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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
z0 i2 x, ?+ h. D' L3 Q7 Q& p1. predict_fun.m为主程序;
% c7 p; P$ s2 G( o' Y7 d1 n2. timeseries.m和 serie**pan.m为调用的子程序
7 H7 U0 V( a8 l5 d! [! i/ N0 C7 _! d6 ^- S: C$ C V5 Z+ x" y4 K
function ima_pre=predict_fun(b,step)2 t0 R% y4 y1 o
% main program invokes timeseries.m and serie**pan.m* Q/ k) J/ e9 i' L' S) Y3 P7 ^& P4 N
% input parameters:
3 j$ y/ m0 E9 t0 D; |2 P# z% b-------the training data (vector);
3 x9 P: @3 m& c; ~% step----number of prediction data;
, |- p: S- R( x2 [9 o% output parameters:% N5 a) j: S0 j
% ima_pre---the prediction data(vector);
6 b4 O, d7 j" s R$ ]old_b=b;2 F' g& f# N1 i
mean_b=sum(old_b)/length(old_b); d+ B; I' B" l) X
std_b=std(old_b);
" A; L+ e. k; Z/ n. e: Eold_b=(old_b-mean_b)/std_b;
f2 j/ R$ f0 [+ o9 D- q[f,x]=timeseries(old_b);
1 y1 U4 Q; u8 B9 a4 N' [* mold_f2=serie**pan(old_b,step);
- D: M. x' E) F5 S% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;) g% z4 b( O3 k H: o+ }& ]0 Y( r: P
R=corrcoef(f);
8 X/ q; v- d/ }4 ]' ]6 q3 f5 @# N[eigvector eigroot]=eig(R);1 }6 t* O. m. D; Y+ \ G
eigroot=diag(eigroot);4 Q) s Y4 ^2 U# L7 W# A# U
a=eigroot(end:-1:1);
3 i' f$ ~4 \ `, Kvector=eigvector(:,end:-1:1);2 e0 g" l% W, A0 c: p
Devote=a./sum(a);0 k+ a! }) j* j. [2 G5 p" ~3 r
Devotem=cumsum(Devote);
9 ]. J' r( [- y+ y' ym=find(Devotem>=0.995);3 ^/ s% F( g3 g/ U: b
m=m(1);
% Q! {( N1 l1 }% `! D& x* \V1=f*eigvector';
' R! T* B3 J3 O/ l& XV=V1(:,1:m);& F, H& P- C! t% `
% old_b=old_b;" f" {% \! W* i; x' Z$ E
old_fai=inv(V'*V)*V'*old_b;
2 ]0 \# ?) e- F) Ceigvector=eigvector(1:m,1:m);
, d o5 @: a ^ b L% V, ufai=eigvector*old_fai;3 C% T' O$ b( R( K+ x1 T
f2=old_f2(:,1:m);
- g/ w D- |/ c' f/ w2 Npredictvalue=f2*fai;0 ]! y1 _9 K8 v" Q
ima_pre=std_b*predictvalue+mean_b;
! i5 |# r$ l$ }7 {, b/ a$ d: W
4 x4 }! ^* n% }4 y/ M% C4 T/ I1.子函数: timeseries.m
3 _: P1 D% u9 L( u" Q% `* G% timeseries program%
/ e$ L6 I& I6 C8 \2 g0 c% this program is used to generate mean value matrix f;# E& C$ z. u2 d
function [f,x]=timeseries(data)
3 ~5 `/ X& q/ ?: T( Q% data--------the input sequence (vector);
0 n# p3 p8 u& Q% f------mean value matrix f;1 K6 K2 i4 z" \" _
n=length(data);
, E4 R- y1 ^9 ^. W3 rfor L=1:n/2
% ?6 p; h9 p! j7 z nL=floor(n/L);
, _, U7 x) k- U. B7 h; Z for i=1:L) ]- M1 ^6 f0 O: E
sum=0;
! w+ ^8 @: p$ l! h for j=1:nL
' N. N R& f8 m. J' ` sum=sum+data(i+(j-1)*L);
# {" @& {2 W) i( M& m9 ?+ Y" v end: [4 a$ N5 r' f* d# l# A! y
x{L,i}=sum/nL;
z4 ?- G( Q: Z/ N* t end
* G3 Y* c' Z$ S4 L# C3 x7 u, Nend
/ y4 p ~2 g& ~1 NL=n/2;- q) A7 n" o1 ?3 E8 v
f=zeros(n,L);
* q) c+ t4 f( N0 @, j# p3 `% kfor i=1:L) z+ H& U% L1 P$ H
rep=floor(n/i);1 M" R v- m$ I+ T1 y" O* p; Y3 ~
res=mod(n,i);1 P- e. `' w1 n! @( }. q) x% h$ A8 E
b=[x{i,1:i}];b=b';
# j) g/ \$ w6 X/ ~ f(1:rep*i,i)=repmat(b,rep,1);4 l8 _" A: r- H; ]" ]/ q
if res~=0
/ [# c* N- n/ r* p0 m v/ g8 _& H c=rep*i+1:n;1 U' {$ g- X! f, N5 f
f(rep*i+1:end,i)=b(1:length(c));9 r* l2 \- [4 d
end
7 J9 ?* y9 V7 aend
3 b: u! z* V$ X
2 p r+ a p2 ]2 J$ g; z% serie**pan.m0 q. X, i3 W6 M9 B6 `4 A& e* D
% the program is used to generate the prediction matrix f;
2 c4 V8 J' x* L8 m) K) _6 |function f=serie**pan(data,step);
, w$ f- S/ C2 M; r7 Z%data---- the input sequence (vector)
; v( I1 w3 s* C. J% setp---- the prediction number;
$ J0 [! T# f# dn=length(data);. V7 U/ V5 ?0 Y7 A: n+ I6 C1 {2 _
for L=1:n/2* H$ y# U. L: \. N& }8 C8 w# I
nL=floor(n/L);
5 j7 u( \" r) O% a6 e6 m for i=1:L5 |& i( S# A$ q/ D
sum=0;5 S2 }+ ?3 {7 J
for j=1:nL
0 o' o8 z _. s! @' b' q9 W sum=sum+data(i+(j-1)*L);
! ?- s6 d' A( [7 F4 |( h/ B end
' ] C* e( w# v# m# D" w x{L,i}=sum/nL;8 b3 Z' x# C( V9 ^: D& q3 r
end
" k' H& f* r2 ~) H1 ]7 m8 Vend9 \5 J+ \. x+ C1 [
L=n/2;4 i: Z5 n/ D, n# f0 R6 I
f=zeros(n+step,L);
9 [* b- y/ y% lfor i=1:L
" {8 ^; Z- Z @! t# d rep=floor((n+step)/i);
+ d6 u$ C( R4 x8 k" m res=mod(n+step,i);
+ i8 |0 F8 r# Y7 z/ F b=[x{i,1:i}];b=b';
& m0 H$ o' N1 r" q( e/ o% w2 n5 J f(1:rep*i,i)=repmat(b,rep,1);& c2 U% L. g5 r* P
if res~=0
7 _- l' z" F) L4 ], [2 j c=rep*i+1:n+step;% A) `& [0 ]8 S3 I3 M# k% Q
f(rep*i+1:end,i)=b(1:length(c));
7 g3 b' I0 @' r. I! U- Z3 \ end
+ s, ]5 C. Y9 @3 ]# q9 g2 uend
6 n' B5 F9 ~! W2 [2 r# m; n2 w7 B7 b, s( F1 `
二 最短路Dijkstra算法- X/ d$ I9 D( B6 `* ]& Y
% dijkstra algorithm code program%) U5 S# j$ J4 a; G5 T
% the shortest path length algorithm5 h7 k. t: X/ K, y$ V: l! e
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)1 R) I* e. |- w7 b2 |3 [
% Input parameters:
" X* p2 Z) u. M6 x4 c: b4 v% D% Input_weight-------the input node weight!
