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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" D. D D. q: C: O* r" P& s
1. predict_fun.m为主程序;, O8 A+ Q4 Z2 V% B' G1 T
2. timeseries.m和 serie**pan.m为调用的子程序
3 D5 y6 Z3 i8 [/ R1 \
& K/ y; l) x$ w+ t! K; L2 Qfunction ima_pre=predict_fun(b,step). c+ C) Z; Q7 ?& b- Q
% main program invokes timeseries.m and serie**pan.m
( E& C/ I7 k, K% input parameters:7 \7 {9 Q! j' j: T
% b-------the training data (vector);, c8 d- Y3 [, _1 a6 e
% step----number of prediction data;# j3 G( m4 E& `+ K' P
% output parameters:7 y8 ]" N8 \% M! F
% ima_pre---the prediction data(vector);
' F. B- h2 h4 C% C: m0 V% n% jold_b=b;
1 k- S+ r" y/ Q2 E* Zmean_b=sum(old_b)/length(old_b);$ l0 R9 B0 r0 c+ t- r# D: ]$ P
std_b=std(old_b);- @7 B* E0 U- z- F. ~( f
old_b=(old_b-mean_b)/std_b;
/ ]) O# _* P$ f( o# d8 e1 I[f,x]=timeseries(old_b);" U0 k* m2 t1 ~* u" t
old_f2=serie**pan(old_b,step);, ?- `7 g `7 @ d+ {0 d& ~
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;
5 \, _8 V/ T7 Y1 [6 h! ^R=corrcoef(f);3 f( c5 ?& W8 h# Z9 w' n& @
[eigvector eigroot]=eig(R);; Y) H y; p0 Y9 b: u3 A" Q( e
eigroot=diag(eigroot);5 f+ M- F! C* I
a=eigroot(end:-1:1);" d: v' x1 E. b# y5 l6 r$ g
vector=eigvector(:,end:-1:1);/ g7 _; L) d. [+ K; m: c
Devote=a./sum(a);# G; p3 e( g0 S+ g9 ~' m) y
Devotem=cumsum(Devote);4 M3 m l6 k- S+ Q) K) L
m=find(Devotem>=0.995);( ~1 `3 ?0 B/ Z) q. E
m=m(1);; z: F/ g" j N: R
V1=f*eigvector';
9 T n2 `! t) ?' S5 E$ |V=V1(:,1:m);- z( ^0 y$ O5 _+ c# O0 l* f/ U K
% old_b=old_b;" t ]7 P% v Y0 k ?2 m0 D
old_fai=inv(V'*V)*V'*old_b;
+ L7 L% c3 h; }# u, ?1 Keigvector=eigvector(1:m,1:m);! j3 I% }1 S5 A! X! ]8 D7 g6 d3 [
fai=eigvector*old_fai;# U6 a' D, K% H C4 H/ Y6 {
f2=old_f2(:,1:m);% u+ b8 \2 n" x( a5 k, V; x( q
predictvalue=f2*fai;
6 ~3 N: Q6 N- Z, V0 ?+ z! y$ X$ mima_pre=std_b*predictvalue+mean_b;. C! {1 B4 _. ] B$ Q ~3 Y2 {' |0 @
( ?0 f m t+ ^1.子函数: timeseries.m " j( Y% {: l/ G( S$ L y
% timeseries program%) o2 M7 |4 G1 T8 K
% this program is used to generate mean value matrix f;
; m5 Z0 L4 S% R+ J1 ^3 k* o" hfunction [f,x]=timeseries(data)
# R$ R$ u9 P: \+ b T3 b% data--------the input sequence (vector);& a/ h ?' f, Y0 }2 Z
% f------mean value matrix f;% @5 u1 i6 ]3 U, T2 m- D2 F
n=length(data);
5 q4 H9 q0 b/ j" M" Sfor L=1:n/2* r+ E% S( G# S1 N- n( y2 S
nL=floor(n/L);* v+ C. ]0 m# j
for i=1:L0 y* [3 j" M8 v: y" p
sum=0;7 @2 x' `. T4 d' ]% [1 w
for j=1:nL
3 I, u+ V+ `& O sum=sum+data(i+(j-1)*L);
. x* }' _/ u4 H' i* O end
1 Q4 J0 Q% g A1 v x{L,i}=sum/nL;) E0 [$ ]1 @* ~) a0 r2 U9 R
end
! S( b+ o% ~% A- p* ]9 dend+ `( `7 q1 ?: j; V+ \/ T
L=n/2;
' s) d. y- D) d# z6 b7 \9 t Lf=zeros(n,L);
$ t5 }1 Q: S. C1 D) pfor i=1:L% r+ q* Z' `: {. a5 `( ]/ H
rep=floor(n/i);/ X" R$ z$ ^. H, v" y* N% T- Y
res=mod(n,i);% B6 O$ ~0 ?2 r3 y% M
b=[x{i,1:i}];b=b';
2 H1 i7 d0 B8 o! K- U6 m f(1:rep*i,i)=repmat(b,rep,1);
; C* y) |1 d% R E+ F. {! Q if res~=0
1 w2 ]0 r. @+ l4 C3 l" |9 N7 \8 ? c=rep*i+1:n;
% _/ t5 a/ U. r; \- r& B f(rep*i+1:end,i)=b(1:length(c));
0 G& s2 e% @& w/ [; l" V end
, W1 Z# ~6 H4 }' w) Rend9 l, ^ L) m- r* i
H; M' m5 ~" \2 J* [: j
% serie**pan.m
) X2 |2 Y1 u8 m$ Q' s3 x0 n% the program is used to generate the prediction matrix f;
; n! I" i' C! ]6 F- xfunction f=serie**pan(data,step);3 M7 K; n1 c% S. Q' p! z: Y
%data---- the input sequence (vector)
7 _' B. v: H1 {* _! g% setp---- the prediction number;
' v4 P# C4 C" |" F: Z/ u3 u- W# In=length(data);
& _6 g% S* M& L) o8 V/ B/ g+ |for L=1:n/2) y5 i. A2 p- U( V$ X# {, _+ A
nL=floor(n/L);: a3 H4 M6 B8 D, g0 p/ O$ I: e( h
for i=1:L
2 n f. C+ E) a) q, g3 j; d' L sum=0;
& t7 e$ t7 m( w for j=1:nL
6 E- |- d% s$ c% V. R: S sum=sum+data(i+(j-1)*L);& _, ]' q& t* ^
