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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 s/ ]+ p3 f/ V
1. predict_fun.m为主程序;
& C6 B d9 y0 s/ U2 S& }: ?& |7 r0 P6 |2. timeseries.m和 serie**pan.m为调用的子程序' C- [$ p" S4 |2 {- t" B* Z* l
) {8 w9 E/ l- N- P, S' Z# {* C9 f
function ima_pre=predict_fun(b,step)& q2 J2 w) I4 _) V, z9 ?
% main program invokes timeseries.m and serie**pan.m
1 Q" L% x; z2 ], `+ q$ H' Y% input parameters:6 p) a9 e! s7 A3 q: x5 k+ r
% b-------the training data (vector);
6 I& N6 _. B4 n& s2 d% step----number of prediction data;
; E0 z! V2 A) M( v% output parameters:# H- e, q7 Z' Q4 b6 L5 [
% ima_pre---the prediction data(vector);
0 p y. P: v8 o L" j4 @old_b=b;, y2 s' _0 Z- d. T& k/ Y
mean_b=sum(old_b)/length(old_b);
F( f( a2 T8 nstd_b=std(old_b);& e- P( P6 A, z7 M
old_b=(old_b-mean_b)/std_b;* a, O1 ?0 p2 b: Y3 ^% w: [
[f,x]=timeseries(old_b);" G/ R+ a) T& o& m( B- f5 _" v
old_f2=serie**pan(old_b,step);
: l l8 ^" i2 O' i% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;; X: T3 v( f3 H! {
R=corrcoef(f);. a4 S- ]8 G$ N: g/ {
[eigvector eigroot]=eig(R);' V; ?( f+ a! U) @2 R {* P8 B( A" J. U
eigroot=diag(eigroot);
. G. u& Y, T- c( |! h0 ~a=eigroot(end:-1:1);% i9 R8 z% @7 A
vector=eigvector(:,end:-1:1);
2 \! i* q" Y: P) @+ `Devote=a./sum(a);
) D* l" B+ x) Q5 i- TDevotem=cumsum(Devote);
4 p: a U; G0 \) s2 ~: O8 Vm=find(Devotem>=0.995);' }+ I$ F" n. z9 l1 W# Q
m=m(1);
! \' t! k E+ U- _9 e" PV1=f*eigvector';
; `0 [' `+ x9 X5 |6 s; P" a; E- ]V=V1(:,1:m);
+ u, `- j% l& o! _: s% old_b=old_b;/ O+ a9 l6 L% p! G& `
old_fai=inv(V'*V)*V'*old_b;% f$ Q& p7 {( [ S9 {1 g$ I
eigvector=eigvector(1:m,1:m);- Z. u1 Q% h/ m& i/ j
fai=eigvector*old_fai;2 [* o% t5 b+ C4 P# o: D" O' X: k
f2=old_f2(:,1:m);5 f% E) ~- s* C( c9 _
predictvalue=f2*fai;
- t2 G T, L" Z4 o8 M* {) qima_pre=std_b*predictvalue+mean_b;! o$ o, d% u2 M, m
7 x ^$ }- c6 V' }* @
1.子函数: timeseries.m 5 f) ~+ n* {2 q6 L
% timeseries program%3 A* x. Z; H5 c" G/ x1 `9 W3 F" q$ K3 ?
% this program is used to generate mean value matrix f;, F# \1 n, y* p( I8 W
function [f,x]=timeseries(data)
% G z5 U4 {! J5 n. g% data--------the input sequence (vector);
: L8 G& I2 t$ I, N" X, y% f------mean value matrix f;
7 L+ z* u% C4 ]3 [0 z( A% tn=length(data);- s% r+ }: B! ]) a, ~
for L=1:n/2
# C5 X! t2 x& a nL=floor(n/L);
6 \% `! W/ y$ Q5 E( J% @3 m for i=1:L1 S. H* ^& s6 A: c2 U
sum=0;
# L# @- v' i3 E. S J6 w" R for j=1:nL" {0 u7 ]$ j) ~. ]7 M
sum=sum+data(i+(j-1)*L);$ s1 t U2 D& j9 S
end. l9 x* c9 h: _& J! I
x{L,i}=sum/nL;
! a9 i2 _ U, d( M" f* I# Y end
. i2 j7 _4 Y& A- i6 }( Lend
/ m0 R. {* U8 ]7 F$ ?L=n/2;
1 y6 e( a5 ^% U+ Af=zeros(n,L);
7 z& C% c. T, Q$ G+ m9 Efor i=1:L
% J6 U# A4 ^( B( U" U3 w rep=floor(n/i);
% o3 _: R. K" c- S0 ]$ S. n res=mod(n,i);
" U2 A$ K* m7 a) l b=[x{i,1:i}];b=b';# D0 V+ @2 B" t; U, ^
f(1:rep*i,i)=repmat(b,rep,1);
+ W' D' J! Q0 s8 a if res~=0
B6 A8 p8 o( s1 q c=rep*i+1:n;( m- M; x* Y) P) i0 D7 n2 ?