$ H# |$ s$ C9 @+ a: v% start--------the start node number;8 f& v6 [, \' f# W n. w. I, W
% endpoint------the end node number;1 p3 M! A5 h N/ X4 p7 y1 d( o& F
% Output parameters:
9 K4 _; a4 k: z- n$ p& b% path-----the shortest lenght path from the start node to end node;- u, E/ \# `& y2 a$ U
% short_distance------the distance of the shortest lenght path from the+ y" @/ q% D! s* X; d. P9 w
% start node to end node.. X D2 `2 y) }/ q k; a# }
[row,col]=size(Input_weight);
" H* [* a4 T0 v
8 p( D9 O: p3 \- F6 X%input detection
! o$ K J! r4 |" x% aif row~=col: k e5 z. j- G3 d4 i* p
error('input matrix is not a square matrix,input error ' );
2 S1 h7 O; H, `7 e* bend) a7 W! t- T% a/ x
if endpoint>row4 I5 i }. F, h' ~/ n
error('input parameter endpoint exceed the maximal point number');8 r" V6 c4 h* t; ~3 b: u, j4 |
end7 L& u# j" w8 e+ M8 k
. M! Q% } P3 A0 [%initialization8 K& a" }) L1 d' a: r( _
s_path=[start];0 R8 B$ i3 C2 k( l+ \. q) Z" H, [
distance=inf*ones(1,row);distance(start)=0;
4 p& Y+ k9 ]6 y: l$ \flag(start)=start;temp=start;$ u x Q. g& v4 k8 a* Y. H
# p6 i) s' Z9 T I9 R) {3 H- C6 \' T
while length(s_path)<row3 |5 W$ d3 @ |1 t9 i
pos=find(Input_weight(temp, : )~=inf);) E' j2 O. r7 g* r1 b7 H$ \1 p3 R$ O/ P
for i=1:length(pos)
6 r1 A. X* S2 R3 j: H if (length(find(s_path==pos(i)))==0)&8 m. `- d: K2 F9 O5 i
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
' H7 F' D) v- D- j$ ` ?& ^ distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));% A& y2 Q7 r! W7 S; D+ s& P4 s
flag(pos(i))=temp;% q4 {+ S6 T& C& W6 @$ v( D
end5 f* f# }6 ]0 L1 r, ?
end0 h5 e: n8 f; C) A1 J3 I( y* C: `
k=inf;7 I: G0 m% k: g& V5 E$ T
for i=1:row! z r: r- c3 y1 G
if (length(find(s_path==i))==0)&(k>distance(i))# D: w1 @3 S1 s" ?
k=distance(i);' R, u1 Y" L! U2 ^ w
temp_2=i;
e+ V1 W! l- F, ?; N$ Y% c end5 M/ o6 P" e0 U0 K( R
end
" M& _( {9 A5 y% d' P s_path=[s_path,temp_2];
9 D% @ H, S7 {+ Q9 p/ Z0 _& V" B temp=temp_2;
7 v9 K) x2 Y$ w9 Y5 I: Xend7 q) R4 u8 Z0 F4 y, _ D
) e2 B8 D3 G R; D; i
%output the result/ e; j/ b8 M: T
path(1)=endpoint;3 I" r) z& E; U
i=1;8 ?- G7 K* b* L+ q, V7 A
while path(i)~=start* s- f" g' v: [+ w1 v
path(i+1)=flag(path(i));9 ~7 ]" c' h$ R/ C8 f
i=i+1;' r# d9 k X+ ]" h0 H3 J
end
" M" d0 x! y+ Q& Y1 h6 x3 L9 F, K. v4 Lpath(i)=start;
G6 a: k2 u: c; V* Ipath=path(end:-1:1);
2 y# j; i% J; |' ]8 p5 g3 Eshort_distance=distance(endpoint);* @! h S* ~. q+ H9 t2 }1 t( _
三 绘制差分方程的映射分叉图
. D% X4 o* d1 X0 ^
" B! `2 v: c4 P% `7 Mfunction fork1(a);
8 S4 r8 r |: F5 S7 \, x
3 q. W4 c3 O; m4 \* e# {* z% 绘制x_(n+1)=1-a*x^2_n映射的分叉图" C z' h' S8 B$ _, y; U' Y. o
% Example: : C A. b3 Q$ B* q+ n C
% fork1([0,2]);
+ Y! R1 y9 P! uN=300; % 取样点数 $ b% d$ M+ H9 |1 N
A=linspace(a(1),a(2),N);
$ ^: N6 E) v6 {8 ?/ k7 U) Ostarx=0.9;
5 h" y P4 H# _ W( iZ=[];) }$ V7 h4 a! _6 ~
h=waitbar(0,'please wait');m=1;
9 {. M2 G8 Y9 S6 L! \" s1 j6 hfor ap=A; ; B, p' X9 j/ x
x=starx; r9 \3 C7 U: z2 H; w. P% E
for k=1:50; 9 d0 M2 _& G. D# c Q: x3 n/ t
x=1-ap*x^2; 7 V! v+ k- F; @: v! K: A2 S
end 7 }! G ]0 G1 y9 M4 I3 p3 c
for k=1:201;
' m% ^: [" j6 Z2 T& |+ A, [ x=1-ap*x^2;
6 R8 {* D& }/ v Z=[Z,ap-x*i];
3 L: @. d9 Y( [, b" g4 b, ~ end 9 | F5 Y: a# o4 [
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
# Z5 V/ h" p' {+ c m=m+1;! x$ T+ X: Q. L' B
end . A& V1 V" d# x; C# X9 T3 I% {
delete(h);! `2 Z( d1 K$ U& y; I3 C) V+ R
plot(Z,'.','markersize',2) 1 y! r: ~4 Z/ n$ S% n6 d' A
xlim(a);
# n, n m' i8 ?# g; S2 Y/ M( B( |+ J- R6 B3 ~' q |& F
四 最短路算法------floyd算法0 W. Q1 j+ S( `. V6 K
function ShortPath_floyd(w,start,terminal) 8 _, w3 D0 G" n+ G M
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
# R; B1 b& t/ G+ j0 L+ A; O%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
; J+ N- K* z* s/ T; T" v) A%start-----the start node;/ |- N* j3 s5 x7 x
%terminal--------the end node;
Z2 w/ \6 y* _n=size(w,1);
3 N0 a: u& p) j$ q9 F[D,path]=floyd1(w);%调用floyd算法程序