end: N5 r0 t* w+ A4 W- [7 z
x{L,i}=sum/nL;1 |. F' T4 e9 n- z; b/ D* w+ N+ s$ I3 A8 p
end9 d" k4 i4 I( ^* t- ^+ J- e
end
) {9 F6 d/ N. S2 `L=n/2;; P; o# ~! f0 n. H, ?. T5 V
f=zeros(n+step,L);& @1 v, h4 ~7 `4 N/ }* H( t$ s
for i=1:L
8 s- B# G# ^2 w rep=floor((n+step)/i);
- V @4 d4 ?- ]7 j res=mod(n+step,i);
( M8 ?+ t2 P4 A* g b=[x{i,1:i}];b=b';
3 N; g3 D* ?7 x2 h f(1:rep*i,i)=repmat(b,rep,1);- j. P/ V; y c, I9 T
if res~=00 P: S4 S A3 m' f3 m
c=rep*i+1:n+step;
" C# ~, I& S! @* K f(rep*i+1:end,i)=b(1:length(c));
( U$ p* N2 R2 F+ q( |; ~4 C8 t end3 f! }, z. ^1 b* n
end) H: {* f/ {( ~9 `, W# ]
* x5 ~& F" r# i c2 H$ h/ f二 最短路Dijkstra算法& b$ h5 v$ s/ x9 `$ X
% dijkstra algorithm code program%
5 m0 h+ ` Z. v M" ]( z% the shortest path length algorithm
& p" Q% g4 q" o# Vfunction [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)4 V+ m1 f- ~2 ?8 g
% Input parameters:
4 `: t' z# N: K6 G- B' ~& |4 k5 d& d4 _% Input_weight-------the input node weight!5 q. {4 s0 d; B; E' P- K* U$ \
% start--------the start node number;2 i% i4 |' d3 ]) Z, T
% endpoint------the end node number;1 \9 A( ^( R. g7 g( Z* J
% Output parameters:
, J5 o5 K* X' `' K% path-----the shortest lenght path from the start node to end node;0 y3 p4 @% f( }9 M
% short_distance------the distance of the shortest lenght path from the
% u' D1 m/ d# L- ^3 g4 \7 R$ \9 T% start node to end node." o( t& h5 L$ y! p& Y* @3 K) F9 }
[row,col]=size(Input_weight);
/ J6 W# h- R3 r$ n) |9 r8 m6 ]( |, g' I" Q2 ]) p) |
%input detection
& h k% C, L* k8 `% iif row~=col+ l( G; R! o a7 I
error('input matrix is not a square matrix,input error ' );$ N+ D. N% x; V, Q9 d
end* Q5 \/ \5 P" U3 j
if endpoint>row+ H1 c. a& Q4 y) D* q1 t: Q
error('input parameter endpoint exceed the maximal point number');
! ^. e; V" g0 E5 t% z: uend
7 u/ J i" j3 s6 ~, m0 g3 f. |! G' y4 D8 R) V$ m/ h
%initialization8 u( V6 y! u2 Y3 |4 j" E9 X5 M
s_path=[start];+ J1 {% |7 Q3 o- I* {8 x- l( e" i6 ?
distance=inf*ones(1,row);distance(start)=0;
2 z- U" _/ s/ @0 Uflag(start)=start;temp=start;* c N( [& X& d
% e/ J: M4 d3 V: u/ ]
while length(s_path)<row
v- T% r) P( S+ {* r# X: X2 u7 w pos=find(Input_weight(temp, : )~=inf);
* G( e6 R! h% v# p: G! r: h" O6 c for i=1:length(pos)
4 B" W+ C2 R7 u3 X+ b' S& c/ f; |$ O% ~0 k if (length(find(s_path==pos(i)))==0)&
- Y- f6 Y: v9 x(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
4 f' U! X+ w' ~: {" Y distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));7 @ Y6 z+ x4 r. j2 J
flag(pos(i))=temp;1 j/ j9 {" @0 P4 X4 b
end
" k+ [& v& L) h2 I$ | end
: v! V0 q* e. W5 [ k=inf;
1 ~' s% D% c9 j7 X8 { for i=1:row; j* C/ R; T+ ?: Z& g1 S
if (length(find(s_path==i))==0)&(k>distance(i))1 A! J% j5 ?& L4 Z5 e
k=distance(i);0 J! h0 r1 [1 z! J8 G( \
temp_2=i;
6 h+ m9 _5 O0 p+ c5 Z end2 D2 G5 |$ V- \/ i5 O, M7 ~# Q$ G$ e- c
end
) x5 ~# H: I- A6 N s_path=[s_path,temp_2];
" h9 Q- F$ Y( j8 I) Y. _ temp=temp_2;
) N, Z6 H R/ fend
8 ?8 {2 m9 e& n% v3 l- x
. V# Q. h8 n' ?5 P: c/ h%output the result& h$ ]6 x! l% c D
path(1)=endpoint;( d/ Y: k( \8 |! [$ |2 m! h& p
i=1;$ T; y( V, R: t5 l4 \3 d
while path(i)~=start
% l3 O( _% R1 L path(i+1)=flag(path(i));0 p6 @, Q; p1 E( p5 N
i=i+1;* q2 I9 U0 c! V! t# u# T% Z# e: V
end% l' \7 ~8 E: K6 ^) g
path(i)=start;
" [; y4 K5 ^, j5 d Hpath=path(end:-1:1);
- a/ o, X' g! D# S' V+ T0 zshort_distance=distance(endpoint);9 |- y. M5 Q+ p4 F# m/ `
三 绘制差分方程的映射分叉图
1 i8 J8 J7 ]5 y: S& h( R6 a4 w, M* Z4 ~
function fork1(a); 3 O* J1 L9 o* c. }: {' D
& r& n* r. W v/ y1 u# ]
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
" X |% h% G+ u) G. z ^8 s3 h$ b' g0 p% Example:
3 ]1 q7 L M# u- [, \4 w% fork1([0,2]);
. U1 N6 H! \ l/ {/ a; AN=300; % 取样点数