f(rep*i+1:end,i)=b(1:length(c));+ \2 j1 d$ o w. z
end
+ p6 `( L+ Z: l5 [- i* Y" gend
7 e2 K# V: v( Y' \ k
) R* Q+ Z. V' j1 c2 k/ T% serie**pan.m
, Y y k" h4 I' P' I% the program is used to generate the prediction matrix f; / G ]: s+ }- S' [* z4 X1 n
function f=serie**pan(data,step);
( b+ B- M+ ?5 m( b$ z# Z6 D%data---- the input sequence (vector)
; m- g5 x: b6 C( F& |6 K% setp---- the prediction number;
% s. ]; y4 @: h8 H9 ^& t; c3 hn=length(data);
: k8 g J2 u( i# [& G* R9 K) Cfor L=1:n/2
: U8 {8 T7 m& X& i: J) D nL=floor(n/L);! D' M; w w9 g4 m0 _' g7 S# h+ I
for i=1:L
5 W$ [) l) x7 Q" ?3 P sum=0;
. J: U0 w) H" [0 R3 n7 @% ? for j=1:nL
0 o* x l7 c2 z4 R. R* f sum=sum+data(i+(j-1)*L);
4 ?8 C# A2 g9 R( J- L- a0 n end9 G/ d' F, M+ E) O) t g; {7 Y |
x{L,i}=sum/nL;1 v# v/ a, f, y& l/ q. T+ @
end5 D/ }; ?8 a7 b. l& a' e
end
. z' C% H% d5 }3 mL=n/2;
7 g0 z2 J* ~4 [+ b, p& m% Xf=zeros(n+step,L);
[7 @) s x: F& \# rfor i=1:L
/ _- T, n M$ i0 n8 e: M2 _$ \ rep=floor((n+step)/i);/ M* K. N& C- S( x& W
res=mod(n+step,i);
7 {; X3 y* R, ^& c8 O8 I+ B b=[x{i,1:i}];b=b';
$ [& G1 P& n3 r f(1:rep*i,i)=repmat(b,rep,1);* v5 a8 v/ N5 y. L8 R# ?2 A6 s3 n
if res~=0# p; X. \( r! ]& }- Y
c=rep*i+1:n+step;6 W. ~' U- K, R# }8 H, X3 A
f(rep*i+1:end,i)=b(1:length(c));
# ^3 Y3 b* L" Z, h" L% m6 K end8 S2 p6 C) N7 L5 b% F* R/ Z$ c
end$ t ~. ?6 t9 L( H; d
4 i1 J" e8 t$ s4 y二 最短路Dijkstra算法( _- J3 C: l! v9 ?9 { ]0 {# y
% dijkstra algorithm code program%
/ I; f) D5 y! B+ D! P) y' `% the shortest path length algorithm; `8 |) i, U: o) G5 D+ g
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)
9 q/ }, A$ V- s8 h% Input parameters:
, x/ g* P1 L5 Y+ e& i% Input_weight-------the input node weight!
9 j- D7 S- S2 T% start--------the start node number;$ g1 b7 @' ^* @ B
% endpoint------the end node number;9 k# J2 |% S& O: v/ Z1 w" Y+ p
% Output parameters:' B! ~4 x; `8 [5 H! @
% path-----the shortest lenght path from the start node to end node;* u( t4 I$ t) I( F9 x
% short_distance------the distance of the shortest lenght path from the
, n9 ]! j! ]2 ^- Y; c% start node to end node.
) ^ l$ F) | @% M' p7 `. X[row,col]=size(Input_weight);
7 {( b$ O, e, s5 ?, g2 b. U5 J0 X% O" R1 [! d0 {+ m7 X- ?
%input detection
* H" ~% Z- [/ Y: |' kif row~=col
4 J g7 @1 P2 M& k$ h3 I error('input matrix is not a square matrix,input error ' );
5 \- R% B; t! \. T Send+ H( f2 Q, t1 \5 W( N6 ?( H9 b* P' f
if endpoint>row, \; J6 L! y) U7 K$ m/ U3 h e
error('input parameter endpoint exceed the maximal point number');4 f1 X- {- R* m4 l$ j
end
$ ^7 d8 Z% j" ^: O3 e) I' L, r! ?5 _3 Q
%initialization5 P9 z( {1 u) l, V: e: I- `2 q
s_path=[start];! D4 S( i4 M3 Q, o; _2 i, g
distance=inf*ones(1,row);distance(start)=0;
' q2 [6 D I) vflag(start)=start;temp=start;0 V5 l n2 `0 _6 `: F3 O
4 |& I4 D6 l- y1 I7 V0 L; v( O5 ^while length(s_path)<row
; h7 ~5 {. _ j pos=find(Input_weight(temp, : )~=inf);
: }- P4 `5 ~0 t6 E for i=1:length(pos)) m/ Y: |! a1 F
if (length(find(s_path==pos(i)))==0)&
. M/ T' {1 u9 _, [* w3 `! R(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))* L7 S8 N% m f' B
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));( M4 {0 c1 P. v" q/ S. G( `7 x
flag(pos(i))=temp;
2 |: G! B4 V$ \9 |" Q end. }+ b9 Y/ K- g: G3 ^
end
- B% l3 j9 x) i. t" W; s; B k=inf;
( Q0 N- L$ V: L G1 } for i=1:row ^4 A0 H @2 I) _
if (length(find(s_path==i))==0)&(k>distance(i))
& M5 X1 @4 M, Q) J1 p k=distance(i);
1 ]1 q k4 u) Y temp_2=i;8 @" d. t0 x9 a- z' n4 ^
end4 n1 S# U1 c" o
end
3 k* l) {( |7 k4 u4 i# J8 b! b s_path=[s_path,temp_2];
) I7 v- k" S! }1 c temp=temp_2;& j6 t/ y, A, ^6 r7 U# K! a
end: K( r- P+ Y, ]- C
; _( R& @1 p3 p- T7 K' x4 | R# j%output the result
8 I# F' r' Y( B2 Lpath(1)=endpoint;, d- {- N+ Z D2 v0 V
i=1;
4 o0 C, D$ t* Y9 b: ~- f) |while path(i)~=start; G8 s5 ?8 O* B& g0 j! U8 [; N
path(i+1)=flag(path(i));
- X H* f3 `6 d* h& L i=i+1;* E& H2 F3 F3 G" x9 i
end. r3 N0 d. i) e @+ i9 J' |
path(i)=start;5 i" u; x6 K" _0 g) n7 X
path=path(end:-1:1);! d/ e) h' X1 A# R& D8 [/ S+ y
short_distance=distance(endpoint);
; x1 {$ w" v# B! a) N三 绘制差分方程的映射分叉图( W+ e- b* {/ J
$ P" o) _9 l6 f( d- G# lfunction fork1(a); 7 z# K# E( q; d: \+ A
" Q& ^0 o( B9 p7 D( G2 _6 g# S% 绘制x_(n+1)=1-a*x^2_n映射的分叉图1 E- T( `1 [- |1 S+ J2 H" }, h
% Example:
4 o) Z: F. \0 _ r/ f# k2 n% fork1([0,2]);
3 G, z! {) S2 U! b0 y" GN=300; % 取样点数
