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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; F D& \3 ^$ j
1. predict_fun.m为主程序;# `+ P' a. M$ j! F
2. timeseries.m和 serie**pan.m为调用的子程序
" b c/ X0 r& H, h$ y5 N! N9 ^; X
- k/ I$ S) N2 {: ^" j function ima_pre=predict_fun(b,step)1 _3 E1 v3 ]' p5 Q$ F
% main program invokes timeseries.m and serie**pan.m1 g& F7 N; [2 `( o2 X4 f% R
% input parameters:7 u' `- J8 n- c. v3 v$ ], `
% b-------the training data (vector);
. g. u$ Z' H% u* x3 Q% Z+ Y % step----number of prediction data;
0 m3 Z: @$ _: d % output parameters:
/ `& {- z' @! ^- G; v+ b % ima_pre---the prediction data(vector);
0 F6 u; P) [- E old_b=b;
# C1 ?; ~) Z/ Q! a, H: q& O$ N( d mean_b=sum(old_b)/length(old_b);
+ Q2 p) G) m. K5 l std_b=std(old_b);, O7 i" g G8 s
old_b=(old_b-mean_b)/std_b;
! X3 y; e9 E. y2 V2 ?. x5 D [f,x]=timeseries(old_b);& A- E# \& f2 e' X# y) w" K/ j: b
old_f2=serie**pan(old_b,step);8 A2 C: h' b5 b. F* g' h( o
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;( x) f6 m Z3 T2 R1 _. v6 }
R=corrcoef(f);5 p/ i2 t7 |& q. m5 I' l3 @5 Y
[eigvector eigroot]=eig(R);1 |, @, m. x' x* T/ W* B/ ?/ U
eigroot=diag(eigroot);
8 ]) k+ u. g; K a=eigroot(end:-1:1);
9 W2 x3 h- U/ y- j* h2 o0 h vector=eigvector(:,end:-1:1);
; J, E* H6 G. [; K) s Devote=a./sum(a);) b! F9 o x0 k% y
Devotem=cumsum(Devote);- C2 G2 h7 D( i: U$ n$ x. b# ]4 q+ a
m=find(Devotem>=0.995);: ]; r, Y6 v6 B
m=m(1);6 t7 j: b) B+ w- x' S/ j! r! D
V1=f*eigvector';7 v2 r& y% z+ c) q
V=V1(:,1:m);
3 K0 J0 J. w3 c7 C0 b# g % old_b=old_b; z& C- d V( F( w
old_fai=inv(V'*V)*V'*old_b;0 b7 T3 u4 ]; p: T# T
eigvector=eigvector(1:m,1:m);
K3 g. B; d, U; Z# X' f( \ fai=eigvector*old_fai;
) t( n3 l( R7 C, _; F+ i# q f2=old_f2(:,1:m);* Q, F% B. t. {. ?' i2 P
predictvalue=f2*fai;% F) P7 s/ u$ i
ima_pre=std_b*predictvalue+mean_b;; y1 m1 T9 O; t0 v
: F; y, Z1 }5 d J6 ]! z4 p, O3 s H2 V
1.子函数: timeseries.m
^$ y3 B1 U' |' } % timeseries program%; V" ~, V4 w+ m& b6 q' H! E
% this program is used to generate mean value matrix f;
, x4 B8 s) @) z: P1 k: \1 s function [f,x]=timeseries(data) 9 T0 g5 V0 d$ J; h( o
% data--------the input sequence (vector);# Q, ?6 A, b2 G. q: O
% f------mean value matrix f;
) _' u! K; D2 t8 O4 } n=length(data);
