [* { for j=1:n4 F8 v! \' H5 T) g) n* h# ?& y! ?
if D(i,k)+D(k,j)<D(i,j)* ^$ S! a2 l @0 P8 K a
D(i,j)=D(i,k)+D(k,j);%修改长度4 C D* c4 t: @ {8 E: L+ J
path(i,j)=path(i,k);%修改路径. O7 j1 t2 d( ^! `8 `% T' T
end( n4 z$ @/ c* z' A( R5 G$ S& \1 y6 B
end
7 @1 |& u7 s, u4 O' t2 u+ y end' D2 y0 P% q' v! ^
end/ |, Y- |8 ^1 a W1 r
! T+ w C. _: H/ i# ~4 O7 ]+ _0 J r
五 模拟退火算法源程序
4 ~, O3 G2 r3 X+ k* gfunction [MinD,BestPath]=MainAneal(CityPosition,pn), |# W2 X# \* |- o1 s" }
function [MinD,BestPath]=MainAneal2(CityPosition,pn)
2 B; r, F8 z) k; t%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 u* \/ M: f9 a' Y) l
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
1 a8 d) A! d2 G1 A7 m" |. k8 G" K% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...5 P0 r2 O3 X0 y% M5 |
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
! l6 p' m8 c. T. Z% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
& t- @- P* a- T- M) U( K4 f5 _% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
- V; ~, }: P6 O
8 M, O' y3 P+ O8 O%T0=clock3 @. O* i2 T6 U3 E9 `6 d8 M
global path p2 D;
P) G( Q9 U( F5 y[m,n]=size(CityPosition);4 t. h, L: z a8 a r4 ~
%生成初始解空间,这样可以比逐步分配空间运行快一些
1 V, s6 U( [5 E$ }7 z/ K* `! [+ P* { RTracePath=zeros(1e3,m);
% K' P# G1 S. e$ p# u/ Q7 KDistance=inf*zeros(1,1e3);
$ S- o9 f0 k0 [* k2 v2 u% R7 a* p4 `- V" o5 y
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...4 C! i4 ?. w# x4 D" Y/ m
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
! W% c! B1 l' ~* T- Q& R%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵); J' n7 p( q: Q5 A5 h8 c, c0 I
for i=1:pn0 z Q3 T" n7 m
path(i,:)=randperm(m);%构造一个初始可行解
, O2 G" @7 T, P# Q, l& z+ S" D6 Gend
$ X t' w6 {: R( J/ y& ot=zeros(1,pn);
/ n7 I6 r4 z( t& r/ u& m U$ Np2=zeros(1,m);- |! Z/ g% z$ j9 e( T
8 i" H' X9 R/ \7 u# t9 V: k0 @2 w' G
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );: p, L5 h6 v4 M4 t3 b8 ^& n, k
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=' ) ;
8 B; G* ]- e# V O; a%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- E9 b8 y$ ]( U% J8 _, {
%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) h8 s* Z) Q! z+ Z. D%人为的使初期 iter_max,m_max 较小,然后使之随温度降低而逐步增大,可能
: q* w6 c, r3 N5 s%会收到到比较好的效果( B$ h- T: q1 A: ]9 v4 d
+ }4 n! K6 }- M7 N. JT=1e5;0 T. i: k8 b( y2 [% z3 |. `( i