! S- a# A T# a& ]1 I ?- lA=linspace(a(1),a(2),N);
9 a1 M& G2 @( _+ P- o8 W4 @starx=0.9; 6 E0 q. n9 s9 C- b
Z=[];
6 o/ F7 t: V4 m8 }5 }; ~* jh=waitbar(0,'please wait');m=1;, [* p) \% d$ O& f# t% j( P( |. q
for ap=A; 2 [% x9 N1 R# ]. T% t
x=starx; ( i! L3 {' Z8 I0 T9 Q, ?1 [' |
for k=1:50;
7 C" o$ y$ J7 q; N5 m( e! b' g% ^ x=1-ap*x^2; $ @2 n% d; C5 f7 z0 ~1 ?$ h, _
end / {0 _: Z; p, x/ J' c9 l
for k=1:201; $ J( f4 C8 s+ n b6 |0 v3 @+ _: p
x=1-ap*x^2; ( q- J+ \/ \* ~* v$ }7 P
Z=[Z,ap-x*i]; " c, s( t" e) Z6 j, M
end 0 b: p3 S6 t- N& d
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);, d8 u" e- D* `8 @
m=m+1;! h1 q+ T8 K* s6 i
end M8 z, X" b2 f( ^) ]4 ]. a
delete(h);
% _* ]! N' F9 { A& Cplot(Z,'.','markersize',2)
3 u' \' m0 w* h7 O1 K* wxlim(a);& \, S5 w' L( g7 x/ d0 Y0 u2 r
7 j' J7 a7 w/ i, `) P7 q8 f4 V- q四 最短路算法------floyd算法
: D( m) W- J2 Vfunction ShortPath_floyd(w,start,terminal) * F0 s5 G& d4 P1 H2 w0 U3 O# e! i+ }
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;% J9 w. y& N" H! u0 x+ }- h
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
& h3 A4 w, Q* m4 N5 H%start-----the start node;$ ?& M7 ?3 M4 G% I! L: W# u+ n
%terminal--------the end node; $ R% S8 n, d6 U5 a8 ]9 e
n=size(w,1);
& B- j8 }4 ]6 r! N* y- z9 R3 S[D,path]=floyd1(w);%调用floyd算法程序
: k, r" \; Q3 G N
( p6 S) Q* X' U* r%找出任意两点之间的最短路径,并输出
4 W$ ]9 `8 a6 W' k7 O' y" T- Vfor i=1:n! h- }8 k! r" d8 C
for j=1:n
% ?. A" @! b1 P" v3 X! T. n- f6 z Min_path(i,j).distance=D(i,j);# {3 N; _. I# f1 }
%将i到j的最短路程赋值 Min_path(i,j).distance
- V' M$ }% I! M2 W' F/ U %将i到j所经路径赋给Min_path(i,j).path
5 m& W/ D6 ` z3 B. \8 \" E Min_path(i,j).path(1)=i;9 {' [2 y) e- V" j+ A; B' E% |, o. D
k=1;' X0 x7 ^8 ?- R# t, [' E% z
while Min_path(i,j).path(k)~=j
. a1 O7 N8 W- H" c7 J k=k+1;1 ]0 X, @8 A: y/ M' p% Y: K
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);: y+ J) \" {2 B- v% {6 ]+ k4 V
end7 B$ A( V. c: n2 z) y8 [/ r
end0 g. w! D! i# H1 @9 C+ D8 e
end8 ]5 i" p; G) m! J8 B
s=sprintf('任意两点之间的最短路径如下:');) p) `& t% B) m h
disp(s);
6 W% U N* ?! Gfor i=1:n& N' d' U" _* N& M9 J
for j=1:n
8 o) v, p7 v1 Y1 M8 G; I7 m s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
/ r j/ s3 }8 H) D9 F6 I# p ,i,j,Min_path(i,j).distance);
( P& G+ E. e& m4 v disp(s);+ k/ B5 E) v, K* I
disp(Min_path(i,j).path);! ]- J0 p6 H7 k! W! `( t
end w: o4 |2 @( z& q
end! w7 Q: e5 p2 z* B; }
0 F5 U# v2 a! s5 _! ?5 G/ v%找出在指定从start点到terminal点的最短路径,并输出% X% |1 N( F$ ]" \
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...8 p# K% O G e6 F% w
start,terminal,Min_path(start,terminal).distance);9 I$ e" ?4 |% X! x
disp(str1);6 l0 c7 L( X# @
disp(Min_path(start,terminal).path);3 Q D5 t2 N+ Z" `2 k# \
7 \9 e% T/ g. {* m% G
%Foldy's Algorithm 算法程序* @: ]* I2 C9 R6 x2 E+ u
function [D,path]=floyd1(a)- i3 l% q/ F5 m% H/ J- Y
n=size(a,1);/ }9 {; F: m0 a4 U. d4 m% X; r
D=a;path=zeros(n,n);%设置D和path的初值
/ C( i+ X3 H4 Z' L, O+ @ Efor i=1:n% ]4 v6 G {+ B. E* h& p. J1 e: [% _
for j=1:n
$ e$ ] M1 i, m. ~ if D(i,j)~=inf4 h6 Y0 _2 @3 E% Y/ j& K3 g* R
path(i,j)=j;%j是i的后点
/ k4 ?9 U) M' Q1 `4 F1 O* b end# E, ~8 w# D+ s, s) H1 _* k
end
- {8 F; @+ L. [4 \. A7 Vend0 V: w- D5 t' P' ]- ^# u# B) K
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)! j9 }8 u# ^- G9 H$ G1 I/ U
for k=1:n( H. Q; \) Q" N6 L+ H0 a
for i=1:n
4 E% y1 @& a( `: p, ` for j=1:n
& O" d* J5 J7 G W( @2 d( z% s if D(i,k)+D(k,j)<D(i,j)
( n% \; u. a& s% ^2 ]# W0 S D(i,j)=D(i,k)+D(k,j);%修改长度% G/ X, _- Z5 T1 {: v: U8 @" Z9 u
path(i,j)=path(i,k);%修改路径5 z9 P* U$ n3 X- d8 Z+ i
end, _$ U* L: L2 D; V% [; f
end
7 E: [* @& m) [6 T( c. F( K ? end
* w( G6 Z9 q! k) H3 yend
: d* n3 |0 @9 Z
) x7 r* |; D; x4 M8 O五 模拟退火算法源程序; ?8 m/ b5 m% J% ]! q; B9 O
function [MinD,BestPath]=MainAneal(CityPosition,pn)
! P1 Q& s( Z: Pfunction [MinD,BestPath]=MainAneal2(CityPosition,pn)* r8 n( v8 V) T+ m: Q+ b! A
%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" Y8 k: a0 u; q( X
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...8 |& n _; r1 ~- \8 H' N. n
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...4 P, w6 a: ]8 ?0 q) y) ?0 k
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...5 e4 {6 k* p$ F6 }' }3 n- ?0 L) `
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...6 s: I* H% W1 L2 A+ L: b+ Y
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];! W T5 T3 ~/ H4 H% S4 `
) D3 ]2 g# n. V% n5 V
%T0=clock) ]+ y: ~3 }$ ~7 A# W; ?