! P, [: h. N9 a; P" Y- o for L=1:n/2, n/ S& s2 y* e$ _0 Q/ D, U5 O
nL=floor(n/L);2 l4 @& m4 c' [
for i=1:L
# Q3 @( j$ K I0 q" ~$ g sum=0;% h) M0 q0 e3 n4 P) |/ ?
for j=1:nL
& o O5 k, p- }" l& W* u sum=sum+data(i+(j-1)*L);
4 l% D/ L4 b* R0 j+ w( j end
+ Y) |- J* _) u, t0 A% A( w x{L,i}=sum/nL;
( v/ ]5 L @9 ~1 L' h1 d end4 Q- H" A3 s/ F' `. D& r
end
Y: S# s2 q& e: | L=n/2;
$ y' Y: y% l1 I f=zeros(n,L);
) N3 F, M7 O" o+ m for i=1:L4 d4 ~+ F) O c# w$ H
rep=floor(n/i);
7 e! G" p! r/ B) e; D. ]+ O res=mod(n,i);% y5 B! p5 J0 u5 z3 W
b=[x{i,1:i}];b=b';
! v! C, K( E! P6 c* d f(1:rep*i,i)=repmat(b,rep,1);
/ Q8 a2 ?/ a! v" ~7 r3 o6 ~& \5 c$ m if res~=0! T, P/ G- X! a/ B( m* S
c=rep*i+1:n;
, q2 O4 f3 F2 `6 V1 F. o0 _) p% Q f(rep*i+1:end,i)=b(1:length(c));% B; ?5 W) S# A! {
end
- i2 K% _# a$ w/ t end
" l. T r; x% X4 X6 ~
8 _. y. c% r2 f( h: z % serie**pan.m$ b+ F% H/ Y! x
% the program is used to generate the prediction matrix f; 0 C2 @$ Q7 Y' ]# X% O$ u) a
function f=serie**pan(data,step);
( @( b, g/ k1 g0 U1 F6 b8 ~ %data---- the input sequence (vector)+ {2 b. _/ m) V* K+ Y+ S
% setp---- the prediction number;4 {; b8 E B$ H3 H" S. t+ ~
n=length(data);8 D6 T6 w6 S% H! W, r* E! O3 R$ l
for L=1:n/26 z3 q$ e! A2 N* \. l
nL=floor(n/L);' z) O2 N" y4 [$ C
for i=1:L1 g7 C2 v7 Y/ [# K! h
sum=0;
) c: z+ p! P' ^& q for j=1:nL
/ b" S3 `3 k: L1 Q4 p! ? sum=sum+data(i+(j-1)*L);) j3 x3 \3 \% U+ h, J, t. ]4 U5 i
end7 k9 M7 V1 g3 S1 J+ A
x{L,i}=sum/nL;% R- S1 U+ V: [
end
- ~8 _; J6 ]0 `( N( e end' n5 k# X9 F' v2 T; Y7 f' V
L=n/2;$ ^% J% o0 L: R- u" I% S
f=zeros(n+step,L);" ]1 y2 A- C% p) e$ I
for i=1:L
3 Y7 l) @- N. s" ]4 w. c rep=floor((n+step)/i);
) @/ L+ b/ j% \- X4 { res=mod(n+step,i);
! y8 P3 u( f [3 c3 e& D b=[x{i,1:i}];b=b';8 w& K1 H. h3 s% u& ^( U, C- j
f(1:rep*i,i)=repmat(b,rep,1);2 D1 c* f. N5 N$ f' h
if res~=0
! E4 W3 g) N6 A" m6 X) E" ^ c=rep*i+1:n+step;# q) S6 j- t% i }
f(rep*i+1:end,i)=b(1:length(c));
5 n/ H5 v1 j1 v end
0 l8 {9 v5 \/ v8 E3 P' x4 f G; _ end
8 A( q" M+ ?7 h) b 7 G, W& ]3 P1 A f, I2 X
二 最短路Dijkstra算法
R; F* v' f: I. @; e8 f2 U4 s' S % dijkstra algorithm code program%- _ h0 c6 y& K
% the shortest path length algorithm$ T7 v' I' r. F* G" w, R
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)5 s& u _ M& d4 I) r4 J) o7 O' @
% Input parameters:
: R) N* Y/ D! z- f( w' X0 A4 \ % Input_weight-------the input node weight!% A- W5 y& E) r% f
% start--------the start node number;
4 k4 O! u, _8 @3 s % endpoint------the end node number;# x$ K1 s' t" K8 L
% Output parameters:& }+ F: |! ^" W4 C% G' z+ v
% path-----the shortest lenght path from the start node to end node;
0 _- T/ H4 ~. s' } C; Q6 V % short_distance------the distance of the shortest lenght path from the
. r! `% U2 z- K6 U' R$ y % start node to end node.
