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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8 n% f4 ^( r. q
1. predict_fun.m为主程序;) P0 L" {% @: G9 F2 i
2. timeseries.m和 serie**pan.m为调用的子程序
. `6 I2 J. o# w- l$ C. O- f+ I* d7 {9 ^( a. U. \* G
function ima_pre=predict_fun(b,step)9 y& Y' K2 T( M: w' G$ `
% main program invokes timeseries.m and serie**pan.m. ^( j$ \3 Y* M% `' Q7 H
% input parameters:
. R- I/ H; z- h. L' y; d% b-------the training data (vector);% g2 g/ Y' P. V, Y% ?
% step----number of prediction data;
- G7 |4 h: Y$ @: Z; y% _% output parameters:
7 d$ z. o) c7 L4 l5 ~1 _% ima_pre---the prediction data(vector);$ d8 {5 ?& d( L
old_b=b;: q6 U" N! h$ k4 O* q: P
mean_b=sum(old_b)/length(old_b);: Y( U7 f) W5 _9 j! P8 P
std_b=std(old_b);
! N: w; i# p/ n1 Z1 cold_b=(old_b-mean_b)/std_b;" I, i: X4 {/ S! C9 V1 T
[f,x]=timeseries(old_b);3 S; W3 N; C+ a
old_f2=serie**pan(old_b,step);5 J. w# q5 w7 L
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;
7 f7 }* C2 |+ e. M6 S+ kR=corrcoef(f);
# `3 h9 c* P8 p% ~" [- Y[eigvector eigroot]=eig(R);
& H3 N6 a6 Y3 y+ L$ }eigroot=diag(eigroot);6 a$ W8 K/ b+ r0 U/ n7 o0 A
a=eigroot(end:-1:1);
, T O; ^, ^5 H1 tvector=eigvector(:,end:-1:1);5 t0 n, w7 S7 Z, Z; e: v
Devote=a./sum(a);/ R# O% x* t, t; a0 z) o- `
Devotem=cumsum(Devote);
% ]5 F- n/ ~7 f' Wm=find(Devotem>=0.995);. ]6 a$ z6 f' @! x+ P/ [7 M
m=m(1);
4 \$ h* \, _& n3 m9 b( MV1=f*eigvector';) i* i3 r# O' _, i
V=V1(:,1:m);2 Q, U# R3 ~4 ?7 p c5 x
% old_b=old_b;
( ^: X* B4 Q4 Z% L+ oold_fai=inv(V'*V)*V'*old_b;( n3 Y) D) ^8 S1 V( R# ~
eigvector=eigvector(1:m,1:m);
1 O3 o7 x$ h/ V: I8 Q( U( Nfai=eigvector*old_fai;
9 J! N, X5 K$ @f2=old_f2(:,1:m);5 C8 O8 A" ]. K) z4 h1 L) y
predictvalue=f2*fai;* E& G3 h# ]* K
ima_pre=std_b*predictvalue+mean_b;
5 j1 |; y0 {$ f2 Q! z8 Z! a( p& i, [ w5 E: U+ @
1.子函数: timeseries.m
* M/ Y2 r& `8 C+ @& e' ?/ C% timeseries program%& T3 s0 q3 E. v: _! U' C8 H* F5 R
% this program is used to generate mean value matrix f;
- N+ ^2 h/ H! U8 n) Jfunction [f,x]=timeseries(data) : @, L: x& t) |- P% @; g5 v% @
% data--------the input sequence (vector);2 L/ o; N8 ?+ v2 S
% f------mean value matrix f;
# [. X/ h }% A6 F- Y- in=length(data);
7 A; E9 A' w' Z' W2 l8 Xfor L=1:n/2
0 N% h, U3 }/ G+ v+ E+ d% _ nL=floor(n/L);
+ I& q- d$ X2 w; @ for i=1:L' Q, L% g, a' x3 Y% t! t
sum=0;
/ F. j) V& g' M3 [4 B" [ for j=1:nL
+ x$ w. L! @/ J; ?. ^. d6 p sum=sum+data(i+(j-1)*L);
3 m2 T6 }- |1 T end
1 [5 ]2 [ a- t: R- v x{L,i}=sum/nL;
I( Z. `$ H' K9 n$ } end
$ ~8 M. v5 F) F8 ~ M7 q8 ~end4 Y9 e' B- x( B6 n- `* `' x
L=n/2;
. I, D% R+ E$ Y0 J8 @f=zeros(n,L);2 @1 ]- u- p. ~: F2 {0 z
for i=1:L3 l! E0 g# X; l% X1 @
rep=floor(n/i);
0 Q2 { O$ o+ _2 g3 r res=mod(n,i);
2 k/ @& m- u! b4 P# a6 R! Q b=[x{i,1:i}];b=b';4 p; I, M4 E1 N, a9 w. p
f(1:rep*i,i)=repmat(b,rep,1);
" ?+ s6 Q! _9 O3 a/ e4 w6 x if res~=0
5 Q/ n$ n4 K& d f. D4 {' ` c=rep*i+1:n;+ T% Y0 V4 y1 @. L# C
f(rep*i+1:end,i)=b(1:length(c));5 n( x% ^" `" k" [ W* }$ P
end
+ w. s+ Q9 ~) K3 Hend
5 h& Q( f2 K( X' `& Q7 J
5 n/ \1 y: Z: U- y7 [, k% serie**pan.m
' q% Y* u5 |2 r7 o6 K% the program is used to generate the prediction matrix f;
4 E) Q" z7 o A9 L s4 wfunction f=serie**pan(data,step);+ @+ S( P3 d" I; M7 S: i" G( E8 a
%data---- the input sequence (vector)2 F6 I6 k! I4 g$ Q# }7 _
% setp---- the prediction number;
; x" ~, c+ Z yn=length(data); D1 P T! u7 T( _ I
for L=1:n/22 V0 E% v9 S0 Y* Q3 b) B1 c
nL=floor(n/L);
& I1 r6 ~: n1 ^5 X* f, j0 V for i=1:L, `7 f( m4 D5 E7 p6 m$ N
sum=0;
: l/ U o9 R. E x$ p for j=1:nL
8 |" M0 ~* P' W0 E9 @$ {# O sum=sum+data(i+(j-1)*L);
6 c6 D# q# W- I d% w* L end( W) A( a) c0 \$ _9 R$ l
x{L,i}=sum/nL;: x! d8 {' m8 x+ d7 ^$ _" h; U
end- Z0 u1 |4 ?: w+ r& s
end
. `! H0 M! Q7 BL=n/2;, X& g* N9 ~) Q: K( L, x7 W
f=zeros(n+step,L);7 ^, u2 B% D1 v9 b+ a) l
for i=1:L4 ?# B! N0 k/ s7 Y' P2 d/ g$ u
rep=floor((n+step)/i);5 l1 e* e+ u f
res=mod(n+step,i);% u& T) v/ q! b! Z3 `5 ]3 _
b=[x{i,1:i}];b=b';
" K7 C" P- m. I8 {) {8 L% ^ f(1:rep*i,i)=repmat(b,rep,1);* s& \7 ?* P+ e# U& [; v: b; R4 i
if res~=0- p( Q! _/ z5 a; |0 O, T
c=rep*i+1:n+step;+ [ s$ n) ?4 p) H; h( y5 C
f(rep*i+1:end,i)=b(1:length(c));8 x5 x9 V; }3 \2 J7 ~, Q# B- }) }
end, P4 p6 r7 N9 n, C
end
1 r' y. v* A: \/ Q, }2 R+ V9 ~; ?1 ~
二 最短路Dijkstra算法) v. U+ X9 U7 P: l, v
% dijkstra algorithm code program%. v# u) w9 w5 H+ k k/ C9 T
% the shortest path length algorithm, c; x5 n/ V$ P- S4 |2 \# t
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)/ [3 `" n0 I6 l. e8 l
% Input parameters:5 q; P) V( N+ b' f4 G( Z' X' D/ `
% Input_weight-------the input node weight!
