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TA的每日心情 开心 2016-11-7 00:15
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[LV.3]偶尔看看II
一 基于均值生成函数时间序列预测算法程序
' \% E9 D& [9 k+ C' @; C 1. predict_fun.m为主程序;, _7 b+ A& ^. a: S7 n, M
2. timeseries.m和 serie**pan.m为调用的子程序
b! n! N% a: k0 M) T. ~
: D6 Q/ ]+ g! o H function ima_pre=predict_fun(b,step)
+ w' E7 m# x, T& y. e R( k0 G % main program invokes timeseries.m and serie**pan.m# t5 R k, L B5 r* d, y1 c+ ]& j
% input parameters:! Q {$ J8 M) N1 ]+ J
% b-------the training data (vector);- _* z7 T: m, l; q- j
% step----number of prediction data;
* q! ^1 ]7 {4 a % output parameters:7 \4 x; x% b; M$ y$ B! O
% ima_pre---the prediction data(vector);
1 \! I/ p2 ?7 V; A6 D* B8 y3 T old_b=b;6 ~3 j# ?/ ]) x9 L, K; _
mean_b=sum(old_b)/length(old_b);. e" S" k( R& y$ ^ x6 V
std_b=std(old_b);
* h+ M. L2 v C# M, X& a* { old_b=(old_b-mean_b)/std_b;
1 S+ I/ w- H _. h( N2 p [f,x]=timeseries(old_b);
' w ?' p! Q- X% p, q" {0 N old_f2=serie**pan(old_b,step);
8 T$ u+ e. ^8 d# k* f! m % f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;# b, w" O6 W3 i6 K# x2 S2 O
R=corrcoef(f);9 n! B) A5 r ?6 p7 N
[eigvector eigroot]=eig(R);
: s9 @$ W" ]( N9 ` eigroot=diag(eigroot);
6 Q, P9 H v( e- O a=eigroot(end:-1:1);
9 u9 J6 u9 f* C& d: z; Q9 V vector=eigvector(:,end:-1:1);
# L; g* H, X5 j Devote=a./sum(a);- z4 [ T& L9 z `% L. D
Devotem=cumsum(Devote);* I+ {) I+ x2 H7 C! P5 i
m=find(Devotem>=0.995); ~7 i6 G3 m5 i
m=m(1);
% S' n! ~/ H! w- r t! L V1=f*eigvector';8 c. h- k; A' n% {# U
V=V1(:,1:m);
* ]' V( E. r1 ?* z' F4 a; w$ Z' M % old_b=old_b;& {. z& V ]6 I# ~
old_fai=inv(V'*V)*V'*old_b;
8 K$ f$ p) n8 o5 k0 K$ n, M# _9 | eigvector=eigvector(1:m,1:m); Q# X3 w3 |- c2 i* g: S
fai=eigvector*old_fai;# X* e T' d |8 u. c/ t
f2=old_f2(:,1:m);
# v, T _' [/ ^/ p( k) l. [ predictvalue=f2*fai;
* _/ i; P4 h+ I ima_pre=std_b*predictvalue+mean_b;
8 M& z+ G1 q( h4 j+ I
# d0 A1 F; ?6 l% g 1.子函数: timeseries.m 0 x% n8 |8 @% Z' N3 `9 y
% timeseries program%
/ A7 z1 V! E9 w8 g % this program is used to generate mean value matrix f;
* f( g" B$ E) N0 m- Z' a" K# ^ function [f,x]=timeseries(data) # b/ N2 ? V3 E/ {* R3 [
% data--------the input sequence (vector);
9 `+ j2 X' H9 t0 y! J % f------mean value matrix f;
* F( S) A6 P% N2 l+ k, b& C n=length(data);3 E8 c1 Q6 E5 D0 i
for L=1:n/2: \) Q$ p; a% q! r* j
nL=floor(n/L);% p5 a" ?2 V" j9 \5 o- p) W
for i=1:L2 B6 u6 G# d6 d" S* d! s# D+ c
sum=0;+ u6 X! b8 q3 l7 a( W* [0 d
for j=1:nL u Y2 w. ^3 E1 y
sum=sum+data(i+(j-1)*L);
' r; z- P5 t" e9 e! B end
* q# ~9 o2 m# ?0 m o x{L,i}=sum/nL;5 W% r+ a/ M/ r7 x y d0 t
end+ l8 M9 B0 Y2 D* l9 x: I$ |
end
; W5 e( O9 V/ Y0 [9 u L=n/2;# w& X& U( U. g( l6 Q) T2 L$ e
f=zeros(n,L);( r) f- V% t9 ~& d+ U* v
for i=1:L
* I5 i; B+ u% g" w' E# q z rep=floor(n/i);& Z% F; T2 \" h7 ?% Q* x& b5 a1 V
res=mod(n,i);
% r) r. f/ N+ P) E3 S* G ? b=[x{i,1:i}];b=b';
! F2 E2 C9 w5 d5 U f(1:rep*i,i)=repmat(b,rep,1);1 T' A! j! L$ n) y% t2 H- o/ y1 _
if res~=0
9 |4 X4 t1 l8 r; I' h c=rep*i+1:n;
: j5 o3 J% \& z6 u f(rep*i+1:end,i)=b(1:length(c));
( W4 P* R0 Z, A1 Z% \% B end
2 l Y* p# Y. J" i end
5 F3 ~4 e+ r/ V: I3 }! A3 r. _) b - \6 w, f8 I! t; G1 J6 x
% serie**pan.m
' D9 Y9 T2 p( a, @ % the program is used to generate the prediction matrix f; " ~# n0 q* U% |5 D0 r
function f=serie**pan(data,step);6 T5 ^- w/ m- P4 i* m: f* k' A
%data---- the input sequence (vector)# `9 y0 r+ F" ~$ a- Z0 u( Z
% setp---- the prediction number;
9 S0 |; P+ x2 |& Z: a! p. P n=length(data);
( X. u* ~' J& i. ^ for L=1:n/2
3 r* h" h1 k3 r b, W8 x nL=floor(n/L);
" i5 T& P4 w5 @" A- } for i=1:L: Q% ?- Y2 Q' P p) X9 m
sum=0;
5 Z6 u, P/ A. e( c: d for j=1:nL) p: E( j; R; |4 o) h5 o
sum=sum+data(i+(j-1)*L);: _) F } `9 F* n/ ~
end5 _! [, y( |" t0 e
x{L,i}=sum/nL;4 d& y; u* L/ i9 y( Z
end
6 @. V! r( Z' e# T end4 E. g$ l. [$ k0 @% ?