1 b6 x$ E* [- M- n t [row,col]=size(Input_weight);
% Z: B) z, ~0 ]2 p- h$ } & w7 c0 r$ i- v2 k0 Z
%input detection
) A) P0 W& n0 @% _- c if row~=col
0 ~- r2 S, w7 u0 h error('input matrix is not a square matrix,input error ' );* c: k _9 S G/ Z
end
5 ]+ ~( j0 J: C( [ if endpoint>row4 j' l- L* W. q; _+ [
error('input parameter endpoint exceed the maximal point number');
0 i, D6 H/ B) L! \ end
* Y) z" I; C/ s+ {
" L3 p( @! |+ i6 n( ]: \ %initialization
; ? P! r8 ^' y s_path=[start];) F* E# w" }" N5 o& B% W1 p# l
distance=inf*ones(1,row);distance(start)=0;/ e J6 K! S' P$ {! x3 \
flag(start)=start;temp=start;% E B4 y1 D7 B# t% A9 H
; c6 P& E9 P; t. _( t9 j) N n
while length(s_path)<row
, ? P0 A& `' m" a4 H/ J( U pos=find(Input_weight(temp, : )~=inf);
* y* C9 _* [. l* R8 X for i=1:length(pos)
4 h$ N: `7 ?8 \3 i% p/ T if (length(find(s_path==pos(i)))==0)&
4 z2 ?! J3 x& s- T* u, c5 p (distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
$ P' {% A0 U: _9 ~+ t! X }- R7 X' \ distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
! D3 [/ V& i5 D- o flag(pos(i))=temp;
1 p7 `- j* m2 I end
0 F# n: P# `% P2 F: \# Y end
, X; ^ H* B8 n3 A' ? k=inf;! ^0 h2 _! s# b* h. A0 ]
for i=1:row
) q$ V n7 \1 F! ^ if (length(find(s_path==i))==0)&(k>distance(i))
! ?7 Z" N. A' X1 q k=distance(i);% @6 I: T8 H/ g! t- E' R
temp_2=i;
/ }8 ~5 _; Q1 T: W) D" f end
9 i2 o+ R5 P9 }' ?: t6 H end
V0 N0 Q- ?8 C( k! P& {- U% ?# F s_path=[s_path,temp_2];+ b6 C# H: m9 N6 ]% w
temp=temp_2;
, M* T& _. H1 n8 N0 x8 y7 h& u$ T end
0 l F1 M/ @/ Y0 |$ a/ s, { * `. p" B0 M# j0 X* D3 c+ ?6 L
%output the result
. o$ V2 t# q. w. ^* V: |' B path(1)=endpoint;- z" U0 H3 ^& ^) \' c8 H
i=1;
" V8 q! [% N; _+ U% H; \4 ?* b3 X' V while path(i)~=start
: ?2 J: f, n& [; k, Y7 c path(i+1)=flag(path(i));
! O- }9 h3 Q: e i=i+1;
+ t3 u" ]4 `! E k( o$ o9 C end) ?5 O5 d" z0 p$ _
path(i)=start;
: Y+ c1 E2 X, \$ Y# v path=path(end:-1:1);
/ `& v( s3 f, K9 Z short_distance=distance(endpoint);9 r& X7 V/ ~" ^* m! A$ `
三 绘制差分方程的映射分叉图
& F7 `0 y; n/ n$ B. C
8 t# v5 ~. E7 n function fork1(a);
, x3 J! o: _' N$ C3 l% Z. R - m+ k( N$ i% z5 y
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图0 j* e V4 N) D4 f* X; g' q
% Example:
5 C# D* o5 S0 F % fork1([0,2]); 9 B0 a2 W( W* ^8 B. E( o
N=300; % 取样点数
; r. c* K1 K5 Q( z, }* [! ^ A=linspace(a(1),a(2),N); 8 S$ v9 ~4 }9 c" j, {
starx=0.9; * t/ ^/ {* J+ S( T$ _
Z=[];
3 ?5 U0 K1 w5 i8 Q h=waitbar(0,'please wait');m=1;2 Z9 T+ A* n q
for ap=A;
) b9 a0 V1 G v+ ` x=starx; / t6 i) S" k5 O
for k=1:50; , P1 j8 j& h/ a! C# b. n K1 _
x=1-ap*x^2; 3 I0 \9 ^ G, ~9 x+ Y
end
. i& V% H: d: E; d) e for k=1:201;
" V: g3 L0 l) A. c& s8 p0 z x=1-ap*x^2; 8 U8 E3 @$ _* f/ B% M
Z=[Z,ap-x*i];