global path p2 D;
8 W. A# Q* Z) H1 |( Y0 k1 `[m,n]=size(CityPosition);
6 N" y# |; Q1 @$ H9 ?7 q%生成初始解空间,这样可以比逐步分配空间运行快一些 P, |" ?8 y' Y5 r# A
TracePath=zeros(1e3,m);
/ M f) i4 ~ D0 I9 u DDistance=inf*zeros(1,1e3);
* J6 s0 W# p' {: u" R8 E7 u. l5 D7 e4 {5 z
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
$ u b3 r1 q0 Q% ?: C (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );5 P& t1 J2 S% c# N
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)7 ^3 L! y; J2 `7 L9 ~
for i=1:pn
; J5 [8 Z- L' c, I4 U& G path(i,:)=randperm(m);%构造一个初始可行解
2 [/ [" S7 ~9 R& x% M& u+ [end: n& v8 A' F! ~4 b7 y- i
t=zeros(1,pn);
+ h* n' ^% F" O up2=zeros(1,m);0 g' k# U6 H6 v, M8 ? W
8 {5 K1 Q- R$ f p* O- Miter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
4 s, D: `) p$ h# Q' {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=' ) ;3 E0 E. b/ L% }% d' l. d& ]' Y
%如果考虑到降温初期新解被吸收概率较大,容易陷入局部最优
6 g# Y- m; t- {& @1 A$ e9 D%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' p( ]5 t# t" W l
%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* v" s& B# D; J4 ? Z% f+ k%会收到到比较好的效果
# l7 s( l5 e! L$ K. M) u2 x) v
T=1e5;
, {5 W- m% s' k7 `8 @0 kN=1; U7 D& Q( z% M0 p! u
tau=1e-5;%input('请输入最低温度tau=' );; l9 i. U1 u: a, X# K
%nn=ceil(log10(tau/T)/log10(0.9));6 X3 \4 V4 T- `1 ]5 O2 X
while T>=tau%&m_num<m_max
: X& X t) o9 G& ?; a5 M iter_num=1;%某固定温度下迭代计数器# W7 f; U" y* z( y# K3 M
m_num=1;%某固定温度下目标函数值连续未改进次数计算器
" s: @6 Z* |6 [, l1 i %iter_max=100;
' m, b8 c4 u5 i. E %m_max=10;%ceil(10+0.5*nn-0.3*N);
, a! q# C3 m# X8 p# s: ~2 Z% g& G while m_num<m_max&iter_num<iter_max( p: {$ j- f$ W1 d( H4 {% H9 U
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
; b5 b" e7 d$ H& u2 Y3 s9 o3 p %用任意启发式算法在path的领域N(path)中找出新的更优解
r% l" X# P/ _& K2 c for i=1:pn
2 d; a) T) i2 T. J9 ~ Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
4 G0 U( N2 e3 m6 L& U9 n+ p%计算一次行遍所有城市的总路程 % {6 R% ^- }' f7 R* B/ D
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线! @, M+ U3 e( X {
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);+ m; I' q a- ]; \1 y
end- ]$ v4 N; m8 y. g' `% N( i/ |/ k0 z4 F
%Len1* s2 Q& ~3 S. Q H, O/ \1 u" j
%Len2
3 l4 {. j/ N$ x. [+ g V# U$ n5 G %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
5 X3 ~" ^3 M' f) Q% [6 K R=rand(1,pn);
3 f8 L8 z5 O: i* y# c x0 \ %Len2-Len1<t|exp((Len1-Len2)/(T))>R
/ u0 c# C4 W( s: y& C3 o/ q if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
( y' `* y+ y0 e! ? path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );7 t |; g1 I, j( S& A
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));5 q" \0 o; _1 L4 I; l
[TempMinD,TempIndex]=min(Len1);: r5 c U% q9 n. o, f. N& Z0 y
%TempMinD( h; R; e8 e0 B7 G0 r; V
TracePath(N,: )=path(TempIndex,: );
# g7 m1 O' ^' c( r* b+ Q- A% L Distance(N,: )=TempMinD;
5 Z/ h6 F4 G0 \6 l N=N+1;! C( N9 i7 ^" u# {# L& u
%T=T*0.9
5 R8 j& U0 W0 J. L0 L m_num=0;
! S! [+ y* f: p/ {& p else
' p% Y/ ~/ G. q) z( w m_num=m_num+1;: |( R% n K" t3 A. a
end9 n$ x# a3 S9 L& e1 k
iter_num=iter_num+1;
5 \2 a$ N3 J" s$ z, y" d# t" c: } end2 x6 D: A' B. g: t7 B' b; O+ d
T=T*0.9
# W5 R& F$ o1 c# M8 j%m_num,iter_num,N
2 ~6 R) Y( W4 s2 U* A+ ?2 a G& G& Oend # F& C9 r5 B0 ^# L! G' s7 N
[MinD,Index]=min(Distance);0 T7 `; u- h& i: r, i$ ]
BestPath=TracePath(Index,: );6 p% A4 V& M1 W9 _ z: G: }
disp(MinD)2 b5 V( }0 y& l
%T1=clock
, i, N3 G/ K4 p, B6 N
% |. Z s- S1 G) o & d5 ^4 V u. _ Z. u. L& X4 I" i
%更新路线子程序
- M) V" E. e2 V1 B! D: Tfunction [p2]=ChangePath2(p1,CityNum)9 V# @3 d8 }: f1 [' i
global p2;
2 H5 A$ H$ x0 k/ G. @while(1)
8 G3 g- _/ _2 z R=unidrnd(CityNum,1,2);
/ ~9 Z; u$ e" p" @6 q if abs(R(1)-R(2))>1/ c. q5 K" V! p! o* l+ ~) K
break;2 w$ b0 g3 a2 W/ ?8 `* r
end8 i9 }) H% V; h0 v3 w- _7 v0 {
end
, r7 y$ |3 E" z) \4 @$ a3 U* W7 j: RR=unidrnd(CityNum,1,2);0 K3 ^% }8 w1 W- I8 G* i+ z
I=R(1);J=R(2);' @0 t, i6 D" A% X" b5 j
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
& X0 Y' v5 j: z+ b4 o9 Q/ {%len2=D(p(I),p(I+1))+D(p(J),p(J+1));" Q" K" \' M3 h0 K+ G
if I<J
! w4 f4 Q4 w1 i2 O/ v$ g; X+ t I. L p2(1:I)=p1(1:I);
/ k" @/ L8 h' b1 z4 ~ p2(I+1:J)=p1(J:-1:I+1);
- n! e6 ~; g: l4 ]$ R P- p/ [ p2(J+1:CityNum)=p1(J+1:CityNum);
# b& ?& z( k Zelse* i3 B$ M ? c2 c, T% }
p2(1:J)=p1(1:J);
5 X7 ]; a1 x2 T4 T8 I2 F, W# E4 U p2(J+1:I)=p1(I:-1:J+1);
) t8 v- \, v: Q; ?0 q9 I p2(I+1:CityNum)=p1(I+1:CityNum);! r" X3 X: x$ Y) { {- {2 }
end: r* m6 Q/ f' }" b- ]. B# @
" `+ n/ A, a; x2 P- y3 K
六 遗传 算 法程序:1 @# z5 M' a' W0 I: y% n7 t6 y
说明: 为遗传算法的主程序; 采用二进制Gray编码,采用基于轮盘赌法的非线性排名选择, 均匀交叉,变异操作,而且还引入了倒位操作!