N=1;, Y& e9 V, I$ o9 p3 j
tau=1e-5;%input('请输入最低温度tau=' );* Q9 D$ v1 t8 d4 Q* `( J
%nn=ceil(log10(tau/T)/log10(0.9));
$ f0 |: [ J1 m, O, xwhile T>=tau%&m_num<m_max 2 ^: f! g0 i2 R3 Q5 t
iter_num=1;%某固定温度下迭代计数器
9 o' w R0 ?/ ]1 l7 P m_num=1;%某固定温度下目标函数值连续未改进次数计算器' A) s0 K) h$ p0 v; ^, K# e
%iter_max=100;
! K+ k2 t. g1 N( u %m_max=10;%ceil(10+0.5*nn-0.3*N);+ u/ Z. T3 [* l3 y
while m_num<m_max&iter_num<iter_max7 l& L' l7 i/ D% O+ t
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
) n! r& o. a& x* g4 l, @ %用任意启发式算法在path的领域N(path)中找出新的更优解' M( H3 _2 ^* ~+ }, B. |1 }
for i=1:pn
0 ^+ Z+ L; L0 B T Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
, Q T# U' w+ {( {%计算一次行遍所有城市的总路程 " z# b) F$ H2 |! J
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
7 T( j1 d* }6 _5 P7 \ Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);: b9 p E; k+ A
end( s7 J9 D+ Q7 P6 L, w, W
%Len1
3 N0 T# j1 @" @$ B6 m %Len2! J6 }- Q( D- M8 @8 l& w( {- x2 V$ p
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand9 Y, u# w, C% Z. K' l: y- Z2 n
R=rand(1,pn);
# h% M: p1 ~4 m J %Len2-Len1<t|exp((Len1-Len2)/(T))>R; F, k$ w9 r8 z4 ]3 w+ H+ o
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)$ p/ X) E4 I$ k+ Y( L& t
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
7 @: U2 w6 e5 O Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));$ c) [# Y/ `" f0 u% E4 L9 t
[TempMinD,TempIndex]=min(Len1);
( w! ]3 Z- o8 X9 `& ~) q" G %TempMinD
2 n, c9 C( k5 ^2 N* Q2 I5 {2 h TracePath(N,: )=path(TempIndex,: );: s" N! O+ k" s' ?- z6 m- ?( V2 p
Distance(N,: )=TempMinD;. A3 F1 q, S# O0 l% n4 o) X% }1 t9 ^
N=N+1;# H: d! z' W; w# ~" `+ E
%T=T*0.9
: G1 `7 C# U1 Y1 S/ Z' q' @ m_num=0;
( Q9 T) p7 H$ K$ A7 r9 [ else% `! f6 F) s. h# q% b- Z
m_num=m_num+1;8 ]& Y; A5 d& E/ j, _0 v: E w
end
0 A1 N/ y7 E4 e: j7 I0 k. t( B iter_num=iter_num+1;3 P( U, z- ?) I/ s5 ^/ o* O
end, f. H: P- `1 R6 |3 g7 T
T=T*0.9' _; T5 O- f; H: c9 J; @
%m_num,iter_num,N
! ]( Q% {8 }2 y7 u' f" vend
% p& p+ e6 ]0 K4 Z[MinD,Index]=min(Distance);
1 C( K; q; c1 Y3 v7 t8 NBestPath=TracePath(Index,: );
, N1 p4 d# h) Edisp(MinD)
) A3 f/ ?6 J; f%T1=clock; H3 u3 l6 a; c6 U: ^
0 o2 C2 F2 ^. t1 X + Y. r1 d! w. T& M3 W$ q
%更新路线子程序 4 J/ a9 j: R: r& E! q9 g
function [p2]=ChangePath2(p1,CityNum)
" e7 v, b# I9 o1 ]% p# {' Vglobal p2;