, W4 g& ^ c2 O& i- K3 H end 5 M* C" v) b* i) `; W
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
7 H7 I* B* w1 z0 ] m=m+1;5 D9 C( O. ]9 n" Z' ?
end
% z5 ]( D0 R' h! Z3 }7 |8 B delete(h);2 Q1 r" n Q, W" ^ r+ N+ X
plot(Z,'.','markersize',2) ' a& T, a; D$ }; ?7 F5 S; Y! `4 i8 N7 G
xlim(a);
1 ]- P9 ~8 O5 X- |) d/ K 6 [9 Z/ b+ g& A
四 最短路算法------floyd算法
0 B5 Y/ a7 c3 Q/ F9 ?" C! a function ShortPath_floyd(w,start,terminal) 2 g1 r4 |5 N( x% Z/ x
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;4 j4 T2 g! n0 c7 |, y
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
* W, l% w5 E) I5 d! }+ t# h( @" P %start-----the start node;
6 \+ g+ W; L- f. u %terminal--------the end node;
. p" C* J# `9 M' r8 _# J n=size(w,1);' o6 M( J8 K2 q/ Z/ E* [- {! p
[D,path]=floyd1(w);%调用floyd算法程序7 _8 y$ d$ c) F% P$ D2 q# I& a
9 d+ i& Y7 ]) C* C' z( w, L %找出任意两点之间的最短路径,并输出3 @# b$ A" n Y% {
for i=1:n1 z- S4 u @ P- d* C
for j=1:n& T4 ~' n. L+ W1 T& x# U
Min_path(i,j).distance=D(i,j);
, ]9 v7 X. ?6 T& ] L3 s: \ %将i到j的最短路程赋值 Min_path(i,j).distance
6 W% D0 s/ ?, S4 y$ u% y9 } %将i到j所经路径赋给Min_path(i,j).path# V% \1 L& y9 O' r2 j) }) q+ @
Min_path(i,j).path(1)=i;, s n3 g& s; X i; A
k=1;
. D3 G. ~3 A6 T1 k8 N% V8 R0 p while Min_path(i,j).path(k)~=j# x1 j! l2 W0 {( S# J" Z" t; i& C
k=k+1;
) R- k$ z' u4 `5 X. H Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
0 x9 i7 O0 T2 q* S* [5 W/ i* M end
! a9 o0 I( b7 T' ^; s" U! @ end9 k1 }/ j+ u7 W+ ]. A& g
end0 o% I0 P" u& z& f/ Q1 s
s=sprintf('任意两点之间的最短路径如下:');
& k. C# v; j# |/ ?; ]8 {9 z. ] disp(s);
: A2 K. s& R& G5 S. f1 \ for i=1:n! C& V, G9 e" X3 [; N
for j=1:n
& k) N3 |( ~4 X- m s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...6 ^ B+ Q, E0 ?4 H; ~* }' _( u
,i,j,Min_path(i,j).distance);
0 i% D' d! @) j( [ disp(s);$ E" C' l8 c& H) m! T' y% W
disp(Min_path(i,j).path);1 s$ ] K0 v2 @+ w
end( H( Q1 O3 [; ?) k2 q! m6 D$ Z
end; M5 S3 e- a: y
`# o5 X* Q0 q# ^' y %找出在指定从start点到terminal点的最短路径,并输出
. y9 I: O4 z" V W str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',.../ d8 h1 V* e* L5 T" S1 \* x
start,terminal,Min_path(start,terminal).distance);7 ?2 k+ l' m7 Z1 v n
disp(str1);
9 ^' a( L! `( h) q( |6 f- f- A disp(Min_path(start,terminal).path);3 K) i. p5 P# i
% }, Z8 u! @6 `7 \# p- P W+ \
%Foldy's Algorithm 算法程序
