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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; [: _$ v* b; A% I- Q1 H6 v
1. predict_fun.m为主程序;2 x# \6 S% c- O( H u' V4 T
2. timeseries.m和 serie**pan.m为调用的子程序
3 J% g* E3 E; V& C& ^: o
) V5 B5 W ?# z# B8 Ofunction ima_pre=predict_fun(b,step)
" T: ]( Q7 N2 O. j% main program invokes timeseries.m and serie**pan.m
7 R7 H8 {( ]4 y! _7 O/ [% input parameters:
. i* a$ ~0 ], y* @0 S' Y4 i% b-------the training data (vector);
7 s7 D* z. \# D' G% step----number of prediction data;
1 X- V6 `. ?- p4 V7 U/ V% output parameters:; r$ u: I5 C- u3 Z Z. K; b) W
% ima_pre---the prediction data(vector); M+ }& }$ V9 @; m. J( A, D
old_b=b;( U+ c7 u: P# h- U2 I
mean_b=sum(old_b)/length(old_b);
! E( i3 e, B! Dstd_b=std(old_b);" L6 v$ A, L! @9 ]
old_b=(old_b-mean_b)/std_b;
( c; o& j1 B& I' G1 K3 W4 k[f,x]=timeseries(old_b);, E+ h. J u* J( _) Y
old_f2=serie**pan(old_b,step);
/ Z f1 c+ p" w& [1 e% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;
7 L% q5 V7 W' WR=corrcoef(f);
1 z3 I; b- r+ g' Q% l8 q% k8 w1 F[eigvector eigroot]=eig(R);$ f% E8 R4 ?: A. E# U) h
eigroot=diag(eigroot);
9 f) N! E. k" q2 t1 |, va=eigroot(end:-1:1);; N8 X0 @& j# a, v3 {7 a
vector=eigvector(:,end:-1:1);
4 `: {0 u0 B2 ] QDevote=a./sum(a);
9 X5 A% O$ K9 GDevotem=cumsum(Devote);& d7 Q7 x: h9 N) G0 G/ C
m=find(Devotem>=0.995);/ I1 k6 b' Y8 h9 t" W2 X
m=m(1);, f( o! B, Q- L" l
V1=f*eigvector';
9 u1 l' I# d8 Q& _1 U; gV=V1(:,1:m);
( q" I' S- w% |7 e1 z' d% old_b=old_b;7 }' d7 d5 _+ ?7 Z& r
old_fai=inv(V'*V)*V'*old_b;
1 x$ Q3 H- p5 Oeigvector=eigvector(1:m,1:m);! z9 A) v b" A4 D
fai=eigvector*old_fai;
6 R, O6 o7 K1 Z- j! ]' lf2=old_f2(:,1:m);. e0 @7 Q4 z- k+ {8 h3 N; s3 F$ B
predictvalue=f2*fai;
! v7 D( N6 j3 \ima_pre=std_b*predictvalue+mean_b;: I9 o* e& d& z
3 | K+ ^3 x% g$ J; t1.子函数: timeseries.m
* b% K: h6 m8 A$ l: G% timeseries program%
# q c( T' a8 j4 `: B1 P; A3 Z% this program is used to generate mean value matrix f;. J& L5 H7 ?0 B) Q
function [f,x]=timeseries(data) % U1 l, b3 ~, v
% data--------the input sequence (vector);
$ E% Q+ |, V: I' o r% f------mean value matrix f;: g& _2 O( ~/ o) O
n=length(data);
) ]$ E9 y+ y/ q. b: q8 rfor L=1:n/2
! j: H" D0 G. W+ h nL=floor(n/L);& a, G2 M3 C5 n t. z- ]8 B; R
for i=1:L
" b+ W& A3 o: R6 P sum=0; e3 C& }8 i5 Y* y& ^' ^: [
for j=1:nL; H j9 i: @. z% d6 r4 b
sum=sum+data(i+(j-1)*L);6 Y( }6 A8 l- x6 F; l; Z/ K
end' ~" F5 g; _# J! e
x{L,i}=sum/nL;; X1 g8 M+ y% ~9 S2 o) R+ b V
end: c1 f4 ?9 i: o+ m& p( b/ A
end
; B- V l/ r* I8 c1 r! n! ?L=n/2;/ f7 w2 q2 p A- S( i' O
f=zeros(n,L);
* i* B( K) l/ f; E# Lfor i=1:L
% {. i, X3 w) i+ ?6 d6 s4 r rep=floor(n/i);
: c0 c% o% I, D; }. K res=mod(n,i);
& w" s/ Q0 e* K- e! } b=[x{i,1:i}];b=b';# S& Z/ J! G! {) J
f(1:rep*i,i)=repmat(b,rep,1);- t' ]% p/ t8 [( u! f* `
if res~=0
! E! C3 n: f8 X) a c=rep*i+1:n;
D6 R! Y' E% c" @7 M f(rep*i+1:end,i)=b(1:length(c));& Z, T' t8 K- U4 E6 W! ~# F
end j2 v7 L# p& O
end
! y& T6 A, ~5 z0 i' f: U
U. L1 S; C9 m/ m# d8 \) t% serie**pan.m2 Z3 |8 z: r4 A: y% S
% the program is used to generate the prediction matrix f;
% I' K0 Y- {1 bfunction f=serie**pan(data,step);# v: ^3 Q" q* \$ q4 R2 d, Q5 G
%data---- the input sequence (vector)" H; V' ?9 H+ I' K, G# H( S1 u. c
% setp---- the prediction number;' J8 q* \$ c7 P4 J' t; C
n=length(data);- K) K0 w! q. b U6 {. X, O& N5 Z$ \1 r. x
for L=1:n/2; t3 U% A# ]/ j: Q- C* ~
nL=floor(n/L);
9 t) C/ L* Z* V; _& F+ D8 _5 ? for i=1:L
Z, Q' d5 ~$ a" n* H1 U; |$ m sum=0;9 U" y* r X( [& n: c$ x
for j=1:nL
# e2 A+ v3 F0 f5 j! j7 q4 m sum=sum+data(i+(j-1)*L);
4 O' Z$ ^( M h! C6 I+ S u5 f end
6 V; o; V, q) {# r x{L,i}=sum/nL;2 f3 M5 s/ k9 s$ L# C. {% j8 S& @
end t+ d* ~* W. R1 c( w
end
2 x& [; g; q, A7 L. @; V Y$ gL=n/2;$ X4 B$ y1 k8 Q/ U# g9 ?& u* B4 {
f=zeros(n+step,L);+ z) R& i0 x" S- v
for i=1:L
2 ?5 \6 P1 S) I0 x L& o% _ rep=floor((n+step)/i);+ ~6 h2 W) U. Z+ M. f3 x) e M# D$ L
res=mod(n+step,i);. y% N8 s( n; a9 e
b=[x{i,1:i}];b=b';) R8 `0 [8 s7 f$ U- G
f(1:rep*i,i)=repmat(b,rep,1);( q+ E1 q' r% E0 D. D) F; G* A
if res~=0$ [+ i0 ~2 _& i- d
c=rep*i+1:n+step;0 r4 {/ D3 c) d2 f4 z! V( x! z) j/ c) `
f(rep*i+1:end,i)=b(1:length(c)); p" [8 F5 c! W+ ?$ ]
end% | C8 ~. W$ t9 K+ D$ T
end7 P; s) P6 t9 Q3 y) a5 [) f/ e
" \9 \. i0 O8 S# t; e2 ~5 W
二 最短路Dijkstra算法
, V. g9 H; [! m, P2 i* h4 T% dijkstra algorithm code program%
, }. w$ Y& M& G X5 y0 c% the shortest path length algorithm# q) e3 K: a. a5 @2 s% _ g# ?