- A, R; T! G# }+ y! a5 M( S, o% start--------the start node number;3 s# }8 S( @4 A7 n7 P5 l
% endpoint------the end node number;
% ^4 C3 S2 R6 s% Output parameters:& f: J# t; r0 P: ~6 U% |
% path-----the shortest lenght path from the start node to end node;' _1 L+ f# L/ w& P+ W1 i
% short_distance------the distance of the shortest lenght path from the
5 G( B& E8 @! B- j/ s% start node to end node.1 P j0 L8 ~0 T: @# L
[row,col]=size(Input_weight);3 t8 C- ?1 Q. J0 s6 }
9 X! E1 B5 i' e/ h; R2 _/ U+ _- z%input detection4 v o5 f3 T, @. c# ?. I( W
if row~=col
9 u* X. A/ n; H error('input matrix is not a square matrix,input error ' );
3 A' U3 u* G, B. [end p; x* V2 K6 G, u+ l, r
if endpoint>row- ]! b+ g0 k& t# r/ B2 W s) o
error('input parameter endpoint exceed the maximal point number');
% E; L- Q3 C" C' g0 E& x$ s2 |8 ~end
: p! o+ K7 r7 h% z6 I# l7 C, [ K: G! c
%initialization' F P- w; d" k
s_path=[start];
5 t$ ~5 w2 t. x2 c! Wdistance=inf*ones(1,row);distance(start)=0;
( I; ?9 B3 P$ r2 @; J% Uflag(start)=start;temp=start;
9 Y0 R+ t3 y" _9 s5 e. J) y! a
' b, W& a1 S. \4 q# j2 ~) {' Nwhile length(s_path)<row! e+ M% L, r7 r2 S: E D7 @% _
pos=find(Input_weight(temp, : )~=inf);
/ ]9 n4 b$ p9 n& d, c' e6 f for i=1:length(pos)
r- Q4 b' Y1 I3 ~3 `7 ~ if (length(find(s_path==pos(i)))==0)&
3 l4 N6 s0 I3 H2 ]# r' U. y(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))0 T. T+ E) T4 o0 \3 k' E& t1 g V
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));# n2 z& C5 d0 N! I+ U9 q7 W
flag(pos(i))=temp;
/ D5 e. Y" Z8 M% g: T: F' L end
; T0 O2 v; p, H, z; \8 c) _$ ] end
. R- X- @. o! }5 d k=inf;
' P. \9 q& ?+ I* u for i=1:row% ~4 C, x- I1 m2 v: Z
if (length(find(s_path==i))==0)&(k>distance(i))8 [5 v" G/ g8 o
k=distance(i);% A) |% g9 s& n4 F% f8 V3 [
temp_2=i;/ b( G6 g1 }: Z8 x
end B Y( \9 d! I H+ _
end. \0 q, X! K/ t6 J2 z5 u0 o
s_path=[s_path,temp_2];
0 B) o. X9 D5 i+ D: L temp=temp_2;
+ p, ~% e. t+ E2 A$ Rend- _6 r9 r8 M) s/ }& b' v# V
. E' c: ^; ^0 g7 \' _% l" Z8 l%output the result. }% g4 l9 A$ j/ E2 o" o
path(1)=endpoint;
( ~" R/ w* F0 q1 S$ D* K0 T1 }i=1; P# l: X7 r. |$ B# ?& n% \
while path(i)~=start
; u. O f% v; i5 U3 }0 G0 L+ p path(i+1)=flag(path(i));( r( x$ h2 c$ l. Y% a) i
i=i+1;
4 L$ k" b/ }( x* H, ~end: v& S) d8 S4 I; Y+ \, G( z
path(i)=start;
4 f t2 O, T& |2 S) hpath=path(end:-1:1);8 O$ F2 S8 f" s. f9 u, d; _ ~
short_distance=distance(endpoint);; A- @3 s+ c! k
三 绘制差分方程的映射分叉图
$ ^+ n! o) a, Q/ `2 [3 d7 ?- v& h, j+ T7 i( n
function fork1(a);
$ H: F7 E6 _+ S* L
/ A a5 h3 G1 P: N" _ u2 {% J% 绘制x_(n+1)=1-a*x^2_n映射的分叉图- t5 ?4 ~+ }& t' A# \
% Example:
7 k, W' r. O+ |1 U) b P: i% fork1([0,2]);
# f' Q6 q: D: }+ S7 @% L" R vN=300; % 取样点数
8 T" `2 O4 x; V- FA=linspace(a(1),a(2),N);
4 O/ j" j3 Q' L, K3 N5 |starx=0.9;
2 T, Z* O( c) A. j0 tZ=[];
4 R* @% L3 P/ F; }h=waitbar(0,'please wait');m=1;
5 v7 v# R) L- ffor ap=A;
) l4 q9 Q9 a3 C2 ? x=starx; ' ?, O! y0 c4 M
for k=1:50;
- _/ q0 i6 U. d- S x=1-ap*x^2; - _0 r( S1 `. e9 @* N1 G) O
end
8 c- O7 C( N5 |. I+ C) a9 E+ [ for k=1:201; $ k2 }/ z5 N+ n# U
x=1-ap*x^2; 8 Y; v; B7 c. ~( _& t
Z=[Z,ap-x*i]; 9 n" Z. }+ t+ \2 @$ T R
end 9 i$ E# I/ }" h6 D- i- X! t& N; i