, d, c" H! W+ P$ Y$ v" k: R. e* P8 r; l2 [% _: J1 d
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
l0 P, H2 K1 d% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
5 o+ M( ~- `, n: q) a$ S% Finds a maximum of a function of several variables.! n) G' A, y) Q* x0 X. D6 \
% fmaxga solves problems of the form:
9 x/ R% l* k8 j8 l1 D% max F(X) subject to: LB <= X <= UB
! q# F' u% O1 M; k, z7 d# W% BestPop - 最优的群体即为最优的染色体群. v+ _1 W8 l4 V4 q% a# e5 i
% Trace - 最佳染色体所对应的目标函数值
z: s6 F( r! D- N% FUN - 目标函数
, _ V$ ^- Z' w }+ F+ D% LB - 自变量下限1 M7 E4 D' Y, G3 D1 k! K6 h) M0 G& \8 L* a
% UB - 自变量上限
, @) I- I+ |8 [; T. t% eranum - 种群的代数,取100--1000(默认200)2 [. e$ v* t' \0 L* r
% popsize - 每一代种群的规模;此可取50--200(默认100)
5 F; A0 {- T0 z4 ~5 ?) _) P3 e- z% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
% f' ?) Q+ E, K% K/ i. e. X# j% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)* X2 t! G' [4 w7 S+ c R
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
2 w8 ^; V/ b0 K! S2 j& ]% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
/ ~, T' M; @5 q# m& M%码,option(2)设定求解精度(默认1e-4)
* t W8 E f* i2 y R%2 O% t" s; |% ` H6 M
% ------------------------------------------------------------------------
; b4 e' k$ P/ J) O; T1 o# [8 ~8 a) |5 x
T1=clock;
& g7 G. ~! a* ~7 | b' p2 y( lif nargin<3, error('FMAXGA requires at least three input arguments'); end, L, S0 s3 n) A: u1 M" a- ^1 k# n
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
5 } Z r \ `" i, \% Lif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
- S. k/ H" H3 r2 V2 [if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end- w5 E1 o2 u+ G3 K. ^3 ]! L: P1 p
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end: X) J4 N w7 |: [& [0 Z7 R
if nargin==7, pInversion=0.15;options=[0 1e-4];end# ^1 A" \9 Q8 K) h$ r2 T4 t
if find((LB-UB)>0)1 e6 V2 z$ C" t$ a: V" e
error('数据输入错误,请重新输入(LB<UB):');
* m7 e; F/ X7 U* U% bend+ C# |8 {: Z4 [' s- Y+ C8 A
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));& X, B" K- @% U& ^
disp(s);9 r1 S/ I3 \) P9 B0 b
: z: N: D2 i. ?2 Y) d' D/ }global m n NewPop children1 children2 VarNum
& O: d8 E9 S L" i0 W6 R: }8 f7 e; L" X4 n
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);' x6 c X9 i9 m w; |# j( E
precision=options(2);%由求解精度确定二进制编码长度
" _0 o ~# X: S- y; ~- S6 Qbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
* a$ Y( A' A5 @6 {& @8 ^) e+ b. Z[Pop]=InitPopGray(popsize,bits);%初始化种群
; u' h# Y* f/ s4 I, B[m,n]=size(Pop);4 f3 c* B4 |& `: [& D( m# B) A, P
NewPop=zeros(m,n);4 m7 |% v: R0 j6 A1 x
children1=zeros(1,n);
! L4 Y2 d: p. m" u& h5 bchildren2=zeros(1,n);
4 K! x5 r$ Q) k1 C( Hpm0=pMutation;
! L! R2 w- q }7 z5 X# g; rBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
: Q4 w) P7 u- p! P0 tTrace=zeros(eranum,length(bits)+1);6 I8 |5 A$ E1 |: V2 V2 n
i=1;2 }5 u$ ~3 t9 C
while i<=eranum& q% W+ r0 d6 Z; D9 ^
for j=1:m; ^0 a% d+ X7 O# p$ l0 m/ k
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
4 T& P0 n4 h! z3 D- ?+ M end1 b6 W1 L/ C; c3 u8 c
[MaxValue,Index]=max(value);
& p% ]) n. r: w# [/ m5 P BestPop(i,:)=Pop(Index,:);
0 N# [1 U* n1 I$ S3 F Trace(i,1)=MaxValue;9 a3 M( \" v( ~3 `8 |* s7 w5 u
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
: U* z8 n8 [& X: R; d2 c8 V [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择7 p, c1 z1 Z3 f8 y* `/ b: r7 S
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));4 ?7 ~8 T/ G# L% Z
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率4 D7 [% R% {) D* s$ }0 i
%round(unidrnd(eranum-i)/eranum)
. s7 A% D% r* F* g4 } [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异$ A; f7 M5 ~+ f) g: U/ s
[InversionPop]=Inversion(MutationPop,pInversion);%倒位$ B- |4 i) w7 [
Pop=InversionPop;%更新
2 t+ s/ d9 |# F3 i4 j4 X3 XpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); 2 h7 j) B0 J- Y" d; c
%随着种群向前进化,逐步增大变异率至1/2交叉率
( C/ |' B& H( \- `4 b+ ` p(i)=pMutation;