L=n/2;
# T* h Y( w" j f=zeros(n+step,L);
5 U5 A* A; A4 D# ^' }2 W for i=1:L' X3 {" b$ p: s" J; G. M3 y
rep=floor((n+step)/i);% c" ?3 J! {" j2 X' r6 Z5 k& u7 p1 q$ k
res=mod(n+step,i);
, v' V7 |1 c ]. N) w; I( H# b b=[x{i,1:i}];b=b';2 Z- V3 p9 w, r: J" l0 a7 w
f(1:rep*i,i)=repmat(b,rep,1);
5 T3 p, p# i0 ?. ~8 t+ @9 U( c if res~=0
1 y! f5 ^9 @7 N% ^- x c=rep*i+1:n+step;
5 C, W9 `0 \/ a# D5 r f(rep*i+1:end,i)=b(1:length(c));8 q9 }7 C! v/ q& \ y1 U
end/ o7 \4 [: K( w3 k6 B6 c
end
5 t- Y+ V; J( v( t. J# N3 f
5 v. Q: L) {+ j( g, u6 `9 m2 t/ M7 J 二 最短路Dijkstra算法: D' X0 s' B- I8 ?+ V. s5 H% b5 e
% dijkstra algorithm code program%
$ y2 _% `& U9 s % the shortest path length algorithm* [: C. j6 F3 i6 N
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)! p" _& }2 |% L @7 c9 \# @
% Input parameters:
' C9 }6 s1 ?0 I9 S3 q+ V7 N % Input_weight-------the input node weight!* _3 E+ G3 ?" E
% start--------the start node number;9 E* ~0 J3 _: y: N% p' M( ^4 v
% endpoint------the end node number;$ z5 {) S7 ]0 c
% Output parameters:
/ e0 u; _! m2 [. Y( ^! h e % path-----the shortest lenght path from the start node to end node;' R: ~" `% L" u9 L
% short_distance------the distance of the shortest lenght path from the
6 k0 Q& E8 b# H5 s % start node to end node.% L$ ~* D( {. Z
[row,col]=size(Input_weight);0 c. {( ~; B: N
3 _ F' q* V+ ? %input detection4 U- v# X; l! W1 g
if row~=col/ [0 [$ v/ Y& U2 X3 z% A& N
error('input matrix is not a square matrix,input error ' );
4 {/ m. S* v: C4 @; H! n end
- I* U* {3 t& P if endpoint>row
9 C0 i- K! T& d8 b+ q9 w0 m error('input parameter endpoint exceed the maximal point number');7 D! B$ O1 o1 p9 k0 E9 [+ S1 g4 }
end
% [: Q4 A& ~7 D* f+ G0 ~
% j7 S* R! R5 ~( h' q+ |. X %initialization$ k% [* O+ u; v' O7 ?: c! e) T
s_path=[start];
5 r0 B- D9 S2 ~/ d: t% D9 v9 ]4 n distance=inf*ones(1,row);distance(start)=0;
' I/ A2 w& }. s+ j% V) s flag(start)=start;temp=start;
2 C+ m' C- {1 Z
3 }( `* }; X0 {; J* H$ e& i0 U while length(s_path)<row
5 O4 a7 m) v" A2 w pos=find(Input_weight(temp, : )~=inf);2 S& g' ?' k( M" G3 g; H
for i=1:length(pos)
7 ~1 s, o8 P9 k3 Z2 [, S3 a* ` if (length(find(s_path==pos(i)))==0)&& ~5 |$ b! c& O: l$ k9 E7 q
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))6 v1 I7 j1 D# d/ i: K Y
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));5 @) h4 i) p. [6 P8 a% q0 ^
flag(pos(i))=temp;. p/ @6 u' u0 S G
end
1 N6 }9 R. q& y( j end
: @3 {9 | `5 A k=inf;
0 L4 N0 E" C7 g7 v; T( T for i=1:row
$ J9 c, J2 L0 W1 q) v, W. N if (length(find(s_path==i))==0)&(k>distance(i))5 r" N3 K0 l; o! `# h
k=distance(i);
- E' J* o* H2 T5 T temp_2=i;" I d1 P2 f9 b& o3 E
end0 Q1 X; V& v7 b8 a
end
, b* e: @1 X$ G! L; H s_path=[s_path,temp_2];
4 g5 T M4 F; ]1 Q+ ^+ d temp=temp_2;
8 n" o) b# x( N" t- u6 @4 y end3 a( q0 n2 h! _7 D8 G- {
, X! x7 n/ [0 R- o# E+ | %output the result
7 ^+ O4 f$ {: N$ M l path(1)=endpoint;
- L3 p% t) E' `3 y0 c5 t( q5 V% _8 c, ^ i=1;4 y7 X: t$ S, P5 e
while path(i)~=start
' }" V5 v+ J5 m' Z9 E/ G" T/ q; h path(i+1)=flag(path(i));
7 r: h) z" a2 g i=i+1;
$ b6 i) X% c1 J9 Y2 B; h: q* c end/ N" Q1 e5 F3 F! L; r$ `% U0 z
path(i)=start;
/ X2 G3 S# D$ Q6 j0 v$ f' C path=path(end:-1:1);
5 z+ a% G' Z8 F5 L& z d0 d- r short_distance=distance(endpoint);# e# W7 e& w) A' L* H/ ] j# E
三 绘制差分方程的映射分叉图) F4 E8 h0 f7 b$ u: u. o" A
9 o( a' Y. C# A& c$ e' w8 @4 S8 h function fork1(a); 6 y0 q- E. L8 o0 o$ y% L3 ~
; Q0 J4 E, j; @* c % 绘制x_(n+1)=1-a*x^2_n映射的分叉图5 E0 t$ G; o2 \. R" Q; r
% Example: 0 u9 k5 ~/ }$ N3 |
% fork1([0,2]);
5 a: Q) H; Q. I1 n J8 W9 r( s N=300; % 取样点数 - u& m" z( m8 B+ v" u h
A=linspace(a(1),a(2),N);
6 a# u# s# k5 i: { starx=0.9; / _5 `8 O) ^! c, G
Z=[];' U. H6 E0 f, k! {& I! y3 W: X
h=waitbar(0,'please wait');m=1;- N* Z0 Y& I }+ b( M/ U7 p
for ap=A;
; W# X3 [! W* Z: q# Y0 A x=starx; + C; [0 W% m9 b
for k=1:50; 4 ^0 J' G4 {6 Q- f! ~1 C
x=1-ap*x^2; - L. m) U* W8 b; m) M k! x