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
7 ^6 b% R% S4 a% Q m=m+1;
- P' F. ^8 V* ^1 \end # t2 r7 K1 O) G5 V; U
delete(h); c0 f/ z! T8 M! j$ X7 B8 e
plot(Z,'.','markersize',2) 5 ] n: U& v& H+ h# U: m# d
xlim(a);
6 A7 W+ i( b7 R- s7 l
% S$ T: }3 G: H四 最短路算法------floyd算法
" c7 q5 |7 U( K( a$ `) p6 Pfunction ShortPath_floyd(w,start,terminal)
i* w6 K, w0 c%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
* a1 V& q; |# M. z%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
& T9 @7 S3 w; b9 p: B%start-----the start node;* ]( I: ~# h- @) \
%terminal--------the end node;
$ {6 J; a( C7 ^7 f6 L2 f4 g7 @n=size(w,1);1 j5 ] t- |7 U
[D,path]=floyd1(w);%调用floyd算法程序
$ l6 X6 Y) j) p) ]! b6 w
& E+ a# h9 s, h& Y%找出任意两点之间的最短路径,并输出
2 `! r) M6 Z$ t* H" h/ Cfor i=1:n
% a9 Q3 W; ^5 @4 |3 n& h, D for j=1:n/ e$ ]: v& p; _8 U
Min_path(i,j).distance=D(i,j);- M3 A* ^+ ?3 ~. I
%将i到j的最短路程赋值 Min_path(i,j).distance# q/ g6 z9 d. Z3 _
%将i到j所经路径赋给Min_path(i,j).path: z) d% C* @9 E/ I; e7 D( L, h
Min_path(i,j).path(1)=i;5 H ^ d8 J; H+ ~+ T% ~7 [) q
k=1;
# U3 N) |5 O! Q- a y while Min_path(i,j).path(k)~=j
/ `% o& r+ h, K# e k=k+1;# Q; w$ J9 `( L! [+ ]# A
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
4 z E7 a9 Z! n, r: \: A end% b' Y# }+ G7 o5 F) p
end
& j% b) t u; H2 C' P+ L$ Q. nend1 `" I7 V7 W0 u( p r% l3 u5 v
s=sprintf('任意两点之间的最短路径如下:');3 h8 [. [# E4 b5 S/ t; d
disp(s);' A4 [2 h, M$ w
for i=1:n
+ p0 f* E, K2 c" A for j=1:n6 c1 q0 g C5 I f- P
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
# s F& t. u3 t6 s ,i,j,Min_path(i,j).distance);1 K2 ~3 W- }% g5 {: l1 o+ A) I0 c
disp(s);
* g- j' N6 P% J* D1 K0 ?8 D disp(Min_path(i,j).path);% A" {1 E8 U; I6 G% \- ^3 f: J
end2 ]. o6 m! q$ o( g; n5 S# E
end
4 F2 ?# q7 ~3 _, e/ n5 s9 O7 [5 p# P3 a S" B4 F
%找出在指定从start点到terminal点的最短路径,并输出/ ~: Y R. b- e
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
8 f* {" L" V: \ start,terminal,Min_path(start,terminal).distance);
" X% s- K5 J' d- q) L8 L$ ?disp(str1);
8 _: \* t2 T; p3 R: A& G5 Ddisp(Min_path(start,terminal).path);1 ?' D3 K7 g$ Z2 y m4 k+ Y
8 x# x8 M! S+ u5 Q6 j6 V. b
%Foldy's Algorithm 算法程序
! ~7 m1 b/ p1 Q' t1 ^! Qfunction [D,path]=floyd1(a)
5 c: k% w# l+ k. O k5 [7 rn=size(a,1);
- v5 }) [6 n U/ A, }0 h/ kD=a;path=zeros(n,n);%设置D和path的初值( f9 F5 G. q/ u3 J e
for i=1:n
# g. u* y5 z; H2 y+ x- F for j=1:n
+ S* ]$ w2 d/ i: B if D(i,j)~=inf$ B! I9 x( a$ p( F8 ^
path(i,j)=j;%j是i的后点6 j# J4 B: x* I( A+ H. V+ _' m
end
( ?' {" r5 v; J, ^# \( c end4 e0 {- I( r+ z+ w- H
end. I Y2 d% I3 N/ Y7 \
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)$ B# ]9 ^1 L8 }7 q5 l) C
for k=1:n
6 Z# C7 ?, x% D( n7 ?) l' E0 s for i=1:n+ s+ ~! y h1 p% G- N
for j=1:n; l0 d" T6 Y8 }0 A. B a/ F
if D(i,k)+D(k,j)<D(i,j)6 ^. a' |! r! @! ]8 a! i
D(i,j)=D(i,k)+D(k,j);%修改长度
7 @2 B3 q" m. S" I5 \ path(i,j)=path(i,k);%修改路径
4 _# ~) B8 O. T" L9 T' n' v) ] end
7 ~2 ^# e& t% c; @# w+ ], V. C8 m- R end- F! ], w C C& P- M0 Y/ u6 L
end
8 u: I6 d! i9 F$ g) ^. F4 Yend
6 q/ I5 V u( o* a; B6 X4 A e6 e* ~5 H. ?. n% G
五 模拟退火算法源程序
" N9 J' d- t( `function [MinD,BestPath]=MainAneal(CityPosition,pn)% A# \3 O0 K q9 W4 ~3 ?