4 q% _# b/ e# I5 T4 J0 u$ \
( Z' S% m% @" ^0 y& V8 I) r+ v5 S%找出任意两点之间的最短路径,并输出
; g7 I) I# @, U" ~for i=1:n- v4 d! \' _" g8 ]' X# `: _
for j=1:n
, t1 S! r% e$ ]4 R- u' L" D Min_path(i,j).distance=D(i,j);, Q6 q5 w) o/ o* a+ h/ X6 O- k
%将i到j的最短路程赋值 Min_path(i,j).distance) |& u! P7 a8 h* i5 s& \
%将i到j所经路径赋给Min_path(i,j).path
" n" O+ A7 R9 A. ]. i+ U2 | Min_path(i,j).path(1)=i;
6 V3 q W" P2 u, L: Q- \ k=1;
7 z( O: ^! ], J while Min_path(i,j).path(k)~=j* }( h# A W% Z% O- s7 n) b
k=k+1;/ ]7 P$ O6 O/ d; k+ r
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
2 W" n- J! e2 g. ?! ` end
& k$ W- U; c- I1 m end
7 C6 U' w0 G4 J L0 {, D! eend
" U& B6 ]. Q' F6 `s=sprintf('任意两点之间的最短路径如下:');% A4 Q& ~ S4 _+ }% \
disp(s);% q+ H! |% z$ V8 l7 a8 Y
for i=1:n% B: a4 V/ H+ A. X$ c
for j=1:n
& J5 z' L) c1 S* Q7 a s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...! Q9 a! {. Y2 t' u" J
,i,j,Min_path(i,j).distance);
, O) a# Z- m @0 _9 W disp(s);( v3 i0 u5 d0 G5 I6 e7 w
disp(Min_path(i,j).path);% i! ~8 x2 `+ Z7 p& b
end
& [" t# `. L' n$ Z9 f; oend& K9 l; i3 T0 K/ C! O8 x
, l" O: e. R! L/ Y+ R! g%找出在指定从start点到terminal点的最短路径,并输出
8 H/ H" _( Y5 u$ N2 @% B+ l" _% kstr1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
X$ c9 T; [% }4 W h* x start,terminal,Min_path(start,terminal).distance);
O+ u6 Q- y1 r1 y* l/ r4 gdisp(str1);
" {. \, H* N0 x+ }# }1 Vdisp(Min_path(start,terminal).path);
^0 S- z* @3 x
9 _9 S9 X& c2 y; N0 ^& f%Foldy's Algorithm 算法程序
6 `& b* f( O5 O( i" sfunction [D,path]=floyd1(a)& V. _- i6 {. `* b N V
n=size(a,1);
& S3 ^! I% V0 w6 |5 ~- M' h* k8 ZD=a;path=zeros(n,n);%设置D和path的初值
4 Y4 g) m) g- n* A! vfor i=1:n1 g; r" a& D! x
for j=1:n
* e8 H8 } `0 i/ g- t if D(i,j)~=inf' f% ~- c& m- e r" w6 r* @
path(i,j)=j;%j是i的后点8 R- Q7 P: o- {8 j
end
7 ` |" `+ ~8 q7 L) v* o+ V end% h- `* _6 y5 D3 b2 p0 ]: Y3 |
end
7 }. G+ ~6 ^$ N5 u%做n次迭代,每次迭代都更新D(i,j)和path(i,j)9 r/ m F" R* l6 U
for k=1:n
: o! j- B2 r4 y0 C7 L for i=1:n
$ o' X( A- C6 c3 G for j=1:n0 c. g7 v4 t5 }4 y
if D(i,k)+D(k,j)<D(i,j), { S! t* h. j9 p
D(i,j)=D(i,k)+D(k,j);%修改长度
, O6 ?2 z: k- i$ p, P/ F4 X& ? path(i,j)=path(i,k);%修改路径% H( V- r$ r( {7 b8 X
end
: p4 m) R3 i* j5 A) T, R" C2 X end
6 `2 f6 n* ~# X end9 Q. y6 j0 b. G2 J
end2 A+ E5 d5 }5 h8 v3 S
' }+ M* f+ m; ~1 \, _五 模拟退火算法源程序/ {* a; L' M$ p9 W% D
function [MinD,BestPath]=MainAneal(CityPosition,pn)
$ F e6 V/ Y3 d6 J6 |" C3 F- J- afunction [MinD,BestPath]=MainAneal2(CityPosition,pn)' p& @: ?( [8 n( }6 g
%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 \( s" q( V% W8 d1 E% _
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...3 }) e1 Y- K) I" ~/ b2 _) o
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...3 ~6 _: x# F+ N6 R
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
! A6 p& N$ @3 h/ I! Q( I& B/ U% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...2 e4 L# B" ^( V9 t, Y7 R! t# o
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
. l7 t6 r5 B( c3 c z0 ^8 w9 d/ Q" _9 [7 {# M* r ~. R
%T0=clock
/ p" |; z7 g' Q9 {global path p2 D;
( n3 n* n$ K6 J7 c! p/ |% v/ h6 L[m,n]=size(CityPosition);
" O- m/ V% ?7 `( G* v4 J( N' s%生成初始解空间,这样可以比逐步分配空间运行快一些
+ ~! {* W8 ]7 c! `, kTracePath=zeros(1e3,m);
# [+ I/ `, S* H) QDistance=inf*zeros(1,1e3);
4 a8 ?3 B) l9 u% p7 S0 {
4 z; A; { T" s/ L# \7 j1 KD = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
# q! U+ F1 M6 l, {2 C (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );% b: N# h& f9 \' `5 [) t
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
- K2 R* O' V+ g% P" K+ h2 U* K1 |for i=1:pn8 J6 X3 }- K( @3 {1 O3 E
path(i,:)=randperm(m);%构造一个初始可行解
, h4 n3 g* A' n7 D1 U7 Z6 [end
5 p8 A$ W. N U7 L& }, zt=zeros(1,pn);
1 A2 A H8 D; J7 d' F zp2=zeros(1,m);
/ F( r8 ?2 H( q, j% A$ B, H: h* D3 I$ T
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
) j0 C* A" T2 U1 N. fm_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=' ) ;; ^! O7 V3 J3 S% h! B