end
" E: Q; O" w. K0 C, _ for k=1:201;
) i; d0 G H: S$ n: @, G; i! Y x=1-ap*x^2; 7 n0 D) x) ~3 a. T4 J; T
Z=[Z,ap-x*i];
# T' h p7 X0 ?& ?6 x1 k end 6 G, P3 z2 _- U. d' Q& N3 l+ j s
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);8 _1 l1 z& m( z( r! u% g
m=m+1;' ~$ ^" Z5 Q! f$ q4 u
end 8 q" }/ s( O* ^! ^3 s
delete(h);
7 U8 J H! ^ B+ a plot(Z,'.','markersize',2)
$ i/ Z8 S9 O1 [& ^) | xlim(a);" c5 m8 d+ S# f/ F4 F; Y
. |6 k8 g+ l2 l2 Q, Q* W
四 最短路算法------floyd算法
! |$ R/ z1 I1 F' I' V# \, L function ShortPath_floyd(w,start,terminal) 7 y! Z& m& f9 r( V$ ]
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;0 ]7 d6 z$ b( d, b
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
' y! b7 b5 @. G4 M %start-----the start node;, G- `6 L% R. R9 c
%terminal--------the end node; ; { @, c* u, |1 r! q
n=size(w,1);; Q- \' d0 b5 j- y( G* V. L2 N3 B
[D,path]=floyd1(w);%调用floyd算法程序
/ o+ D- a# _% Q 4 a9 O3 ~5 r3 A$ m
%找出任意两点之间的最短路径,并输出: A3 L' k( y6 A1 A
for i=1:n* k0 p; G5 L! B, l1 C( H9 e! c
for j=1:n% |9 P8 o6 e0 L7 |! E
Min_path(i,j).distance=D(i,j);
1 r. s9 e0 d6 \! \ c j %将i到j的最短路程赋值 Min_path(i,j).distance
$ x8 \4 d) \7 v# }$ Q( i) T# ~ %将i到j所经路径赋给Min_path(i,j).path
. }# E# _+ ~! }6 X5 F6 j& A5 `' W4 c Min_path(i,j).path(1)=i;0 v5 ?9 t1 H5 |. {' R* ~
k=1;
0 b4 p5 Y' y% I% \* v while Min_path(i,j).path(k)~=j3 T1 f! H ^2 }; W& ^
k=k+1;4 g! r# ]7 Q( q0 X
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);6 o9 i4 {% ~& ~* y4 H
end1 Z6 A1 |0 [6 Z6 \9 i4 q3 m0 D
end
, i4 R, a- b8 e6 h% ^4 [ end9 M; F7 v: O3 n o9 ?! ^9 O
s=sprintf('任意两点之间的最短路径如下:');
3 L7 G& ~6 o6 l0 v0 r disp(s);3 ]* M+ M; b4 O. W: U* |
for i=1:n
! y; Y: r2 m1 J! V# \7 d for j=1:n
/ m V% B' ]/ U2 ~, B2 p3 H9 r. r s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
* w7 Q9 {% U; Q; Z' `" s- T i ,i,j,Min_path(i,j).distance);: M: N; O- Q: ?3 G) U
disp(s);# V7 P# R8 v1 e8 f: q6 a3 j
disp(Min_path(i,j).path);
. U a# s+ N3 l6 r1 S. R- i end
% X" A" b% [% }2 P end
' X/ @# f7 e0 s' p+ R
- b+ q! N3 V, B- J$ [; A" X# g. @ %找出在指定从start点到terminal点的最短路径,并输出0 G' R- k" E, S7 c" F
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...9 b( L" E3 d: ~
start,terminal,Min_path(start,terminal).distance);
: w+ q8 S1 u' I1 u1 p disp(str1);
! q; u/ J# L# b* l: ~ disp(Min_path(start,terminal).path);
. g8 R4 }0 @' l3 L; |9 d
7 q2 I# w: C4 `# \9 v: m %Foldy's Algorithm 算法程序
$ {3 c7 X" I7 D9 _ p$ U function [D,path]=floyd1(a)
/ W. r' l6 V1 B n=size(a,1);
; z$ q+ m/ W/ e' _ D=a;path=zeros(n,n);%设置D和path的初值: }; p2 v b9 C% Y; Y7 v
for i=1:n6 w; ?0 N( h# W4 z
for j=1:n
. M( _* r* p) M- a. B+ e( S if D(i,j)~=inf/ g4 R- J7 E' q- W# w5 S
path(i,j)=j;%j是i的后点
3 P; I* S7 D: a& {, j end
" J3 p' r( m: V# M1 h* x; a; G8 z) L end2 C- J4 S# ^( _) _/ D0 X
end
; g6 ]6 h# l( v6 p %做n次迭代,每次迭代都更新D(i,j)和path(i,j)
! p' Y) l4 O) f3 O9 L/ @ for k=1:n. V9 B8 }8 g0 f, `
for i=1:n8 B3 l( u) Z' \( V" J, O- d9 W
for j=1:n: f7 |+ L; A' g1 L2 h. W# o% C
if D(i,k)+D(k,j)<D(i,j)
+ m/ Q& x% }9 Y( l3 l D(i,j)=D(i,k)+D(k,j);%修改长度
% j1 x% |9 F5 o$ I4 s. i% J* s path(i,j)=path(i,k);%修改路径1 g" A: v" K/ ~0 y
end+ {6 q4 X. `" H" U+ X0 K/ c
end$ S" n' ^' V" D. b0 d
end3 B$ S* C0 M" z/ i) ]
end( I* a# F* ?) {5 |+ W" E
( a1 `( U6 o/ x$ x& e 五 模拟退火算法源程序5 b1 r# O' J0 w# J
function [MinD,BestPath]=MainAneal(CityPosition,pn)
. F2 e2 A& U+ J1 u9 _ function [MinD,BestPath]=MainAneal2(CityPosition,pn)
* `7 W* v1 O9 Y+ U %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
8 c" S% l0 M* m %CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
q. X6 L, X4 ]+ K- x % 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
/ P7 b4 d$ _3 y8 i) c2 A % 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
9 ~% L8 @, \4 m, B# N7 i6 E, u % 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
# W* x) o, I! H. s0 \9 k % 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];& j- {) X7 B1 V! J4 A0 w/ w
; O2 u7 p6 s% j$ e7 a2 e %T0=clock4 {" b" u3 k. y L' B