function [MinD,BestPath]=MainAneal2(CityPosition,pn)! P6 |' j% j! B* W
%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( U# D; V% D. c. Z
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...; U# Q4 K# H. m7 W
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
" m! N7 D% z8 v# Q) ~" @+ C- {; }0 D% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;... g$ g( n) X' u( O
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...) ~- t) N* w( T3 R% s( @% ~
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
! H( A; Q' r7 K* p( a" ^
! k! ~9 _6 x' ~$ G. ~5 a0 a%T0=clock" S4 O5 ~. d* n: a+ o
global path p2 D;
[3 m1 s0 B$ t8 w( q" E( W& |6 K# {[m,n]=size(CityPosition);
4 T. K/ ?+ ?. R. e" s%生成初始解空间,这样可以比逐步分配空间运行快一些6 m5 p! x5 f# @% O! m' h
TracePath=zeros(1e3,m);
" H- `; t6 [1 NDistance=inf*zeros(1,1e3);
& [2 ? N- T' _3 Q8 h
. R& u: J& L$ c2 z* vD = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
, T7 \# h$ i4 a3 M4 }8 } (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );& U- [3 n e0 s! ~+ c: ]
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
! m X. B) B$ l% i" l6 Q9 ]3 @2 l$ mfor i=1:pn
# j% A$ T) D. o path(i,:)=randperm(m);%构造一个初始可行解
4 S+ `) M i& I/ {* n7 `' B! b$ Kend
" n- x1 u) d: nt=zeros(1,pn);
3 v- `6 B e' U$ x! P! l& Ip2=zeros(1,m);
& W1 h/ T# _. l5 i
8 G8 `7 J% [& \, J% t' O6 C1 Q$ @iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );$ u9 S# O! m8 b! g7 I
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=' ) ;* f: w2 |8 m0 ?5 Y4 R3 s3 Z
%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
0 J0 P! I3 b* H u' B1 p%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
, Z5 y3 t9 ]2 a$ E%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
% F5 M4 U8 C( o. B- M O! k( l%会收到到比较好的效果/ j* P# X5 T( F
# ^! r, A& S! MT=1e5;1 T7 M3 b' v9 \; s# W5 W3 m6 {
N=1;: w" ^ I; N2 o( \& l- u/ c! t
tau=1e-5;%input('请输入最低温度tau=' );
3 p) q/ n5 V* |2 w5 b; ?%nn=ceil(log10(tau/T)/log10(0.9));3 C, T: p6 H4 U* q8 t
while T>=tau%&m_num<m_max
8 f$ S- A, q: l iter_num=1;%某固定温度下迭代计数器
4 k1 T0 f* ~0 u# { m_num=1;%某固定温度下目标函数值连续未改进次数计算器
& D8 q3 b) r. `, d %iter_max=100;
0 m2 ^! V% F- ]; X/ M %m_max=10;%ceil(10+0.5*nn-0.3*N);
1 D) |% ]. g2 x while m_num<m_max&iter_num<iter_max- |( H5 _- s+ r. o* s6 |1 b9 r/ L+ M
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:8 c2 S1 Q5 R' a- ^
%用任意启发式算法在path的领域N(path)中找出新的更优解
. \( [4 Q {6 l' e1 n for i=1:pn% f5 L, L: M8 t/ p4 S
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
$ K5 H% l; X# q" T9 m% T* f2 c4 t%计算一次行遍所有城市的总路程
" A( `* k5 P. [5 I [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
. S+ Q5 _+ [" ]& A% W Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);2 ^" {9 G0 i% }4 a
end& f) G' v- Z8 ]
%Len1
/ ^: r! S. B# e %Len2
9 H" g0 k; u4 v" v %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
) J, i5 W" f0 w3 W% e- D( F R=rand(1,pn);3 \# F3 S8 z; {' M! h
%Len2-Len1<t|exp((Len1-Len2)/(T))>R
B% W8 H$ S h4 S if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
9 p" |' o2 c' l T* ?* {; z4 B path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
* G9 E( Q9 ^+ d9 _+ L7 A Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
& c- H# N4 ?4 W3 J$ J [TempMinD,TempIndex]=min(Len1);
$ t. N$ ]7 Z2 E1 r* B) J1 I %TempMinD% [5 A. t5 c& D. M/ b, y
TracePath(N,: )=path(TempIndex,: );
. {' Q/ H' J+ S* w/ I Distance(N,: )=TempMinD;
$ f b8 ~7 @2 ^+ r, E N=N+1;
! a. K) Q# t) w. E1 M. \; M9 `. ` %T=T*0.9' d% [5 K. C8 ?! y; G
m_num=0;
' u& i# k8 K) ~1 v) G% q. c1 X else
# J K+ I/ b( V& I: o* k m_num=m_num+1;
) k0 @# @) `" B; W* ^: A end, p; H* }; N: H- S" I' b! m
iter_num=iter_num+1;
' H R P5 {; w6 Y# v L' d% o end
! ?( g; O! N ?& z9 C T=T*0.9
! R: M6 i7 L7 ~%m_num,iter_num,N
4 [1 i$ a R' o5 a% f- S: ?end
8 @; N3 K) P0 R9 ~* ~[MinD,Index]=min(Distance);4 A7 |& j) ]5 z: S
BestPath=TracePath(Index,: );& ^2 F: N/ j, Q6 w6 W, N/ _: k+ u
disp(MinD)- A9 L' K3 Y7 g4 \8 E( |" J: w
%T1=clock
w& P* B5 e9 D) h
/ J3 F" u! ?5 s 4 |$ b& _" E ^
%更新路线子程序 : z- `" k- s$ m
function [p2]=ChangePath2(p1,CityNum): r9 m& s; O% N. F9 o1 O( z2 ^
global p2;! l+ o+ V( ]) M' J6 g
while(1)) G+ O: P/ M: m
R=unidrnd(CityNum,1,2);% j' Y7 l2 S P# D
if abs(R(1)-R(2))>1
) X, J) t6 L. }7 |6 J break;5 K8 E" f4 A/ p! J$ U8 }4 b8 b7 b/ E
end
; W9 `& X* F; nend2 e5 ?9 w: Y k3 h
R=unidrnd(CityNum,1,2);
& z: x4 `) }1 q% h" w% l* Z+ nI=R(1);J=R(2);
2 K6 ]6 m1 C4 v/ [0 M: h%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
9 S, @5 J, j, K8 Q, H" r%len2=D(p(I),p(I+1))+D(p(J),p(J+1));! Q# o% v. N9 l) H% M4 N! T0 m
if I<J
3 | T, q: W. s! v, i; h* K* v p2(1:I)=p1(1:I);
' a& M9 x/ K' ^3 | p2(I+1:J)=p1(J:-1:I+1);
( Z, q6 W; l- z- H( {! X, v' @) O p2(J+1:CityNum)=p1(J+1:CityNum);1 H. v3 {5 E5 y
else! u# y9 _9 g3 z' X" J
p2(1:J)=p1(1:J);, u# ]( b; _% `" |7 T- J0 L
p2(J+1:I)=p1(I:-1:J+1);3 S0 B! Q% m! H% Q/ ]
p2(I+1:CityNum)=p1(I+1:CityNum);% X* }* f: ^, K+ r9 H
end7 @7 H+ Z5 ~7 U" C+ A" Z
# o) b) [6 q% \
六 遗传 算 法程序:
# x! {( f. S: ^' X/ }- M$ |& o 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!6 c5 z$ X) {, E( l( |
) a2 ]; M$ q; S, B: Wfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
7 j/ s9 Y! d3 d' ~% _% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) # a" w/ V+ S% B% s& R0 _
% Finds a maximum of a function of several variables.