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint), V9 B+ b) u8 n* ^
% Input parameters:
- W( Z ?, O9 c2 n7 Y% Input_weight-------the input node weight!& I1 n+ Y. ]* M: j) G2 ]& Y# H) w
% start--------the start node number;% s( o% n% C a5 P8 ^5 F! D5 j; D
% endpoint------the end node number;, d7 r# G' J/ f0 a t. [8 [/ ~
% Output parameters:$ W5 y4 z4 [/ k/ E( \: O3 b; f8 d
% path-----the shortest lenght path from the start node to end node;
6 P7 r, ?5 ?8 r) J- L% short_distance------the distance of the shortest lenght path from the% F( H9 K5 U4 D1 b6 d& w0 |; f5 d
% start node to end node.
/ Z- U |0 d6 n6 m. B[row,col]=size(Input_weight);# N0 E e9 h& m, N2 f
" m) S9 S2 ` U%input detection4 o- _, E7 Q4 Q6 g$ j
if row~=col
# }1 d1 Z' u! e* Z3 `5 }! H error('input matrix is not a square matrix,input error ' );
: M3 a/ R. o/ v& w2 ~# ^end) g) u6 ^8 b0 E; x1 R+ i
if endpoint>row7 ]: M2 j6 v+ \
error('input parameter endpoint exceed the maximal point number');- h1 ^! D5 B# l8 G( L- }1 l
end
, m% _/ ]6 k% f i7 D, F: e
9 I* P$ v0 P8 u6 u' O; U$ G%initialization, ~5 b w- H: o5 X" s" b
s_path=[start];8 I* v& S. Q6 G# C+ c
distance=inf*ones(1,row);distance(start)=0;- ^. F2 x. D9 i
flag(start)=start;temp=start;: z- o$ h- T9 U& p7 Z' P
! \0 j" g* Z3 B+ Z; c/ y
while length(s_path)<row& f9 `+ _) a( k: E) m( E
pos=find(Input_weight(temp, : )~=inf);
$ `& D% v7 I* e for i=1:length(pos)
* s+ m% h, ~/ j1 @ if (length(find(s_path==pos(i)))==0)&
( } [/ n: W' d(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
; Q8 c Y& O0 v% q- N H distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
4 G/ E! R5 c! _6 ?) m1 t, d6 p+ i flag(pos(i))=temp;0 e5 V, D6 r$ U+ {; ^
end8 u3 [' x2 ]$ Z; X7 h
end
6 w, e; ?, p" N8 e- Q k=inf;! @% r/ A: h6 K0 I, h3 A) g, b3 ~
for i=1:row* R2 ^3 B: R- F$ _- g @8 D, ?0 R
if (length(find(s_path==i))==0)&(k>distance(i))( F3 X$ f) d% F2 s
k=distance(i);
) q& Y1 R. p! u7 r# o7 U temp_2=i;8 n9 x1 |- C- G8 D0 V) R
end" e& ]1 G: N1 Z6 Q* x$ n
end. b3 }4 i4 S6 L4 b `1 b+ u9 v4 U
s_path=[s_path,temp_2];$ c5 A& B0 `; m/ p s+ E) v
temp=temp_2;
9 g w% N. E$ p) a0 H' g9 ]; zend
! ?2 T( k+ E, \4 T8 V8 W* S9 E1 T$ H7 h- D' U7 |3 g
%output the result
" e) n& K4 j" Tpath(1)=endpoint;4 r" i! k) c3 w' _$ C- N) P: M
i=1;* D& f2 u: ]" P2 R1 D' s
while path(i)~=start
$ n5 f4 H! h* c: C path(i+1)=flag(path(i));
, g7 i+ J2 Q% q i=i+1;
' q# `6 e' |7 d# n0 Z8 J7 aend
6 s! |2 S/ Q1 R6 _2 A) z& c6 O5 M1 }path(i)=start;0 t- a8 f/ v. A& N! A
path=path(end:-1:1);
7 d/ ~" g- [* ?6 M9 I, b" U; Cshort_distance=distance(endpoint);, l% J* Z) `# u8 |' P$ ^
三 绘制差分方程的映射分叉图
, l4 c! m, X2 f2 q1 L C" K+ e/ i6 g7 A& H1 @
function fork1(a); 7 G1 p; \ U: a4 ~
! F3 F/ D" Q) G+ S% {6 g
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图& }9 `7 m2 S3 P2 s7 S6 }3 O( y
% Example:
9 [' u2 |5 U. D& U4 L% fork1([0,2]); ) m2 I: i( X( o) m' r
N=300; % 取样点数
( v# N& I! c+ U" pA=linspace(a(1),a(2),N); 0 w# L* N1 Y( `3 S8 c2 O0 j
starx=0.9;
' K) n9 Y: L5 @& [( `% q' iZ=[];, ]# B) J5 r w; |5 M. d7 B
h=waitbar(0,'please wait');m=1;
# c* H# I' n' j) ^; Z) R, g5 xfor ap=A; $ {$ K0 E$ }8 K6 _
x=starx; 6 v7 i( O9 n( [5 n9 G8 h( F
for k=1:50;
0 s' w, J2 f) y8 r) V3 w- I; V x=1-ap*x^2;
6 H4 B) a; C3 J, l! V; a end 3 e4 R M( r' ^0 z- T* Q
for k=1:201;
" r- f' D3 t) @# Z" k0 s x=1-ap*x^2; ) p" @1 `' _ P5 c4 {1 I! T
Z=[Z,ap-x*i];
, O& v( r: o! d7 s+ p5 P* c end ! O6 x! W6 T% Q; q( T0 s
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);( M3 {$ |& I x! q9 Y+ f