& J' |5 D' Q2 aA=linspace(a(1),a(2),N); ) a" n: q: U: U ?' b4 h7 _
starx=0.9; * ~0 g9 ~) I9 t( H. Y+ q4 i" T
Z=[];4 i) @ b( r8 @+ l
h=waitbar(0,'please wait');m=1;
; t: R9 t3 C5 ^: i F; Gfor ap=A;
& f9 N. f9 }* Z* Q x=starx;
( P$ ?' h* {5 m0 a" N' p! q for k=1:50;
' p* |" `' E, r W ^; | x=1-ap*x^2;
7 B; i" Y2 |5 o# W" G( A0 U end ; d8 I" t% l- }0 H: g/ N" V
for k=1:201; 2 U; G2 t) q9 D4 H
x=1-ap*x^2; 9 B+ _! R1 I6 U5 s5 C8 d! s/ K& w
Z=[Z,ap-x*i];
+ A+ ]6 \; a& I# \ end % C( e8 }. g( k7 i* V
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);5 O$ W3 H0 `4 Q" K. r$ K
m=m+1;
/ t% q9 V) m+ H* G. o$ G' r% Iend
" R( x5 T% e5 x, i" z& Bdelete(h);
9 ^% k3 C: w6 v `: ]plot(Z,'.','markersize',2) . J( {6 k- k# F* A* n- P$ N) h6 R
xlim(a);9 H* |: \; b$ g+ T7 [
+ `* ~! L* r5 A& U9 ^
四 最短路算法------floyd算法
+ F1 ]+ z2 @4 P4 Z6 x6 H$ L. {function ShortPath_floyd(w,start,terminal) ( S y; O$ S8 ]: c7 N
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
1 _+ z8 B5 X: B9 ]%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
% U; |1 R8 g. _' R) s0 l9 G%start-----the start node;
( n8 l, h2 d m2 V( w%terminal--------the end node; 2 }, g/ j( r$ G) G0 Q8 }
n=size(w,1);8 {. S! ^) y r1 d+ P
[D,path]=floyd1(w);%调用floyd算法程序
+ L7 r: b' d6 z
; Y* R% P# m# E$ r- p# ^* R B9 g1 N%找出任意两点之间的最短路径,并输出6 N- o3 o5 h% z5 y* z% {
for i=1:n5 o6 l7 i7 ~/ L( V
for j=1:n
" [9 J: U& X" G2 d% `8 {1 H Min_path(i,j).distance=D(i,j);+ J! b" T' E# B2 T0 M; b" t, z
%将i到j的最短路程赋值 Min_path(i,j).distance$ r8 n7 j" q) Z8 P! i
%将i到j所经路径赋给Min_path(i,j).path
2 B O) g. i) _6 u" q+ c! u% E Min_path(i,j).path(1)=i;1 H' V- [; s7 Z$ O* G
k=1;6 b. n3 c# z+ N" C9 i% A
while Min_path(i,j).path(k)~=j4 o8 I& i7 K# ^0 n
k=k+1;% v3 n7 M0 r; o) _0 M* n
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
4 S. g8 V) O7 r2 r. }( @$ | end
# |4 M7 f, P$ K end
9 ?9 ^3 D# l5 N" I# ]) Kend
& x5 F. s: v9 r/ a; Os=sprintf('任意两点之间的最短路径如下:');- j' @4 }- I/ X: n6 {" Z
disp(s);
9 J' Y' Q: Z/ _ H( d+ wfor i=1:n0 C: ~$ Z m. g- M" i* e1 R
for j=1:n+ {( p- o/ g3 u1 b9 u0 W" Q4 p
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
. C- c7 l5 [) M" e ,i,j,Min_path(i,j).distance);
1 I2 f2 G+ j k" K# j' u disp(s);
! T. _' ^. M% t* n4 I disp(Min_path(i,j).path);, V; {0 V: \: g8 d4 A
end+ i3 @$ Z3 Q: M& `& h
end
$ k8 M- @! y* }8 O+ m. g. |
1 t$ I. g7 j) f# Z%找出在指定从start点到terminal点的最短路径,并输出1 ^9 n7 A: }- K T/ [
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
1 a. |; [( J$ h/ |: C. V3 C1 K start,terminal,Min_path(start,terminal).distance);- Z+ s5 S( r' k5 d
disp(str1);
# _- E5 n' g( w# Kdisp(Min_path(start,terminal).path);5 X+ ~& [) ~8 A# i4 O, k
8 \4 Q/ d; Q" f+ G# ^( Z0 \
%Foldy's Algorithm 算法程序
# k7 {. ^. u5 O* }' w) qfunction [D,path]=floyd1(a)$ k! }0 ]# `' h* u# R! L
n=size(a,1);$ j+ w- e& O9 K% V, x
D=a;path=zeros(n,n);%设置D和path的初值/ Y5 P3 {1 [/ v" {8 c
for i=1:n
8 z! U3 @0 {7 D0 |+ O% q9 \' V for j=1:n
7 ^5 a% \6 ~6 P) F0 _7 [! \0 o if D(i,j)~=inf* Y# t, J) T- |5 O6 E
path(i,j)=j;%j是i的后点
5 L! E: N- T4 P# f: V! X- ~5 X end0 U$ [6 X, S7 W% W+ V: h) y' F
end# W$ |! p3 `6 E3 r6 y, g, H, V
end
5 n/ u8 P K/ K%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
+ }4 c1 C* J8 c0 U- g0 pfor k=1:n
4 }( D9 `( I. Z( F' y* R$ v for i=1:n
* l4 G# l9 W3 E) S5 s; K for j=1:n
/ H3 ?- c- S$ R f: e2 k- { if D(i,k)+D(k,j)<D(i,j)
3 [/ P% q: w3 d" ?1 C4 c' I D(i,j)=D(i,k)+D(k,j);%修改长度6 x( {& @, n+ ]$ W. G k
path(i,j)=path(i,k);%修改路径
7 S6 W: B" z; |; L8 D# V end- P! x8 A& X& O
end5 x+ M$ u7 B( j" O) @3 T
end
2 u8 z" }0 M. cend
: I- |* u* Q! n2 y# b/ ?: o$ x
五 模拟退火算法源程序) m3 @: @2 {5 t' N2 Q% q
function [MinD,BestPath]=MainAneal(CityPosition,pn)% I4 j( C3 \3 a$ H- {