, P* }5 c' X! B, y H function [D,path]=floyd1(a)
W- `( _: u7 d/ I! { n=size(a,1);
6 @7 x9 j& \) v& k. e z& v4 O- _* K6 }2 {4 A D=a;path=zeros(n,n);%设置D和path的初值
5 }. y. Y# b, ~5 a! M& A) D8 j* s9 T1 J for i=1:n
1 a8 i) D, ]" f. Z1 T' w/ e for j=1:n! S9 M: [" M9 L5 o2 y
if D(i,j)~=inf
3 ?7 E. {3 H3 G path(i,j)=j;%j是i的后点
. I( w1 I( x, L4 [& M end5 T; e$ T+ s) A' m* q+ o; p
end& t+ J8 e& b- o6 R) N
end
9 N. K7 G' X1 k& s% W1 I y5 ^4 ]- B9 j %做n次迭代,每次迭代都更新D(i,j)和path(i,j)
/ P/ s0 ~ ~( K for k=1:n
: y! O6 ~9 u" h for i=1:n
& q/ s" `# d( r$ N for j=1:n
. g- V, Y2 L1 G5 x; i if D(i,k)+D(k,j)<D(i,j)/ I. r& _2 a3 \- |" I \9 c
D(i,j)=D(i,k)+D(k,j);%修改长度
1 F/ W, Y$ W+ I6 z# k path(i,j)=path(i,k);%修改路径* B0 \; w4 V$ O
end
5 W0 D$ y# F# ?' o end8 \2 B* I# ^2 I# U3 P
end
2 r/ _2 t+ F5 S1 Q end7 f; b) U& Y9 H
% C) p# K) | m0 Y5 Z 五 模拟退火算法源程序
) M: e6 e/ t6 R2 a; } function [MinD,BestPath]=MainAneal(CityPosition,pn)
( I; U- u* @. @. r6 r% n+ \ function [MinD,BestPath]=MainAneal2(CityPosition,pn)
/ o# p6 m. i/ f( f1 O* V( y+ Q0 j6 s %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
) l3 {* Y: ^) X' E7 Z- ]6 L %CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
% P4 k5 F) a8 i4 D. }3 O % 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...$ `8 i j$ V8 G. g: X% _
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
% N- `) o- f) d2 x+ q x % 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...9 G: ~# {. K, j8 N
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
. U) b! _( X' q
+ ]7 b7 d0 C4 R A. C! m %T0=clock, _$ B2 ]' _: O/ B0 S
global path p2 D;) z0 b: @% D* J$ j
[m,n]=size(CityPosition);4 n& o3 d2 ~7 X( G( _
%生成初始解空间,这样可以比逐步分配空间运行快一些! \; j4 L* C5 k- X5 P
TracePath=zeros(1e3,m);+ V0 R3 r0 L8 d3 M: F s- N. k- p, N
Distance=inf*zeros(1,1e3);# i8 @. g% h3 M0 Y$ U: ?
7 s7 Z. I+ g& g
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...$ A/ s& s; u3 r$ A* i! r( c
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
$ x. H6 }5 s$ h3 P& y %将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)6 o: G) E+ g- F7 o; t& U$ k% a" d, C5 o
for i=1:pn
8 r% |, [: f' K% q! c0 _6 E# V path(i,:)=randperm(m);%构造一个初始可行解- M; `* a) g2 m* d) a6 D
end/ B9 a* M( ~( J' |- v) C1 Q
t=zeros(1,pn);& K6 `. {( x( X8 B/ G
p2=zeros(1,m);5 f) S9 g! B# Y3 |* _+ ?