5 H6 D0 d6 G$ D) n) {while(1)4 v' z& l4 w: @) h* ?
R=unidrnd(CityNum,1,2);9 T- m" t/ J& A5 e+ b
if abs(R(1)-R(2))>1
6 n, i) d1 ^- j) A0 i( w* v break; [8 \: a9 l) T; A: Z
end
" e$ }8 D4 ~$ z+ I; ~/ K* ?1 Uend
4 w7 i7 w2 g' s% q: F$ L; pR=unidrnd(CityNum,1,2);7 R) x3 {; g4 h, h0 W
I=R(1);J=R(2);6 i3 u, `% n! Y3 b+ [
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));4 z1 P) s9 }( b O( V: X3 H; ]
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
' W9 R, j8 \9 Z8 pif I<J9 `7 A t) t4 X0 ~
p2(1:I)=p1(1:I);
- h v5 }& }2 O) \' n8 x p2(I+1:J)=p1(J:-1:I+1);
' K, ~; G- a- J p2(J+1:CityNum)=p1(J+1:CityNum);
# a3 U2 a N; g$ G) Qelse
+ S% T3 v. Y; d6 @" W- _! a p2(1:J)=p1(1:J);
, P5 C& M2 K6 K- Q$ r p2(J+1:I)=p1(I:-1:J+1);9 v' b+ c# f6 J/ E1 X$ r: D. }1 V. v
p2(I+1:CityNum)=p1(I+1:CityNum);* U$ V! B, A. Z; ~- k5 T
end* |2 ^* W, i. P F3 @
6 a+ d2 y- V p; E1 M六 遗传 算 法程序:
4 O9 S6 R5 X# }. c 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!; L3 V6 S u# G. ^
' `3 p( R6 E4 o' V/ ^! } g
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
4 J' |' {% F$ K- ^7 [% Y% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) * k7 R% v2 d0 S9 U7 G; J* u$ f
% Finds a maximum of a function of several variables.
9 b5 q' [. o" {1 z4 C% fmaxga solves problems of the form:
5 m, y$ y" J2 J! _$ L% max F(X) subject to: LB <= X <= UB
. b" I/ u1 @% r/ t+ Y' A& F% BestPop - 最优的群体即为最优的染色体群! G3 o4 s/ w( W
% Trace - 最佳染色体所对应的目标函数值
/ O* [ Y0 z" A; e* @, N% FUN - 目标函数
: w+ z* F' `9 B( x, u% LB - 自变量下限
1 ]% b: }$ G& g* b4 I8 h% UB - 自变量上限
1 v, L/ h$ Q: U' B( D h% eranum - 种群的代数,取100--1000(默认200)
* V/ f' K! n" d C8 Z% popsize - 每一代种群的规模;此可取50--200(默认100)4 I3 K4 E( s: Q$ G6 b, Y* \
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
/ v1 ^6 J, K1 L( k. L) D9 t, x% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
* G9 e u& P$ u6 H) h% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)8 s3 g! {' N& \; x9 @
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编, o; S' {' O5 `2 {3 t4 A
%码,option(2)设定求解精度(默认1e-4)
4 Z7 s1 {: E/ f% f& ~+ P" }5 T%( [1 ^% [2 k- e- E
% ------------------------------------------------------------------------9 w) }: b$ z, s K# N. o: L
' C6 m3 y; x$ ]T1=clock;) n$ z' g. ^5 v
if nargin<3, error('FMAXGA requires at least three input arguments'); end3 ]. d2 |6 ?( h. u0 b1 G6 z3 u! o" j
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end$ S& p/ q. a$ ]& |2 C
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
% H; N, P# e# l- B( C( U* N6 `if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end* {4 g8 I# @ [# S; ?- t% V% T
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end# u0 [: w' Z8 r0 N! P' \1 ^; z: J
if nargin==7, pInversion=0.15;options=[0 1e-4];end) J+ u/ a% I9 z
if find((LB-UB)>0)
. g6 i* ^, v. K1 |% r* q) o ^ error('数据输入错误,请重新输入(LB<UB):');9 r, ]: U: l; x9 s2 z0 `/ A1 e
end8 E7 L E& ?5 d; D H; O. o: h/ b
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
' u0 N9 L% p* }: Tdisp(s);/ Q$ B+ k+ {% z. c9 ~0 b
6 |; `6 O' P' E: o0 y3 _0 a, p
global m n NewPop children1 children2 VarNum, ?7 J+ K- ?0 ~3 Z1 s7 i6 O) j
4 }+ C! A1 j1 O" j* ybounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
% Q1 V( r6 A$ A1 r1 G7 _, `precision=options(2);%由求解精度确定二进制编码长度 r! |4 ^) |. f% V8 j
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
+ M. |. K5 t, @5 j2 D0 H[Pop]=InitPopGray(popsize,bits);%初始化种群4 n4 }* u, A4 Q4 E. T
[m,n]=size(Pop);3 k+ \/ b; k3 s& B4 ~8 X% a( E
NewPop=zeros(m,n);
$ S. D( F4 y# P4 nchildren1=zeros(1,n);; |# N# p- b, n( ?