function [MinD,BestPath]=MainAneal2(CityPosition,pn)9 p ?' s7 P- h( C5 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2 \3 Y8 h) F/ o: C- G
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
# {" k0 ]/ v% S( |4 `' f# @% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...9 ]. g$ c l" \5 a
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...) Y& M F* w: W) [# Q
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
+ A& h6 U5 p6 I/ }4 V& p% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];0 ?* l3 q" b- g; ~
! [# Z) C0 ^0 U1 C' l1 T
%T0=clock
1 U% r! E# ]4 Wglobal path p2 D;
+ u A/ c4 I/ s+ E/ A, m4 r5 t2 V[m,n]=size(CityPosition);
0 z A- P3 f4 i9 d5 D, H. S%生成初始解空间,这样可以比逐步分配空间运行快一些! b& ]; [+ [# I; q+ U4 C3 f
TracePath=zeros(1e3,m);
9 L+ K, u2 y. ]% G! V8 [0 VDistance=inf*zeros(1,1e3);
! M; y' y5 Y; u+ N; B. g7 z( B2 b1 m# l
! A/ T$ D* T) z# b i* YD = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...# x: `' `, o, t3 ^9 q
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
4 @+ T4 y& s: d. c6 ]) ?. n%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
8 b8 T2 E% U! h ?6 |% Bfor i=1:pn
0 P. }. ^1 A d& ?3 c4 m path(i,:)=randperm(m);%构造一个初始可行解- G/ r$ a! _& J3 J% s" p
end; ?( _8 {) e) d* b' b$ d0 T
t=zeros(1,pn);
; D% u1 {5 \% E3 _: Z0 ?p2=zeros(1,m);
2 q0 P6 a2 y& ~; K7 `' u6 E5 `! f( E) @% @/ X4 l. v
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );8 x* Y- h0 O& a+ g3 a
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=' ) ;
) o( N& |! t3 M x%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
' }; m& C+ b( c+ [& j4 b%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, J& h. z+ M' R* D. q
%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
0 ~. s) P. X1 L%会收到到比较好的效果
, a) p- B3 H o. r! p& Y* M. s6 Z+ v
# o w F( ^, {$ n9 K0 W, dT=1e5;
7 `6 Q3 j) _7 @1 D/ V* [N=1;
6 @! u i5 ]* stau=1e-5;%input('请输入最低温度tau=' );
+ W$ i/ a4 p* N7 t%nn=ceil(log10(tau/T)/log10(0.9));
: B1 J: \1 w9 Awhile T>=tau%&m_num<m_max 6 Y: ]1 h7 q4 J( w' i. s$ |4 c
iter_num=1;%某固定温度下迭代计数器
$ g$ q# c! {$ ^" C* b% a m_num=1;%某固定温度下目标函数值连续未改进次数计算器
5 M: {' K" A- E/ { F %iter_max=100;: g1 p0 j/ x% h
%m_max=10;%ceil(10+0.5*nn-0.3*N);
+ a4 ~0 \) O' e/ l, R3 w( | while m_num<m_max&iter_num<iter_max; P$ i4 F% t7 w# m3 @* L& f
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:+ y1 X# ?, c5 N* e6 \3 q
%用任意启发式算法在path的领域N(path)中找出新的更优解3 g. Z" r% z4 X' ?
for i=1:pn
5 d: H. i% g7 U/ x* g* y Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
) \/ h( x8 |/ r. J, V% r7 ~+ D%计算一次行遍所有城市的总路程
8 }. K# }+ S8 J5 a' Z7 i [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线" f% I1 L @; t( {9 ~; G
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
$ _/ A# O3 R/ k. | end
8 L4 \$ z" G+ | %Len1
: l5 w9 }1 |4 E" y# h' _, V %Len2
9 Z" C; a V& p7 e. }& E) i %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand; A3 z: j: q5 m, S6 n+ ~, q0 W9 }
R=rand(1,pn);
1 ^* t" s- P; O8 Z# q V- ] %Len2-Len1<t|exp((Len1-Len2)/(T))>R
1 c1 P; i; w8 b# o& u( R: f" a if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
+ B& [1 E) S3 B2 [, C7 e path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );; r& a& S. y; V$ P. O% y r% C
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));( P4 m8 H$ G2 \" [+ e3 f
[TempMinD,TempIndex]=min(Len1);4 i6 d9 j! v& [: V
%TempMinD
+ ?8 J6 ^7 f- ^3 g TracePath(N,: )=path(TempIndex,: );+ S% L% r. I# [+ E4 }. Z
Distance(N,: )=TempMinD;
7 ?6 o6 V& \8 Z# Q7 B N=N+1;& t% c$ P* r( u y9 V* ]* @8 b2 v) _
%T=T*0.9( z. |" X4 O- S9 g7 b
m_num=0;9 \( ^+ ] [5 }
else S8 Z( L8 Q1 Z
m_num=m_num+1;
Q i8 K$ Q/ L* g end) r! [9 g% N& L% k, V$ W: M3 Y2 u
iter_num=iter_num+1;" Y$ B9 l# a" Z( M$ E" u1 |
end% L0 G* A C0 |" S+ L
T=T*0.9& ]/ j' K: Y+ W7 m" ?