%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
. a1 z- e, [8 r! s%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! ~' ]; [8 C% m# U: ] _
%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$ ^' U6 G8 H$ ~9 ?/ T- q1 Q& g
%会收到到比较好的效果 R- ] H* X" X: h; w8 f
/ r3 }% y! w* K* C0 x w. w6 Q
T=1e5;
' H$ B) O: ?% Q' g: Q5 m. ?N=1;3 o V* ~/ m2 C- D) N" m. U1 \
tau=1e-5;%input('请输入最低温度tau=' );7 b U2 Z) Q* w; j( X& f. j
%nn=ceil(log10(tau/T)/log10(0.9));
& N* H( ~6 z' Y- Twhile T>=tau%&m_num<m_max
4 }( f6 X+ U' d6 N4 p% N0 g5 x iter_num=1;%某固定温度下迭代计数器+ g- l @5 Q! c: |
m_num=1;%某固定温度下目标函数值连续未改进次数计算器7 i0 \# R8 k9 D7 C: I
%iter_max=100;4 D5 T9 n; N& n7 C1 k$ P0 T- n0 ?; I
%m_max=10;%ceil(10+0.5*nn-0.3*N);
g1 y* C+ C, Y5 I; n while m_num<m_max&iter_num<iter_max
0 M, `' N$ v, _# q6 O7 q8 p %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程: B7 w: w% W( K- a
%用任意启发式算法在path的领域N(path)中找出新的更优解$ G* B( ~( n2 ]- m+ B9 |% B
for i=1:pn1 ^% |2 I. m5 e: g% H/ p
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/ d6 F% h8 }
%计算一次行遍所有城市的总路程 3 F6 K6 z5 g& X ?* X. c" [/ a
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
5 E$ X# H7 n4 R5 { Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
" O- p- }% J! G7 a6 w0 r end
" d- J3 B6 T" @! t$ t %Len1# h) S: l! p- \, \; {/ z; Z. t
%Len2
4 U- n% e" @& L# X! n2 H1 c %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
9 e6 e: A. a. p R=rand(1,pn);% l, [+ O+ {/ L% J8 T! q
%Len2-Len1<t|exp((Len1-Len2)/(T))>R
( Z% c( I, y- k# D) x5 E# I if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
, m$ d4 |0 N5 l path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
, |8 w, @- i K Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
& v" R) q2 } J [TempMinD,TempIndex]=min(Len1);1 L* B. w- b+ }" Y
%TempMinD
8 Q; f6 w9 {5 ^, Q" m TracePath(N,: )=path(TempIndex,: );
?0 H$ _: M$ ]# I- R5 r: i& ^/ Y Distance(N,: )=TempMinD;
3 t- x- j5 L0 h8 a0 N N=N+1;
0 r$ y9 `* @! o, c/ F %T=T*0.9. ~" S+ \2 B# X* W1 q2 [
m_num=0;% x" }+ Q9 z5 {, S# o
else
. e7 v; c& [7 O7 t- k0 k m_num=m_num+1;0 B# M7 p$ d' i* B& H8 a
end
" }5 b6 ~8 s& o/ ]+ B7 l) u iter_num=iter_num+1;! h; L) K/ N6 Q& D. Y9 T
end
( Z* A$ @/ q& x4 p$ x* s T=T*0.9) U# m# A' S% i4 @) B: M# t0 o
%m_num,iter_num,N6 Q* V& C% U% k/ v, p
end
( [: C( a8 w" q! w5 n[MinD,Index]=min(Distance);% @5 q& f! U5 B$ i# d( X+ f' M. [
BestPath=TracePath(Index,: );" t& a( F5 e) x5 _% s
disp(MinD)& p0 i( \: d, {$ `/ f
%T1=clock
# ^8 D3 k5 W: Z3 Z
7 B7 N$ e, y2 b i" F" f 2 H) W' D2 m4 H+ ]
%更新路线子程序 p% K4 a2 o0 k
function [p2]=ChangePath2(p1,CityNum)4 d1 H. P2 J( i
global p2;
6 \ L: K; f- v v* Y. c7 xwhile(1)2 r% O3 w0 Y, A& ]3 C7 q' y6 S0 d
R=unidrnd(CityNum,1,2);
# z: l" e( P. P if abs(R(1)-R(2))>1) S! ~# G6 B) k+ f# l) ^% }" `+ x
break;& y% F3 A+ ~( l$ P; k' R1 V- N7 f( [
end/ f& J3 l' J1 n8 E( w
end/ b: Z3 [+ E+ b! }6 k+ `0 D
R=unidrnd(CityNum,1,2);
4 D5 h# E3 j: n" N* u8 P5 @! A. iI=R(1);J=R(2);
o$ m) v1 d/ T9 G f3 y%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
8 U: S4 l5 s J5 Q1 e%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
# ~4 N, g! ^- H2 Xif I<J
J$ u! ]4 g% M/ l$ J8 A' a5 J p2(1:I)=p1(1:I);
4 g* H* X( B# q1 o* W p2(I+1:J)=p1(J:-1:I+1);
* g9 Y! o+ o* f7 Q p2(J+1:CityNum)=p1(J+1:CityNum);
- [3 @/ d8 e* Y6 X9 i7 Lelse
5 r' C& |- x9 F2 s m6 L9 @; e7 g4 H p2(1:J)=p1(1:J);
! ?* G1 K- a- `0 C& z) f! Y p2(J+1:I)=p1(I:-1:J+1);' I8 K1 ]2 p$ E( v; h: P$ j
p2(I+1:CityNum)=p1(I+1:CityNum);8 W$ @, g8 r0 G) y7 l" h
end5 p. ?9 k8 N0 v) N0 b9 b
7 y$ o+ n: T: L- ^# q
六 遗传 算 法程序:9 D$ v1 t% k. o+ k6 w
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!. a. ^* t: `3 o6 d' J
$ A/ ^/ s- s0 |/ K" W Lfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)1 y* ?; z1 C7 n' {1 ~" B
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) 5 B' z, b* P8 S! m3 G
% Finds a maximum of a function of several variables.