children2=zeros(1,n);
6 r/ o) ^0 _) N5 O qpm0=pMutation;, @/ g2 j* I# l5 M5 Z. a# t
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
( ], h; Z1 C3 z) t* YTrace=zeros(eranum,length(bits)+1);7 ~: g8 `5 \5 E3 V8 T
i=1;, {0 C- j D! W
while i<=eranum
& Y" M( m- i4 E5 C2 A/ y for j=1:m
5 `$ `& s8 L( \ value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
. B( Y# l( k; a) ?+ K* { end
& m+ |3 Y! u/ E& c' b# i- Y. d [MaxValue,Index]=max(value);
4 C0 f [% Z% k) G( y/ z BestPop(i,:)=Pop(Index,:);
' C* Y3 y7 o7 U8 M Trace(i,1)=MaxValue;4 b! z% P* i% C# @9 u1 E" k
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);, D$ B- F& L- i" v% y
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择) ^% X5 h! s. E( K
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));& m' O( k- Y V% N8 E
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
( j% V- \; c& V %round(unidrnd(eranum-i)/eranum)1 y t0 ^8 H% b+ U/ b* ^
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异+ z9 x" f3 a( Y1 u3 {
[InversionPop]=Inversion(MutationPop,pInversion);%倒位2 P/ k" T; | L8 U
Pop=InversionPop;%更新
' r% l) [) t- ipMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
; D2 u" @! B Y%随着种群向前进化,逐步增大变异率至1/2交叉率3 ?, C& ^' A+ c% Z* S1 I
p(i)=pMutation;
; \- O( X) T, U0 _ i=i+1;
. ]; y/ T1 a. N, p! Q5 Wend. s) D0 K5 {* w, ^4 J U, M' L
t=1:eranum;. B: c" b8 I* a! O: q8 G. F% b3 C" i- _& I
plot(t,Trace(:,1)');: C' L( l1 O' @% Q2 q6 J3 s$ c
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)');
$ j) n& C \+ Y+ i3 e[MaxFval,I]=max(Trace(:,1));5 G8 x& Q& p( Z! j5 L2 U$ C* g
X=Trace(I,(2:length(bits)+1));' {4 P2 y% l0 o6 f) x! C4 g
hold on; plot(I,MaxFval,'*');
0 F; K& v% F! m# R& | P0 |! @0 D6 ttext(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
4 u" f" K6 W# Q( X+ `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,:)));
$ ~9 s$ ?7 K- w( Z! ]disp(str1);- q, p* ]8 g& h7 _$ @6 f% F" V) f6 N# |: U
%figure(2);plot(t,p);%绘制变异值增大过程# F8 e- ~2 J0 ?
T2=clock;9 i( l5 D q7 T6 O
elapsed_time=T2-T1;4 p% M% k, n& |) ]4 M1 I
if elapsed_time(6)<0" A1 A& y6 R K. o
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;. I2 {! q( a7 o0 p2 N% z/ y* q! d
end
* l4 i, P" W2 M# m4 @0 ]# d; j' ]if elapsed_time(5)<05 p6 z2 y8 C7 h J/ @- V
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1; c U) P3 p# s2 f- t' g# E0 w
end %像这种程序当然不考虑运行上小时啦- M. r' }+ ^ G
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));, J+ H& P, J! x, i9 w
disp(str2);3 e7 n6 ]. u1 n s* W
* [0 u* d- u% W" S& M) r" ^ m% D2 z7 C/ y% K
%初始化种群