%m_num,iter_num,N
2 Y$ w# C- e& ~& ~9 L/ eend
9 ?1 f! D% Q! k[MinD,Index]=min(Distance);
+ q& U& f+ o7 J/ ZBestPath=TracePath(Index,: );
" B+ v& {+ C% _disp(MinD)
! v9 K# W {6 o: l%T1=clock
4 X5 \/ q4 a, ~/ N5 w/ W* d/ q
8 M# \# ~4 J4 w* y1 B i, F/ |$ n' [) Y
%更新路线子程序
/ K2 x! k/ k) a7 _4 `. @7 V: vfunction [p2]=ChangePath2(p1,CityNum)
: |) M+ q% `& p( c A6 p0 dglobal p2;4 [8 |3 X& P2 ?! w" l7 l
while(1)# d: D' J! B: l$ Q
R=unidrnd(CityNum,1,2);# L& ?; e2 B$ w3 A4 |1 c7 _, q
if abs(R(1)-R(2))>16 y- b, |0 s1 i3 U
break;* n- `' e' Q8 W' r
end
$ k( [8 X+ {; T! F% |" {+ Pend
& d$ s, v( P7 CR=unidrnd(CityNum,1,2);
4 e& ?. m( X5 fI=R(1);J=R(2);7 y Z' n3 q* J% V7 D$ D* d
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));: v2 n/ P7 b2 K
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));; h! j/ S6 W; D$ B9 n" {3 c
if I<J
2 \! N/ q4 n/ j! f8 t p2(1:I)=p1(1:I);
- ]- D0 A. y. S8 A p2(I+1:J)=p1(J:-1:I+1);
9 F" `# n' A$ c# a" Y p2(J+1:CityNum)=p1(J+1:CityNum);
' v1 U, n, O% s- q2 b; c8 P9 Welse& P& i; F- k/ n: M5 c
p2(1:J)=p1(1:J);
' ^# q/ P; ^" a4 A p2(J+1:I)=p1(I:-1:J+1);1 O- R, P; T9 d- _( e9 Z9 `
p2(I+1:CityNum)=p1(I+1:CityNum);
, B1 m) C3 ~" M7 B. [, U; dend
' p: C* N, j: |. S2 {
& u* _& W% l3 A* ]. X) k六 遗传 算 法程序:
( s j3 l1 R1 I2 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!: g; f5 J, g0 Q, a3 t" F
( m' C& f1 P/ Yfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)2 q {* z7 }6 M* \
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
% k* s7 e7 M/ m; d7 C2 C% Finds a maximum of a function of several variables.
" r1 [7 _: u5 T) p7 C: U% fmaxga solves problems of the form: $ v8 y t& x: t% u( N3 b/ w9 n
% max F(X) subject to: LB <= X <= UB
( B4 h( A+ O0 Y% BestPop - 最优的群体即为最优的染色体群
, H2 D) |; p% c% v6 U/ b% Trace - 最佳染色体所对应的目标函数值! K4 k( u/ H8 J8 c* F
% FUN - 目标函数% I2 C+ |7 G% _ ]' Q
% LB - 自变量下限. K B2 h; p6 w3 D
% UB - 自变量上限
; Q" x0 i" [ U0 [% eranum - 种群的代数,取100--1000(默认200)
1 h9 M3 x1 G5 S# L0 G' i. o% popsize - 每一代种群的规模;此可取50--200(默认100); b8 M' z0 _& N- S
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
) z3 N% ^2 V5 N9 c% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)& E0 t/ Y3 [* ]$ @; o' j5 h# P
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
9 G9 u# Y, i: @% H% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编( [) V$ z) h% i+ M' k1 P* _8 B4 c
%码,option(2)设定求解精度(默认1e-4)
1 [0 h5 A0 o+ \/ E; f8 T%) O& L2 |, ?, H6 ]. G
% ------------------------------------------------------------------------; k0 P: o* n* [' n
/ u S Q" s3 Z, B
T1=clock;
6 ]* T! @& y6 Pif nargin<3, error('FMAXGA requires at least three input arguments'); end
' I8 k7 A% h/ p. H3 I8 dif nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end6 a' m# w7 N7 [- M& l
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end; _: ^$ n6 X- O& l7 [
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
9 ]2 M+ P0 ]: }# S) u+ vif nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end5 |8 D5 _4 _; r! v& p" o
if nargin==7, pInversion=0.15;options=[0 1e-4];end
/ ^8 E, I0 B7 k: w) U; qif find((LB-UB)>0)
3 _6 n, A# @2 g+ U4 J# t error('数据输入错误,请重新输入(LB<UB):');
% d0 l# m2 W7 u, x6 q0 x9 {end8 n. u. t& Y. d& S: V; b
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
3 M* C. e+ ^+ s1 B: b5 |! U9 Fdisp(s);
6 i5 M) d3 F8 l# P! p2 V. [
6 S, S4 m! S; T0 Q$ r5 }. e9 g! y4 eglobal m n NewPop children1 children2 VarNum
7 t6 b: K9 W; X0 i9 H
) T; y: P3 x2 a7 b* y) F. hbounds=[LB;UB]';bits=[];VarNum=size(bounds,1);' {( a$ M, |/ @1 m/ D
precision=options(2);%由求解精度确定二进制编码长度
/ G# I4 D; ]! I5 pbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
, L6 @2 |7 Q4 K[Pop]=InitPopGray(popsize,bits);%初始化种群
3 N' ?- r/ X: g0 x# N& _3 q[m,n]=size(Pop);
9 M( ~& |9 q0 m5 d" UNewPop=zeros(m,n);6 L- Y$ s# X& G2 O, Z% f6 r
children1=zeros(1,n);5 }' R* E/ ~4 L
children2=zeros(1,n);
5 {5 t) X1 S- i& Y% t8 ^/ Z! U( G& hpm0=pMutation;& Y% x9 f( p! L. R+ m h
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
& s: J9 m& c$ f" Q( \Trace=zeros(eranum,length(bits)+1);% U' V3 M+ F$ ~. f: f5 M# K9 ^
i=1;4 a: W1 n# r. P4 u; l- ]
while i<=eranum/ W L) y7 F1 u2 h
for j=1:m, U" p/ o2 q, Q/ ^$ M5 H
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