& n$ a: u) K0 q/ S" G' D. J% fmaxga solves problems of the form:
% T* l' G% E9 U: D% max F(X) subject to: LB <= X <= UB
3 B1 v/ S" J4 Y" m1 x% BestPop - 最优的群体即为最优的染色体群
% {% u! Y, E) v9 q$ l* R0 o% Trace - 最佳染色体所对应的目标函数值
- q0 @: I5 }1 M p1 x% FUN - 目标函数
0 A7 W& S$ {7 e4 d% LB - 自变量下限
$ `1 n* T. }3 N; H* P' a2 e% UB - 自变量上限
9 [. l+ s1 Q3 v# a% eranum - 种群的代数,取100--1000(默认200), ^% i8 }+ F6 T$ }0 k; R
% popsize - 每一代种群的规模;此可取50--200(默认100)
- i' |6 K8 F: J5 j( @/ p% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
5 K4 c% r* @6 y& c5 l% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
! a0 j y# u9 Y" l* a" K! v% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
( ]) l+ e o. x% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
0 k1 V T! F& l, T3 \% v%码,option(2)设定求解精度(默认1e-4)
+ d# s, X* D0 f6 J2 ?4 g%
' B+ h; x1 V$ ^% ------------------------------------------------------------------------
8 }& S6 ]0 Q# c- i- n* n" }
5 M' i4 ] E# k8 V! [4 dT1=clock;
% o* y" ?. T2 r/ F& [4 uif nargin<3, error('FMAXGA requires at least three input arguments'); end/ C6 l( a% y, a; a" e' |* ]! I* P
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
4 }. K! E% X1 r. fif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end- J+ _4 d; u6 r" R( T( D' t* F" ~
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end5 E& g4 q1 N& p% w5 d
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
5 z+ G2 K2 {1 C2 Z: mif nargin==7, pInversion=0.15;options=[0 1e-4];end |3 S% }3 z8 s" l7 d
if find((LB-UB)>0)
% V& p+ B4 \- S8 k/ _/ g error('数据输入错误,请重新输入(LB<UB):');" R5 s- C) L$ ^1 X3 O" ]* u. u
end7 F) {" S% v' }: D
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
9 b y9 F7 D5 u1 l/ Q6 ydisp(s);) U& `+ F' a. O' p" u) |( P2 P" s
( Y9 T$ `& Q/ n0 ?; Uglobal m n NewPop children1 children2 VarNum
8 i0 \, v9 f9 `- \1 [2 l& S8 L& i: t/ r8 Y) y
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
' |4 i b U- E! ?' v& Oprecision=options(2);%由求解精度确定二进制编码长度
2 ] z8 W3 p, `7 _4 Nbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间+ F Z- R- X4 ~# n$ k
[Pop]=InitPopGray(popsize,bits);%初始化种群& n+ P) Q: A" g( u6 S
[m,n]=size(Pop);
1 ]" e# A) O7 \# r/ A6 X: V( HNewPop=zeros(m,n);$ l+ p, `7 i9 N. _: M
children1=zeros(1,n);
! N9 {: d# F- wchildren2=zeros(1,n);8 }1 d$ w( u0 t; t8 K, G4 X
pm0=pMutation;
& j( w( K; m9 |& cBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace8 h. w4 @& J( O+ U/ e* c( C. h" V
Trace=zeros(eranum,length(bits)+1);
' m" Q B, @8 w" k. J: _5 ti=1;
" p6 A/ ^" e$ @3 ~9 b z4 Fwhile i<=eranum' P3 [6 Y4 Q. R4 f" y" Y
for j=1:m
. P: K5 [' f) {# _ value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
- T6 F: D' L/ f$ V3 n% H2 F end
* A# k6 P% R0 r" I$ D [MaxValue,Index]=max(value);8 q& D! Y9 k% u
BestPop(i,:)=Pop(Index,:);! W8 u& Q t ]4 r# e! k
Trace(i,1)=MaxValue;
) s: A( E9 e2 U6 I Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits); r& }" y2 F4 m U
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择+ B; M# p' t- E4 |: U+ i, O0 h( U; g
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
5 o* g, V2 N5 ~! _* e9 O%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率4 G3 B& x" V, s5 Y2 L
%round(unidrnd(eranum-i)/eranum)
h0 G& {2 L/ k5 k: A8 b7 v, l" E [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异. g' h+ c) z1 ~
[InversionPop]=Inversion(MutationPop,pInversion);%倒位0 y0 i9 X4 c/ @. P
Pop=InversionPop;%更新
! h9 Y, B* |! j" b& SpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
