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升级   48.42% TA的每日心情 | 开心 2016-11-7 00:15 |
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签到天数: 7 天 [LV.3]偶尔看看II
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一 基于均值生成函数时间序列预测算法程序/ ^3 L" h1 O8 ]( h$ e! k' n. Y
1. predict_fun.m为主程序;
' B. P! _9 M5 y% i' V, w2. timeseries.m和 serie**pan.m为调用的子程序
: l1 |) D- T1 X w6 |6 L% i& U) q2 V' R3 |; g. p; z6 j* t$ ~
function ima_pre=predict_fun(b,step)
2 I. I$ o6 e$ C* V% main program invokes timeseries.m and serie**pan.m7 H: [8 R, L6 ]8 _, e
% input parameters:
2 Y9 a1 X# r, m- a3 u4 o3 }0 r9 ~ R5 d% b-------the training data (vector);% q7 @, {& t& A9 o" ]! o3 b M
% step----number of prediction data;
1 p' ]; r4 E; h" p$ C% output parameters:# J! A8 f8 ~' K& u. k. ?% g
% ima_pre---the prediction data(vector);
* J6 @( p3 V6 B0 \old_b=b;8 s/ p( i& U: T2 A
mean_b=sum(old_b)/length(old_b);
, C4 _2 A0 |% I2 w( j0 vstd_b=std(old_b);
! g: l% g& b; A7 s" a" Hold_b=(old_b-mean_b)/std_b;
9 A: L S& R4 k5 ^[f,x]=timeseries(old_b);
% B/ D' E P/ M. t' Lold_f2=serie**pan(old_b,step);
2 T" W* l9 m4 W* p7 {/ K% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;8 x4 e. z( Y7 ]5 i2 }& M% E
R=corrcoef(f);) P, n4 C4 O+ b( d, A9 e; U
[eigvector eigroot]=eig(R);
) ?" _6 r* t1 Jeigroot=diag(eigroot);7 g6 P0 I' Z# W0 W! o6 O; ]
a=eigroot(end:-1:1);
1 H( F( @/ J, u. i0 p2 G! l& h6 ovector=eigvector(:,end:-1:1);
4 o# B4 k" ]( _# {4 P6 EDevote=a./sum(a);
8 {: r Z! h% Z0 t0 W8 g; dDevotem=cumsum(Devote);7 ~ g1 h9 O1 B
m=find(Devotem>=0.995);
9 S: N& J- V* h9 {: O4 ^* \m=m(1);
6 T- } R" U& s m) ?V1=f*eigvector';
3 T h) ^; V, U( ^2 U- nV=V1(:,1:m);
$ [- G3 v& w! x8 k; `3 ?% old_b=old_b;
3 q1 g; p& O/ {4 Iold_fai=inv(V'*V)*V'*old_b;" W' J# t! i' Q5 h* `2 ]& f
eigvector=eigvector(1:m,1:m);. W6 a: v9 ?0 I3 H
fai=eigvector*old_fai;# E8 [# T. x7 d! S! Q& i, r
f2=old_f2(:,1:m);
+ m2 Q* P5 t& F# K: @3 Tpredictvalue=f2*fai;; Y: x5 C! O6 w
ima_pre=std_b*predictvalue+mean_b;
4 c. j, q3 N, p: R" R) T' }) p- W" I, E# h' c0 J! P
1.子函数: timeseries.m % E1 @& B+ k( X" d3 h4 x& m' a4 q
% timeseries program%
2 f( D4 ^: I2 c5 o, m% J% this program is used to generate mean value matrix f;3 Q1 T, d' `1 a) T" A' m7 ]( ^( F- V, k
function [f,x]=timeseries(data)
- u3 W- T. {4 ?. X5 c8 |% data--------the input sequence (vector);. T) T) }. G+ F5 U ^; ?% f2 d' \$ {
% f------mean value matrix f; y7 ~( M! S7 X9 ~
n=length(data);1 K% N+ |' m1 z8 u
for L=1:n/2. \- K1 t# B3 g$ t+ f7 j5 `6 p. A
nL=floor(n/L);$ |! l9 H0 j0 y
for i=1:L
& k! w% _2 g% {5 D sum=0;
4 G8 ?" c1 O" s. q, I for j=1:nL
; o2 @0 B5 V! ?+ B! L sum=sum+data(i+(j-1)*L);
6 J: b$ U) R# N* F end
8 V5 X2 j4 v5 }. s4 {+ V; K x{L,i}=sum/nL;* i {" M3 s# ^
end" K9 [3 N: G u! L( O
end
7 o( l0 N6 q5 C0 f# D' t; X. e; UL=n/2;0 Z/ q. f; B3 z9 }$ J( B
f=zeros(n,L);6 X+ I+ R3 p: w" w
for i=1:L3 T# ~, W5 |! n0 q
rep=floor(n/i);+ _ S+ v5 B# |4 A
res=mod(n,i); u& F3 p, x/ |% z) p
b=[x{i,1:i}];b=b';
* W# F7 F0 d; A2 m" ]% O: y f(1:rep*i,i)=repmat(b,rep,1);
0 h7 ~1 K2 o q+ v3 K1 Q if res~=0
+ `& y7 K! Q# |. [; o( ] c=rep*i+1:n;+ s+ W% ]0 @# o3 B1 k2 \
f(rep*i+1:end,i)=b(1:length(c));
% [5 e2 @* j# k) V end g5 w6 H d4 u4 q7 D; l9 Q- A
end1 Q5 ~) R( k4 f2 e1 h" e% O% a' l q
$ K3 N3 s: P r% serie**pan.m7 Z: D$ y* D8 q2 o6 l. B
% the program is used to generate the prediction matrix f;
) }( t1 R; p+ Lfunction f=serie**pan(data,step);+ Z" A' Z, t+ Y( |) N/ [" [4 r
%data---- the input sequence (vector)
. [* e- \, M" l1 V% setp---- the prediction number;
7 k w, H/ P: `" B- M4 M) {9 F4 Rn=length(data);! T: o7 P1 B# ^$ g# z5 R! B
for L=1:n/2
5 u6 M X3 a3 Q3 Z nL=floor(n/L);: h/ Y$ [. _6 P$ Y& Z. j; _9 j
for i=1:L2 r0 X$ m- w3 V
sum=0;
8 U6 D" e, O2 e! L J. x4 T for j=1:nL
+ z2 r. U! r8 s' Y8 T8 O sum=sum+data(i+(j-1)*L);
7 w( l' u5 O" M# i& a end. o1 H2 I( ?. N" v* F
x{L,i}=sum/nL;
; W/ L+ l4 Q- | end
; o8 f0 o5 o$ B# X" }end* P% C9 r; _& ]. G' ~) U6 A4 D
L=n/2;/ R5 M0 _6 O0 q3 D: ]
f=zeros(n+step,L);, N$ _- y1 h: V9 d5 ^2 `+ V1 ?