global path p2 D;7 O2 U* t" V1 ?7 I/ q: F2 E
[m,n]=size(CityPosition);
: e% R* A* I0 K5 m$ R %生成初始解空间,这样可以比逐步分配空间运行快一些9 z; l8 g0 l" X0 u N0 o0 E) W3 e
TracePath=zeros(1e3,m);
. p$ S% `, z# I4 P/ b0 w: R Distance=inf*zeros(1,1e3);
/ w( V) ?2 v; r) p; |) f3 c
- k5 ]" O9 X( P D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...# A' K7 S! v# ~* B7 g* C8 d1 T. i
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
* i, L- ]% h, g! X %将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
6 ]2 M4 X1 `$ I for i=1:pn1 M' ~: X; j7 V5 |
path(i,:)=randperm(m);%构造一个初始可行解; y7 K3 F) s @5 J. s
end1 t1 _8 X8 V8 z5 I/ L
t=zeros(1,pn);! Q6 }6 c7 z6 X; c, K* g: ]
p2=zeros(1,m);. J! W# _7 t9 Z2 [5 r0 d# m" f9 d
/ J+ g) j2 b7 x }( k/ J; G" {
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
* J% p1 J" h7 | 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=' ) ;
$ V1 V( p+ a }# O %如果考虑到降温初期新解被吸收概率较大,容易陷入局部最优# |6 V8 S4 q- `4 ~# k3 i! A' c! n; {* k
%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
$ D/ s0 K1 p- I8 T( ?% D" J %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
- K2 S8 m3 n2 A" P, C( x( n ` %会收到到比较好的效果
7 O: o; X( e# R. u7 ^ " ^* o3 r0 M; W' V% c
T=1e5;
) D b8 m- ?5 b2 J1 ^ N=1;
4 C- L# {" r6 A" k8 ~ tau=1e-5;%input('请输入最低温度tau=' );
/ [6 u4 U+ p. \; d/ V9 w( d* v %nn=ceil(log10(tau/T)/log10(0.9)); B& C& O; e# J# Y
while T>=tau%&m_num<m_max 3 {& `- ]3 [/ Q: v' ]
iter_num=1;%某固定温度下迭代计数器
8 x9 {( h6 B0 M( T+ F- b- o* @ m_num=1;%某固定温度下目标函数值连续未改进次数计算器8 O3 D$ b$ U, O: \# j& D6 N
%iter_max=100;
6 g7 ~, | {. I8 o/ D& U %m_max=10;%ceil(10+0.5*nn-0.3*N);2 m) M: v/ V& h# l$ w3 t
while m_num<m_max&iter_num<iter_max1 o; d1 t9 p9 V9 A! B+ E; z( f
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
X8 I2 F/ r* C& E/ y( [ %用任意启发式算法在path的领域N(path)中找出新的更优解
) w2 O$ y" ^* e2 s1 d$ s" n for i=1:pn( F. e4 j) d# Q( c2 Z
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);/ N4 V) S1 N# p: D$ m
%计算一次行遍所有城市的总路程
3 j0 ]# w* e8 D: n3 H3 j [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
9 ?( p1 q! l* g; v! k. Y Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);- Z, w4 I0 |. A' Y. R
end5 _& R$ R: [8 c/ Y, H! ~+ r5 d
%Len1& T) J* Y7 |$ ?, Z
%Len20 x% C& g+ E G3 S8 ^( ?. [; f
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand: c9 r# Y' o- Q7 U% T
R=rand(1,pn);
' b, U1 l% m' S/ {" V+ v4 z4 [, | %Len2-Len1<t|exp((Len1-Len2)/(T))>R
. j3 q- a$ i5 e" q. ~' {' m+ \ if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)+ Q7 Q2 e6 n1 B6 E" S
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
, {6 X7 R% [% @1 ]+ {7 \8 O' o Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));$ t4 I* @ f$ y* D
[TempMinD,TempIndex]=min(Len1);) | R8 k6 `/ E5 Z, {+ x
%TempMinD
! c* W: r9 a/ U1 y7 b d2 ? TracePath(N,: )=path(TempIndex,: );( L* m1 B* _- a2 m' Y* @6 G
Distance(N,: )=TempMinD;% e: H5 i8 `. F" l8 S
N=N+1;
: f u% J' s! S; n7 v %T=T*0.9' X2 z2 j" u: h9 d- P$ ?8 ~
m_num=0;2 Q# _; U% r3 N- q
else
! L9 J+ r! D- h; u3 k1 R' \ m_num=m_num+1;4 x: o2 i; B8 q# z. ]
end
5 T8 `, B" O" }6 |2 r0 a iter_num=iter_num+1;- }, \0 l9 m* f, j% ^% a
end
% N9 R7 a, x: g: {" l6 b, ~$ z9 B T=T*0.9
5 \- P% d3 C' Y %m_num,iter_num,N
# H+ N/ [! @/ V7 X end
3 _3 u" T0 P* D" H, l1 @3 I [MinD,Index]=min(Distance);
. j& S( }+ F2 Q( I- C BestPath=TracePath(Index,: );
8 ]7 B# f9 A0 `9 z n3 a7 k4 x disp(MinD)0 w6 ~3 {& L& ?0 Y) X0 L
%T1=clock! p1 a4 k6 d% f, x- Z! ]
F4 o4 U5 b/ J Y! p& f8 U. v- x- F
%更新路线子程序
0 A& I( h' l9 r function [p2]=ChangePath2(p1,CityNum)$ ]; i3 O, h- w4 _
global p2;
( j J( L: z0 l) p3 H9 w while(1)9 j: V! U3 ?5 B; A. ~
R=unidrnd(CityNum,1,2);! W7 _" M( \# A( f- X J
if abs(R(1)-R(2))>19 c& M3 f3 q' \* }! n
break;
: _, v u4 u' S end
0 x. H/ J* |$ `' S5 x( N: O+ P end. D Y! T$ N+ U5 i& \
R=unidrnd(CityNum,1,2);1 [& w8 L4 r1 c& p, O" e
I=R(1);J=R(2);8 y6 ]/ \8 n- p8 f- [+ T