" {' B/ X. K0 g* g1 N6 ~%随着种群向前进化,逐步增大变异率至1/2交叉率
\) b( Y. N( G. Z4 Z p(i)=pMutation;5 W9 r! u' H2 f: K3 D {& i8 [
i=i+1;9 M8 y( X; @ c# L
end2 u8 ?- |5 I3 x1 r, }' |/ K W0 Z
t=1:eranum;. @6 o3 ]3 V+ d: Y/ h1 T4 Z: u! `) X
plot(t,Trace(:,1)');
$ B. k7 T5 ?5 x" Ititle('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 l. B0 K# a/ T8 k! Z: X4 b( P[MaxFval,I]=max(Trace(:,1));! r6 P2 ?" G, Y) W0 d0 }; h3 G) Q
X=Trace(I,(2:length(bits)+1));
5 U k9 t* X3 ghold on; plot(I,MaxFval,'*');) N3 j8 j( e& [6 y/ l& c; o$ {$ I
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);: l3 o& n1 U$ F2 h* i" @$ q
str1=sprintf('进化到 %d 代 ,自变量为 %s 时,得本次求解的最优值 %f\n对应染色体是:%s',I,num2str(X),MaxFval,num2str(BestPop(I,:)));
7 K- w6 s+ K) E) Y) D9 |disp(str1);
' x0 G. |$ J" b/ ?* s6 f%figure(2);plot(t,p);%绘制变异值增大过程
, y* v; k. N, n/ gT2=clock;) b6 K+ v' d# Q4 X- w: {
elapsed_time=T2-T1;
" B0 w5 | q- X, s" U2 D: q) vif elapsed_time(6)<0
7 Q; C1 f7 M! M9 Q- n elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;% V9 ]" z# T% [2 w3 d+ Y7 m
end+ e2 S k H+ q& G# q
if elapsed_time(5)<0- H& W/ Q: W' c% E% A" @! D
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
y0 r+ U+ Z$ F. \5 ~3 k, I% ~end %像这种程序当然不考虑运行上小时啦6 V! g/ B6 H+ n9 v w
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));
9 ^# ]! J/ K; N5 e. _+ }: adisp(str2);
6 ` L; Q% j3 q- t! l. i P- ?/ X- f, }4 V D% B4 P
% o) M8 ]1 [9 Y# s1 B
%初始化种群% \7 `0 N$ F5 h8 v8 U
%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
3 Z# u8 u) f% u- o8 xfunction [initpop]=InitPopGray(popsize,bits)
- E& I6 t4 f2 }) xlen=sum(bits);
* y( e9 q# Q* A: C8 K. \ Yinitpop=zeros(popsize,len);%The whole zero encoding individual& ?& ]5 z/ B+ f0 R1 T
for i=2:popsize-1: w( c$ U n- K [1 U6 R8 k1 N* }1 D& a
pop=round(rand(1,len));& a1 `/ d0 @$ ~. ^$ ?
pop=mod(([0 pop]+[pop 0]),2);* Y( B0 M; `% x- a o
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)3 d1 y/ B5 ?2 E4 q
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)( N2 W& P8 }4 f, B+ A5 }6 i2 b. s7 E5 |
initpop(i,:)=pop(1:end-1);# ?! m0 q3 D( V0 N
end
7 l2 E9 G9 s8 i, ~8 J. jinitpop(popsize,:)=ones(1,len);%The whole one encoding individual6 t* O3 ~3 D8 F3 R2 s
%解码/ } E9 O: Q$ M
3 F. v7 c( }' T5 ?6 @) L8 y7 I
function [fval] = b2f(bval,bounds,bits)7 O% T; i- A6 k4 T9 a( e7 {
% fval - 表征各变量的十进制数
& E) q# ?. {, f' P% bval - 表征各变量的二进制编码串
3 N3 ?8 Q) I" G: ]% bounds - 各变量的取值范围& R+ u7 i! r4 c+ n5 G* C
% bits - 各变量的二进制编码长度; P2 I& n @2 W: y
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
! ]! X9 c3 M2 w CnumV=size(bounds,1);
' K) u! F6 m D. l. ^cs=[0 cumsum(bits)];
. ^% R' T" `5 z9 Ofor i=1:numV
" L4 m, Z8 j, N* Y( p# K a=bval((cs(i)+1):cs(i+1));
V+ W2 s& h7 L: y fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);( Z. `2 N; d! v3 l: D
end
. h N* Z/ t/ W%选择操作
+ i8 w" ` U7 I( f+ i0 ^- J%采用基于轮盘赌法的非线性排名选择* S! d! F, f' I3 J: I4 j2 W
%各个体成员按适应值从大到小分配选择概率:9 c% n" g! }% D
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=11 S, k! E# j3 A! W. e: n: Z0 n
" q1 s- v6 p7 a: r M" ?) v
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
' ^! J% |/ f& J8 M6 \3 s$ }/ xglobal m n+ E* z. h0 m$ g& V* }1 A/ Z/ A- Z
selectpop=zeros(m,n);
8 M" f) ]2 r# f1 u4 \: e0 j2 Rfit=zeros(m,1);- _* f8 G+ m! p4 {
for i=1:m' e) T( [1 L, U e2 `* |
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据7 j* K" X: Q7 a0 {* S
end
/ X$ U, A, K9 G: @; U7 w2 U* Rselectprob=fit/sum(fit);%计算各个体相对适应度(0,1)- Q8 o. T0 n8 A: V+ E% ?