, m- }- ~' s+ z8 H4 Z$ f end) h7 F& W% @) I7 T: S$ H+ L( ~9 h
[MaxValue,Index]=max(value);
h: g& P1 P& d+ H/ ?8 i# Q BestPop(i,:)=Pop(Index,:);
, y' h- U/ e7 Z1 T% v9 g2 G Trace(i,1)=MaxValue;
E3 y) h. |0 d2 u" a& h( E Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);/ Q7 d9 {) T$ _% [1 y
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
' L5 d* S# m. x( U! C[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));4 I9 B% W+ y' g+ [8 q, x
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
6 {, g' L9 E" O" H) e %round(unidrnd(eranum-i)/eranum)2 w1 x# ?) i# `5 K) i7 h% X& K' e
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异9 c5 Q- a) I p0 ~
[InversionPop]=Inversion(MutationPop,pInversion);%倒位( ]2 ]2 w5 i/ R9 T: g1 R& P8 R& k* g
Pop=InversionPop;%更新
9 b6 ]) ^& |" D2 TpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); 2 a2 L1 Y' T5 f- T5 D
%随着种群向前进化,逐步增大变异率至1/2交叉率
+ G$ [( w) _% Y9 x p(i)=pMutation;
8 _2 b' n6 a! X+ _0 ]# a i=i+1;7 j8 V( W+ R5 Q
end
, Q$ }2 {, u' \8 ]- I6 t2 V3 Xt=1:eranum;
8 ?+ W3 c3 L! jplot(t,Trace(:,1)');
; r! A3 |) E% I0 ~0 M4 c5 i3 L) ftitle('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)');; K/ X5 P. k! i( A
[MaxFval,I]=max(Trace(:,1));7 |: u. ]6 H; Z
X=Trace(I,(2:length(bits)+1));: I# C7 \: J8 K0 ^6 m }. s9 ]
hold on; plot(I,MaxFval,'*');, }# G7 f1 N# T" L! `2 V- }! H( c
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);6 T( g4 s/ E9 s7 ~6 V
str1=sprintf('进化到 %d 代 ,自变量为 %s 时,得本次求解的最优值 %f\n对应染色体是:%s',I,num2str(X),MaxFval,num2str(BestPop(I,:)));
8 }* }' W' N# {# ~. S! O8 ~1 udisp(str1);, p' k9 }2 u1 I- j: ~1 [$ @
%figure(2);plot(t,p);%绘制变异值增大过程
' R m! c2 K) e8 L, c' |" yT2=clock;1 e- n a( k4 N8 Z7 ~: D; @( N
elapsed_time=T2-T1;/ V) s3 Z/ m2 Y
if elapsed_time(6)<0
# g) _+ A. G1 a' z; Z elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
% e4 w& Z# T0 F) Q/ }7 p# o$ Nend
3 N5 s6 R* q' R" H2 E& P( O: D$ s/ bif elapsed_time(5)<08 }# a$ S7 ?9 } w- b
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;! ]# B6 E8 l* _/ z
end %像这种程序当然不考虑运行上小时啦
* k5 G, A1 ?: q) [) Wstr2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));
2 Z. o7 y/ D/ [0 g: r% J" a+ V Odisp(str2);
( q7 i2 t5 j# w7 ]' ~. v% I# k+ m( W K7 }6 h* K: R4 T
' j1 A1 z" a$ E- e, e4 j% ~/ k7 T%初始化种群
7 z& Y, `% }, j j, O7 W3 x+ N%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 w g. l% k) o- s8 Kfunction [initpop]=InitPopGray(popsize,bits). j: |* Z( ^) t. x5 r
len=sum(bits);5 c: s1 W, L) m$ f
initpop=zeros(popsize,len);%The whole zero encoding individual0 Y- }2 e& L" C' u3 d4 h3 ?
for i=2:popsize-1
( d$ i( F* } `. {, G2 I- H pop=round(rand(1,len));
2 t* \: x2 G+ [& {6 I6 O pop=mod(([0 pop]+[pop 0]),2);
% ~( M+ V1 e: s %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
) p6 r# r' J5 L" e' c3 U: t1 z %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)5 w9 l$ y* i/ y5 q7 k+ V; }0 p
initpop(i,:)=pop(1:end-1);
9 b5 \7 x; A" P, iend9 N6 |' E2 j% @1 a( l }3 Q
initpop(popsize,:)=ones(1,len);%The whole one encoding individual2 C" H' m0 ^+ s1 w9 X6 u* T
%解码+ x7 V( S2 S7 D* f4 q3 W! v
2 M" z2 C5 m& Y% i8 l( k+ Wfunction [fval] = b2f(bval,bounds,bits)
1 h- Z/ {) ~0 m& f& |3 n8 ~% fval - 表征各变量的十进制数' `( W: Q! ]1 i+ v: i; S( s) O8 v
% bval - 表征各变量的二进制编码串# D) V1 w k( ~9 |6 l' o3 Z7 |9 u" m
% bounds - 各变量的取值范围+ Z8 X, @; U2 B" j) b4 C
% bits - 各变量的二进制编码长度
k- n" k j' q+ W& [scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
\" `% ^) P! r$ d% h8 v( V t0 C+ GnumV=size(bounds,1);! W, n8 U7 e! n, Q O- {
cs=[0 cumsum(bits)]; 2 n. \# s( k6 W! e5 A) y1 Z
for i=1:numV
0 [+ d% W0 K* a% z6 S2 @' C+ [ a=bval((cs(i)+1):cs(i+1));
; a) W, a$ B. a! ?, |( z6 t fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);/ u& q1 ?* k8 q& b2 E
end
& a& ^4 s- D4 Y4 L! z; B$ u%选择操作, B) V# ~( G1 Y v6 A y( i! A
%采用基于轮盘赌法的非线性排名选择3 C# }7 }: s! W
%各个体成员按适应值从大到小分配选择概率:
' n2 K j2 a5 J; B, N; U%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1
, [$ Y1 E+ q) g6 i
6 {! k, w3 \# J# B; qfunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)' M, U8 B( c' c$ o6 k6 V
global m n
0 W% j9 N/ A6 O; k: `7 e. n' Iselectpop=zeros(m,n);
( l# \" p$ G, Y u u7 {fit=zeros(m,1);- P4 h3 Z* h: W0 ?- M( F4 b
for i=1:m
9 Q) G1 j# m# s" a0 a; V" x fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据0 X, e6 ~5 T7 `2 `& u