for i=1:L+ g& i& \: M5 K( \7 L4 R* L6 X
rep=floor((n+step)/i); @6 E; w6 d' H% F; B- ^9 {) Z
res=mod(n+step,i);
' X$ L* i' ]5 S$ }2 s+ _ b=[x{i,1:i}];b=b';5 G: f8 l2 Q" O- ^) G q v
f(1:rep*i,i)=repmat(b,rep,1);
# H0 l% M# m/ S! J if res~=06 D2 ]! X! Q0 j/ i C. [- e
c=rep*i+1:n+step;
[ ^9 m0 K& t X f(rep*i+1:end,i)=b(1:length(c));
1 ?& n: X0 `5 T2 P; U end* ?; x" H1 L: v; l9 `- Z
end9 P$ a. }' m4 s# `9 H6 A6 P# `/ \
: x. i, j' T4 d _二 最短路Dijkstra算法. ]6 a) z; J" m" e
% dijkstra algorithm code program%
2 E; g; a9 R/ Q$ d# C% the shortest path length algorithm- `" \. g: ? A! H! `& x, X* d
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)
: y; j/ s& ~4 V( i. z9 T% Input parameters:
' ?* M! n8 C ^/ ~9 p# Y7 w% Input_weight-------the input node weight!
$ X; L8 Z9 v% O% start--------the start node number;
k7 J/ d- j0 A- T2 @' e% endpoint------the end node number;* X8 j; v* N" P$ _& U7 ]
% Output parameters:$ B9 b8 a# y$ @4 h) A$ F/ o$ B
% path-----the shortest lenght path from the start node to end node;
& S/ p$ i% a* G9 C- n3 e( q# X! }! u% short_distance------the distance of the shortest lenght path from the- d% Q6 d$ O/ Y# o% N
% start node to end node.9 j# E7 p7 d8 n2 \8 C1 p
[row,col]=size(Input_weight);
: k; C- f2 j/ {$ F
2 ^$ s6 f; W" K2 l3 K; h0 {8 Q) t: f%input detection
4 _& V- N, R0 ]3 W1 }if row~=col; n' b2 @. G" L: s( ^; |
error('input matrix is not a square matrix,input error ' );
6 }/ {+ }: ] E6 a* vend& M: @+ b2 i C
if endpoint>row
/ O; f& ~ ?6 G% ^/ A, K& Q9 U error('input parameter endpoint exceed the maximal point number');
1 r* n/ a/ P/ k7 ~, uend
( J" I5 [* c0 q; j4 ?) H
) K7 V8 _+ A {%initialization/ `- R4 d* Z7 ~1 h% t2 b/ t
s_path=[start];4 z& a7 V0 e, i. ^' T
distance=inf*ones(1,row);distance(start)=0;; D) q* S1 D3 D$ K" @6 t
flag(start)=start;temp=start;" R o* k+ m* W# H. Z
: d1 Z) w# l$ a7 Q' `" O7 \while length(s_path)<row
3 r( R$ r) Q6 w" h8 s# ~1 x pos=find(Input_weight(temp, : )~=inf);
; e( M; o/ @3 l" t2 c) c for i=1:length(pos)
# _! {% N' Z( {' L: Z if (length(find(s_path==pos(i)))==0)&6 G2 k7 s% s2 w# T* G- o, o- u9 {
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
4 {1 D' r5 C# G- U" w: O; b$ w distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));" F& Q ~1 p! [
flag(pos(i))=temp;2 {4 v/ b, z3 \7 M
end
# B- v+ _; W/ C: e5 M end
( P& }& u2 k& c4 M$ c% F k=inf;
& n$ \. h; W: Q for i=1:row7 Z3 Z) \8 T' b" B) i
if (length(find(s_path==i))==0)&(k>distance(i))
1 X+ }& ~, X) b$ _6 C& C k=distance(i);
# W2 u" p: U- n+ C) { r. i temp_2=i;# i, {; K+ V9 L
end; d. Q6 L, a: L: \1 H
end; U. A: G! i! G- N' Y# P" J
s_path=[s_path,temp_2];
# h( U6 d+ [% C J+ G temp=temp_2;
8 F0 V: l m3 G6 }+ uend; a! x" C* ^5 Y, K3 K7 @
& D% x5 ^3 ^9 S" X$ Y5 k
%output the result
: ~# t/ `. C7 s5 f0 gpath(1)=endpoint;
% w$ H3 o$ S, I1 J! S* v( I) Qi=1;* b( s; I% i9 J( Y3 p
while path(i)~=start
2 U2 e/ s- i* A: S( I path(i+1)=flag(path(i));3 j q- E% U0 T* \+ D
i=i+1;
* U/ V1 J; W, }( l# @end
4 X+ ]# Q9 D1 z3 K& upath(i)=start;: `0 [: J+ o2 [) T; z9 P
path=path(end:-1:1);/ I0 H; k8 o8 r/ O9 i
short_distance=distance(endpoint);% ~" J- e' ^+ @6 m4 w) G
三 绘制差分方程的映射分叉图
& E: f, l+ Q. o* C3 y/ {- n3 Z5 S( G# M/ G0 w, \4 W; A
function fork1(a);
* ~2 ? d( }6 ?" k
6 z A2 }8 z! c7 P4 G v% 绘制x_(n+1)=1-a*x^2_n映射的分叉图/ N/ a1 d# z( P' Q% \
% Example: . i1 r) k2 O: l# R. ?7 a3 o8 ?) v) y
% fork1([0,2]);
/ T, Z; }( j! nN=300; % 取样点数 9 L0 G7 [3 x% `6 M7 n% S( |# {
A=linspace(a(1),a(2),N); ) W) R1 B2 Q) I0 m: [+ L
starx=0.9; ( S' V' a6 q/ p
Z=[];
# R5 [ b( K+ |) @ |: uh=waitbar(0,'please wait');m=1;7 F& v! q, p& e, o
for ap=A;
/ L8 m2 M8 }, J9 J0 m* w$ Y" Q( y4 x4 K1 | x=starx; . D8 B* T9 |9 v
for k=1:50; ( i1 n6 C7 ?3 d4 p
x=1-ap*x^2;
7 y' G" z2 `9 k end " Y8 f: ~- Z0 M1 g3 B6 K
for k=1:201;
2 g( I. Y& H5 ]% c: b" W1 l x=1-ap*x^2;
+ E4 ?1 r9 l/ [7 j4 r2 ? Z=[Z,ap-x*i]; 7 u3 g2 U# T8 W: d6 q$ D1 }6 X
end
6 R6 s. o- l4 X1 T; ~7 u waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);# C+ d& d" ]3 z" n% ]7 ^
m=m+1;* H O9 X7 n$ d/ W! @5 H: i: v4 ^, f9 R- d
end 0 {7 P7 g$ P8 v4 U/ }1 C
delete(h);1 Z3 R+ i4 o* ] r% B" G
plot(Z,'.','markersize',2)