+ Y1 F; n0 X7 S: F7 p! `5 D/ k! e
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );2 p$ @$ y% O# s. B1 K5 Q! O6 l1 ^7 u
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=' ) ;
; j6 p& B+ A, m8 q %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2 k/ I" e8 F' `7 _2 f) w! k" O, F
%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4 {$ `- a1 z" {! y. F
%人为的使初期 iter_max,m_max 较小,然后使之随温度降低而逐步增大,可能
q& s3 a- u9 W% e %会收到到比较好的效果2 N. F1 |" P0 `4 |. [
2 ]' P% M: L2 z) e
T=1e5;, O7 G% m: p9 v1 b0 z0 K& j
N=1;) y6 ]- {% Y" F6 g
tau=1e-5;%input('请输入最低温度tau=' );+ i: ` p* q8 _
%nn=ceil(log10(tau/T)/log10(0.9));* S; T" e9 M2 H' |* n6 w
while T>=tau%&m_num<m_max
' c4 V8 ]- p! V. e iter_num=1;%某固定温度下迭代计数器/ K/ q6 o' ~2 F, G& g7 m6 t
m_num=1;%某固定温度下目标函数值连续未改进次数计算器
9 Y$ P" N' P8 M9 W+ H8 a, W5 ^" B %iter_max=100; ~2 ]( q( e9 J7 X( Z; V- B' U
%m_max=10;%ceil(10+0.5*nn-0.3*N);
4 K. V! Q j' b while m_num<m_max&iter_num<iter_max
# h3 M8 V6 V" X$ v6 z V %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:5 o; R; c, t4 G" Z+ j; X9 I# S
%用任意启发式算法在path的领域N(path)中找出新的更优解2 {3 X$ z: t3 ^( e. F, S+ T5 X$ k6 i! _
for i=1:pn9 J1 R+ ^0 |, q
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);# G, s6 I6 ^: i/ H# p
%计算一次行遍所有城市的总路程 / u/ E" F7 Z' c* s
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
! M% q* O: M F- t5 [9 l$ N Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
! |5 [! J- T3 _5 K end( `" t9 S, x" t! c
%Len1: M3 e0 T! |6 ^
%Len2$ l% t, n. ?8 h, O
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand# n+ r: J9 q& Q5 V
R=rand(1,pn);: v8 Q& d% x* L5 r7 n
%Len2-Len1<t|exp((Len1-Len2)/(T))>R
$ i; L- M( M/ Q if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
9 |+ u/ ] v! F6 q1 a path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );4 O: C/ p+ j ]" z
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));- W8 d. b8 n" C7 b
[TempMinD,TempIndex]=min(Len1);) v" u' N2 {* ^
%TempMinD
* f, I5 A5 n, p TracePath(N,: )=path(TempIndex,: );
" G2 p/ {( T0 y H Distance(N,: )=TempMinD;
, ~- O2 f+ D2 w! Y N=N+1;8 z- U& i: @" M/ L5 K
%T=T*0.9
! v5 f3 Q, Q( z" \& c2 I m_num=0;
# a8 M6 M6 K' O. C! D* ~ else
8 x# c4 `8 J, G! V% Y m_num=m_num+1;
2 b# J" t- p' r2 y end
6 U% S! M a' I! _5 j iter_num=iter_num+1;
' o. {+ {, Y C3 a( G end* F2 k& a# R5 J( y8 ?" j
T=T*0.9
3 J9 W V& o! g9 r! S1 [7 N& Y" I %m_num,iter_num,N
: z4 [- t5 Y' h4 K! J7 L/ t end * b8 l9 D$ Z% O1 P2 ^: ?
[MinD,Index]=min(Distance);% T( @' `) u" U) T v
BestPath=TracePath(Index,: );6 {) O3 v2 t' s, s9 e" f1 \: y
disp(MinD)
7 ^! t T+ I2 Q+ v %T1=clock
% d5 Z! d/ i/ z6 F
]( t6 z4 T7 e& L
. b1 |( Z. T/ ]( ^) ]* @ b %更新路线子程序 ( a L) s; a& n9 ]9 [% M c# S
function [p2]=ChangePath2(p1,CityNum)
]4 K$ m# H! q9 N global p2;9 ^, Z5 c2 b$ a+ ]
while(1)
" j! N5 g* D$ \, V# A% o R=unidrnd(CityNum,1,2);
$ t1 I1 Q* k0 n; f if abs(R(1)-R(2))>1
1 W( S" }; q# }, |- A break;
' y( x; h9 }% `+ U end
9 k4 g5 i* D- T1 C5 \9 u/ z end0 D7 }1 o% z1 n/ x; L2 W
R=unidrnd(CityNum,1,2);
6 X& C* H: c, d! U& V I=R(1);J=R(2);
& w4 O* Z! y6 T %len1=D(p(I),p(J))+D(p(I+1),p(J+1));% v8 T/ N* I7 H/ i; _+ b8 T( m
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
, e% X: Z( Y, L2 ?$ x if I<J
' O6 k, G/ ?; F3 M p2(1:I)=p1(1:I);
- j! W5 {3 c' e p2(I+1:J)=p1(J:-1:I+1);4 h) K2 x. L, N! e. e5 w/ Z
p2(J+1:CityNum)=p1(J+1:CityNum);
9 O5 l" K3 `. P- ?. |) Q5 ~ else
1 ~3 M1 M4 ^: r+ N4 ] p2(1:J)=p1(1:J);
* o+ S) F9 {7 u$ Q& D p2(J+1:I)=p1(I:-1:J+1);. O: L2 c+ y# u s/ i- X" J* R5 N
p2(I+1:CityNum)=p1(I+1:CityNum);8 ] B% @! m5 z
end, Y3 H! o& N0 O. U2 \+ g& |
8 B: B1 G \2 ?3 \0 d
六 遗传 算 法程序:; b5 i1 I/ K# O( a
说明: 为遗传算法的主程序; 采用二进制Gray编码,采用基于轮盘赌法的非线性排名选择, 均匀交叉,变异操作,而且还引入了倒位操作!