' _& R7 o; ~- \5 e. _- O* Q%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2 k0 X: [$ n0 ^$ J6 y
function [initpop]=InitPopGray(popsize,bits)
# M# K, l' t3 p' o) K1 Glen=sum(bits);
5 U2 M# H% Z& Y) q/ o, oinitpop=zeros(popsize,len);%The whole zero encoding individual
: K, V# A. J& e; [2 Ufor i=2:popsize-1: x5 v$ a* ^# o8 I' H+ c
pop=round(rand(1,len));: q$ n, x" `- z0 ]( J- V
pop=mod(([0 pop]+[pop 0]),2);: h k7 Q7 v0 V2 g( {* c' w
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
) F& B! M! |3 y9 J %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)# p o# N0 I; d( j& ^" H
initpop(i,:)=pop(1:end-1);7 V# J9 |! d) W+ v+ ^
end
* t% x3 j H Linitpop(popsize,:)=ones(1,len);%The whole one encoding individual+ D& M& W2 h! j; L0 Y& o& T( L
%解码9 \" N4 h; [, I5 U
8 J1 K V1 w: r. z+ a% u7 tfunction [fval] = b2f(bval,bounds,bits): `4 i r: @" i# n& {/ O j2 R( s
% fval - 表征各变量的十进制数
S' |2 m9 B" w8 M7 T2 A% bval - 表征各变量的二进制编码串
3 p- z' N; a1 X* _& F3 `9 \% bounds - 各变量的取值范围
% J0 R. K* ~. F3 b9 J& u' L% bits - 各变量的二进制编码长度; ?1 J! n# y2 k8 V0 q
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables+ E1 y# _7 m: `, c3 L
numV=size(bounds,1);# r) c+ a6 R1 y7 j' @7 y
cs=[0 cumsum(bits)]; ' V" P% s6 N9 u3 f/ b1 Z$ c9 X
for i=1:numV
3 v3 \. |/ W4 M+ `0 `! [ a=bval((cs(i)+1):cs(i+1));
/ Y, H0 K7 ^( g9 \) n" ?3 T3 I. A fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);) P, b) j& Q& v3 n$ s
end7 Q. w, U5 ^1 K& h- i$ G
%选择操作; m2 f9 w& N% q0 n' W
%采用基于轮盘赌法的非线性排名选择
5 e, ?( n) G- U8 Z: `( }%各个体成员按适应值从大到小分配选择概率:
/ q2 s1 g) n& P, h; r%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1) U0 Y6 c: [2 T( C0 n
! V! ^- L4 T" ?9 c
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
2 I h' R& S' w' C& }: F% K( n7 mglobal m n
$ }6 O- R6 m% R7 N0 @selectpop=zeros(m,n);$ j0 f/ H/ i6 i9 A4 ~! Z
fit=zeros(m,1);) e1 f3 x' V. r0 A0 R$ t% j/ h
for i=1:m: J, a' o0 S$ }
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
& G7 ]- p2 b2 J) {end0 x7 m% ^7 g; C; j. c# K" w
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1) `4 U6 T; { U& y
q=max(selectprob);%选择最优的概率. j$ P0 L: l3 f/ V$ e% s' K6 [$ y! x' [
x=zeros(m,2);7 _* \' z* B H; S: w( m: p% p
x(:,1)=[m:-1:1]';
/ ^9 V. D! W" X) X2 \; R' P0 s0 b- T[y x(:,2)]=sort(selectprob);' U, `( _1 {* z' w) T% p% I- g
r=q/(1-(1-q)^m);%标准分布基值
1 D. d0 {2 p4 j% Z$ H# qnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率' t$ \/ }3 T9 h- x
newfit=cumsum(newfit);%计算各选择概率之和
' s' j, o+ c) ?' Z4 T1 ^rNums=sort(rand(m,1));
% R; N8 H" {1 W5 N) `fitIn=1;newIn=1;
7 Y- g* i. a- w7 lwhile newIn<=m