4 {4 n! T9 u; R. r# J: @xlim(a);
1 |8 m8 y2 G/ I1 P7 G/ Z4 Z5 l% b& X' J+ N
四 最短路算法------floyd算法8 n8 O4 L. ~( M U) r* {
function ShortPath_floyd(w,start,terminal)
7 T0 ^, I d( G6 p%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;. U4 `, B- z1 g6 x* v
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];( Q& m- y' h# x K: y
%start-----the start node;( a% W5 Y3 E5 ^
%terminal--------the end node; 7 ~1 Z* y* w$ U0 u
n=size(w,1);
& i# L% r! Q* c/ |; j[D,path]=floyd1(w);%调用floyd算法程序8 r% g! V8 d- `2 O: ^: H8 q. r) B% n/ s+ V
- v- l7 i. G/ L%找出任意两点之间的最短路径,并输出
( u) T: {6 X `for i=1:n
( L* m4 L% j; x1 P5 E, i- F7 D# e+ u for j=1:n
0 s- v c% s; A# r) J5 O ^2 s% U3 W Min_path(i,j).distance=D(i,j);! o" o S; R( X3 Z( _
%将i到j的最短路程赋值 Min_path(i,j).distance
4 c3 Z, g) B7 T; g) f %将i到j所经路径赋给Min_path(i,j).path- L" N4 K3 {+ u+ V9 s
Min_path(i,j).path(1)=i;3 S6 ?$ ]) R) s6 b1 L4 O
k=1;( U) ?. S( F" I. r% |* h
while Min_path(i,j).path(k)~=j8 i% u6 R* [5 i4 B
k=k+1;
; v$ x" J( ~1 H1 m Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
+ ~! u! q Y+ i; _6 s4 M end
. ?. @/ N5 u) V& n end- b& B p( g$ X% R- |
end
4 X1 D; B+ ]! J# ]s=sprintf('任意两点之间的最短路径如下:');
& W2 b3 I% o8 z: L. _5 u9 Bdisp(s);3 q9 c) A0 o, E8 F, j, v1 E ^1 y2 ^) f
for i=1:n; c1 l* u9 G T3 g; u
for j=1:n! K B I: B; l$ d8 h3 ^$ L
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
5 H, k2 {1 e+ k; ? ,i,j,Min_path(i,j).distance);0 R! H$ @' `7 c5 F2 D
disp(s);4 ~+ ]; Y- g% G1 W% [" Q1 o
disp(Min_path(i,j).path);# p0 i3 k; k$ r' N5 q$ U' B. w
end/ D7 h4 Q3 ^0 c. ^+ B
end+ @* m. f' S2 r6 }
, g! }- t h! z
%找出在指定从start点到terminal点的最短路径,并输出0 v" e F( y7 w4 @+ o2 E
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
1 H+ w" E! O- r% n% E start,terminal,Min_path(start,terminal).distance);
; H: o w G2 R, ?disp(str1);1 l" s% L) E* \( g# C" l
disp(Min_path(start,terminal).path);& A9 O$ V6 z2 X9 {
. n: O3 V5 E; v$ d, g6 j
%Foldy's Algorithm 算法程序
6 E8 |" @ q3 U. I3 i% S' N5 lfunction [D,path]=floyd1(a), }; }! O1 Z1 b" K" ^6 S
n=size(a,1);, v3 @3 P' D) O1 Z) |
D=a;path=zeros(n,n);%设置D和path的初值
$ t* m: l* h: I* |for i=1:n
% T5 [% r9 N" E3 S' z5 @% S: C for j=1:n4 c- h. J- d8 E# X5 g. s; q5 a
if D(i,j)~=inf7 l/ e( n3 r6 P% C- k: F
path(i,j)=j;%j是i的后点
% O/ n8 O w6 M8 W1 W, }; b+ x end: B# d1 a. c o3 L7 ~2 M# v+ @2 X/ C }
end3 B$ S& w7 \' ~7 P$ C
end( c' u8 B+ _& U( s7 W, H+ I9 e B6 t
%做n次迭代,每次迭代都更新D(i,j)和path(i,j) c. L' _6 U! B: K" F
for k=1:n
7 g8 P! R' }/ V$ O3 G for i=1:n( F# ?( [* t. h% T" |
for j=1:n
. l3 P: i" x; [4 M& Z% Q2 h if D(i,k)+D(k,j)<D(i,j)
2 I( Y O4 D# t# v& O# c' S o+ h D(i,j)=D(i,k)+D(k,j);%修改长度
) f4 K( U/ X8 t8 d" G path(i,j)=path(i,k);%修改路径
6 b7 y, D5 E7 K+ g3 u end
* }6 R7 p0 f+ m: A! R! p# \ end& i( C. b K9 }( W5 X+ q4 B- t
end
6 h& }4 s! {! n* O: Kend
8 O$ L4 A8 q# F( Q
# h: K* O: b- h O五 模拟退火算法源程序& I3 r0 P! S: x, b8 Y; T( h
function [MinD,BestPath]=MainAneal(CityPosition,pn)
# W6 ]& P3 B4 V: F& hfunction [MinD,BestPath]=MainAneal2(CityPosition,pn)
8 `& u( |% ^6 F2 c2 D$ o%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
* C+ d3 `1 o' z5 U1 G" n+ ~%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...3 n$ }+ k1 k! a
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
/ ?+ E+ J8 x$ W5 B9 f* c% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...+ Q0 L7 J3 y2 d; I
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...; @ O/ O/ I) o, } f) M4 C8 U% h
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];0 |8 g8 w, b" v0 |- O9 t6 o
8 [# O+ U. a6 N7 {% n, K; {1 z%T0=clock: \; d* r7 {" p5 Q
global path p2 D;
# u, [2 y! J: v[m,n]=size(CityPosition);
0 l2 R, L7 L# O% I( \8 q: a%生成初始解空间,这样可以比逐步分配空间运行快一些
; x! V& [% A9 T$ ?+ f- D7 g3 o6 R' yTracePath=zeros(1e3,m);# V4 X& r, }- \
Distance=inf*zeros(1,1e3);1 F# `6 ^3 W9 v0 t# l k
$ J6 k3 s$ x. L7 d7 h" s! D3 {D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...5 W9 ]# }' n6 f5 B
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );1 h! X- O3 N( h/ p* s
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
7 G5 z) C" y- v7 B5 b* G( x0 F: n0 Vfor i=1:pn+ q3 o( ?9 ^/ O3 f9 s6 f
path(i,:)=randperm(m);%构造一个初始可行解+ J" d9 J& Y$ P5 c1 W
end