m=m+1;! h% }7 j: S( ]3 Q* m0 S1 f4 B
end % F6 y: z$ m6 u# Y% w
delete(h);; U" |! Y, R; w
plot(Z,'.','markersize',2)
, F. }2 [8 m' v5 J& Txlim(a);( S* K, d! Y1 ~) p. V1 J" A \
% W9 ~/ n) ~- v, c四 最短路算法------floyd算法7 m1 l( W5 }7 N6 o+ v, C
function ShortPath_floyd(w,start,terminal)
+ k& e- P0 w- Z7 N( M: _%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
6 S, s# A$ g5 n1 S8 u: t5 w9 V' }%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
' E) o# ]* R& @# q) R3 u: e; w% @%start-----the start node;8 P# ]) v3 k8 ~1 Q& j; d, R7 g! G
%terminal--------the end node; / q* R8 M$ @ ]0 \) c
n=size(w,1);0 d% ?3 l$ ^1 ` V6 S: k! M1 R4 }
[D,path]=floyd1(w);%调用floyd算法程序$ G$ F8 V2 m$ [) c! ^4 ]' y
; A3 g' a" w' @* Z9 P; {%找出任意两点之间的最短路径,并输出4 [1 D- n0 A+ N& k& Y8 S F
for i=1:n/ C. p7 |: x0 S' G' c' X
for j=1:n* Y |( k. W) i5 h, ? u2 ]
Min_path(i,j).distance=D(i,j);
7 D/ C% O' q. o8 t %将i到j的最短路程赋值 Min_path(i,j).distance8 M# W2 \9 a, d
%将i到j所经路径赋给Min_path(i,j).path3 s4 z6 o( C. R0 r8 U
Min_path(i,j).path(1)=i;
0 u$ j( [$ W- r, T( N; ~ k=1;& B; v( b- b! _: Z6 O
while Min_path(i,j).path(k)~=j& h' V- D. O$ }1 r0 H
k=k+1;3 h: ], i4 A- f, S( x$ q* {
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);# v6 \- j4 i3 z& \
end
6 j4 a% |2 n! v" t end
& t! T6 S0 F6 i4 A) ^5 m0 xend) X w& h/ |; J% e/ ]; P8 `: m- m. I- F
s=sprintf('任意两点之间的最短路径如下:');
% l# v1 `8 l+ r6 P9 d5 D6 _9 Gdisp(s);4 ]7 C% Z [% D1 N% P& q
for i=1:n
& T" Y. a( L; ~# G j/ ~ for j=1:n
" _# y6 @# `1 [' I. c s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...5 ~- c( R& P) X0 G; A1 y" F) D/ s
,i,j,Min_path(i,j).distance);
( H8 p2 `% d4 ~4 E H& _ disp(s);: K( x1 |! A' Q6 `% ]" l
disp(Min_path(i,j).path);$ _4 z" e0 R* p' e( @' N
end
) J6 j9 t" r3 V# Jend
6 {8 N+ U( U @/ a' h+ n' T% v9 n) ^' Y9 a! ?/ [. Z
%找出在指定从start点到terminal点的最短路径,并输出4 R8 r( |9 w2 Z. h
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...! {6 b+ }4 Y" P. A+ a2 O
start,terminal,Min_path(start,terminal).distance);+ Q' T# t* n6 X# Y7 f
disp(str1);. B' l' h; a# [
disp(Min_path(start,terminal).path);4 \6 r" ?: S8 c* g
" j# i |4 x: r7 K5 z
%Foldy's Algorithm 算法程序
: y/ o+ i" E& g5 F6 | Ufunction [D,path]=floyd1(a)
: }% c. ^& d' X: i8 u- q! kn=size(a,1);
: k. S3 M7 L4 K! U1 QD=a;path=zeros(n,n);%设置D和path的初值% X' c# O5 y" G1 _2 s5 }
for i=1:n# ~. s5 z" _! x) K! @6 v
for j=1:n
& m! M6 \; r/ y G8 u$ j2 V if D(i,j)~=inf
. m1 P! w# j1 [+ h/ s: R8 J path(i,j)=j;%j是i的后点+ |) J; b$ ?' C8 B3 P
end2 k7 g# o* _7 F5 ~
end: [4 J* R; R/ [% m( P! T# j/ d7 ~6 s
end
, {2 C' l) e1 B/ V. [%做n次迭代,每次迭代都更新D(i,j)和path(i,j). r9 F; Y9 q0 z! f/ V0 }3 ]
for k=1:n
, s1 D' x; a+ r" W5 _ for i=1:n4 G: D- Q6 s* T; O$ P6 c
for j=1:n" o& x0 }/ F- u
if D(i,k)+D(k,j)<D(i,j)
4 A8 c* l: g6 P3 E% \5 \4 [% ?0 H* g D(i,j)=D(i,k)+D(k,j);%修改长度9 `" R( F; h0 t6 [* O8 ?4 M: G
path(i,j)=path(i,k);%修改路径
5 L4 ^ o% q, ^ end
. h: a2 B, R$ v% `3 t end
4 s) Q5 d, W# i; ^) E5 j& v c end
! w; Q# x6 M0 l3 t% M0 fend( t0 k2 U3 }+ ?% E" i" T y
$ N) @6 w3 D' [: b1 L! d7 e
五 模拟退火算法源程序; Z2 R; B K* g/ O
function [MinD,BestPath]=MainAneal(CityPosition,pn)
9 F! }0 F$ [5 {4 A5 E" Jfunction [MinD,BestPath]=MainAneal2(CityPosition,pn)4 G( `) r5 q# O; ?; W% S {. j
%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
$ f! d8 B/ r" M1 I: l$ c9 O4 o%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...) B9 x* Z5 p3 b2 i" ^8 [/ S9 y
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;.../ ^2 A$ l/ X( Q- i1 j" _/ v+ v