. P* A' c/ \/ x' u1 Y5 |; t3 X if rNums(newIn)<newfit(fitIn)/ D) k" `7 B+ r! k# R+ u
selectpop(newIn,:)=pop(fitIn,:);5 S$ G7 E1 L9 V" f I8 a
newIn=newIn+1;4 }' a9 Y' h5 [( T9 N) V
else
8 x l g3 z6 o8 B. u fitIn=fitIn+1;$ S$ P' i+ @/ J! d) j Q X
end
# ?7 w! c: t" ?- b$ aend" }% b+ R. ^. x+ p
%交叉操作% r5 S; r/ \% y! I9 u7 l8 ^
function [NewPop]=CrossOver(OldPop,pCross,opts) o9 {# }% B0 C/ X8 j4 s+ l; ~
%OldPop为父代种群,pcross为交叉概率' A$ }0 j |8 f- H) Y- R
global m n NewPop
8 M* Z5 b! z/ s4 f8 _# }r=rand(1,m);
% X H* J, S( [2 m, k4 my1=find(r<pCross);
: W9 Y3 i) W c! G" i s# ry2=find(r>=pCross);
9 y. Q% `* I( \len=length(y1);+ \8 z% ^$ y6 V- l
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
: @0 o' \) z. t7 c2 J; H y2(length(y2)+1)=y1(len);2 m2 Z! Y8 T. z
y1(len)=[];
; r( i# s `, Q6 k, jend
' C( G) G1 C4 m8 i, s5 h9 l. o$ [if length(y1)>=2
6 ^8 s) `! ~0 X# ^1 I: t for i=0:2:length(y1)-20 S/ b$ h1 J! `$ U0 O' O
if opts==0
# L4 b9 T4 e- @$ q Z4 p1 ~; f [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
- D4 s0 O# D- A# f else h% N0 J C* F- h0 y+ ]. u
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));- E, r4 Q! l7 G0 A
end
Z# o0 j j" b- I0 C' O( k$ V end
, v. X% x& E7 k P: wend
* {- }# h% H- g# n1 pNewPop(y2,:)=OldPop(y2,:);
/ m9 S# r% J4 z' [& Q7 c% o- D. W6 i
%采用均匀交叉 % k x1 U: N3 V2 O5 D' O$ [
function [children1,children2]=EqualCrossOver(parent1,parent2), N X0 ?) E, d1 n
0 `* Q/ P5 z+ Q$ G
global n children1 children2 ) y4 q* \3 _: u
hidecode=round(rand(1,n));%随机生成掩码. p* c% ]& M' F' A( y
crossposition=find(hidecode==1);( l) _* v$ j, N3 ?) a
holdposition=find(hidecode==0);
3 a# s* R0 ]' L4 g. p* @children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因7 k6 a. M4 e3 i# ?4 n& r/ O" |
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因# S& [6 B$ A5 F! t' T3 y! a
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因2 Z+ d c8 z" y
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
/ g# F7 s# T& s0 D3 ?4 F+ h
- ~' }! v- B# \) x8 q) G%采用多点交叉,交叉点数由变量数决定8 ~2 E8 e7 Y/ N( X7 u3 g3 P5 R
& ~3 `4 Y: a+ G. o2 Z+ v4 Mfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)9 E7 X" z5 p! @: i# a" M7 H
2 U2 ^! [& _3 Kglobal n Children1 Children2 VarNum
: v( e5 z/ M! X% p6 [5 `5 W5 [3 VChildren1=Parent1;, C1 i# v; x2 b0 h9 ]2 }* B
Children2=Parent2;- s# f8 f, ]2 i
Points=sort(unidrnd(n,1,2*VarNum));
, C' h1 G* X4 H4 ^# P: `/ b9 rfor i=1:VarNum
7 D2 ~5 s0 K$ i9 y5 S, U Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
) q7 f+ U5 _2 W# J$ z+ K Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));4 j" J R; S) o" Q. D
end7 ~) G! n5 C- P) i