% U, _) r5 c$ O) O- g9 ]t=zeros(1,pn);
* A3 f* _& \+ j" p4 w: J% jp2=zeros(1,m);. Q2 M+ z6 Q& h0 @: c0 q: O
$ `. y# ?) r( f3 W( C/ n( S
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );9 ?8 A/ T( w9 _
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=' ) ;
+ L5 U( X; b6 o- Z* b" |" n%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) y v, }; ~, D4 R3 U$ |1 S6 `
%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
' C$ R# X1 v& V6 |; g3 J! F" r%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+ b! Y! L' K( g+ b3 q
%会收到到比较好的效果
% C' Q0 q$ J. c- g5 U1 x0 Z o1 }2 w1 p T- [9 i* @/ I D
T=1e5;
9 D6 P! W* ^5 z5 l* u' KN=1;
) I+ p7 ]' m7 m+ h; x% Ctau=1e-5;%input('请输入最低温度tau=' ); b0 t0 X+ l2 {& V& {9 Y+ A5 l; C) J
%nn=ceil(log10(tau/T)/log10(0.9));
. K! u; }5 M N* u! Twhile T>=tau%&m_num<m_max
+ E; G9 i% W) a- }4 k iter_num=1;%某固定温度下迭代计数器
! o# m) A* @& B" } m_num=1;%某固定温度下目标函数值连续未改进次数计算器
* r0 ]' V0 o9 I- s3 Q" I$ H %iter_max=100;
# r* F" q1 D' I, @) ~. i %m_max=10;%ceil(10+0.5*nn-0.3*N);/ t5 p) v- D: G; c/ `* f- i! ]
while m_num<m_max&iter_num<iter_max) M' N, v' L; G$ b
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
& ^* w2 \# T+ f! Q: b' { %用任意启发式算法在path的领域N(path)中找出新的更优解
[. Y3 W! o8 {4 z for i=1:pn. a* t+ \' i$ t; M5 R
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
: a7 v& m6 A: d5 O$ B6 s%计算一次行遍所有城市的总路程 * P8 [: C; s- T' t& p
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线# Y8 @- W1 _+ V5 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))]);- ]! v* S% d; x+ t
end
/ S4 v4 `. n/ Z %Len1
$ b% p. s* [5 _: k. n1 m %Len2
& C8 k: W. Y0 ? %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand+ i3 ^( C4 d" l6 q
R=rand(1,pn);
$ s4 b ~* `5 @" B %Len2-Len1<t|exp((Len1-Len2)/(T))>R; U9 q, V0 ^' [( o7 ^* T0 ?' `
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)# u* ^' y8 F! g
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );$ A6 ?2 {) \; y' c! G# m
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));* y: |' F% `$ h2 z% p3 k
[TempMinD,TempIndex]=min(Len1);7 M0 I! z6 o' Q& O1 G
%TempMinD
3 j# n/ X2 a. u; ^$ C: ]9 \ TracePath(N,: )=path(TempIndex,: );
# h6 n* T- B7 D- c7 E4 w Distance(N,: )=TempMinD;: q- |1 V3 N4 |. u
N=N+1;
5 ^. T! M; n+ m ]9 g; k %T=T*0.9
. @. p1 B6 }/ _8 S) v/ h m_num=0;
0 ]) E2 o/ h, g0 t2 e+ [ b0 F else4 r: e6 p; ^- l3 C& e7 p
m_num=m_num+1;/ M* @4 m0 D4 i: _. C
end) Q* ?" w- P4 m9 ?3 t4 r/ q
iter_num=iter_num+1;
5 N6 v7 p# ]. i" V end# b. a2 x; }, A% i0 N) e2 R' M0 `
T=T*0.9: N9 X8 s+ @: @! N5 v+ h
%m_num,iter_num,N" e% h' Z: Z# U' v4 }! Z ^; g
end 0 r! c1 ^/ Y( Y4 ~* T7 X
[MinD,Index]=min(Distance);5 @0 |, ?, o+ d: l( P
BestPath=TracePath(Index,: );; x( C/ u* m+ I
disp(MinD)
4 k' @+ J0 Q0 J& F" |" h; G' A%T1=clock& l' b; }& i( x+ [$ I C
; Y1 w6 t. S* x9 v N/ X * K. R! J( N {8 l) m8 P
%更新路线子程序
I! t6 {+ l# m! l& p( q# \function [p2]=ChangePath2(p1,CityNum)6 C+ }/ O8 ^2 r" ]( `
global p2;
. M+ U/ V! ?. k( A8 dwhile(1)2 e/ F" ^$ W p4 D& V+ A
R=unidrnd(CityNum,1,2);
/ k" n. h7 U9 X( y6 `! [ if abs(R(1)-R(2))>1
! M' e( c# q0 ] break;& B0 r, a0 e! `" e
end# g1 n2 K+ L) H% S( L
end% d7 V! @) E1 K" U
R=unidrnd(CityNum,1,2);& ~, _4 P2 r8 k* I
I=R(1);J=R(2); {" }! a6 N& z
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));5 W1 |. }0 W- E- d) M& Z8 S
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));6 z% {' x0 O4 Z# w) ]4 i
if I<J/ ~- f/ Z. N; Z0 ]
p2(1:I)=p1(1:I);
) `) f3 m1 d- d7 w" G) n p2(I+1:J)=p1(J:-1:I+1);( A: P. g" S- _3 {5 n
p2(J+1:CityNum)=p1(J+1:CityNum);
1 Q* M6 o. R/ T3 H0 @3 d4 pelse* L5 ^# A9 l1 G7 J6 H& a: q' t: K7 d
p2(1:J)=p1(1:J);6 t$ T) L( _, \8 @+ r
p2(J+1:I)=p1(I:-1:J+1);; x5 \5 ]; {& f! R9 c
p2(I+1:CityNum)=p1(I+1:CityNum);
, h5 I! J- k" e, f( M. G Qend
5 A$ N. O! ~: y. p- ^' j2 K7 W5 G
6 p; x4 ~: ~$ i! B2 B六 遗传 算 法程序:- y$ y: S+ v* y' W, q2 S
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!& m$ p1 ?( E; P! K! E: f
3 L3 \1 M. W1 i; r$ o& e# e4 Qfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
|8 z" H5 o3 U1 }' O. \% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) 8 Q( p( p4 B$ `8 y9 ^' E# m
% Finds a maximum of a function of several variables.