%len1=D(p(I),p(J))+D(p(I+1),p(J+1)); S6 a: {2 ?" V
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));' B9 e( o2 i$ l: C3 a- {1 @1 l
if I<J5 B7 R0 [; [9 X1 X/ z
p2(1:I)=p1(1:I);
8 `+ O1 k- N% ?6 d p2(I+1:J)=p1(J:-1:I+1);/ s% i0 ^+ U8 |3 \ Q) F- r
p2(J+1:CityNum)=p1(J+1:CityNum);
0 D2 j0 }' i& x5 h2 y! u' W else! `! Q2 S p8 M
p2(1:J)=p1(1:J);( g7 C9 T/ V* _ h9 z# N
p2(J+1:I)=p1(I:-1:J+1);
% N1 a" f P) z( g3 A9 i p2(I+1:CityNum)=p1(I+1:CityNum);) A- f k. O5 l( b4 q
end
4 y" c5 J3 l/ S2 c: C
2 ^ j4 [8 z9 @4 H0 v. B. E& L9 g 六 遗传 算 法程序:
* P! n# t7 ?1 Y p( x9 c# r 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# m" k0 x9 Z0 N6 j - J- U2 c# H% a1 l
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
" M. F+ J- `3 t3 f7 V4 h1 ~3 v % [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) ; e7 N* E0 }, m- M# ~. f
% Finds a maximum of a function of several variables.4 w! F# a6 E! B3 j4 J- }; I U) i
% fmaxga solves problems of the form: - f, B7 n, v: b# e7 c0 b" X! W
% max F(X) subject to: LB <= X <= UB
6 X) o" a' }/ O# v6 s+ V( ^ % BestPop - 最优的群体即为最优的染色体群- Z7 d# e1 F: | ~) x6 `8 t
% Trace - 最佳染色体所对应的目标函数值
; G* o6 Y6 w5 d4 {5 q! X3 R0 C % FUN - 目标函数) l6 X k$ s+ ~% V3 B! Z ~
% LB - 自变量下限
/ K" K4 g, Z7 w' f M0 N J % UB - 自变量上限
" Z% |& {* W* d2 |- V; O& V# [ { % eranum - 种群的代数,取100--1000(默认200)
+ d( g" i! V$ h$ J1 Q, j % popsize - 每一代种群的规模;此可取50--200(默认100)8 I. @$ F5 h; l. s
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
+ A0 J( a8 b( [/ ~ % pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
& P2 M! Y# R# G5 n* H3 E % pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)' M8 I1 b. Y' r' R9 F
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
3 c( N) Q, p, ^6 d7 j %码,option(2)设定求解精度(默认1e-4)
{2 B2 m6 W" l- A0 j4 S- `- X %% e/ R. N1 F. A; \, |+ V
% ------------------------------------------------------------------------! C: k3 a# T5 K) g J1 c& i
! k1 u1 }. I0 Z1 X2 z7 F
T1=clock;0 L0 \8 B: Z- i6 n
if nargin<3, error('FMAXGA requires at least three input arguments'); end$ {4 [8 y3 |7 v9 d; E7 O7 H
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end0 N5 B4 T, B2 _4 r2 [; D
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end8 X! C" T' n9 r5 P
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
3 h$ G" Q s: S; S if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end" q7 b9 ?2 x0 {, g" R) H
if nargin==7, pInversion=0.15;options=[0 1e-4];end
0 e5 `2 P( V6 O" o% U3 R6 y if find((LB-UB)>0)( s. ^ C8 w! J0 }1 j
error('数据输入错误,请重新输入(LB<UB):');+ E" s2 D! R0 @' _& X* g7 w
end( z9 y7 K( \$ G' i+ {8 b5 T8 Q
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));7 A0 e" p( M: L" z9 y' C5 t
disp(s);5 s# ~" O4 v' X" D$ \
2 q1 L+ m. k0 v( e" e
global m n NewPop children1 children2 VarNum4 g5 Q! P: y8 P' v- X, r
3 X1 M6 J) Q/ ?* ?( c( R, J bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);2 w4 x/ p8 K% c" {% N' h# g
precision=options(2);%由求解精度确定二进制编码长度1 Q7 x$ H" w; F0 a: M4 k
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间7 D5 } n; W' W. q! Y0 o& d
[Pop]=InitPopGray(popsize,bits);%初始化种群1 E- {+ J" l b' ^: ~
[m,n]=size(Pop);. o* T/ X) k8 v1 ]7 H1 x, W& j
NewPop=zeros(m,n);
" t: @% N. r& I/ m+ k2 Q0 h$ H/ U children1=zeros(1,n);4 I/ H- V) g& E# e8 u5 p, p
children2=zeros(1,n);. ^& s8 ?$ T" Y3 ^. `3 o$ f
pm0=pMutation;
" U4 b f# |0 O4 |3 ^* j5 G1 {& U BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace* ^: @1 }% [% L& D
Trace=zeros(eranum,length(bits)+1);1 i: _3 M2 f6 X' p. R5 i6 R
i=1;
. ]& `5 a# P% o1 |1 j while i<=eranum# p# g3 k# F& x) ]/ y1 a+ T
for j=1:m
# Q" ~8 h# D7 n% E. l value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
& S7 {( D# G4 ~ end
- `) C* m8 ?2 k1 l+ k+ u, _ [MaxValue,Index]=max(value);
1 I4 ^* [+ P+ R) Z/ B BestPop(i,:)=Pop(Index,:);
8 I, `" R: L5 E- T& E4 Q; j Trace(i,1)=MaxValue;