8 L6 d, g! I' N# }4 j M# u( S i=i+1;7 H/ H; t/ ~9 D
end
4 L8 n% A9 t* T$ \5 [2 X5 K$ ot=1:eranum;/ m7 ]+ X* J/ Z# `) _2 O
plot(t,Trace(:,1)');8 K( L& R, y' `+ r
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)');
6 E5 Q, `+ A7 Y' \& {[MaxFval,I]=max(Trace(:,1)); v- r% Z9 U; D
X=Trace(I,(2:length(bits)+1));/ m( Y! }$ J S
hold on; plot(I,MaxFval,'*');' U6 |/ t, H4 O( P
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);5 O* E4 k6 Z3 o* Q1 J6 D! O
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,:)));
; @, N+ w$ j! ?2 |disp(str1);
# ?9 G% U& B! @/ ]0 ^6 U# L2 F%figure(2);plot(t,p);%绘制变异值增大过程
- F) ~( i4 G: l% W! F6 P4 Y% TT2=clock;
5 c/ k7 y% w, Oelapsed_time=T2-T1;
' }+ W3 z/ ?5 a* ]2 rif elapsed_time(6)<08 ?' W% k0 W x) i
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
' L) z; @: O- D4 G/ a" vend
1 U7 i) D. S( M0 @" [- Y9 _. jif elapsed_time(5)<03 a9 j& ~+ U. ~& y6 J8 v: ]. y
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
! u1 |8 B8 g: s7 kend %像这种程序当然不考虑运行上小时啦2 X- X0 d# n' Z2 Z& e
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));
. C1 v+ s( y* @disp(str2);
( P9 a. ]7 \7 S: W7 ^ H& K$ @! V# z. z8 h
0 d. J6 {2 {) F) m%初始化种群
$ K$ J: H* J+ k%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7 y; j1 x) a. S% p/ N s9 a) r. X# W. A
function [initpop]=InitPopGray(popsize,bits)
8 k: A/ D7 S2 t0 T3 f y/ Nlen=sum(bits);$ h Z* j" K1 J) R( w
initpop=zeros(popsize,len);%The whole zero encoding individual
4 |; j+ k' T) f+ C: t2 d8 Gfor i=2:popsize-1
, o' N5 h) o4 n/ |* L- p# D( C+ z pop=round(rand(1,len));
7 c7 a+ V! Z) _7 t, {# U pop=mod(([0 pop]+[pop 0]),2);
- X& K l ~# s2 W8 E %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)1 ^9 P0 G- [9 M. S
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)0 n; C5 S: ~7 i# c! z( \
initpop(i,:)=pop(1:end-1);
$ H& v3 ]$ W. `6 Hend
/ K U! o6 d( Winitpop(popsize,:)=ones(1,len);%The whole one encoding individual, t1 m2 F4 E! u1 _* d
%解码
( Y. n$ U2 B# q* v7 N
3 v' q! ^& h* \8 [0 t+ g, afunction [fval] = b2f(bval,bounds,bits)
2 |4 T9 H, F5 t0 k C% fval - 表征各变量的十进制数
2 V" o# f' t9 @+ x4 O" g% bval - 表征各变量的二进制编码串
# q5 U3 s6 I' ^" F1 Y% bounds - 各变量的取值范围) k; T+ P S3 H7 g( l! r# C
% bits - 各变量的二进制编码长度0 D0 F2 K& N0 U8 L9 u7 Q/ M/ D
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables7 M, P. M( z% Q! u. E0 R+ R
numV=size(bounds,1);
0 u8 W) z( A$ _" Wcs=[0 cumsum(bits)];
# J. Y- }- i8 g1 h5 g, G/ u9 zfor i=1:numV8 Q/ r* g& Y; u
a=bval((cs(i)+1):cs(i+1));
j+ {6 {; T. g$ ]1 g3 V fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);% Z5 ]1 O+ _4 w* j
end
4 C1 X8 s9 y8 w% e+ b* u! s%选择操作" N/ L: {4 A7 Y2 Y, n& X
%采用基于轮盘赌法的非线性排名选择3 l; t+ I7 Q& R
%各个体成员按适应值从大到小分配选择概率:0 A' h( ]! ~' h0 z
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1, c5 }' E+ J! `& B
9 Q: l |% g: U) P+ Dfunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
6 W! e' i# o$ \; t8 Nglobal m n
- Q- Q4 g1 a2 e1 A0 ^) k5 }1 Gselectpop=zeros(m,n);2 G2 i/ d3 S- y4 |9 A! x T
fit=zeros(m,1);$ b r8 \" E9 b# Y, e H
for i=1:m g9 T: J. h9 A: ^9 F0 _& A
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
, N& t( e8 y) r I; Mend
. E3 O }. \' z$ `" vselectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
! t4 C X9 N2 o' p: _$ H, }q=max(selectprob);%选择最优的概率5 o' b1 A* W6 h9 n0 }
x=zeros(m,2);6 U9 J1 p/ r9 t* o: J
x(:,1)=[m:-1:1]';
, T$ ?+ b8 b* f; t J% E[y x(:,2)]=sort(selectprob);0 n8 v5 X! p3 [% U3 X7 U+ k. i7 |
r=q/(1-(1-q)^m);%标准分布基值7 h8 G0 v$ l2 ^+ w2 V
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率+ a2 j1 F m5 V" W
newfit=cumsum(newfit);%计算各选择概率之和. L5 K( f# H4 ^$ @ }
rNums=sort(rand(m,1));
; N8 f4 f0 X. z# ~" C; gfitIn=1;newIn=1;
% e9 n3 g0 d5 ]" p g+ u) `8 ~' Lwhile newIn<=m# b6 s* K0 G8 u8 h1 R9 C
if rNums(newIn)<newfit(fitIn)
- l) C3 @+ L0 a, ~1 c, Y( j selectpop(newIn,:)=pop(fitIn,:);
! S$ ^; S% W% R- U- \ newIn=newIn+1;0 h9 Q! M3 \8 [ m# s) j
else
; k- E7 H, O- Y: U5 @ fitIn=fitIn+1;! Q# o; f" h$ H