5 L: S; h7 g! m. H% fmaxga solves problems of the form:
& R+ [$ ?9 d8 B* O7 h% max F(X) subject to: LB <= X <= UB & b4 J8 U! ]; X; v: g" N+ g9 b3 Y* ~
% BestPop - 最优的群体即为最优的染色体群: U" I1 J4 ]. F- S
% Trace - 最佳染色体所对应的目标函数值
9 M% |. f0 ~: z* G9 b; l; v% FUN - 目标函数
, O1 ^- J1 x) E1 h, k! W4 z% LB - 自变量下限
; v& Z5 R# u3 r, I5 V# R( u% UB - 自变量上限
. m* I+ s& W, w& Y4 k" A* Y8 Y% eranum - 种群的代数,取100--1000(默认200)) ^' J0 Y9 Q3 i/ y
% popsize - 每一代种群的规模;此可取50--200(默认100)
: q' o' B0 d5 P8 X6 x% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
; v1 g1 b# D: S' }+ R0 n, O% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)7 L2 q% A. l) ]* g! E/ b7 a8 e6 w7 j
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
, T1 m& @1 l' h% e' g' b2 l2 P) M% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编& h' y0 K' M% |9 P# A
%码,option(2)设定求解精度(默认1e-4)
) K% \& A$ d" ~7 N%
; Z- q; J1 |3 ` N+ M1 R3 I% ------------------------------------------------------------------------
8 }, h& g& F3 d5 w" T$ t5 `5 t3 P, }
T1=clock;
! E1 L" ?) n( z% O2 Q5 D! i: Fif nargin<3, error('FMAXGA requires at least three input arguments'); end
% Q1 b7 G; x0 k: E" ?! K3 c( U4 cif nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
% ]0 H9 ~% T* g, _/ d6 p; x6 B" iif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end3 ^* w, u) c) ^" ~4 v
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
) M; h9 Q* e4 z: z9 vif nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
1 @% B/ w4 A- p+ \if nargin==7, pInversion=0.15;options=[0 1e-4];end
, c! y# T" Q( O# m, H6 Jif find((LB-UB)>0)- e# z7 G% O7 U1 t; U
error('数据输入错误,请重新输入(LB<UB):');0 f9 a; k6 n/ ]8 @
end
& d4 ^# @8 t/ v8 S; [s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
) N7 N6 W0 a7 R: A5 I3 |* idisp(s);
" k: ]" z ]% P
, t& w: C2 M& k$ P7 C0 e. gglobal m n NewPop children1 children2 VarNum
$ J% V1 n6 N0 g+ E4 e" M6 s3 A; [; X1 S& b: P: f! e
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);$ N; M' P- o3 a$ U5 `' j) X
precision=options(2);%由求解精度确定二进制编码长度7 p S+ j4 y8 Z) a( R4 L
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间+ ]: s. t( s! |8 W" P. o$ m1 u% z' l
[Pop]=InitPopGray(popsize,bits);%初始化种群
3 R- T& B1 a+ ` R* J[m,n]=size(Pop);7 p) u) v( s+ Z
NewPop=zeros(m,n);2 N l) `' c; B8 q
children1=zeros(1,n);$ t0 m% C% g4 ]5 |+ Y4 N. N
children2=zeros(1,n);6 V) _4 U( A3 z1 R: O
pm0=pMutation; N: U0 k5 K* ~$ b: q( G8 v6 N" I3 t
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace1 M! w8 R; m" _- E
Trace=zeros(eranum,length(bits)+1);
/ k& K. U. }: ~6 H8 p8 ~( fi=1;
" \5 M! e4 ^6 P) nwhile i<=eranum
. r8 e7 W- h# m3 O8 \9 c& k& u for j=1:m
; Z( u7 _+ r: Y! i value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
! f3 H+ O" f' N9 [' Z end& H: S& q4 i. N( f; q4 Z5 [2 M: ?