end
# e/ T+ D' x+ `selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)6 D; `+ ?1 W1 J& |
q=max(selectprob);%选择最优的概率
8 F8 g g1 q& lx=zeros(m,2);. V5 D: b4 e3 G, p$ `- z2 Q/ q
x(:,1)=[m:-1:1]';
4 C3 ~% @ {+ @" o' W[y x(:,2)]=sort(selectprob);; o5 o! m+ e w# g. a' e
r=q/(1-(1-q)^m);%标准分布基值1 R+ x" F4 ?* m( S
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
3 L' i" s# W( ?; r3 y0 q: |0 Mnewfit=cumsum(newfit);%计算各选择概率之和
a& n+ U2 N* [. J% D% T* E! WrNums=sort(rand(m,1));
- x4 e5 x2 l! a+ dfitIn=1;newIn=1;! W8 \9 v2 J, H+ S8 d
while newIn<=m7 ~ u' o- x3 P* f1 P0 Y' V
if rNums(newIn)<newfit(fitIn)" ?$ l: o- f& e/ {/ F
selectpop(newIn,:)=pop(fitIn,:);
6 s/ o5 _3 @) i; D newIn=newIn+1;
! h8 I# |, [# Z! @+ q" x else) R' \9 Q3 j8 R7 n. M
fitIn=fitIn+1;
: k' ~! ~& |: n6 ~1 n. x9 c end
6 c B5 t5 K$ u( U5 t, kend
, l! k3 H5 o" W1 Z/ s%交叉操作
& _+ C+ e$ E! m4 i. Kfunction [NewPop]=CrossOver(OldPop,pCross,opts)6 C {( Z( A/ [% x
%OldPop为父代种群,pcross为交叉概率
. O3 e9 `/ r1 [global m n NewPop - D! {! Y8 C, K( Z
r=rand(1,m);% ^9 X8 K2 y2 v: j) M- j- P
y1=find(r<pCross);3 J6 u8 x) @# p" p: B/ O
y2=find(r>=pCross);
6 I( h" @' B( B& a& g2 i( a& hlen=length(y1);
, M4 [$ V" A! |0 u3 V1 Cif 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+ c0 g2 ?2 r: c; o t) K
y2(length(y2)+1)=y1(len);4 s: J1 W- ~; \" ]+ F; J/ o# {
y1(len)=[];
( K8 ^5 C2 l# U" v) `end
& W6 [/ B5 _5 r: L& G: l3 V) fif length(y1)>=2
2 Z+ d: E2 E. S6 Z. b& x for i=0:2:length(y1)-2
, w6 k, A; m& \8 D4 m% H if opts==0
: f6 c* R2 ~" r8 Z: a Z [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
' F7 Y" f& ?5 Z+ @ else
) J; q& @9 I8 a- P- U: v [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));) q+ w" v$ [% H& X( l- A
end% d4 V7 }" A& {0 s' r
end
" w7 S/ |- I; \end
$ I# T- F6 p1 YNewPop(y2,:)=OldPop(y2,:);: f9 s2 C* _$ O+ t
* d) I4 a3 o& b$ d8 j%采用均匀交叉 $ g- y4 @$ T. F6 X9 z* a# C
function [children1,children2]=EqualCrossOver(parent1,parent2). Y+ w1 Y1 E5 ^: m
- x' u) D3 V5 \* V6 ~
global n children1 children2
8 e% {, _$ ]$ Yhidecode=round(rand(1,n));%随机生成掩码
- k/ G' {( U( s2 o+ V; fcrossposition=find(hidecode==1);1 U0 r1 R& k# Q
holdposition=find(hidecode==0);
6 z' i! F' X/ q0 {children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
; H/ {9 o7 o9 V6 D$ @children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
, Q& ~9 G D& h) Xchildren2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
. y+ f% Q1 o, Z1 [children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
1 I Q; i5 c8 T% r) o0 y' e/ ?+ Q5 A3 d7 b( C2 r) [; Z3 s- |4 H
%采用多点交叉,交叉点数由变量数决定
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function [Children1,Children2]=MultiPointCross(Parent1,Parent2)
h+ N6 g) W* m8 @5 g G1 E6 F( V5 x' }. w9 D
global n Children1 Children2 VarNum
C, V7 f4 U9 M c( \$ V C! |Children1=Parent1;
. p0 J1 [5 R! d3 u+ iChildren2=Parent2;
1 [1 j6 k3 D; Z" `6 Q/ sPoints=sort(unidrnd(n,1,2*VarNum));
7 h7 W. P! c. g' @4 l- nfor i=1:VarNum
- x: N& A8 R+ J& Q( }8 o3 L0 ?5 } Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));* H+ H N# K b/ v7 Y% `
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));5 R* i/ a" y+ x M5 G2 t
end
/ _9 I/ A' q" p: M
) Y1 o% L) s/ G2 I6 Y4 Q) S+ C%变异操作- z' K/ n1 g5 p; b1 T' x" c
function [NewPop]=Mutation(OldPop,pMutation,VarNum)
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global m n NewPop6 p& l( g/ j, t* C1 _) g
r=rand(1,m);
$ m0 m9 D5 i9 ?+ P9 c" Rposition=find(r<=pMutation);
2 _) u( J! T% E2 S3 k f, ~) B+ w8 Nlen=length(position);
3 F) C' m) y( w3 D; ?0 Z4 Sif len>=1. y5 Y6 S7 V- N$ m8 n
for i=1:len" K% w" t9 h2 Q% Y0 Y
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点% f* K8 \5 L+ N2 C G8 c
for j=1:length(k) v8 O5 h6 `' H5 z+ `) N- F
if OldPop(position(i),k(j))==1
% Q& m9 ~6 q1 B% g4 @ C0 M OldPop(position(i),k(j))=0;
5 ]1 d, l, c* L% k else
7 g0 }5 D% r0 }4 k7 b OldPop(position(i),k(j))=1;
* H* Y9 L2 R6 | end; h A! L; W( I/ e6 Y
end
5 A# I7 q% B0 l6 Y end
$ z0 f$ W, q& n4 k0 t6 Eend
4 W% Y+ {* B9 @6 u3 f9 |NewPop=OldPop;+ e- i* F& I: U/ a; L
2 w9 O; `# S( d- Z: |
%倒位操作
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function [NewPop]=Inversion(OldPop,pInversion)