$ G; C0 v. {: _8 ?, Z
%变异操作; [: I( C$ D: N% t. X( j
function [NewPop]=Mutation(OldPop,pMutation,VarNum)0 S% z Z" \! u% d( @4 B# ^3 a
& A! \9 X# k' a% w+ t- K
global m n NewPop& b0 _% R+ R! s) A
r=rand(1,m);
4 ^- m1 h7 u( B% [. Jposition=find(r<=pMutation);! l! V, k! h2 z/ s0 @$ V
len=length(position);) E2 H& M8 L7 E4 Y0 e# Q" ~
if len>=1
3 T/ r2 |4 e/ u7 R7 w for i=1:len/ }& B' k0 ]1 _# ?% |/ e
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点; i( G- l- N4 u5 [# I( z$ }7 ^( h
for j=1:length(k)
4 j7 H/ Q$ Z( j9 S* K if OldPop(position(i),k(j))==1
3 ~# b c1 |& Y2 h OldPop(position(i),k(j))=0;) | o1 F, e! J4 ]
else
. V4 Z+ j [/ \+ r' R6 K8 _ OldPop(position(i),k(j))=1;1 a9 h, U+ V) w" l- J. S
end6 E! X5 a; C2 _; q
end* t% M3 P9 w0 n4 o
end
1 ^4 S8 D* e' w7 wend* o# s6 o1 r- p D5 [
NewPop=OldPop;+ }; g6 a/ T+ N& W' J
0 ~* Q9 N8 a1 f% S%倒位操作
0 p D# q$ m8 q) e; w# h0 y; g( j; L0 q% m9 a& R; L3 b* o1 e3 j
function [NewPop]=Inversion(OldPop,pInversion)
J, S) n' d# B5 M7 G
' Q* F' ?2 k! Y+ h$ |global m n NewPop
2 p/ l" D( c4 b# n. \NewPop=OldPop;
1 W3 y% @( `: L7 Ar=rand(1,m); g5 p' V+ I: `4 P0 L# Z, p
PopIn=find(r<=pInversion);! ]+ Y$ _9 l5 ^" T! m
len=length(PopIn);
) Q/ |$ m: x! K1 Tif len>=1
! p8 h* k: x) L3 i$ c for i=1:len" D1 s) q3 F" g3 S
d=sort(unidrnd(n,1,2));
; e: c8 G1 Q% e4 _+ B if d(1)~=1&d(2)~=n' x; x$ l9 V& @1 m6 p. o
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);2 k8 ?1 ^1 y. Y7 H) U& `& D
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));0 q/ T8 R$ L3 W0 ?
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);6 ~. G8 q: A5 G8 H0 a
end0 O. w2 {' a: w9 A4 t0 e) m
end
& ~& [4 }- K4 ^/ ^2 cend: ]) {( {+ ]( O
j( d) |3 p' k; |/ P) l七 径向基神经网络训练程序
4 n' {& I, v3 R% z( y& }- p
( o3 ?; c8 ~6 [3 V- A1 k4 S3 Jclear all;/ \$ P7 o% {% f4 c8 o Y2 z
clc;
8 L* j- R0 I1 a+ Y3 C%newrb 建立一个径向基函数神经网络5 C* ~4 x9 e# Q* P3 a3 K
p=0:0.1:1; %输入矢量9 m3 c5 S3 \' I2 c U
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
6 e. |$ G! `7 hgoal=0.01; %误差3 I9 U8 s: Z3 F
sp=1; %扩展常数2 X; T. C3 p' z3 n
mn=100;%神经元的最多个数
; D" `1 x4 [* H" ddf=1; %训练过程的显示频率0 K9 H4 n% N/ @- R( E' U
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络) j: d4 G; L& `
% [net,tr]=train(net,p); %调用traingdm算法训练网络
+ r0 O) b& a9 r/ N%对网络进行仿真,并绘制样本数据和网络输出图形
5 y6 I( y8 f& E" M7 l' p' Z4 z0 z6 aA=sim(net,p);: r) X" V4 W3 {, q
E=t-A; B: ?0 n! J) }( z& M
sse=sse(E);$ y3 j) S. \8 [
figure;
0 J! s3 U. g2 i" N; Q+ e- Rplot(p,t,'r-+',p,A,'b-*');0 Z+ `9 y" y% {8 N% H
legend('输入数据曲线','训练输出曲线');
: A; N4 }4 O5 y" D9 e# gecho off e. E) y6 X4 t6 ]5 n! ~