[MaxValue,Index]=max(value);
) p, r$ V" N* b BestPop(i,:)=Pop(Index,:);$ a# R: S5 x; t1 k$ P/ \+ [
Trace(i,1)=MaxValue;
6 K& y \4 c6 a Y1 f/ Z Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);* G9 {, D3 n. n1 j( w
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
1 f( f' Z4 {# u7 H$ @[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));+ H( Z" p0 t5 W) y* U
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
3 e7 u, H/ K5 F1 J8 P9 u! ?$ |) ` %round(unidrnd(eranum-i)/eranum)
9 P7 O: N' _: |/ Y [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异 u0 Y; }, L; E7 A2 |& A$ s
[InversionPop]=Inversion(MutationPop,pInversion);%倒位
" p+ o* V- y0 Z) R Pop=InversionPop;%更新
' ^2 w0 p: d" F* d# t! o' C. DpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); 8 H! K1 I' h# `& b+ e0 H
%随着种群向前进化,逐步增大变异率至1/2交叉率$ G- L1 n" U1 k6 G
p(i)=pMutation;
& w$ W/ E) h# L i=i+1;1 i3 ~7 T) v9 a& ]; R9 M
end
: H8 }1 [( n _% p* At=1:eranum;
+ E1 e* p% U' T/ q! gplot(t,Trace(:,1)');
* A. }6 @8 _- w- C |4 Jtitle('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)');: V- A2 Y- z4 I2 [- l- J0 z
[MaxFval,I]=max(Trace(:,1));
7 O/ k, W/ d( n0 |X=Trace(I,(2:length(bits)+1));
/ b0 W* S: [$ L: Chold on; plot(I,MaxFval,'*');1 M' n$ l5 J& G
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);8 \( V; s+ _1 h! u! z7 o1 m" 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,:)));
/ G. ?3 p) Z7 |1 V2 bdisp(str1);2 R& j( u" [2 \5 F* V9 a& [# p
%figure(2);plot(t,p);%绘制变异值增大过程
! [5 _+ [% P+ |* W! |T2=clock;1 s2 v6 x# b3 w! y0 Z0 A5 y) E
elapsed_time=T2-T1;( m6 c/ |' ~6 o& {. l! ~ `$ c" u
if elapsed_time(6)<0
/ ~: s7 B2 ^- d1 A. a+ L$ ] elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
! D- L3 m7 M; N( M. x" A$ G3 {end
; r2 z+ x- u2 E; X1 Eif elapsed_time(5)<0
; Y) M4 G! F. h0 M" Y elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;( z4 ^3 v6 f' ~) |
end %像这种程序当然不考虑运行上小时啦
, { n e% U0 Q. |: lstr2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));& k+ G/ Q: ^3 i+ ^9 y$ n
disp(str2);
( x/ o% W; ~0 f( s8 y+ i- `( u- p" b, L
9 z0 {+ G! L; G; {* C) {3 ^: U( U%初始化种群
% S! P! l# N' 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
5 a' R1 x) O, o" g- }function [initpop]=InitPopGray(popsize,bits)
$ {5 n. }3 K5 z, r7 K% Y" vlen=sum(bits);
( a" S9 N7 l. `initpop=zeros(popsize,len);%The whole zero encoding individual
' T- T0 I' y# r, Qfor i=2:popsize-1
/ {" L! G* m) o9 i8 N3 q/ ` pop=round(rand(1,len));
4 h2 R! q2 F) J' ]/ B* W pop=mod(([0 pop]+[pop 0]),2);2 E- C" W2 v; ^$ k2 q- F; u9 R
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
4 m! f9 ~% e2 t7 z %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)4 t) l, T, l" b7 n4 o
initpop(i,:)=pop(1:end-1);$ s) }( u5 z( A/ C/ M) ^! Q
end& t* D! S9 ?) v9 G' y6 Z; Z+ i
initpop(popsize,:)=ones(1,len);%The whole one encoding individual
. e9 }1 s% i5 R. G8 X%解码
0 E$ u4 E7 [: n+ H( k: F- E. G! k5 e, s6 J$ m3 ] C( r0 z) q5 {! @5 P. N
function [fval] = b2f(bval,bounds,bits)4 g, k$ E; W$ d# d8 d$ V
% fval - 表征各变量的十进制数
' F0 e! A7 v" n3 N8 ^0 p% bval - 表征各变量的二进制编码串
; U% |- i9 O& C) Z* r% bounds - 各变量的取值范围
( z _, k; N3 |: e/ y- \% bits - 各变量的二进制编码长度
# }. t9 N& R& k% [scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
" z z7 w7 e. B% A# onumV=size(bounds,1);& t, a8 X% {- I4 b; A, e
cs=[0 cumsum(bits)];
' R; R6 j; b2 ?$ Ifor i=1:numV$ b* J3 _5 Q c# [2 M5 H
a=bval((cs(i)+1):cs(i+1)); j: N3 o5 h' d5 c/ _9 ~8 F+ W
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);+ h, k0 \2 f7 X' j+ m( b
end
- |2 z' N# Q7 `! w; \, u/ y%选择操作+ u l1 A' ?6 _& [; |* K* p% V, ?