0 D2 W7 M' n6 J4 L% x% f Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);$ _) y" Q$ E- T
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择4 X% d- e% r* B- o8 B
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
/ Q8 @/ n6 M+ x2 j %采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
! g8 {$ P0 G6 `; r1 c8 t: H2 X %round(unidrnd(eranum-i)/eranum), z* J- j: o Q) |
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
+ \' j! K& ^, e [InversionPop]=Inversion(MutationPop,pInversion);%倒位
. ]( o" D; F$ E; A Pop=InversionPop;%更新
( f$ q5 w3 B9 B" Q' m* j0 {$ t. u pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); . r- ~7 f4 x. w* R
%随着种群向前进化,逐步增大变异率至1/2交叉率 I3 F4 i0 B K9 N7 r
p(i)=pMutation;/ A) }" v/ X0 @! U; E0 ~ F, w
i=i+1;1 F- h! X- k) h# S: C& H0 C0 j
end
$ z& v8 i2 F" t, e0 F7 i9 I t=1:eranum;
9 Z" a0 K" I) ?( {" G2 G) H plot(t,Trace(:,1)');' ?1 N4 _) P0 u
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)');$ l1 @, Z1 r5 M& u3 o; V, c8 u( F9 w
[MaxFval,I]=max(Trace(:,1));
0 W" W3 O' B- |- E {, u l! R$ f8 ^ X=Trace(I,(2:length(bits)+1));
# K: C/ H+ }; W5 ~ hold on; plot(I,MaxFval,'*');# |0 q$ \! s r* j( _
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
% K& [+ }/ W# ]) e& L/ I- }2 l str1=sprintf('进化到 %d 代 ,自变量为 %s 时,得本次求解的最优值 %f\n对应染色体是:%s',I,num2str(X),MaxFval,num2str(BestPop(I,:)));
7 @% W" O9 ^3 ]0 Q, C# H1 C disp(str1);
& t ^' A/ @# Y2 o G7 b( i& d %figure(2);plot(t,p);%绘制变异值增大过程+ s3 {, U& ?0 C! K) a
T2=clock;& [% K1 v( o' r& {
elapsed_time=T2-T1;4 ~: r5 U" l- \3 |
if elapsed_time(6)<0
, }$ ^% M4 o/ O$ o0 c8 H elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;9 L2 Q1 A: |# E4 R$ f
end
$ D4 \* q3 \& f, q/ \ if elapsed_time(5)<0
* v6 E+ s0 [* f4 w8 v2 u- t# h2 x elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;4 N* t7 Z1 r7 k6 T; ?" D
end %像这种程序当然不考虑运行上小时啦9 H+ _9 P3 A9 @% S4 E- _
str2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));0 h4 ^2 e" g6 z4 l" R' P o
disp(str2);& ` t8 ?% O$ P
& B# ]" L, P! \/ i' V
: q; Q4 F7 F1 j %初始化种群
) @2 i P. L G" {9 J %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: G5 |1 J4 n: h& A/ t& c9 Q4 v. X
function [initpop]=InitPopGray(popsize,bits), T( v, }7 @7 Y2 B
len=sum(bits);
0 I5 v& _8 ~7 O2 Y! V initpop=zeros(popsize,len);%The whole zero encoding individual
/ g1 | {! e1 m& l7 ?; u# A& N+ E for i=2:popsize-1( l, x1 d r: P {" B
pop=round(rand(1,len));0 S( h# @' C: c$ f M- E$ ]
pop=mod(([0 pop]+[pop 0]),2);1 ^# F0 ]. w2 g
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
2 F/ m6 ~* ~6 i( O' T k" @; F; R %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)( ]1 \ Q3 u) C4 b: D/ h4 s% f
initpop(i,:)=pop(1:end-1);
3 J. [- v' R; b! R end5 `3 n3 T/ c6 R0 p& |
initpop(popsize,:)=ones(1,len);%The whole one encoding individual. o$ N# B; @6 H& b+ q
%解码
4 g4 |7 K, Z3 E
# d. m6 {' B# o$ l: _9 p' K function [fval] = b2f(bval,bounds,bits)7 Y3 W! K( A% B& `2 d' k
% fval - 表征各变量的十进制数6 K9 ]$ y3 y$ \- M# q4 p8 o2 Y
% bval - 表征各变量的二进制编码串
+ C* B: v& F/ @3 @& W % bounds - 各变量的取值范围
! g( ~5 M; }) @1 S0 V5 D, u % bits - 各变量的二进制编码长度$ I( G7 q# q5 r
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables+ ^1 C! i2 d; V- G, w
numV=size(bounds,1);9 I6 p' X& x* x, l4 t; u# _
cs=[0 cumsum(bits)]; , ?0 U5 A* }& |9 P& i
for i=1:numV$ M/ m9 p" d' X+ A* o' T
a=bval((cs(i)+1):cs(i+1));
/ {2 W s6 |" g; E fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
: a/ y1 z* r/ O end1 X2 h; I1 }& W) X5 \
%选择操作
* r9 q- P+ x. t: n- {& X; ? %采用基于轮盘赌法的非线性排名选择
/ b* X5 U* g4 g/ R+ \ %各个体成员按适应值从大到小分配选择概率:
5 e9 {( ^9 E J8 R %P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1& R* D; D7 D+ E3 ^& }
0 m, S; U( _5 I: V9 B. M
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)- c4 @/ U- D, }1 W, x/ L
global m n( d- H1 g0 U: P; a2 O
selectpop=zeros(m,n);
! R8 _7 H |! q2 g4 @* K fit=zeros(m,1);! @! Q( n$ w1 R1 R! G7 a
for i=1:m
- G: G, L9 q: Q% _6 g3 ] fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