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
3 z2 N; L5 f7 v# ]9 G% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...1 S$ i+ g! b- Z1 ~
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
" K+ r/ _$ y9 H/ H( X8 b
" o5 k+ {0 S8 ^%T0=clock- ~* V5 h: E7 _
global path p2 D;
2 I: x- i3 g& F" [# C[m,n]=size(CityPosition);" r9 @+ ^% T! _9 Z0 F
%生成初始解空间,这样可以比逐步分配空间运行快一些
. b5 Y5 R3 G3 ~! }TracePath=zeros(1e3,m);
! J6 [5 N+ G* \# g" @+ l3 y/ ]Distance=inf*zeros(1,1e3);8 P S7 }. ^ y5 G0 t* w
2 R+ G" B$ E& o8 [1 b5 P! \$ b
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
. e2 D! S) V/ X# l: Z+ H (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );$ ] n: V, A, E2 ~6 {) E! ^+ Q1 l
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
2 E3 N, y1 |' D4 i5 ?for i=1:pn
n6 E" p% u) L; |$ k path(i,:)=randperm(m);%构造一个初始可行解
8 @5 e4 ?+ ]; B. D6 l; D4 zend
; ]- ]7 p/ H0 _9 J1 Ct=zeros(1,pn);
4 b# g7 p, e8 c. kp2=zeros(1,m);+ ?- V( N( [, y8 r: H
' `' H$ d: f0 P! U. }4 [iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
% W ?' |7 [" M9 \. ~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=' ) ;
5 Q0 S: b( y% F) D. D%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 v0 t c+ Z P P/ h3 g
%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
: P7 ]( M/ O9 i%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' I: J4 u% M/ o3 Q1 z2 x* l
%会收到到比较好的效果4 p( }' u; q4 o. C7 i
! r8 u3 I# a7 u2 m |7 K4 GT=1e5;
' V _9 u" J* N! [% F+ oN=1;
) E! J8 A7 A7 ], A# w" ]) K7 q/ Utau=1e-5;%input('请输入最低温度tau=' );: o8 }) U& O( o) p4 g
%nn=ceil(log10(tau/T)/log10(0.9));0 b& t' }) R7 i8 ]
while T>=tau%&m_num<m_max ' `0 [3 x! o b
iter_num=1;%某固定温度下迭代计数器" c# w; \# x/ U& b8 \: W: e$ s: Q5 x# Z
m_num=1;%某固定温度下目标函数值连续未改进次数计算器
6 y- J2 A$ M. p0 m. y, N %iter_max=100;
: B% W; N; a W. L3 W3 a/ k %m_max=10;%ceil(10+0.5*nn-0.3*N);9 ~9 W. t" o6 q; J1 g
while m_num<m_max&iter_num<iter_max
3 K: m4 w! P4 Q. C& t: R9 v8 A% ^ %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:/ j T0 w5 t( O
%用任意启发式算法在path的领域N(path)中找出新的更优解
Q& Q0 v1 \/ C/ U5 R6 C- W for i=1:pn$ D8 g- i, v9 g4 c. U5 M5 Q' s0 E
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
, F1 k# v1 _7 \. {5 J }8 ]; p( d1 f%计算一次行遍所有城市的总路程 4 d. J/ `$ |" N+ U
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线) }+ V% L+ U0 Q9 [& ^! G+ O6 x- 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))]);
# Q, k* y% X7 b2 h; M1 e end
) {" ?" r3 ^: v1 C0 e %Len1
8 R1 u- k! H( b %Len21 ]2 x' J; o+ I- a ~! R
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand( S% `/ I1 k( _% G( F7 S! h
R=rand(1,pn);
/ b5 ^" O; L9 }6 \' B# } %Len2-Len1<t|exp((Len1-Len2)/(T))>R H0 Z/ F3 g5 e! R" f
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
6 e! y/ H* U7 W; N- a! f path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
' U6 |; ~. K/ P! `. ^ Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));# e0 E3 g" V1 R8 L" B$ L
[TempMinD,TempIndex]=min(Len1);9 z4 Q: D7 S% s" C5 `
%TempMinD
& N6 e* Z! c" _- m' e# C, h TracePath(N,: )=path(TempIndex,: );
, ~/ D+ D0 n! Y6 g& C Distance(N,: )=TempMinD;# x9 D) o! q5 `! t- } n
N=N+1;
4 N$ K. P! Z3 `2 i0 g %T=T*0.9, P% h' ~" }) Z$ a) Q% G
m_num=0;
9 m3 {8 `; R$ Z else4 B) P J& E, G$ y; O8 i
m_num=m_num+1;
( |/ C" t" F9 B8 e end K) l) e8 u( `" D5 d
iter_num=iter_num+1;5 c7 U: B4 C" P! ]& x
end
6 T( q) _! N2 t5 _, |# F. n6 Z T=T*0.9
~. \- w5 ?& U" m- y%m_num,iter_num,N! w* d% ~" \$ f" r+ u6 ?