( c* I4 w/ W" E0 ?( z6 j" r2 ]% fmaxga solves problems of the form: 2 I7 E2 y# ^: n6 L* o$ I& X
% max F(X) subject to: LB <= X <= UB
" v9 B6 E# E3 d A- K8 o, k% BestPop - 最优的群体即为最优的染色体群6 [2 {3 }7 y2 |" T `
% Trace - 最佳染色体所对应的目标函数值: ^5 D- ]# W$ B, d2 ?
% FUN - 目标函数3 ]0 B. R# y6 V: j9 y9 @' J z
% LB - 自变量下限
- w" p7 T1 @1 e, O% R$ \( Z% UB - 自变量上限; g, g* Z, O. T% i5 f( G; t* c
% eranum - 种群的代数,取100--1000(默认200)
2 G) z0 a5 G/ w r) C% popsize - 每一代种群的规模;此可取50--200(默认100)
+ o* P# K# K7 f; t, H% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
9 H- F2 {- @4 |$ u- E' b2 r* i% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)8 ~5 J. Q# |4 V( C6 `: Z
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)$ n. r6 p7 Q: r, j# q. b
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
2 j: _4 x' M4 p% E+ D R; |%码,option(2)设定求解精度(默认1e-4)
) d) `* g* P Y6 ^%7 \, Z& m, S/ s- S' S M5 o
% ------------------------------------------------------------------------
G' z5 W3 [. C0 f- j( j$ Z! e
0 W- F* H! M$ M/ P, m1 V- ]T1=clock;
) B) r4 n2 c2 Q+ p% k, c1 W O7 yif nargin<3, error('FMAXGA requires at least three input arguments'); end6 @: d8 q8 Z4 m: ], h
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end; B+ x, Y* N" }
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
% e7 j6 `8 F; _2 X( v: {if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end @' f1 w5 \4 _ r/ U3 B
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end5 U6 N$ V) V/ O; O
if nargin==7, pInversion=0.15;options=[0 1e-4];end8 Z; ?. N+ [ {$ c( h
if find((LB-UB)>0)
: K6 C. F2 a* A. g$ x- J error('数据输入错误,请重新输入(LB<UB):');/ Z+ N# F' ~2 c
end
5 P% O( A W/ C% f9 _7 M2 F$ g$ Gs=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));; ?9 U' E' L* }/ W0 o8 d% h
disp(s);
4 Y" e' {1 S0 F0 f
2 w% ]/ V! N; lglobal m n NewPop children1 children2 VarNum) c( [) P: [) O' t) [# W
, Y o+ f5 w- A: {, P$ X, Vbounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
- I, i; q2 e' K* _precision=options(2);%由求解精度确定二进制编码长度0 C# y4 O, v/ z9 b3 c( v
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
8 v# o: G3 O, N[Pop]=InitPopGray(popsize,bits);%初始化种群4 h3 i2 v! a3 y3 T1 U' H, g
[m,n]=size(Pop);
' r, c$ i$ [/ oNewPop=zeros(m,n);
) N2 r) N+ q1 C i Ochildren1=zeros(1,n);
7 s; m3 H1 o3 V6 G2 Z9 S+ g# Echildren2=zeros(1,n);
, E; U6 H* I3 C# A; m" n- ypm0=pMutation;% q5 w. H7 H& d: a- x1 _; A
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
- Y! Z+ C# ]# z4 c c7 L7 r0 M4 LTrace=zeros(eranum,length(bits)+1);
# j+ k! l: S& d, M5 @. Y( Gi=1;
4 e( }$ [* ?* a* {8 M Ewhile i<=eranum
9 D6 u) K4 b/ G! q9 z for j=1:m
% h6 a5 {6 i D8 C value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
8 k' }1 f* |2 H2 T' ^* m* i2 U end9 U9 A; X( X' `) m
[MaxValue,Index]=max(value);6 @' O5 \: c1 Z: H/ J8 l3 u S
BestPop(i,:)=Pop(Index,:);
2 h& R/ |# K( m! P } Trace(i,1)=MaxValue;8 {! m/ |" p4 {/ _# _
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits); r+ J+ X- l# O& `" r
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择3 k( g! ]' A5 p
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));: \8 |1 N+ y: n8 J4 d. w
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率+ e9 l. D* d3 V" v
%round(unidrnd(eranum-i)/eranum). }# r0 ^& e- b2 B0 {. Q2 A0 ?8 i+ I
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异* r- w y6 @+ Z4 p. e
[InversionPop]=Inversion(MutationPop,pInversion);%倒位
+ X7 }/ h5 ~9 _" n- f Pop=InversionPop;%更新. N2 L. E" L2 B
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); ; K( Z) i; M& L; ?! e4 E# d