' }6 j( {7 |7 ]* g9 L* n- b+ ` end
7 O. n: o7 R: o; @! z7 s3 n, s selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
@% e; [/ N, t L$ D! h* M) F q=max(selectprob);%选择最优的概率5 P3 \! f% S) H B
x=zeros(m,2);+ L) S/ o' H' v- b
x(:,1)=[m:-1:1]';
5 O; e, G; F- O [y x(:,2)]=sort(selectprob);
+ z0 n$ O% V; ~6 e( G' a+ _ r=q/(1-(1-q)^m);%标准分布基值
, n1 B: g- }9 W newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率9 T' V& ~: m- X# L
newfit=cumsum(newfit);%计算各选择概率之和7 N$ e- w/ s5 v, m
rNums=sort(rand(m,1));
% _0 p% z4 U# m: e6 j6 k" l4 s/ P fitIn=1;newIn=1;$ }) e7 A1 `8 d) \
while newIn<=m: c1 G7 p/ j& w b2 G0 M6 k
if rNums(newIn)<newfit(fitIn)* K+ V; a/ x3 b6 j5 |
selectpop(newIn,:)=pop(fitIn,:);8 g1 D% t" W5 v( r: ` X
newIn=newIn+1; V9 ?# H: g. E
else
/ Z$ H( o! y7 n* k& I* W% ^ fitIn=fitIn+1;1 @ k: O3 V/ C6 v q
end
4 k4 R$ U- D1 `# m. b end% G3 D" o) q3 I) t$ b# ?$ m
%交叉操作
V2 V* ^% X9 ~" H6 T function [NewPop]=CrossOver(OldPop,pCross,opts)
5 R6 V3 B" X# K' m! h) }. Z %OldPop为父代种群,pcross为交叉概率
' J9 }/ H8 s7 g global m n NewPop 0 k z8 ]; l. ?- e' B% Q
r=rand(1,m);
% @/ {% ^/ j; t0 e6 e y1=find(r<pCross);. r& W# Q+ p3 ?5 b
y2=find(r>=pCross);
# F+ `; V6 m0 I9 h1 \ len=length(y1);7 p: T* [4 y& E4 A+ w, W: l& ]( [. ^
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
$ }/ X5 x1 ?' I+ \5 c y2(length(y2)+1)=y1(len);; \6 i8 _" O; G$ o' _
y1(len)=[];" z+ R S3 R' Y- l: ]4 t
end
5 k/ d- E$ i+ J. L$ j4 C if length(y1)>=2; G2 f. Z5 _9 i% h6 t8 g, R
for i=0:2:length(y1)-2+ i& c& K! C0 Y3 l6 u1 M
if opts==0
* s% ]! |6 [4 o' a8 W* ] [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));3 Z* ?4 ~1 S3 H* o+ g6 P _
else$ ^$ z+ F3 ^7 q4 r/ {( ]; M
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
. [8 s, P8 H, l: S% W; |, m* u& G end
) C5 R" k' K; c end * p' q$ b& b" |2 s: c
end" | i; J! p- x7 T" U/ y J: w
NewPop(y2,:)=OldPop(y2,:);
$ v2 q2 h2 p+ s
" U, I: C5 `$ J: l %采用均匀交叉
9 N4 R8 t7 _% S5 H3 m function [children1,children2]=EqualCrossOver(parent1,parent2)
4 T" ~/ ?/ c* p" r* F. L% r1 B* r0 [ 6 v/ L) s" S, M( ?
global n children1 children2 ! _) @) i, y2 z+ @5 Z% G( n; W4 r
hidecode=round(rand(1,n));%随机生成掩码
. Z9 k( g/ R t crossposition=find(hidecode==1);9 H" r5 _( H# o, b/ Z* d
holdposition=find(hidecode==0);) r3 G, q8 K& @5 E
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因/ G3 B: y+ m& g
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因" C( S$ L( i0 N6 _, d$ M
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因: g% j2 J0 f, e2 T( {
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因- ^; M* c( n5 o1 ?" }- D ^! Z
3 l; c, u- Z7 m/ H M3 }) V" Q
%采用多点交叉,交叉点数由变量数决定
" ]+ g5 S, c* U
: q& p& o) C5 d1 r1 X function [Children1,Children2]=MultiPointCross(Parent1,Parent2)
# S5 l7 G! i5 M! @* `
4 s$ x" }% w2 P- Y h global n Children1 Children2 VarNum, d2 q. e0 n# Z; ]
Children1=Parent1;
9 d* M) s% S6 _' G Children2=Parent2;
: u& g# Y6 }8 Z" C Points=sort(unidrnd(n,1,2*VarNum));/ A, v* i, ~6 `
for i=1:VarNum
3 K, l1 @7 v( q( X. ]. |2 T1 f Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));/ e$ t: r; S* X& _3 Q% F
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));. F# P( L8 i: D7 T# D# Z
end
8 u3 b' J* t% K2 y9 C, R! n# K 3 m' M7 [2 }' n2 j( J- v
%变异操作; R5 `1 [. u7 `% ~% ?, w1 H
function [NewPop]=Mutation(OldPop,pMutation,VarNum). t+ C. o! F9 |* D+ {
/ ^1 N' \5 {$ c- |+ A% i' e global m n NewPop
" [) J+ M# \% I5 U- a r=rand(1,m);
r( ], p! l! \: d position=find(r<=pMutation);$ [8 w+ I* h: b& D- t
len=length(position);* t( {2 H( ?0 C
if len>=1% z) u$ W8 ~' O+ I3 T
for i=1:len
% S: s! @2 Y3 ~- w$ G* N k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
: _7 O4 k/ g# e for j=1:length(k)/ ~( w+ [# t4 b% W
if OldPop(position(i),k(j))==1
1 i" Y: X2 h* d& C1 P OldPop(position(i),k(j))=0;3 E8 q& O4 @7 g# X* I8 F) P
else
% N) `: ?* K0 L0 @5 u OldPop(position(i),k(j))=1;