end 0 z' n- F# L+ j+ [
[MinD,Index]=min(Distance);& s2 M, N5 P( t& w* F3 y* k. j
BestPath=TracePath(Index,: );
[+ c$ m/ M& \disp(MinD)
+ _2 q E9 q# O, g: M%T1=clock/ D. Y$ Y- q5 R1 [9 Q2 Q3 P# i
7 Q' c, N+ l3 G
0 y8 g( y& S4 A8 g( B- ?* f# H%更新路线子程序
5 ]7 E2 D) C0 z) M. |function [p2]=ChangePath2(p1,CityNum)5 j2 P# |2 C& B) i G1 W
global p2;& [! F3 G: \1 v( d* b! C: D
while(1)0 y# i4 T- d: W( d; ^
R=unidrnd(CityNum,1,2);
) Z, d4 c. l. V; Z' [/ { if abs(R(1)-R(2))>1
) h" B; `% ?0 m+ F break;' w9 V/ s R5 S8 k1 v) W$ X: X4 C
end8 a5 u) s9 Y. x' d
end5 {7 [; K5 i- A' `
R=unidrnd(CityNum,1,2);
# y( ~! _6 _5 @. H2 J, k0 xI=R(1);J=R(2);; v3 B( L8 ?* [, R2 z: G' }8 A
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
# }6 X4 J6 J, X; c. A%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
$ K. i: }) l3 E% d" Yif I<J
1 U7 i& [. k' v p2(1:I)=p1(1:I);$ P- E7 Q m7 G0 ~3 M4 w
p2(I+1:J)=p1(J:-1:I+1);
* L# s0 S) h9 C% A+ c2 c7 v+ f2 E p2(J+1:CityNum)=p1(J+1:CityNum);) w: [2 n& k! J6 p, j/ T$ A: z4 N* R
else- l$ W/ }: b! p. B# W! U
p2(1:J)=p1(1:J);5 p' m& z+ [% x) [
p2(J+1:I)=p1(I:-1:J+1);& `4 F- x& `9 |) @+ D; O
p2(I+1:CityNum)=p1(I+1:CityNum);
0 Z! I- q2 J! {# {$ l1 @& L3 b4 c+ pend2 Z2 j# S. b5 z; v3 C. F
$ Q0 B, S3 v* A4 w7 J六 遗传 算 法程序:) F- ~, C ^0 `* w4 h6 h0 a
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!+ |0 Q( R1 |* Y# R0 y" d7 q
% M0 E) Z7 |/ q8 a( g% n/ T$ Q% B
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
1 y- w0 E" C$ l; O! ^: q; f% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
/ D" a& C/ W* e" N- T0 v% Finds a maximum of a function of several variables.
3 g/ ?5 n' i! b% fmaxga solves problems of the form:
) |/ }5 L% V- L9 g0 n9 H% max F(X) subject to: LB <= X <= UB
0 W+ K9 Y9 m1 F% J% BestPop - 最优的群体即为最优的染色体群2 K2 e2 _/ i9 M/ W8 R% |4 i$ y
% Trace - 最佳染色体所对应的目标函数值+ c/ H3 \3 o; y
% FUN - 目标函数
$ z' [7 h$ i+ T+ p# n P3 _$ M% LB - 自变量下限
# f( {- Q% v' L5 ]% UB - 自变量上限3 F0 ]+ j% A3 k
% eranum - 种群的代数,取100--1000(默认200)
9 H# M$ D" J8 J2 J. e% Q% popsize - 每一代种群的规模;此可取50--200(默认100)3 i7 m) {" J J3 @5 f; Q9 K g4 d
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
7 I% v: G( A( o+ G% d% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)$ O' v: a8 f& ?2 M0 ?; s
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
! b7 v! ~) e' e1 x9 S% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
7 v7 _/ k, @7 |( s+ T9 s" K: E%码,option(2)设定求解精度(默认1e-4)- r+ ` w% B7 G- M* {
%
% W* x" f3 j+ i, P9 `" ?% ------------------------------------------------------------------------
4 F6 p1 ^" x+ q" |* T/ a* N& r8 a1 }- I$ \. S, ?
T1=clock;5 j2 V& e; P! a8 b- @
if nargin<3, error('FMAXGA requires at least three input arguments'); end
2 g% D6 u! S& D" Rif nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end4 c5 W _7 S3 K& {- }( @! N
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
3 j7 E A0 }# n) m5 W9 z# \ cif nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
- V+ }% p/ W) v0 z$ T# ]$ D- iif nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
" f6 ?4 k( o/ D) l; N, @if nargin==7, pInversion=0.15;options=[0 1e-4];end
% `3 w* r* a ]0 B7 ~if find((LB-UB)>0)
5 W" C( O0 L- B% |8 X8 R error('数据输入错误,请重新输入(LB<UB):');
! }+ T. [& \4 b* q6 Xend$ s5 C% N& Y; i
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));/ U9 y, b, v/ C1 G2 g- b j( q
disp(s);
2 X% W- e) |: M4 h# }9 S: Y( W7 F; z6 R
global m n NewPop children1 children2 VarNum
- r! l7 b& q) |" b( g5 L$ N5 q; ~( `
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);! r/ x) A* J7 p4 J9 G: j
precision=options(2);%由求解精度确定二进制编码长度5 m. J' j4 Q- D8 P6 b
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间, n$ p0 z- p! L9 n2 @
[Pop]=InitPopGray(popsize,bits);%初始化种群
2 M/ y& K+ I: N4 B" f ?0 I' w' }[m,n]=size(Pop);4 {) ]; q9 D4 t. Q
NewPop=zeros(m,n);" K; ~' h1 _3 e$ d% q, X; `) S8 ~* x
children1=zeros(1,n);
2 w8 A4 h) D/ Z! }0 g- K; lchildren2=zeros(1,n);
0 r) U9 Z4 P9 ?* ipm0=pMutation;