%随着种群向前进化,逐步增大变异率至1/2交叉率$ {7 K% d5 G5 N9 `5 ]
p(i)=pMutation;
* ^/ x h* E$ ^( y i=i+1;
" W3 t) _, s2 p- ~end
0 P( W+ _) [- \4 e/ a$ `t=1:eranum;
& R% t, u! @1 F3 m* \plot(t,Trace(:,1)');) v6 r; B* O$ t, o
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)');! M! P% h$ T6 A4 i
[MaxFval,I]=max(Trace(:,1));
! L* X2 J5 ?4 O- R- M9 o- K( D- `X=Trace(I,(2:length(bits)+1));
$ B0 Y; C2 Y) v) bhold on; plot(I,MaxFval,'*');8 r& O$ k; c9 z9 g& D+ |* ?$ ^
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);1 z) j' U4 e7 k7 D$ O; p$ X
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,:)));5 p& u6 Q. ]; n1 D5 @7 J
disp(str1);' ~) R8 j% x! g
%figure(2);plot(t,p);%绘制变异值增大过程1 U0 N: A9 }# D& o2 c
T2=clock;
! `: A" m( [2 q$ n8 i# V, Selapsed_time=T2-T1;
/ f( N- L9 N: @ O6 ~: L5 Eif elapsed_time(6)<0$ x7 l% Q$ ~7 k
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;/ n; I3 ~* {# q) ^% a/ n
end
4 j" E' c4 A7 m6 ^/ U t$ P& uif elapsed_time(5)<0
. q2 d. x2 x/ Y1 t$ ~1 ` elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
. ^6 c0 J& N5 T& h3 _3 i4 Nend %像这种程序当然不考虑运行上小时啦
# B: c: i: p7 f0 f! P7 I, 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));
% B% s1 V2 \' x0 [/ i; T3 Bdisp(str2);
+ g4 z% K1 f: O, \, E/ G6 A
3 k0 c4 b: d) \+ v! E7 O2 y& l4 r2 i0 Z7 ]6 f% p) u# _
%初始化种群7 U; r& n3 p3 |& g/ {
%采用二进制Gray编码,其目的是为了克服二进制编码的Hamming悬崖缺点& x. h% O$ w0 a5 n Z1 ~
function [initpop]=InitPopGray(popsize,bits)
* X( t3 x% [+ l( m( U! ^len=sum(bits);
j3 f! T2 s3 I! ~( _' Ginitpop=zeros(popsize,len);%The whole zero encoding individual8 v/ S }( m7 D0 {; b# Z
for i=2:popsize-16 u7 O' ~1 H! D6 N! y
pop=round(rand(1,len));, Q: N4 M% a. v' [0 L3 X u
pop=mod(([0 pop]+[pop 0]),2);9 P, {; |# j/ H* X7 ^2 Z# N8 z
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
1 J# u+ H# B: x' k$ ] %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)9 C# l: Y5 R t6 ?' K/ {4 ?- t S
initpop(i,:)=pop(1:end-1);
: q. u6 B5 A1 Z) jend
) S" T& d! j4 {3 i6 Z0 d3 S( Jinitpop(popsize,:)=ones(1,len);%The whole one encoding individual
6 ?: S+ L5 A* A0 S& v%解码 ^5 s, |1 F5 o
* {! `$ I$ y9 B+ p' q, Z3 J
function [fval] = b2f(bval,bounds,bits)
: p6 c6 ]9 |/ @- j* [4 d% fval - 表征各变量的十进制数
' s E5 j# M! y3 q% n0 g% bval - 表征各变量的二进制编码串
1 ~/ [5 j2 r. \5 Z4 G9 L8 U& `$ \% bounds - 各变量的取值范围! Z) p1 R. e8 |+ d
% bits - 各变量的二进制编码长度
5 f% L, v7 s! `7 escale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables5 C p8 q: ~% D% c
numV=size(bounds,1);- H4 J7 L7 F1 t6 m8 m- x7 b
cs=[0 cumsum(bits)];
/ b0 }6 d& x- y, vfor i=1:numV4 b {* \0 {1 o+ {! e
a=bval((cs(i)+1):cs(i+1));
$ W( J4 S# n+ _5 ~ fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
+ ]! Q1 Q5 P( @, mend
: v: S) X. |: u0 {+ z% U) P%选择操作
7 n0 I$ G% ^* k* r%采用基于轮盘赌法的非线性排名选择3 l) z; y+ D# U/ v
%各个体成员按适应值从大到小分配选择概率:" ^. o+ D( Y4 y/ s G% K& p
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1
2 w& u- H6 S, k9 J+ k# W
* t7 h& l3 A0 L1 d: F s# t0 i/ `function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)' d7 n7 K& J/ l" |% w2 I
global m n
" l; j1 J5 R7 E( V# mselectpop=zeros(m,n);
& i- c& a5 b& A8 Ffit=zeros(m,1);
3 k" n5 p' j1 A1 P4 [for i=1:m
, O- N: N/ E) M0 L7 g) b fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
: J' X# {2 G: J2 d L' s7 qend
% g7 ^& y' F1 X4 @( q, `3 Z6 Nselectprob=fit/sum(fit);%计算各个体相对适应度(0,1) D9 E' @; \9 e; ?/ Q
q=max(selectprob);%选择最优的概率! g2 Q$ j; O6 U% ]5 J
x=zeros(m,2);- Q) [/ `# O, m+ q9 K. y& C S% r: \! R
x(:,1)=[m:-1:1]';
# ]6 W/ ^8 p# H, Y9 ]) G[y x(:,2)]=sort(selectprob);/ k6 S( F* u# e2 u
r=q/(1-(1-q)^m);%标准分布基值