end2 u1 I, X7 f" C- |' V2 `
end E! f4 A" Q2 W+ h
%交叉操作
5 v% R1 f W9 f4 Jfunction [NewPop]=CrossOver(OldPop,pCross,opts)
& j0 x1 w6 f% d# o7 t* t6 z4 ~%OldPop为父代种群,pcross为交叉概率
( y' ~* Z3 F8 E) `global m n NewPop 1 }/ G. o: j2 u+ Y
r=rand(1,m);
3 z5 T2 {% M: ^( Z/ `1 sy1=find(r<pCross);
& N$ O1 O- i0 [8 uy2=find(r>=pCross);
: s1 m4 D3 E0 z7 j0 s2 o l; o, Ulen=length(y1);! c3 H" b3 j, J" S
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
) Z; M0 {: O" B9 Q% q1 D3 { y2(length(y2)+1)=y1(len);8 E* C8 x4 O" M1 a. R! _* m, [2 X
y1(len)=[];
& A9 Z( U3 k6 X; tend
* s5 V, \. ]* P1 t- Tif length(y1)>=2
1 X V. B. F \1 d) _4 F for i=0:2:length(y1)-2/ d: n0 O% `+ r. g; V3 p
if opts==0" X: h7 P$ D2 Q, l3 s: N4 E9 l
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));' ^: q: U7 q/ ]; e9 U* K
else7 G& K+ F" u" v' j, W [
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));+ d$ M/ H6 ^: C, N
end
: E# x" S# z) t( J7 V end
0 e! c/ e" m7 w- ?" xend
. o: z% I" \& b7 l. a3 ANewPop(y2,:)=OldPop(y2,:);- |0 N% y% N! s# Y8 R5 l) X
! z) Z" N# t, Q' W%采用均匀交叉 - u5 r6 v' x4 f) u& e |7 n
function [children1,children2]=EqualCrossOver(parent1,parent2)
. m- p" ]7 L! C+ p; ?7 O
$ G6 H, B0 w M2 D7 H( Z( Iglobal n children1 children2
3 F1 K& x; f, W# e% K$ a# G% shidecode=round(rand(1,n));%随机生成掩码
/ A$ E, E0 G6 W0 Wcrossposition=find(hidecode==1);! l* k! S7 V5 O$ O1 j
holdposition=find(hidecode==0);2 \' f7 P* J9 k* v, f. C& ~
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
* h( \* N" g0 Q& y7 b7 `children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
% p; K* T+ k1 c7 w; ]4 v. ~( nchildren2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
! o$ s) {& \2 a% P4 o3 f/ Uchildren2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
' N! O5 J) d) {7 e1 l# i* l5 O5 C, a+ c5 N
%采用多点交叉,交叉点数由变量数决定6 V& m* W' K* |3 c2 D/ j# k
4 U8 A: g9 q9 f2 | L4 [function [Children1,Children2]=MultiPointCross(Parent1,Parent2)' v8 ` ^& A# H' N6 d- o
l7 Q2 J, E" G- Fglobal n Children1 Children2 VarNum: C& y( m% C) j0 A# s- S
Children1=Parent1;
" }7 z, S9 L$ c& ]; kChildren2=Parent2;
H. |/ y2 @) i, S$ a8 _* sPoints=sort(unidrnd(n,1,2*VarNum));
9 X7 f2 Y f: l4 xfor i=1:VarNum
- C+ K: ?& |0 g3 @0 \$ L Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));' D/ b3 o" K- L' C8 H+ _" t c
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));8 P% T6 A7 U; d8 `9 H
end; X0 b: X" T V, M5 i# c" A% o
0 E; u1 A- L& o# U8 H4 D, j* w6 o%变异操作
9 I1 M" R( v3 Z6 p6 i+ w5 Hfunction [NewPop]=Mutation(OldPop,pMutation,VarNum)
% y/ [6 @. [ T3 U u4 `/ ]- Q
! ~5 n9 e0 l/ m- R, d' G8 C eglobal m n NewPop. W) a: S/ F/ S/ r
r=rand(1,m);
8 ?7 X$ L/ |& bposition=find(r<=pMutation);
5 m) u9 f6 L% {# w6 u2 Llen=length(position);$ K6 F- z# p6 k$ T
if len>=1/ F, ~* \; `, t: s l% K) o
for i=1:len
y% F8 f8 L4 n k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
1 y) @5 x% ]5 N; v for j=1:length(k)
. x8 w! G- w9 |3 l& q1 K ` if OldPop(position(i),k(j))==12 y+ ^ M L2 v; B! u
OldPop(position(i),k(j))=0;8 F% H- V/ F% ?: e
else
5 u, L7 } H; H; @* I4 m3 E1 B OldPop(position(i),k(j))=1;1 z& _( h+ B/ H( O/ w/ Q/ c
end5 _/ }+ m. Y/ b$ ^7 `; g1 A
end
% P, t* r# [0 d! n' N end# g" w1 y* y1 m2 m- Z3 p
end
0 c r3 f' A$ H! ~! Q* G- {NewPop=OldPop;
) `4 D0 `. N6 I! r# t" |+ X
: p" V3 f/ U z7 a/ i4 M. M%倒位操作, P2 g' m: [, b$ e
, c7 r9 L( T) X& Ifunction [NewPop]=Inversion(OldPop,pInversion)/ I6 f7 D0 h( v+ `) S
$ D7 O1 R: y" Q$ b7 Fglobal m n NewPop: J, e- Z# ^0 I$ H3 X& |
NewPop=OldPop;8 c0 h$ L! D8 a. V' I
r=rand(1,m);
1 J5 o; X) w' S" M$ tPopIn=find(r<=pInversion);! d; s! C7 o& P" }9 ?+ B5 j
len=length(PopIn);
9 I0 j. t/ g6 d! P/ R, Hif len>=1
P j1 Q5 M9 A! g for i=1:len
8 k" V1 z8 b. `; N3 ]+ x) i d=sort(unidrnd(n,1,2));
9 I& |/ Y. E& Q% k7 _' w9 s, P if d(1)~=1&d(2)~=n) D5 }- o" O a* h7 \9 y' x
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);9 v9 I/ S" ?0 s4 s: ?