* T! ]' e( Y( R( O) yBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
8 Y) y6 w9 B4 w( C9 _0 BTrace=zeros(eranum,length(bits)+1);
6 Q; Z5 ^5 F( y0 p5 j/ ki=1;
! r Z& X) B7 f$ t) Iwhile i<=eranum
/ C. V& i, c/ j. \8 X! H: ` for j=1:m
( _2 W% R8 E5 ?2 E0 `8 b) ]1 F value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
: u5 E" v/ r0 N6 _* v end
) H( d- w: w8 H2 S [MaxValue,Index]=max(value);
* Q5 t& I* k" j; R9 \ Q BestPop(i,:)=Pop(Index,:);
5 X: v' R9 L4 c" Y" V- M Trace(i,1)=MaxValue;
O. d; _6 X5 X* N0 E Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
5 R" q& g- b# L3 \# { [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择% L+ n4 w+ C! D }% b$ ~
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
8 e4 ?, M! F8 N6 I%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
9 x8 @, `6 O8 |6 Q# O' T %round(unidrnd(eranum-i)/eranum)- B" N" i: T( \& L% A
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
6 q9 }& B4 x% i [InversionPop]=Inversion(MutationPop,pInversion);%倒位6 l* \- ?) L, ^: o
Pop=InversionPop;%更新
* }7 p d2 T9 ]2 fpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); / X. Z7 A7 O* l( S! w4 U$ T
%随着种群向前进化,逐步增大变异率至1/2交叉率# }- P1 F$ X) r! V. o( S6 }
p(i)=pMutation;. ]) C$ A* J6 w9 G2 g' a* m
i=i+1;
1 @$ I' a' s/ [, aend: n% a: T9 |* |8 c$ _
t=1:eranum;9 U! |+ F8 p$ |5 Q, C/ x. r. t$ R
plot(t,Trace(:,1)');
7 Q ~+ F9 k( g) s+ Ttitle('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)');( Q$ W' [& Z W6 A
[MaxFval,I]=max(Trace(:,1));
4 q9 x/ T3 R7 D3 y) C, @X=Trace(I,(2:length(bits)+1));" C0 U/ e# Y8 t! P# A' T* F
hold on; plot(I,MaxFval,'*');
# p- z# T- z4 ^( Vtext(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
; f# T( O1 }. N! Kstr1=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,:)));- X( L5 ]* F2 w6 b1 n! L3 L; t
disp(str1);$ R- v' L8 m) T) Z4 n" w
%figure(2);plot(t,p);%绘制变异值增大过程
7 t8 T+ G& i& Y7 I$ K/ ]T2=clock;% t4 F5 l/ u; D
elapsed_time=T2-T1;
, \; _+ ]8 G. R1 a8 [if elapsed_time(6)<04 j) E# Q' l9 @# w9 p
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
7 B0 z& U9 w9 t. Zend
$ v$ P' @. D) X Uif elapsed_time(5)<0
, y7 h+ V2 F, @0 e elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
4 V- b& y5 m* @" r( F* E9 c1 |0 J! hend %像这种程序当然不考虑运行上小时啦
' L) ~4 z8 I% F; {" Y/ Pstr2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));' u# o2 Q( j% O6 X2 U1 l
disp(str2);3 e& n) r. b# G0 h7 x- V
8 v& ^2 i$ ~% ?" Q
% q0 Y8 O! @* }%初始化种群7 Q5 h7 `' D* G/ |% ]
%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
- j* P% u/ j- a* Efunction [initpop]=InitPopGray(popsize,bits). W7 C; w; K# H8 j4 i7 c
len=sum(bits); m0 l2 Y0 `. C9 @/ R
initpop=zeros(popsize,len);%The whole zero encoding individual
# B5 j) j* @2 }+ S8 Kfor i=2:popsize-1
n3 W/ s+ |4 S* X5 O5 a! E! c pop=round(rand(1,len));! h5 h- X$ N3 k; P9 P( ]1 _( Z: Q
pop=mod(([0 pop]+[pop 0]),2);
+ V% t% |; D3 b& V ?, m %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
& ~1 U9 u( Y/ ^& A8 ?3 t; H %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
; J: x3 M# g5 V( a! ^3 N. ^) x0 B" [1 u initpop(i,:)=pop(1:end-1);
/ C4 L! v; Z3 U% Gend
1 Q1 @8 q! ~0 u7 G* |initpop(popsize,:)=ones(1,len);%The whole one encoding individual
- ~* f2 E0 `: P' n' Z3 ~% l+ }%解码: ]+ O8 q& T1 ^
( i; y8 S- _) h4 z2 g
function [fval] = b2f(bval,bounds,bits)
" Z7 E( J$ h( x) G7 n) M% fval - 表征各变量的十进制数
% l% w- s8 x1 c1 l4 G% bval - 表征各变量的二进制编码串
, K/ `/ y! V& A7 q4 ]2 {% bounds - 各变量的取值范围" o7 i+ c: g9 L: f/ I
% bits - 各变量的二进制编码长度, c, G2 @2 S( ?! A( z
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
3 R- q) e' i A$ c1 N$ f. R2 InumV=size(bounds,1);5 x, P9 [- l' g" l' [
cs=[0 cumsum(bits)];
9 v. f n1 n" ?- ^for i=1:numV4 u3 U/ k; e8 v) @$ g6 a
a=bval((cs(i)+1):cs(i+1));
5 q3 i& P0 C x9 V6 ? fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);8 v- r5 h" X4 W4 c. L" {+ n: A4 D( d
end9 z% w9 M. c7 }! _9 c& P2 R) s/ W
%选择操作 r' n0 q' e2 }3 f
%采用基于轮盘赌法的非线性排名选择5 m K4 Q0 F; y, w- s. S! z
%各个体成员按适应值从大到小分配选择概率:) |5 ^0 ^3 D# v, u( a