5 f9 f; p ], V7 s& Y$ s
说明:newrb函数本来 在创建新的网络的时候就进行了训练!9 s3 u! J$ m- y. x" J- K3 ]
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,; u! `% C, m) @/ ]0 B# a9 E/ X
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!9 u! }' l9 c/ W+ n, E) _
5 S2 @1 D1 N1 ~$ [ ^9 _' }, K
$ S) x- F% {( R: ?# e) _1 m训练结果显示:% B0 q+ b, w) m3 s) k
NEWRB, neurons = 0, SSE = 5.0973
) o1 w: [1 q& [# A0 T9 ANEWRB, neurons = 2, SSE = 4.87139$ X V4 }/ H# k5 f2 |
NEWRB, neurons = 3, SSE = 3.611766 ]. n+ A3 u& ]3 }
NEWRB, neurons = 4, SSE = 3.4875) h- K, Q9 D2 J" F. W {7 k9 J9 X. g
NEWRB, neurons = 5, SSE = 0.534217
* X/ w4 j& |4 W9 H9 DNEWRB, neurons = 6, SSE = 0.51785
/ E7 x7 y- p- R9 CNEWRB, neurons = 7, SSE = 0.434259
; }# d% r2 f' Y; M, Y1 \3 L$ k6 _NEWRB, neurons = 8, SSE = 0.341518
# C. }: C" I# E" Y* _* a* ]2 m8 ^NEWRB, neurons = 9, SSE = 0.3415191 k; i& C6 o! V# [
NEWRB, neurons = 10, SSE = 0.00257832
" I$ v) [) `' z5 }* o. V/ W6 ]+ E# c2 x# d- J7 i \0 Q& p* D ]
八 删除当前路径下所有的带后缀.asv的文件/ Z$ \/ V+ w0 x: h$ n
说明:该程序具有很好的移植性,用户可以根据自己地8 z3 i# E( | L% N( @1 P
要求修改程序,删除不同后缀类型的文件!
* T6 k2 l) \# X R( j$ z% Xfunction delete_asv(bpath)
! h9 u5 S* a( o J( _%If bpath is not specified,it lists all the asv files in the current
2 t% s1 h! F. _5 A%directory and will delete all the file with asv
5 W, l$ p- O' ?. F" f- R% Example:# r6 t2 x( h" Y9 g0 Y3 l* {5 C
% delete_asv('*.asv') will delete the file with name *.asv;& t; p Q" O* H/ u6 e9 \& r) `
% delete_asv will delete all the file with .asv.( b4 j) `; m0 D* U$ k9 l
3 X( {6 j( ~( N, d* g, _( ]5 {
if nargin < 1& h# A. L, [) {/ o2 s( G0 M: o
%list all the asv file in the current directory
g$ I# R2 d8 X9 I: y) n& [ files=dir('*.asv');
: Q) P& e/ B1 C* b$ y5 H. _. H2 Lelse
4 Z0 U' N4 S" c$ @% find the exact file in the path of bpath$ I; E5 K0 |) |4 C' w
[pathstr,name] = fileparts(bpath);! i# Y0 Z0 t% M! [/ A
if exist(bpath,'dir')$ U# v3 B* |4 s, U( J
name = [name '\*'];
/ ^, m7 D D4 n! ]% K- y1 u5 L: u end- J, S7 U1 ]0 f2 c* u" C/ h
ext = '.asv';
. Q5 u& h3 C# Q( y8 Z! D% g' z3 R files=dir(fullfile(pathstr,[name ext]));
$ H- H. [6 o/ u7 J G; dend
% M2 o9 d# J/ g' @8 ~$ m
& f( X# v! R, Tif ~isempty(files)
& j5 _1 l3 R$ H/ u) t4 D for i=1:size(files,1)/ I! f, E0 w" J' k6 A: K
title=files(i).name;
- B/ V5 X. W6 p; U& J0 j delete(title);
) _6 T# y0 o0 K7 X) {7 C: T, } end0 J/ w8 y- W8 ]
end* g0 i8 ?1 s* \& Q: y! Y8 B/ e
9 U4 Q) R% O! {: C; U, f" S0 q3 o5 s$ ^1 q% @! Z0 Y
同样也可以在Matlab的窗口设置中取消保存.asv文件!* v2 m/ @) Q) I `# E l, L
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