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
2 P3 Q5 S- J. G) _4 C* P4 ^7 F* h NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);+ P6 _+ C/ K% N4 _6 r) }
end- X \# D P2 Q4 P# m3 r
end
5 _1 L6 u2 V7 g- w& ^# xend
$ k- s8 a( j/ x! E% a; m7 g4 L* d! @1 G1 D
七 径向基神经网络训练程序
8 R) k. q& p; l. o+ ]7 w# U
: x& ?- l9 r$ v+ _; [clear all;. Y' N$ u/ @8 y1 w0 d/ `3 T
clc;
1 _. G3 p6 o/ }%newrb 建立一个径向基函数神经网络/ Y% d$ @6 d; r% e2 I
p=0:0.1:1; %输入矢量
- u' @' ^: @0 _# g! O' ht=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量, R9 Y* d6 z2 F/ }
goal=0.01; %误差, b; M0 {$ J( L) J: Y) v' f" c
sp=1; %扩展常数
! e! b0 P. f" w9 q6 z8 Smn=100;%神经元的最多个数
* _/ t7 Z" V. ~6 G* _3 Mdf=1; %训练过程的显示频率
7 T& [( @3 x9 V8 V7 D* ^' y[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
) u9 c2 D* j# f k- W% [net,tr]=train(net,p); %调用traingdm算法训练网络
) ], m/ B! w. Q7 T! L3 Y%对网络进行仿真,并绘制样本数据和网络输出图形8 }, H% ^$ z2 J, M d
A=sim(net,p);+ L# c7 x" I( p2 A/ {
E=t-A;
9 T" B& o5 A7 S. esse=sse(E);
0 c1 J% E# }, @ Y3 h3 g' Bfigure;
9 f8 F( l3 R5 S- T2 H; ]* oplot(p,t,'r-+',p,A,'b-*');
; |' ]. o/ I( g4 A* Alegend('输入数据曲线','训练输出曲线');, J- n. A5 B% F! _ o' P& v% R: s
echo off 8 \9 d' R" n3 {& }3 e
- u! [6 u3 i* U# D* e+ I4 ?( G4 e说明:newrb函数本来 在创建新的网络的时候就进行了训练!* j. k9 E X: ~0 Y& N5 @" A" Q
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,# P6 ^. B( p+ Y5 u6 u
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!1 }; ~1 x$ Y- O; q# ^! W! A/ L2 f. x- C
' e( e4 E$ a9 g; i8 c4 A; i3 z" A% i3 s" I& d. u
训练结果显示:) G7 r& r1 m; U8 W, V: M! k
NEWRB, neurons = 0, SSE = 5.0973
, Y' Q0 r0 x z# o% g1 lNEWRB, neurons = 2, SSE = 4.87139
0 P [1 U7 i" D0 Y8 k% |% [2 nNEWRB, neurons = 3, SSE = 3.61176/ V4 w! d6 b# D! t( _6 t0 v
NEWRB, neurons = 4, SSE = 3.4875
B; U, L5 o( t7 INEWRB, neurons = 5, SSE = 0.534217) T$ o' j8 \+ @. F: F( A; L- ^" A: `& {7 Y
NEWRB, neurons = 6, SSE = 0.51785
# V, B$ M9 V, z: e9 M4 GNEWRB, neurons = 7, SSE = 0.434259# I' B% ?: }2 `1 ]/ C. _
NEWRB, neurons = 8, SSE = 0.341518
, P8 S- Y) g8 L( @: Q$ x# V) [NEWRB, neurons = 9, SSE = 0.341519
: z6 Y; W3 y! n! y! K2 HNEWRB, neurons = 10, SSE = 0.002578322 {3 I( c2 M8 a0 O9 t& q5 \2 Z
' r# H: M% t- z
八 删除当前路径下所有的带后缀.asv的文件9 n, f# W1 z, C; u" a. A2 }
说明:该程序具有很好的移植性,用户可以根据自己地3 }6 [9 H: V7 d- e2 r2 q5 Q$ S
要求修改程序,删除不同后缀类型的文件!
/ R! A! W" w, b9 ]: J5 jfunction delete_asv(bpath)
9 S" a& r( U# k%If bpath is not specified,it lists all the asv files in the current5 a7 d1 G2 `* Q! k
%directory and will delete all the file with asv
* }' n. @3 w) ~4 ?3 L- |% Example:) @: Q3 z: r. n) `5 i4 h& S: N- b
% delete_asv('*.asv') will delete the file with name *.asv;% W; L$ E8 E# C0 ^( a, U% d
% delete_asv will delete all the file with .asv.
) z: N/ \" R+ [# e7 w9 @1 J! m3 `! n! m/ ^0 ]6 w$ C; z! a
if nargin < 1# r4 z/ A* [- l2 ~+ p
%list all the asv file in the current directory" |6 K0 H: \7 G/ i7 L
files=dir('*.asv');
3 I, j* e1 X/ H/ w |; U4 Oelse0 X7 J) o' {1 \6 N& P( Y
% find the exact file in the path of bpath. o. s( |$ J- X& N" h G2 V$ b9 l" ]
[pathstr,name] = fileparts(bpath);' R8 {# y: H; Q, _$ n9 A u
if exist(bpath,'dir')
) ~0 t. d+ [7 a# w( ]4 P3 z, e name = [name '\*'];! q P5 X7 n: l7 P
end4 M* @4 K" ^# z
ext = '.asv';6 p9 i- _4 b5 U; ?, \
files=dir(fullfile(pathstr,[name ext]));2 J! ^% \2 _: V
end" X# P0 \3 n: x: Y* X! H9 s
$ ?; l( O+ L |7 T- X I5 L
if ~isempty(files)5 I# F0 w7 s0 }9 n k
for i=1:size(files,1)
- M9 x5 h. M- c, w, j k+ q. @ title=files(i).name;5 t; T( F f$ U( r
delete(title);! ^1 ]0 u9 [# W* d, C; w
end, i" J4 S x3 C3 _0 F. D# r
end$ o8 U/ M; m' J# w1 `/ M
. V9 a. f7 A. _" {0 z) i2 m4 ?& ]2 D4 P6 W
同样也可以在Matlab的窗口设置中取消保存.asv文件!' S* H2 `% R) x/ R7 X! c3 n; F* A; V& X
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