%采用基于轮盘赌法的非线性排名选择0 t3 a" g3 f5 n: b4 J7 ?- j3 h
%各个体成员按适应值从大到小分配选择概率:+ i1 a0 d6 e" N$ ^) E0 N+ c
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=15 F/ n/ @* x4 ]
; X) _8 u4 {, _; X7 t! xfunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)# V% H( @$ M5 r! w
global m n' ?' d# s$ q( z) ]; J$ `
selectpop=zeros(m,n);9 V( i! w* V; N
fit=zeros(m,1);: i8 ~) a( Q( ?0 z5 e0 l4 e# m
for i=1:m0 k! T6 |% K3 s' V
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
/ ]/ W w {1 Bend1 m( m- |9 s, y8 g$ v$ p
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
7 q4 h8 z0 m& |7 l F n8 N) L/ uq=max(selectprob);%选择最优的概率* j' Q& D. q; v& ]* D- d% ^! l0 z. h
x=zeros(m,2);
. u) S S) A' }" Gx(:,1)=[m:-1:1]';. q, s' J8 V9 a7 ?+ Z% s- m2 w& w
[y x(:,2)]=sort(selectprob);) X3 ^) u3 i% w% }* C/ t, ]( t( @
r=q/(1-(1-q)^m);%标准分布基值
. v! j' [: P7 ?; w Fnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率2 m3 Z# b2 S4 v; Q3 p4 ]
newfit=cumsum(newfit);%计算各选择概率之和
- a d+ c8 J, E% i2 d3 \ H+ L% irNums=sort(rand(m,1));; F8 S% X j0 T- U& m# }9 H( n
fitIn=1;newIn=1;
. V; i& ~% ^# @% u" P( G8 Wwhile newIn<=m0 g u4 y+ v% P) \3 p
if rNums(newIn)<newfit(fitIn)
P' j; L( j" c" Y2 `+ a! T' \ selectpop(newIn,:)=pop(fitIn,:);
1 e; d7 A8 [% ~$ i0 R newIn=newIn+1;
: p; \' v5 p! H/ O; q$ X else
& x( a, b$ W M* n2 B# @$ |7 { fitIn=fitIn+1;5 L2 o, y Q( {9 H- }
end% \, V! i: ^# @; F
end
# p1 H7 f$ m- k2 V! K2 X* p" o%交叉操作
. g$ I! ]9 n2 m5 v. F, L0 @function [NewPop]=CrossOver(OldPop,pCross,opts): n- C) p: q7 g- u3 E# p
%OldPop为父代种群,pcross为交叉概率
! r% c( |8 h/ k6 iglobal m n NewPop ) `2 m8 a* T% @, a& g, G
r=rand(1,m);0 Z: \& P0 A3 ^ G! z: i+ B
y1=find(r<pCross);! J# i8 ?9 O+ G0 @" M, x5 \
y2=find(r>=pCross);
. l4 y* W( g2 w$ h: U4 nlen=length(y1);& {9 g8 U! N( Q
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7 y3 ^$ y# I% g$ W* b2 h
y2(length(y2)+1)=y1(len);
4 ^1 K: G6 [ B% l y1(len)=[];" g; c5 G* p- b9 b4 Z
end
( _$ x y* \2 K, P1 K" zif length(y1)>=21 [. ^4 F" |- H, F
for i=0:2:length(y1)-2+ Y2 F0 U+ [3 j. \9 X: ]: W
if opts==0* o" V- E$ v0 m0 R3 X: Q
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));) E8 X4 D$ B3 V1 k v4 u
else
) m1 E% n* D. r: T2 U9 | [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));6 s4 K F& M7 {. }: |" ~0 e
end G6 _# h7 v& R8 h" g% i4 |7 k
end
# h" ]! X V1 T& _* Zend
1 i( T7 t4 p9 N0 D2 N4 M+ x1 p3 ?* BNewPop(y2,:)=OldPop(y2,:);
9 d( h5 g. Y2 M$ q9 }
8 r' Q6 y8 M1 j%采用均匀交叉
$ A I! _8 W" V, v0 Pfunction [children1,children2]=EqualCrossOver(parent1,parent2)
" K1 p3 [+ o" I. l7 y( U: u/ b
" `% l$ [' |2 Hglobal n children1 children2 & c# [) \; A' I% l. t
hidecode=round(rand(1,n));%随机生成掩码
5 o/ W) E$ @# p) g. }3 ?$ M4 Y) Zcrossposition=find(hidecode==1);! @1 z6 Q# Z: E ~
holdposition=find(hidecode==0);) \# S G8 V2 J
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因! ?+ R$ t: D! `" L
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
' v Q% s- w$ T% O+ n8 p3 X9 k4 C! [children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因! K" A3 W9 E& z2 j8 D( f
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
; o& o9 U8 X+ k- @6 J. \; R
" ^0 g* }. T7 G, W%采用多点交叉,交叉点数由变量数决定
! n/ O* H! i$ G% [8 o& z& Y, b$ R. P4 R* q6 }1 s: t2 ^* G' p7 J
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)) b+ j# I: g1 m+ X, G% ~0 M
0 c q2 g- x' w Bglobal n Children1 Children2 VarNum' e) f- w2 s6 y( e& _
Children1=Parent1;
3 ]! a: {+ I. XChildren2=Parent2;
! h5 X3 c2 X/ }, J2 s; t. } S0 o" OPoints=sort(unidrnd(n,1,2*VarNum));
+ J0 T6 s2 |4 Q5 Nfor i=1:VarNum$ D, b3 } i; E
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));1 h) K* L% a, N$ B& e
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
) h1 S+ ?: D+ a* O7 Qend
) A, q0 O/ ]2 k4 D9 s7 R; z8 f; P9 K5 r7 N4 g& g8 x
%变异操作
, R) @) C$ u( a& \- e$ J8 Gfunction [NewPop]=Mutation(OldPop,pMutation,VarNum)/ J! z, i b$ u; x
4 r' f! w5 t% e( V# P+ Y+ H8 Sglobal m n NewPop2 T5 q% h( u. g+ I; r& `: z
r=rand(1,m);6 ~0 O" R" G2 u2 R+ Q! |
position=find(r<=pMutation);5 u1 X7 Q: _# Q
len=length(position);
6 i( _1 [) J& o0 `5 Fif len>=1
7 e0 Z. E2 V+ O6 O5 y; H/ f8 P for i=1:len
D6 V9 r/ ?- h2 e k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点: ~ ^ ~9 d& b0 I
for j=1:length(k)4 f" i# _ \: X
if OldPop(position(i),k(j))==1
( O( E7 M7 a( c } OldPop(position(i),k(j))=0;' m$ M5 z, { i/ W$ C A
else
; z2 f( g( @: }8 J4 ^0 d OldPop(position(i),k(j))=1;" ?- ], n |. `4 K6 J) {0 a