4 h% m, `( A+ G$ g) C! Y' \5 ~8 nnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
9 n1 e1 G* j2 p# d. S3 ^7 Mnewfit=cumsum(newfit);%计算各选择概率之和# m+ [( f5 e6 s5 v
rNums=sort(rand(m,1)); ~% a- S6 r- m3 d* U: P) w
fitIn=1;newIn=1;* M/ `% Z8 X: V3 m
while newIn<=m
j, l7 P; G+ ^: i7 j% I7 ^ if rNums(newIn)<newfit(fitIn)4 ?0 v) b2 @/ I2 G2 I. ^
selectpop(newIn,:)=pop(fitIn,:);' l: i+ H# N* S8 T& u; B, q) S
newIn=newIn+1;
& C9 r3 \& v0 A$ j3 n else' I. k0 {7 ]# H$ F
fitIn=fitIn+1;
: k7 ~% r1 u& h# @$ P end
" m7 D7 T1 Q9 ~ L5 a8 ~end
: t) C7 p. f- V%交叉操作6 B4 d" D% D0 ?/ I$ c
function [NewPop]=CrossOver(OldPop,pCross,opts)
" Z" b; D3 F% F3 G, F3 ~%OldPop为父代种群,pcross为交叉概率
f- b0 \0 H5 _0 y \1 Y6 Xglobal m n NewPop
3 S5 T/ T& p' m& ?9 m9 rr=rand(1,m);
( o0 ?3 M4 P" d# q( My1=find(r<pCross);
! \7 T) ~8 U- w' l" Xy2=find(r>=pCross);
4 k4 {1 A. U( ]1 y% s3 Plen=length(y1);, |; H# U3 |4 ?8 Y% C3 D
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 t( ?, ?9 N( ?1 r# `" Z0 m6 h
y2(length(y2)+1)=y1(len);. ~% P: D- h* C) b/ L, ]/ F6 q
y1(len)=[];
- w' ?/ J" M9 H2 ~' Mend
* P1 p. I- B0 q4 M2 _if length(y1)>=2+ y4 P+ W3 y1 r. u0 I- [) _+ b
for i=0:2:length(y1)-2
+ p. d6 }% _( a. q- {6 [ if opts==0
/ U6 ~: c/ L, H" Z" @6 e [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
* B/ I5 J4 E% F% G: X6 }0 B else
5 Y; ~' I1 z/ O+ V4 G [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
- x4 j( Q% c5 R! F* M0 t end
) C$ B& v; w& l end 7 y) V; H, G. p1 g. z/ l# z
end) h: f$ O5 C& Y" W9 O: m% B
NewPop(y2,:)=OldPop(y2,:);( ?5 z, O' k! j4 x
0 ~. l9 y/ Y; U: C, h
%采用均匀交叉 ) T* t4 |4 r9 H" M
function [children1,children2]=EqualCrossOver(parent1,parent2)
) {; T) K6 c! X) i* n
6 Z6 G2 _( a4 q; `: `: [global n children1 children2 * V& `! M; c1 F+ p, T* J
hidecode=round(rand(1,n));%随机生成掩码& V& f4 ]1 e' W( ~2 x5 k# k
crossposition=find(hidecode==1);" S7 [4 k% x! @" @" d' L" m, u
holdposition=find(hidecode==0);' R& b# F$ ^: I/ Q
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因2 n) ]" D q% q2 s0 t
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因/ ~* H9 N7 H2 F- P4 {
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
8 A. I: L- c3 v7 }% x. S* R- H* j4 Ichildren2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因9 [2 l( ~ v8 G5 i# Z# S- y
( o# e4 p. |) o. N. w4 V* F ~%采用多点交叉,交叉点数由变量数决定
; X# }# }, O+ G5 Q E
1 H8 _! @% j C0 g' @! Yfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2), ~0 U$ N" u& v; y
; R8 F q3 b4 M" \4 K# f2 }$ yglobal n Children1 Children2 VarNum7 P: E8 N( F7 P2 d4 }1 D# [: ?
Children1=Parent1;
* t6 y! h8 N4 Z( n+ S' mChildren2=Parent2;
4 ]' P3 R1 g2 v+ j& P) WPoints=sort(unidrnd(n,1,2*VarNum));
' A& _% R- W/ I% r) d1 bfor i=1:VarNum
- P- ]& i4 c; f" T! Z6 t7 f0 u" h Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));4 ?$ H( V. Q' K0 e% J9 x! z
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));4 f: C7 e9 C7 ~! h6 D
end
E j2 p3 U2 d1 i$ I
9 t, V) n3 X* C/ B0 l%变异操作
0 n! d+ l! g' X! Xfunction [NewPop]=Mutation(OldPop,pMutation,VarNum): T" n6 V4 ~+ k% ?5 C
1 A5 Q; k1 |- ]$ k4 R) g0 _: t
global m n NewPop1 r+ L0 e3 |2 N9 h
r=rand(1,m);% _5 U* q4 }/ Z4 f
position=find(r<=pMutation);0 x* {5 Q# q6 q
len=length(position);
& J k0 w6 f3 W% Nif len>=1# z% D5 F! [+ O5 ]: z' @5 g, @' [
for i=1:len
9 s$ x/ b! y7 E6 ~8 j k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点" l2 f; y- ?) p) R: u
for j=1:length(k)
% V% r" R+ j) Q1 T j if OldPop(position(i),k(j))==1$ K/ l6 f; Z3 o2 w( X1 s7 }
OldPop(position(i),k(j))=0;, w( e! P; ?) L- e/ K
else; O4 Q4 {/ Z% D/ M8 g- h# f* ?