q=max(selectprob);%选择最优的概率7 k5 n I# }, Q) Y5 u, x% ?( R
x=zeros(m,2);
* p( k! q& o; Y* A1 tx(:,1)=[m:-1:1]';# ?5 r) P% s+ o$ b$ ^0 X( ]
[y x(:,2)]=sort(selectprob);7 x2 d8 b3 B8 c: H; M3 v: N5 s8 p
r=q/(1-(1-q)^m);%标准分布基值: {! p- u, q' ~+ C' r l/ C
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率; H7 }" K4 E# `( J, }8 F* v
newfit=cumsum(newfit);%计算各选择概率之和% ]! O5 _8 @* M! m0 r
rNums=sort(rand(m,1));
- r, ?3 p% z/ E& m6 t7 RfitIn=1;newIn=1;
+ d8 [$ N: Z- }: ]4 gwhile newIn<=m* T: L+ w5 V0 N9 ?6 T0 C
if rNums(newIn)<newfit(fitIn)( w/ _$ D5 h9 ` R% Y( m y/ m$ {
selectpop(newIn,:)=pop(fitIn,:);
, O% d% W2 u. m0 n, C( D k newIn=newIn+1;5 X( U; b% I B6 {
else$ E& w2 m; [% s8 c5 Q2 a8 Z4 u$ V
fitIn=fitIn+1;
( l$ j9 [, w) s9 h W$ _6 ^ end. Q7 e& f2 T( p4 C5 l2 I
end* k. Y( @5 i$ o1 H
%交叉操作% `1 k8 H, U! q, p; j* n
function [NewPop]=CrossOver(OldPop,pCross,opts)) s& v1 s- B7 A- ]. Z {
%OldPop为父代种群,pcross为交叉概率/ ~ c9 n, q/ B. D! j
global m n NewPop ! S/ E5 n+ ?% C7 u K1 M1 x8 ~
r=rand(1,m);
: s; }; h+ T, A$ K" b2 zy1=find(r<pCross);
" c2 c3 @3 ]* C2 P9 O4 Uy2=find(r>=pCross);
; ]+ Z8 S4 M$ @" `len=length(y1);
/ c% ~+ j+ g& E6 J, Z$ Pif 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
5 k! O" M$ p( t4 t- H* a y2(length(y2)+1)=y1(len);
/ G0 X- f7 N! _ y1(len)=[];; m' P) h; F# I
end: l9 B R8 r7 `8 J% b; N$ O! D
if length(y1)>=2
( B$ i0 f) Y/ G% a2 w4 W$ V4 X3 e for i=0:2:length(y1)-2: d( y3 Q% w6 k
if opts==0
( V" D- ^5 \' h% ^ l8 D [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));. R+ N. Z* V y9 y. C
else8 K! [' J4 o0 s
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
# Z4 |7 }( b' n! Z0 f end5 L9 i7 r7 t! g% V4 G$ Y1 |" v4 e
end
0 f6 ~7 \1 |4 J% @4 Qend
! O+ ?: I: z1 b7 lNewPop(y2,:)=OldPop(y2,:);% q; {7 S5 [& P6 d+ ~8 Q
7 h% q8 p! p& B8 |7 j3 E
%采用均匀交叉
6 ~ N2 |) x" O9 Wfunction [children1,children2]=EqualCrossOver(parent1,parent2)
+ d6 k5 i a2 `3 R
( X) x% M- t. X9 |3 N6 _global n children1 children2
/ v- r6 T! C3 `% O7 _6 d8 Rhidecode=round(rand(1,n));%随机生成掩码% q+ M9 H8 Y9 `7 @) U; D( `( \
crossposition=find(hidecode==1);
" @9 H9 M8 Y9 X5 i& qholdposition=find(hidecode==0);9 D: \4 ?8 S7 a, Y3 h
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因) ^( `8 v7 p5 R+ ^' U7 i; s1 B
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
3 A- |: G* T/ K, p0 echildren2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
( ?9 |- R6 \1 P: t- n; `4 Schildren2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
" J Z, B- }# q" x
6 T/ ~4 {+ ?3 R6 M n%采用多点交叉,交叉点数由变量数决定7 D: ?" I# a4 C8 D
2 P' m( w" K+ U7 c. Q: Y# [, [- e
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)' X% l0 Y7 w+ c
* N, X& u n3 h" f2 Hglobal n Children1 Children2 VarNum
6 q* F) Z8 d5 \: {1 Y7 U' Y. f9 AChildren1=Parent1;
& X, J) Y0 L' M' O5 h) |Children2=Parent2;2 p* m2 A8 Q! ]# a# Z
Points=sort(unidrnd(n,1,2*VarNum)); N# e; K& _ |( u- o0 `
for i=1:VarNum
. O! P5 A' h1 J- y7 C( } Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));- e) U4 y0 ^9 L0 s! v
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));8 D- U6 O! Z/ }& T# \
end
" C% a7 q, G7 U. x5 R% e) w3 |' P( s, ?( E
%变异操作9 u9 M: C! M1 i9 j& x. ^
function [NewPop]=Mutation(OldPop,pMutation,VarNum), z ?+ t+ a% u3 d$ K- g
# H& l+ d- s! b0 O; t2 Dglobal m n NewPop. M) j" W: a( I8 z. ~* T4 Z' |; G
r=rand(1,m);
4 S2 S( V! {/ B: R8 c/ ]position=find(r<=pMutation);
9 y2 e# w6 b! R$ |len=length(position);' {+ r6 O5 t$ e% z0 h0 e9 G
if len>=1
1 F6 V, n9 d' l6 a4 d& g' f3 u+ j for i=1:len
: U2 G ^ S# v9 Q# [ k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
% ]8 u3 p" j9 k# ~1 W& z for j=1:length(k) T& u3 ]* k! s" c
if OldPop(position(i),k(j))==1
3 `9 E' i' f9 c* B( g* l$ f OldPop(position(i),k(j))=0;) b7 ^+ C% T1 u& |' t2 L
else
/ q9 R8 v7 [; }. ` H$ U OldPop(position(i),k(j))=1;& R( L0 i& R+ C: z4 f
end
( o8 O8 s& m8 ~+ [- z% l; u/ M/ o: o end
! Z2 P0 ?9 W/ X' B end1 \, j. n0 U4 T2 }
end
7 J* Q; P: g# [3 c9 Q7 i1 ENewPop=OldPop;
+ c- x+ c Z$ R- R- K$ V' _/ f* {8 ^5 Y8 [, u- Q7 J
%倒位操作
! ^1 l8 l) a o& ]/ y5 S. F
) J ]* j1 H% o) }3 k9 r* J/ E3 nfunction [NewPop]=Inversion(OldPop,pInversion)" c: }6 U9 c; T* s- E* ~8 \% y