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=18 Z% ?2 z/ L$ R+ l W( u
. d) g! S& f; [( G1 O! c
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)! ?, ^: c% d1 l
global m n8 |. k5 D. M- ~# `# A) o! [# w+ Q
selectpop=zeros(m,n);
, T8 y: p6 M3 C( kfit=zeros(m,1);
8 w$ z" {' h( Zfor i=1:m
% N; q; [$ n, ^5 p4 {0 n" h fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据8 ~% ^9 P. L) u9 x3 I: j
end7 l. f8 Z0 k& o7 k5 a8 j
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)+ N& |$ q {% @6 |( {6 z. n
q=max(selectprob);%选择最优的概率0 x* X/ s* n& S( B B
x=zeros(m,2);
) t. m4 i1 f2 Zx(:,1)=[m:-1:1]';
# V* H' l! l4 s" u* v[y x(:,2)]=sort(selectprob);% D6 N# W1 K5 c+ D" j9 f
r=q/(1-(1-q)^m);%标准分布基值
: G. @4 e7 x# P+ {) w6 lnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率3 m; o6 n$ e9 \- X% A" L
newfit=cumsum(newfit);%计算各选择概率之和
! {* Q3 F7 R# j5 d) o0 O7 xrNums=sort(rand(m,1));8 k- Q* w7 }" Y; N+ U. ]+ {
fitIn=1;newIn=1;
$ a3 R+ n- r/ l" ]while newIn<=m- P( E* O5 l; z/ m( ~: p! @
if rNums(newIn)<newfit(fitIn)$ Q6 e$ w0 y0 }! ^ B6 r, S/ m( W2 V
selectpop(newIn,:)=pop(fitIn,:);/ W, o6 `: Q% s8 P9 M0 G4 m4 n5 \
newIn=newIn+1;
$ s% e: x I: F) G$ o: P else
9 Z- Q4 P6 I* S, i+ p1 e fitIn=fitIn+1;" G/ M, B" ?7 z, W! h0 S/ r5 h* o: g& D {
end
, c8 t9 G3 U& ~6 Fend0 Y/ C7 g1 m5 u2 O& K: ~% c
%交叉操作
4 Z5 ^* W$ p0 q/ l. @ f2 Yfunction [NewPop]=CrossOver(OldPop,pCross,opts)
: @$ {- \) B8 @! k% e& @%OldPop为父代种群,pcross为交叉概率" h; G) L; X! O$ X$ u
global m n NewPop
$ ~. d2 S9 _) nr=rand(1,m); l+ q5 d8 ~0 Q( ?9 F& g6 `/ x
y1=find(r<pCross);
7 s$ N& K! w7 _: E8 ky2=find(r>=pCross);
9 P. a3 G; S" V, n* Elen=length(y1);7 e8 ?3 G+ w* i( o; K
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* c' r( b/ M! h, s
y2(length(y2)+1)=y1(len);
- S: u! B1 J! `! w3 b( w, F( b y1(len)=[];
0 P8 N* Z, C3 w7 ?# Cend
/ }9 J3 }& }. y' Rif length(y1)>=2
. H ~( P: f& ~7 O6 ` for i=0:2:length(y1)-2 c% s% m+ u, H8 ]9 d5 @
if opts==0+ a, J5 d0 o3 {1 T9 I" h, A
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
" Z4 Y; H6 Z- k9 _ else
& i0 r) {) E# B! _ [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
1 w! m5 h( }9 q' B/ T' H: M end
. e$ I: U) V" v! j$ E# _ end $ E8 L+ m8 i$ ^
end, |" q% e- u$ \' o, R, e% H4 Q' p
NewPop(y2,:)=OldPop(y2,:);9 G5 Z/ ^$ Q) `' G9 v- ^3 w
7 }( C! Z, ^( o! m%采用均匀交叉 - Z7 L+ R# ^8 ]$ ]2 W7 X) x
function [children1,children2]=EqualCrossOver(parent1,parent2); E8 G0 P$ k8 W, Q4 G9 M: R2 t
; W) f# S% F7 m, N: lglobal n children1 children2
* f4 n: |9 |: G Z# A+ V1 T9 v0 z; ?hidecode=round(rand(1,n));%随机生成掩码
. `9 H) d+ i* v9 U9 bcrossposition=find(hidecode==1);# f) i& R* {/ y- {
holdposition=find(hidecode==0);! i7 h& k2 B' H3 o+ Y$ s
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因7 ]7 C' f' p' g- m, S
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
3 Y& }. ]; ]) E1 i+ _' W4 t, M0 zchildren2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因- x- M3 p3 R- m2 }0 h. v
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因, F; \6 X$ H9 Q7 a5 V1 Y
0 _; g2 h! F5 k: h: Y' k# J! i& F
%采用多点交叉,交叉点数由变量数决定$ C) g+ W4 q, J# {1 c# p
" M* e# H( M. p# x4 d
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)' o% Q. f; |/ B- _! |/ _
. N- e* G( P% b2 c, k- R# P* s+ qglobal n Children1 Children2 VarNum) B& x* W. s z' H, U8 H" f
Children1=Parent1;
2 C( }( e, y2 J; EChildren2=Parent2;
+ j8 \8 D8 D3 {# m+ VPoints=sort(unidrnd(n,1,2*VarNum));) x/ S5 _$ s' N7 k
for i=1:VarNum4 k0 b$ l5 o' G/ ~* R1 H4 N
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
* X- ^7 l+ P: u0 g1 ~1 Z Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));/ S! H m! [: p1 B
end8 r& G9 f9 X- }) ^
! ^( M0 O; j9 ~# u
%变异操作
/ l8 Q, C6 ]/ z. H! t0 ffunction [NewPop]=Mutation(OldPop,pMutation,VarNum)$ a& N1 e) f* q3 H& P% z! |7 Z& P
1 }8 N% s' u$ X5 H
global m n NewPop2 c! f4 Z2 t$ L2 X% p
r=rand(1,m);
. U* `" E5 I0 H0 r- U4 k$ uposition=find(r<=pMutation);
2 q5 r( d4 d/ K4 ^$ I1 Qlen=length(position);
" X" q B' C; P6 o/ _if len>=1 N# G6 J& G: b: ?