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P9 p7 b7 i$ L1 U" L8 r2 Sglobal m n NewPop/ {( j% ?, m7 {9 D/ l+ _
NewPop=OldPop;" [* K3 V6 p! m ~ V, M
r=rand(1,m); Z, a3 @4 I M% x7 o6 r0 k# B
PopIn=find(r<=pInversion);
& D2 f+ a4 G7 ^# K, Y! Qlen=length(PopIn);
3 e0 I% t* `! Cif len>=19 C4 ^# x0 ]" L7 Z( ], d) X$ Q1 @
for i=1:len
& C- E5 W* }" H, B% ? d=sort(unidrnd(n,1,2));
F' m5 @/ W7 j( H if d(1)~=1&d(2)~=n
% t# _3 _0 c% b: d! V NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);# e7 c V0 m% Q7 A5 S# I% S9 R3 n+ S
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));3 v7 C- u. r+ C/ \' e0 c3 A# `
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);6 P2 ~& D& W, B/ ~- v
end5 v) r+ j( V. I2 ]2 w
end. n2 i% m5 Y1 A6 h# E! U
end# R2 B* A2 H! I4 c% i6 _' M5 w
4 k! d, N9 ?3 H, p( A) B七 径向基神经网络训练程序
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$ |. K* l; \6 {$ \* O$ v9 Wclear all;5 W2 |; `) v" L3 w) B
clc;+ K6 y$ F% e y+ e2 ]
%newrb 建立一个径向基函数神经网络
: l" l/ X2 [* Y# V1 t, ?" i8 Qp=0:0.1:1; %输入矢量 y/ k; S6 [# b; h+ R
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量, }1 ?! u4 V. K7 ^% @
goal=0.01; %误差
9 v# B. z9 O. p4 e* Q: E' v- dsp=1; %扩展常数: O0 F5 T: O8 S. z9 j
mn=100;%神经元的最多个数1 G: i# t7 T* X1 t, G
df=1; %训练过程的显示频率% U J9 Y/ f v0 l7 r& O* l
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
1 L2 d3 P0 P0 `0 {* t0 B* O% [net,tr]=train(net,p); %调用traingdm算法训练网络
2 \" V# ]5 L7 @$ ~$ f6 I%对网络进行仿真,并绘制样本数据和网络输出图形: L) H3 E3 j) k, x+ _
A=sim(net,p);
$ [1 ~6 T0 Z3 N( N3 y EE=t-A;, g T5 P5 K p" R
sse=sse(E);
$ ]9 P" O- N( Z+ z/ G# y) b' |* Afigure; / a% M0 P# }- h0 ]! g
plot(p,t,'r-+',p,A,'b-*');
5 D: J1 T! [4 t- Rlegend('输入数据曲线','训练输出曲线');8 {( R2 X: M: ?1 t
echo off + k6 L9 {* f! I, s3 h
6 Q4 e( u! J# I+ m ~9 u$ ?说明:newrb函数本来 在创建新的网络的时候就进行了训练!
L1 Y1 [" N# `6 |; |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,/ L$ k! x( ~2 O: _* I
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!
6 D1 a' _7 U+ ~1 C6 t6 a+ A6 l' D0 N. O
2 x" u7 J; z _* [
训练结果显示:' t2 L& A5 W. r: _- c, b8 I
NEWRB, neurons = 0, SSE = 5.09735 s3 K; [7 Y% V: S* U/ W" H# Q
NEWRB, neurons = 2, SSE = 4.87139* E: A+ K, _. ^' v6 A7 c2 d5 F2 [/ v/ O
NEWRB, neurons = 3, SSE = 3.61176' W2 ]+ a! J, Z8 a( z
NEWRB, neurons = 4, SSE = 3.4875
* W( n9 G2 I2 ~# a) hNEWRB, neurons = 5, SSE = 0.534217- ?8 S E5 l5 f8 M
NEWRB, neurons = 6, SSE = 0.517851 \ j' v0 M$ {! u* o; l4 j
NEWRB, neurons = 7, SSE = 0.434259
& V& q" i4 e7 b+ B; CNEWRB, neurons = 8, SSE = 0.341518( k0 l8 \: t7 u7 |2 G% h3 \% m; w
NEWRB, neurons = 9, SSE = 0.3415197 F9 F; a6 p" }1 S% ?6 \! u3 \! S
NEWRB, neurons = 10, SSE = 0.00257832
- H \/ W y) k0 a' q1 d+ K1 W& I! r2 [' Y3 N0 n$ |% q. v
八 删除当前路径下所有的带后缀.asv的文件* Q2 a8 A! V* r: [4 N9 m9 g! @
说明:该程序具有很好的移植性,用户可以根据自己地* g' d: o. L+ V
要求修改程序,删除不同后缀类型的文件!
8 {2 D+ i1 K6 S+ l$ lfunction delete_asv(bpath) ) w( A Z" z8 @( f( v1 h. g+ ~
%If bpath is not specified,it lists all the asv files in the current) J& @8 S5 V- x% i2 C2 R
%directory and will delete all the file with asv
% e# ~. g& s: s! V( v# |% Example:
\4 R$ s% X* t- }% O1 H% delete_asv('*.asv') will delete the file with name *.asv;
9 P9 i# M+ k8 X. o! t& z- w% delete_asv will delete all the file with .asv.3 f" P' o+ t7 D: ]: V
: q N+ o5 O% N1 h/ o0 Cif nargin < 1
1 m8 x w5 N s: p/ k! H%list all the asv file in the current directory6 L. S1 q0 D9 k% T/ D1 G
files=dir('*.asv');. E) K, t! N9 g5 r3 f3 @7 B
else- K. |7 O: y7 v3 S8 |! B+ ?
% find the exact file in the path of bpath
2 _6 |+ k- b4 C' v" B [pathstr,name] = fileparts(bpath);
& s8 j: H0 h5 ?" X if exist(bpath,'dir')
0 r, H, T! F o2 P& G3 n9 y name = [name '\*'];
- h$ C% c2 c9 A3 \$ n% m' Y end: @/ m3 ~7 Q+ r
ext = '.asv';$ f7 [4 \2 j5 L, c3 y
files=dir(fullfile(pathstr,[name ext]));
# ?4 Y9 h7 x S4 Cend
i0 m4 n. w y+ N' H
/ F1 q2 E" C3 N" A; H8 \if ~isempty(files)
* |) N- n( N$ K for i=1:size(files,1)
0 w9 {' P; n9 A' F0 _# F% ] title=files(i).name;
9 [" E: u$ Z. O- v delete(title);$ Y0 b5 @# w4 N2 c9 Z B: y! U
end3 t% k' ^: E! M0 p! C
end
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" ]/ l0 ?' K' N- h1 i4 ?
同样也可以在Matlab的窗口设置中取消保存.asv文件!
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zan
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