OldPop(position(i),k(j))=1;) m3 t$ C4 r8 k9 B; }
end
! b: V# u5 `: m2 } end0 B$ p: M$ i- `; O
end: h8 {% [1 \2 F6 H' a: y M- p; h
end
4 s1 J+ f& f: p& _' K) p$ PNewPop=OldPop;
# c9 C) m1 x2 r* m% g" K! a$ u, i O
%倒位操作
' |+ A9 |/ ^" c8 |/ @! u
& I% E, ]& @+ S1 i: i, W j$ K* I/ wfunction [NewPop]=Inversion(OldPop,pInversion)
7 D/ @& ~/ y% S0 A
1 y6 P6 t% D& J+ P2 eglobal m n NewPop; U @$ g5 J) D# j% A
NewPop=OldPop;
( O" H0 z" q3 Y* n' k$ Tr=rand(1,m);" j* S, `6 F% S6 j$ j6 k: H
PopIn=find(r<=pInversion);5 s0 N/ y X2 C# z8 T; a9 D8 Q
len=length(PopIn);
! n3 I" {3 h2 a# hif len>=1
* N* t P5 ^9 Q for i=1:len
3 A% d% R" \. y9 Q \$ ?' S d=sort(unidrnd(n,1,2));
* ^3 U5 C$ ]8 {) K if d(1)~=1&d(2)~=n
$ E' X) L1 A' e$ V1 \+ F NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
! T, Z- _3 }) Z# y NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));0 m: `2 q0 F9 w/ ?- y* _
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);5 t" n7 a4 P7 j; X
end
% t) Z! U/ x2 u end
9 F( f. Q' A4 ?/ U- N; pend
$ I- P, X0 ^7 l& U& L0 T
2 n' h# g' g0 ?, X$ y- n+ g七 径向基神经网络训练程序5 n- g4 M+ y0 }% |; y
9 z; Z4 u2 W. Q* G0 V
clear all;
4 `- F% t7 D9 }/ Z' x$ i$ |" rclc;- @! @7 K& G s! l6 e+ E9 x' d
%newrb 建立一个径向基函数神经网络
' k* e o3 z: c$ Y; _8 j3 @p=0:0.1:1; %输入矢量
( S! Y0 f0 ]- s; Kt=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量" H5 N, O# G- C0 y! D
goal=0.01; %误差# H* M+ P* O2 v: W' x( r4 H$ o
sp=1; %扩展常数7 o& m! I! a/ x b) t k: n% _7 H- H
mn=100;%神经元的最多个数$ P) s& X, s* s y3 l6 v) [( O3 ]) V4 w
df=1; %训练过程的显示频率
. \* A' h0 V$ Y6 S9 X: N& n8 j[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络/ o+ R1 o& W( v) P2 R
% [net,tr]=train(net,p); %调用traingdm算法训练网络
6 X: o) U4 E A5 o' I. I% q%对网络进行仿真,并绘制样本数据和网络输出图形/ C( a+ L9 i- J5 V V0 F
A=sim(net,p);
& R" {' c' @, e C9 XE=t-A;1 [) P/ u8 P3 q7 W0 w
sse=sse(E);) P! l# n5 I R( Z$ Q- ^
figure;
: v( P& @! f2 [9 F% oplot(p,t,'r-+',p,A,'b-*');6 `7 [) i0 D% {: z. d$ ~5 E) y8 ~
legend('输入数据曲线','训练输出曲线');
$ w6 h! V1 b& Z9 ~) Qecho off 3 ^: ?6 ?. A5 [" d" C9 I
# N& k) h) z D; n& e" a
说明:newrb函数本来 在创建新的网络的时候就进行了训练!6 t; V$ |) d+ ` J" v
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,8 |1 p3 D6 N+ ~5 F6 {
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!
2 z1 R1 L" w2 A3 y. u, o! M9 p5 G- {% e
5 @7 d8 j$ y, B% {/ u0 I8 o8 V
训练结果显示:
9 s* f- a: R5 [4 e, hNEWRB, neurons = 0, SSE = 5.0973+ j( |: [6 m* Q# z$ G, r. L
NEWRB, neurons = 2, SSE = 4.87139! x! T8 _4 u/ H* v
NEWRB, neurons = 3, SSE = 3.61176
+ l0 J, D6 t: CNEWRB, neurons = 4, SSE = 3.48750 i3 s0 F) i# ]( M9 d6 I U5 Q
NEWRB, neurons = 5, SSE = 0.534217& O2 \. z; d4 |) w
NEWRB, neurons = 6, SSE = 0.51785
G8 T, a2 v2 H/ gNEWRB, neurons = 7, SSE = 0.434259
/ u6 i" f: H+ h7 }NEWRB, neurons = 8, SSE = 0.3415181 P6 h0 a l) S' }% @8 f' ]$ |
NEWRB, neurons = 9, SSE = 0.341519: V7 B. w6 g+ h* m8 R
NEWRB, neurons = 10, SSE = 0.00257832
6 K9 ?3 G3 c4 A' r2 J! B5 X. f% f+ h3 y( W" j% v
八 删除当前路径下所有的带后缀.asv的文件
% D4 j, @1 D3 i& ?说明:该程序具有很好的移植性,用户可以根据自己地# ]: l4 O# d, r5 [4 g s9 k/ E3 p1 Z
要求修改程序,删除不同后缀类型的文件!
0 R9 f* g P! o& T5 vfunction delete_asv(bpath) & F$ V! }5 q: ^0 G" {. X
%If bpath is not specified,it lists all the asv files in the current
: L" d* U' p# J% X, I# I%directory and will delete all the file with asv
& s m8 K% k# ]. Y$ b% Example:
* u. w+ F+ J: X% delete_asv('*.asv') will delete the file with name *.asv;
- q4 Y% |& _4 c% delete_asv will delete all the file with .asv.
6 i' f% S4 I/ B m( Z, m0 g+ B
$ d8 Y5 S7 G6 i% Mif nargin < 1
5 m8 c% ?, |& z0 X: F# E, Q%list all the asv file in the current directory0 I; `# P/ ]6 P- M; r
files=dir('*.asv');
0 R+ {! d/ J0 uelse
3 H0 k7 O6 D* {% find the exact file in the path of bpath/ J! Z0 s2 }2 k* T" R& @5 Q
[pathstr,name] = fileparts(bpath);/ u9 E6 D- s+ H, M& ^3 i
if exist(bpath,'dir')
& w. F$ n5 r; g0 B name = [name '\*'];
' ?+ B5 l. \; B3 t7 S; S8 @ X end
, _" M- o; _3 _; S ext = '.asv';
8 [& f E) ~# N: c9 n: B) y8 U files=dir(fullfile(pathstr,[name ext]));7 K; x8 Y \7 G; G) ?
end
- K' p5 l+ ^7 ?. K6 a1 \" W8 c5 }3 _) g7 r
if ~isempty(files)
& v$ M9 ?8 E0 ?( t. T for i=1:size(files,1)& {& x! b) M5 b) ~. `3 f& k
title=files(i).name;
5 B7 u6 r7 v, c# ?! [ delete(title);
4 p9 f( ?: {& z2 Y1 Z end
3 D/ J/ F# ^7 Y* m4 h! bend
1 f+ m, J" {9 d/ {# T
! K# d9 ?# A) F9 f
" G. `# ~0 j2 F+ }( R* A% F4 y同样也可以在Matlab的窗口设置中取消保存.asv文件! J" X. n, y' A! ]& C, @
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