+ z ^9 \- j- jglobal m n NewPop4 ]- g; D, l7 a+ K5 e. ^$ a7 |0 v6 \
NewPop=OldPop;
2 m g q0 W* m. M' Ar=rand(1,m);
5 J6 k, z. V" WPopIn=find(r<=pInversion);
1 C' `% H( B" c- Dlen=length(PopIn);+ P t7 Q( g7 @: @. F/ F# {
if len>=1
) G0 Y! P: d i6 g- `3 y for i=1:len, p/ b; s1 E' {+ s/ ?( V
d=sort(unidrnd(n,1,2));0 Q2 P( C% }/ ^% l$ z0 y
if d(1)~=1&d(2)~=n4 [/ N, M/ O Q( S6 h
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
" w9 h- ]6 E, e, \8 {9 t- t" P6 L NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));! ?( K+ X c8 b8 J& z
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);. H& X; J* a5 t1 b& v
end
5 h8 z8 W5 F1 k- [ end# s7 n( d3 W, {% e7 L
end
; ?5 Q1 M0 K) F' W- T8 F; l/ s# t; `$ N$ m3 l0 G+ I( z9 a
七 径向基神经网络训练程序
1 K" p; _6 B1 p! A* E) T0 ?1 E4 a5 l, a* ?$ t# }' z5 |0 ]
clear all;
4 a$ ^5 Q R: x8 F4 O) \& ]2 cclc;
& w: w: Q* p$ n8 p% Y6 ^7 v3 a- N%newrb 建立一个径向基函数神经网络
& v d: C5 ]! H& q4 g* ep=0:0.1:1; %输入矢量' ^/ J! ~/ M2 G- n
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
: ]. U! O a5 [% r' J7 Igoal=0.01; %误差9 D# [3 X ?. J) }: G9 E; d+ ]6 k' S6 H
sp=1; %扩展常数
( }2 i& [) x9 D3 ? Vmn=100;%神经元的最多个数; Z6 F+ K A s9 R/ }: @! A/ M: I
df=1; %训练过程的显示频率$ g( Q2 F! c# E( t3 @1 e& }& \
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
/ j# ]' K; L! L# b0 e% [net,tr]=train(net,p); %调用traingdm算法训练网络
* _4 v! y# R7 y' L/ E+ Y2 R%对网络进行仿真,并绘制样本数据和网络输出图形" W2 C+ o" W- w6 _1 m( o2 _
A=sim(net,p);
2 ^6 ]2 X( q0 LE=t-A; Z% V, v# v6 ?9 Q& W- y0 W
sse=sse(E);
9 o7 A0 R) J* {- ~figure; z; W$ t& g( u+ b7 ]
plot(p,t,'r-+',p,A,'b-*');* k) P9 I& e8 F; z- J: i. Z" \3 N
legend('输入数据曲线','训练输出曲线');
3 H. ?* g3 g$ A4 [, r3 Z- ?2 Vecho off ! X- E0 p J. ?8 K0 r
5 N( e& V: D/ b# y% u( h
说明:newrb函数本来 在创建新的网络的时候就进行了训练!0 s3 \# z" v1 t. [6 L; S. W" s
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 D' u* X1 O) h" _7 R0 M: M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!
# O/ v) Q: q/ h; Q0 F! f/ J7 Y6 p/ g4 Q
7 W) G: B# V* @" o1 k训练结果显示:/ J; e( M7 q/ r7 f9 f% ~' M
NEWRB, neurons = 0, SSE = 5.09733 b" t8 H4 L+ O$ b4 l) v2 b
NEWRB, neurons = 2, SSE = 4.87139, J" x9 {1 Y1 U/ @
NEWRB, neurons = 3, SSE = 3.61176
) U1 @( O! o, Y- RNEWRB, neurons = 4, SSE = 3.4875- w7 i7 }+ S7 }' ` o
NEWRB, neurons = 5, SSE = 0.534217" V- L# K0 s: C$ x7 O9 I. z4 M! t& n
NEWRB, neurons = 6, SSE = 0.51785
- {, z& C4 k. R! @NEWRB, neurons = 7, SSE = 0.434259
+ f9 a% A( ?, D: L2 |& J iNEWRB, neurons = 8, SSE = 0.3415188 V9 T: x! M* X: h5 y) N* V
NEWRB, neurons = 9, SSE = 0.341519; R2 z; d ]9 O/ q( q! U& n }% ]
NEWRB, neurons = 10, SSE = 0.00257832
/ Z. J3 [: P) @- I
7 D) }0 C/ e6 u) h- @八 删除当前路径下所有的带后缀.asv的文件
4 s, Y$ C' V4 O. P8 w0 H2 v4 J: u说明:该程序具有很好的移植性,用户可以根据自己地5 q& E+ u/ \+ z; m% Y2 K! H' A
要求修改程序,删除不同后缀类型的文件! # P* p \4 n$ L; H/ V
function delete_asv(bpath)
" d& L) n2 g$ `6 N) e%If bpath is not specified,it lists all the asv files in the current
# F; f# Q2 S2 p+ E" Q4 e6 @%directory and will delete all the file with asv
- ~: N4 Z! g5 a; ^8 `% Example:
$ v# \( \0 ]0 L% delete_asv('*.asv') will delete the file with name *.asv;
8 i1 K: i; E6 o! n% delete_asv will delete all the file with .asv.
& Q' C9 V* Z( {: i4 L
' j ~, F+ z, K' {5 {0 Sif nargin < 15 e/ Q' |, g2 r" }7 g
%list all the asv file in the current directory
. n" ]& ]& i) ~, ^8 ~3 S files=dir('*.asv');
% Z1 c- j* E l' M' Selse; l! |2 A. ~) @2 i6 V/ |7 h) J, q
% find the exact file in the path of bpath
: R1 _0 H8 Q! \9 F [pathstr,name] = fileparts(bpath);/ P; H6 f+ w+ v. U3 t
if exist(bpath,'dir'): c1 P. ?5 t0 i( c
name = [name '\*'];
2 z! T$ @( H$ J5 K: {5 G: _0 _! k end, _8 T; m! l& K5 d# i# G
ext = '.asv';. L& r( c' L' p6 A* i( ~, U0 T8 ~
files=dir(fullfile(pathstr,[name ext]));9 `' k6 _& r9 t- a
end7 q; s0 a6 t- }: R7 W
! k- u, w) c& W$ [9 ~2 l: `: |if ~isempty(files)/ Z+ G, s4 `# Z
for i=1:size(files,1)
% z5 x' H% w3 x+ Q: \! N- `6 F: Q2 Y! a title=files(i).name;0 e* o9 l2 i. R0 v) e- G& T: t
delete(title);
( @3 x: ?! D4 @. G( i end; v4 m) ^7 K) \3 S* s2 P
end$ @! x5 [) v1 r6 F( D6 B5 g+ E
4 T8 p6 {; O! V6 A- B# b
3 I# F( d2 r2 X" N0 K同样也可以在Matlab的窗口设置中取消保存.asv文件!
4 m% n! y- B& m6 i |
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