8 A7 E( Q J! k1 T7 Z: ^6 ~ end+ A0 Y9 `2 p& B$ ?
end
- |6 b& j& o! O0 M- ^& A; a end4 L# k8 w! A' m/ {- Y' Q
end
2 n0 o, T8 ]7 C; Y& g o& K NewPop=OldPop;2 f0 p# i! N I, @
0 Y1 v9 R: c6 P3 G0 C$ i0 E %倒位操作
6 S7 s8 Z1 |+ ]. a
+ p& V' J4 b9 e; a: l function [NewPop]=Inversion(OldPop,pInversion)+ x. b) X" j8 w& }. S4 w
' M# B% U9 M5 K1 q& R/ S0 y
global m n NewPop# G: Q6 r) e: V# m- \2 ?% {' d! _& z
NewPop=OldPop;
2 S( t @" N( ?/ ^& S% q; S/ `+ V r=rand(1,m);* w3 f( i: D7 k7 r4 a( M) d% l2 T+ ~
PopIn=find(r<=pInversion);0 {( x( O9 b: s. L0 T/ }
len=length(PopIn);% K3 p# k6 C+ H
if len>=1; \$ ?- t/ K; o5 B
for i=1:len& n, @2 g- _6 e! c7 A3 y/ E
d=sort(unidrnd(n,1,2));4 _$ d0 ?! v, @; f" [- g3 ^3 I& Q
if d(1)~=1&d(2)~=n4 k# Q5 ^" B. D( J; D% u
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);5 C/ n/ {1 V* n8 U4 c% i1 D7 E
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
' m# @! @1 M$ @ h2 E NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n); W. ~! e' i6 p% v1 F( p
end
5 @* H5 [' J' t6 x# U end
8 C& O% K0 d. v0 C end
4 A: B! y" O( s" ~ O+ c2 Z
5 `4 A0 b8 C; |1 a& Z4 P0 o# c 七 径向基神经网络训练程序3 T$ x1 B0 f T* [" s- n
9 D* Y" g# f' }$ h9 y clear all;
) p. `' ]. D$ \* f! P9 q clc;
+ F3 @4 _# b: t %newrb 建立一个径向基函数神经网络
$ u3 U9 d1 r h6 P2 F; }* p% ~ p=0:0.1:1; %输入矢量
8 W$ L6 B7 z9 x2 X t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
; g5 d# W3 v1 k. x goal=0.01; %误差
3 w1 a8 c* f1 p7 W s7 y; l sp=1; %扩展常数" ]4 V0 w/ c* {; c/ ]
mn=100;%神经元的最多个数 p+ D* ~1 ]) p7 e
df=1; %训练过程的显示频率/ k2 ? y4 E/ ~1 `$ j: e& K5 M
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
8 l3 O1 Q1 z' ?0 k % [net,tr]=train(net,p); %调用traingdm算法训练网络
9 @: J# |- W9 L4 ~* m %对网络进行仿真,并绘制样本数据和网络输出图形
; V# ^3 C+ ^- q A=sim(net,p); ^+ w" f% s) Q, `
E=t-A;+ n7 a% z& t/ r# }3 O2 t
sse=sse(E);
( o- S8 f- a) j0 o figure; , Y2 a3 U+ d( h! @8 f1 F
plot(p,t,'r-+',p,A,'b-*');
2 m9 J9 k) ]5 h legend('输入数据曲线','训练输出曲线');
' w! O% @- u% w8 X8 z: S$ ~5 T& q echo off
- K' `1 z( D! U) p' `( z
4 C5 k! M7 ~& B/ m1 e 说明:newrb函数本来 在创建新的网络的时候就进行了训练!; F& p# ]6 ^1 I' Y
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,/ t( h- A( G! ~3 R- i- ^9 V
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!
. I G: E0 ~3 i8 L9 K & y% }' S! y* `
% \/ U, f( G9 C- _+ f 训练结果显示:! e; D9 e; x y5 @, U+ ?
NEWRB, neurons = 0, SSE = 5.0973, ^( C$ u8 @& }1 H
NEWRB, neurons = 2, SSE = 4.87139
, @% ?8 `) r0 H; w R. w NEWRB, neurons = 3, SSE = 3.611767 J6 T! P) c, s2 m: h
NEWRB, neurons = 4, SSE = 3.4875
' Z8 Q; Q& U: e4 J9 h NEWRB, neurons = 5, SSE = 0.534217) G* g! J( E2 a4 P ]1 T
NEWRB, neurons = 6, SSE = 0.51785- u# N Z$ M; i0 K
NEWRB, neurons = 7, SSE = 0.434259
( I. n' R$ [( k! i5 F NEWRB, neurons = 8, SSE = 0.341518' r7 f( u, s/ E' p9 r" y! g! i
NEWRB, neurons = 9, SSE = 0.341519
" |3 [, D! r. m- l+ e# B5 J# a NEWRB, neurons = 10, SSE = 0.00257832& t- @) U& [1 ]
4 e3 `6 L4 b$ \6 J4 v 八 删除当前路径下所有的带后缀.asv的文件
3 w8 n% G6 \) L' r4 c3 ~ 说明:该程序具有很好的移植性,用户可以根据自己地
* m l$ A1 v/ ]( U) V 要求修改程序,删除不同后缀类型的文件!
( ~% q: d2 ]! z function delete_asv(bpath)
! V5 W- D; ]: i% b+ J0 E %If bpath is not specified,it lists all the asv files in the current! k/ W- s, _. v- @# s( L! l% @
%directory and will delete all the file with asv ! B; G; B b8 N( n2 u6 p0 p. r6 [. P3 a
% Example:% a, R& h' C& l- o$ n. i
% delete_asv('*.asv') will delete the file with name *.asv;- J0 J9 U% R7 A V. f/ ]
% delete_asv will delete all the file with .asv.8 I: E: {4 P& C& _: Y- m0 Z. ?. T
0 O* W$ i$ c0 f F) g" e if nargin < 13 ?. z3 J/ _! G2 o$ }! M
%list all the asv file in the current directory
4 ]( ]: K) ~& r5 ~: X) U2 m+ u files=dir('*.asv');, D! l) d/ o# a+ S0 v7 \& ?; b# V6 d5 c
else: k" \" g) G! L
% find the exact file in the path of bpath
+ z" b( Q' ^2 ?! F5 [ [pathstr,name] = fileparts(bpath);
9 b1 H6 r) _; D# m* r8 _0 G if exist(bpath,'dir')# m4 \2 Y3 d5 h
name = [name '\*'];
6 V- ^2 P( U1 o" \) s$ g end
7 G# P3 e& x) k, C, c ext = '.asv';, R5 w& N/ @" @0 { i I
files=dir(fullfile(pathstr,[name ext]));
7 a9 _+ V# ]" y1 c% J end
# K5 V; G8 p' }
. y9 u; B2 C/ B' D- G5 f if ~isempty(files)
9 t' d, v/ _) y" s1 P+ o for i=1:size(files,1)
3 q( _- d1 l) s: ?4 B( N$ H title=files(i).name;
% J8 { Z8 r7 T, [4 [ delete(title);9 M a5 w. | N) o; d i: B. x
end: ]2 u; B1 l- v
end
* G0 c- {" x$ a- ] 3 h" _/ E/ B$ _* ]# @ O W
3 S. [+ A3 \: n/ P8 @
同样也可以在Matlab的窗口设置中取消保存.asv文件!
2 g$ R( D5 D: I# O. p0 M- h
zan