end; _6 _; q. b) D8 P0 A2 T+ v
end2 v" [; G1 ? Y& c& c# H
end! n# m: C9 d6 ~: n, |' d( E' I
end
2 X5 [+ x1 O- U8 p$ l' l/ Z- bNewPop=OldPop;
) \6 A3 Q* V+ n& B* z8 v8 r7 _0 {7 e# \
) A/ v" m3 C4 B9 r%倒位操作: E2 D- D9 L& ^% }
9 w2 W% Y- E. H; L1 ~9 R4 zfunction [NewPop]=Inversion(OldPop,pInversion)
+ M, M4 x S6 {) E$ Z! ]
/ [+ h/ s) `6 \7 ^global m n NewPop
& E% B6 G" l1 m+ hNewPop=OldPop;
8 i* @' q, M7 ~/ [% Fr=rand(1,m);
9 Z3 f0 d1 G! H. dPopIn=find(r<=pInversion);
6 w7 J1 ]/ B8 N$ D* Ilen=length(PopIn);
0 ?) e7 s1 T# |/ [if len>=19 {8 m. N$ {+ q2 M) p: ]$ r' X
for i=1:len j( n; l' T& Q& ~ G3 z
d=sort(unidrnd(n,1,2));3 m* Z9 ~7 l; W5 E8 r; r# g1 T% `
if d(1)~=1&d(2)~=n
i3 l! ^5 c" S( g NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);! g: p/ k' _1 w5 T
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
# ?0 U7 v$ ]' f/ x. {2 M NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
% W4 l) z8 c' F9 {) U& D0 J end- [0 u) Y8 S' b1 B+ a! o+ I
end
" O5 o( J0 @+ R. n) A7 C, U4 m( Rend) r' r. H% v+ m# [+ J. X) T
' B, k5 u, \; v4 ~+ h
七 径向基神经网络训练程序1 d/ z8 F9 h& A# s# b x# h: h
0 w( F; k3 ]* R3 n# z8 U& K; K8 n" f
clear all;
2 \0 `& J1 p* wclc;
+ q) |( L. K) s" h$ }3 P: Z# ]%newrb 建立一个径向基函数神经网络" Q; L; ~* w! K3 G2 S1 U9 `
p=0:0.1:1; %输入矢量
5 {4 Q- _% V$ E6 W( j/ {7 E3 Lt=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
: J2 I' O ?/ n" u2 Bgoal=0.01; %误差
+ }$ t+ g8 @( ~9 s0 ]sp=1; %扩展常数
+ I) y1 q, _8 u3 ^/ c9 w2 {mn=100;%神经元的最多个数0 m, Q7 n& @1 S
df=1; %训练过程的显示频率& i# J1 J" q) U/ v; q* c
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络8 G; q- K5 P7 Y8 d0 ^
% [net,tr]=train(net,p); %调用traingdm算法训练网络1 M) C5 h" c3 n2 X, `
%对网络进行仿真,并绘制样本数据和网络输出图形
$ Z2 z% `: _; ?, [% YA=sim(net,p);4 y, Q- H$ p2 D; s. U6 q! {
E=t-A;
6 W' A! Y5 E0 {3 U- `" @sse=sse(E);- s# O4 c, a$ t. m6 n; k
figure;
* o8 t0 K! b7 k5 c' cplot(p,t,'r-+',p,A,'b-*');3 N4 b5 K& V% r( h- z3 V
legend('输入数据曲线','训练输出曲线');) L0 a* v% E/ t6 O9 ~
echo off 2 R: T+ W1 _: E6 |# n' y
; f6 w q3 V$ d& m' k& c
说明:newrb函数本来 在创建新的网络的时候就进行了训练!
( K; }* ^7 H) L# c每次训练都增加一个神经元,都能最大程度得降低误差,如果未达到精度要求, ]- r3 P( d+ c4 K- J
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!
/ B5 q8 E8 s8 M" v7 g
9 E( p, J; {- v8 \+ [9 |/ P' }# _6 t# }" x
训练结果显示:
, g' w8 Y# R# S3 I5 z9 e1 ?, cNEWRB, neurons = 0, SSE = 5.0973; W* f4 f% ?: ~" z/ V
NEWRB, neurons = 2, SSE = 4.87139 ?% D% Q/ n( g5 R5 d7 L$ B$ z# w
NEWRB, neurons = 3, SSE = 3.61176: Y+ v1 a: \' _6 {5 V
NEWRB, neurons = 4, SSE = 3.4875
2 y H. n3 m3 {5 y0 fNEWRB, neurons = 5, SSE = 0.534217
6 W" Z9 a4 ^( t/ n% ^8 S7 I5 d$ TNEWRB, neurons = 6, SSE = 0.51785
. H0 w8 w& m+ s; {. qNEWRB, neurons = 7, SSE = 0.4342597 s1 D9 W7 S A3 j0 j& r/ _
NEWRB, neurons = 8, SSE = 0.341518
+ i" o; m+ X2 UNEWRB, neurons = 9, SSE = 0.3415193 R. |* M# J/ h
NEWRB, neurons = 10, SSE = 0.00257832, Y* Z3 M. S& S% i/ X- D
" T# J! Z: P2 o4 _% W, a, @# M
八 删除当前路径下所有的带后缀.asv的文件+ J F+ D4 \ t( A3 P% t1 f& Q
说明:该程序具有很好的移植性,用户可以根据自己地+ |1 \' e" Q# h/ z3 M2 }+ D! W5 X" A
要求修改程序,删除不同后缀类型的文件!
z: X! g! K" K W: T$ Cfunction delete_asv(bpath)
- E1 h. P. l4 B%If bpath is not specified,it lists all the asv files in the current2 C6 C( P' ^# \8 [2 K( U7 [6 l
%directory and will delete all the file with asv % m, |$ d0 N$ B* I' `+ a
% Example:
) \ S( Z) E V; |% delete_asv('*.asv') will delete the file with name *.asv;
$ E! z4 Q5 `7 a+ z, \% delete_asv will delete all the file with .asv.3 u/ J* n9 l5 p
' A+ L9 e$ ]/ G3 s1 pif nargin < 1+ |6 l+ o9 \0 I9 L
%list all the asv file in the current directory
5 ~9 r0 J- v0 X! X) Q files=dir('*.asv');
7 T) d1 N! C& g( l* y# relse n2 y% w& j2 G& R5 v
% find the exact file in the path of bpath
" A) U: z; I" ~, x9 D1 L8 A [pathstr,name] = fileparts(bpath);
# t# K% ? Y5 R if exist(bpath,'dir')1 I& f- j3 t) G1 j
name = [name '\*'];
4 O% F1 T7 S- r end
( L) D/ D) y6 G$ A( q0 B3 h ext = '.asv';
; P% R9 m# M! a- ~ files=dir(fullfile(pathstr,[name ext]));6 ]) `+ D) R* |
end
3 g5 v4 `7 P7 |8 J
# Z& ]) w: \5 ^5 \5 Rif ~isempty(files)% x5 d1 K7 e( T- j5 P( @$ }) ^* G1 Q2 q
for i=1:size(files,1)- Q5 A: u3 ?9 N6 L/ }: ]
title=files(i).name;
# d% @- n7 k# S: h2 I delete(title);
# ^3 O" A% y( f3 c end
' a1 S* T) a) u; C& u! |end3 X! S9 ]0 Y9 m6 i
' N# g% x" }9 Y% d3 h) Z. N+ _( W* R, X* x- d
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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