for i=1:len+ `- j" C& \0 c6 k7 E- M
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点3 g. K7 J: T# L% k
for j=1:length(k)& t1 {4 ~! p: ` l/ R+ I' C
if OldPop(position(i),k(j))==1& e _3 L7 B7 D4 P
OldPop(position(i),k(j))=0; x/ I) j2 v8 Z2 W J" Q
else
% |' q4 E3 ~6 J# n0 B: m OldPop(position(i),k(j))=1;1 @2 k3 p# N) O# _ w6 S6 ~" i
end# q% \) V+ X( n2 j0 i2 D+ B
end& }. F0 ?; j3 n
end0 w: b; ?/ i( U6 |' r: b2 G
end; _ m3 o, a) w0 y5 A j
NewPop=OldPop;
0 a% H' g( D. q6 |' q
9 O" o8 b3 L% @; p3 V%倒位操作: ?7 F3 R }- _3 l; |, t, G
& O! G: n) k9 Z
function [NewPop]=Inversion(OldPop,pInversion)" \6 A. l" y2 G2 E. K
7 s0 v' _4 ?- a0 s- U* @$ _global m n NewPop/ E- E5 V) p) k1 g0 }2 L
NewPop=OldPop;
7 N7 L. l4 C4 L! d( b, q, Hr=rand(1,m);* A3 \% b* `' i8 M
PopIn=find(r<=pInversion); S& K- u8 w! P P" h/ a- G2 t
len=length(PopIn);9 w) w" m6 A, X7 v. s4 A8 _7 {9 @' y
if len>=1; ]* W& b# r% G: ^7 q
for i=1:len' E$ {. X8 ?" D# |1 a; b" m
d=sort(unidrnd(n,1,2));3 ]3 {3 D+ E- l
if d(1)~=1&d(2)~=n
4 |' R# k# |% R, K- I. [6 J NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);1 R8 q, O! Z9 \) H4 Y1 I: ~% `
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));' w# i$ l, \% q4 ^ \
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
o8 I) n) Y1 x$ Q* W- ~ end$ G" j- G" J3 l9 _. t
end" b$ a l" }4 J8 Y
end% j9 o" E4 k* c) q* p7 G1 F
l$ D0 X6 G! g) J4 G+ C七 径向基神经网络训练程序
/ r7 Y' {) F5 I/ q, i$ b+ q) V
5 | q, _) E' ^% Rclear all;( R0 \# {6 J5 n* V' n3 h2 k9 N
clc;- z3 O5 z0 g3 l" w5 b {
%newrb 建立一个径向基函数神经网络
/ C- K% F* W- g2 A8 X) U# Xp=0:0.1:1; %输入矢量4 Z9 F! o" f, N2 ^, \
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量8 S; ~( X3 e. W/ m& x! k7 c1 |
goal=0.01; %误差5 E/ R+ b$ K4 z; l+ i
sp=1; %扩展常数2 \! _) p* z2 x$ W6 ?* z
mn=100;%神经元的最多个数: G3 }. j: s. L9 q" z
df=1; %训练过程的显示频率
" {! `: @( I* }; i: k8 i[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
7 F4 r! A7 Q3 _ H/ Y% [net,tr]=train(net,p); %调用traingdm算法训练网络
& z1 I; u- C3 K& M; t4 v$ w3 t%对网络进行仿真,并绘制样本数据和网络输出图形
; ^3 c& w/ E7 V" e, DA=sim(net,p);! d- q8 N4 L$ n4 X) U
E=t-A;7 e0 G3 r0 x7 C- h( T$ k- i9 E
sse=sse(E);% `; z, I* s* o. a8 } L
figure; 0 r) X1 P% W( B2 O; A6 Y9 _* `
plot(p,t,'r-+',p,A,'b-*');
" y8 S$ ~9 u8 f$ }( {% r# klegend('输入数据曲线','训练输出曲线');" m& g! X% N. d0 M7 I
echo off
6 j( j% [) r- K* O* ] y) j) B1 z' h4 Z! G4 k& L. w
说明:newrb函数本来 在创建新的网络的时候就进行了训练!
' |8 n/ L+ j( @% t, Q" c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,4 i% p2 c7 o1 _7 F% P
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!$ b$ T" _* a4 ?5 X+ ~
' I; s0 N# w" g+ E6 p2 L( W; l$ n+ T5 T% v6 y0 z. s& J% C
训练结果显示:
2 g5 W6 H8 g* o- K$ G2 z/ VNEWRB, neurons = 0, SSE = 5.0973
9 C# g; ?" ^& TNEWRB, neurons = 2, SSE = 4.87139
# M7 Y; M, w# C9 S3 eNEWRB, neurons = 3, SSE = 3.61176
4 ?5 N6 Q0 m& X. @: z; DNEWRB, neurons = 4, SSE = 3.4875
: u) a5 _7 x" s6 O* E* v3 R6 _NEWRB, neurons = 5, SSE = 0.534217% b6 y J" g% i0 f9 I: W! A4 o
NEWRB, neurons = 6, SSE = 0.51785; [1 p' S# u; S. e6 F# L$ c
NEWRB, neurons = 7, SSE = 0.4342592 ~! D- [( L% G5 L! k2 V; y
NEWRB, neurons = 8, SSE = 0.341518
6 ^, O; C. d) V' cNEWRB, neurons = 9, SSE = 0.341519
0 w8 |6 K) V0 A- ?1 g) E, @NEWRB, neurons = 10, SSE = 0.00257832
7 l2 c9 n$ @8 \& _" u) I( n) ?3 @4 A( f2 `9 Y( B) |9 J( l
八 删除当前路径下所有的带后缀.asv的文件
6 A: G; `5 M7 x4 s- Z说明:该程序具有很好的移植性,用户可以根据自己地: b5 t7 Y: f' U( F
要求修改程序,删除不同后缀类型的文件!
( x4 n1 M5 L' mfunction delete_asv(bpath)
; ]& ^* g# ~0 G( M%If bpath is not specified,it lists all the asv files in the current5 u$ u R, P- Z. S
%directory and will delete all the file with asv 4 g3 _) B+ t& e$ N
% Example:
' \" t3 u# V0 e' c% delete_asv('*.asv') will delete the file with name *.asv;
6 t. ~/ v" H* G. D0 |% delete_asv will delete all the file with .asv., x, T* Y& I# V1 I
. |6 ?+ R1 R! p6 Z* Oif nargin < 1# J8 v' A0 B# |
%list all the asv file in the current directory
) | X$ _& f+ i2 K4 w; Y files=dir('*.asv');
5 E0 T( n, j2 i+ E5 {2 yelse
" T' Z" \0 ]% F% find the exact file in the path of bpath
; ?4 U, z7 D9 d# ~! K6 x9 S [pathstr,name] = fileparts(bpath);
, y" T( d- V3 L2 h6 w' r2 j if exist(bpath,'dir')" f, f# T4 K% l% M
name = [name '\*'];! N% e* \$ Q# L! T
end' E$ W9 e: k5 n# b" d, `' B0 f
ext = '.asv';
) ^2 C- U" n3 A4 }* j files=dir(fullfile(pathstr,[name ext]));5 l% [" {0 W4 r3 B0 s+ f7 X
end5 v0 ?* `; p5 j! q3 X. y
5 v# `5 ?. h( z( K Z2 j. S
if ~isempty(files)
2 `1 n: I. G2 b/ x8 _ for i=1:size(files,1)
+ b3 M6 K* @! A# E. z2 ^ title=files(i).name;
9 L* [( A6 _3 O delete(title);' m4 U2 t) Y, g3 Y& o7 ~
end
9 ^: \3 o8 o' F L+ x1 Dend
; S: s- \0 r1 O% T+ {+ n
& o; L0 O1 K- R7 `9 X: M& h |( z: t" V. L2 B0 I: {
同样也可以在Matlab的窗口设置中取消保存.asv文件!6 Q. z1 z" c- m
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