! X( w$ T; X, q5 z5 h& d7 H , d+ G; M& B n
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)4 u# H+ o' `$ J) O6 a E0 ~
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
. o6 V1 F; k- W" k, V % Finds a maximum of a function of several variables.- B: s$ s' X3 d; Y; g r
% fmaxga solves problems of the form:
8 O# s( V1 L- W % max F(X) subject to: LB <= X <= UB
! a; o' r" ~3 c" @' ]; M& S % BestPop - 最优的群体即为最优的染色体群
1 ?( L+ f% \4 \' V' ?" H % Trace - 最佳染色体所对应的目标函数值
+ n) f p6 F. j7 J' ^ % FUN - 目标函数/ a6 {! l" T+ q, E
% LB - 自变量下限/ M L9 K/ a6 G
% UB - 自变量上限
5 s1 P( ^0 Z7 C! y6 |5 x' v7 ] % eranum - 种群的代数,取100--1000(默认200)/ `( [6 ^+ d: t/ M, ^
% popsize - 每一代种群的规模;此可取50--200(默认100)
) e- c8 c: [# Y( B* h. @- q % pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)7 P7 E2 m; H2 e' _* B. M
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1), ]4 S7 s+ P0 H5 h. W9 B
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
: M) x" R! s, V8 l- W( G+ { % options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
! S9 t2 h4 }# | %码,option(2)设定求解精度(默认1e-4)
7 c$ L& o. h6 {! `* j; n6 n %
9 _/ H p, p- y7 o/ G% P; d % ------------------------------------------------------------------------
# T! O3 S* [- |! R" A ; v% A3 f7 {5 T: Y% e' B
T1=clock;* N8 L; s2 K% U5 z+ d- x
if nargin<3, error('FMAXGA requires at least three input arguments'); end% w" a( O6 ?& [5 }
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
: Z$ X7 x3 F) T! Q3 T& p& M! s' O2 N2 S if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end& O2 Z+ g. {: o9 \
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
# F/ i8 j% Z: ]: [6 i8 \! q if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end1 d$ m& `2 ?# a8 q8 D' a8 b
if nargin==7, pInversion=0.15;options=[0 1e-4];end
& d r8 z% ?1 W: `6 z l if find((LB-UB)>0)) V: e, S- P* B* j/ n; V2 g" j
error('数据输入错误,请重新输入(LB<UB):');' Y+ G' B6 \& {) |
end' a0 K' W% C8 _3 n( W1 F* ~
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));* j% I% E: h) e
disp(s);
+ p2 r" p) Q% a( m' z
, i! ~0 D3 b8 s" m% |" D3 \9 D; s global m n NewPop children1 children2 VarNum+ U1 j Q0 L5 P, U+ ^4 x
9 R8 X9 \9 q# q8 A# i. q+ W bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);3 Z* ]9 j6 c; C3 y) ^7 t @% Z
precision=options(2);%由求解精度确定二进制编码长度" a, R; v* W* [8 o @
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间) ~& ^% ^5 y o+ d0 u* J
[Pop]=InitPopGray(popsize,bits);%初始化种群2 w/ _ e0 l; K/ S
[m,n]=size(Pop);4 a* c; v& Q& V6 R' a1 i- a7 D- ~
NewPop=zeros(m,n);
' I u7 D! `9 e. k E8 S children1=zeros(1,n);
% i( `! m! r( b/ f$ U children2=zeros(1,n);. _1 e5 A( }" [) b
pm0=pMutation;
1 T& d4 L5 H/ w: \7 |- d: k BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
6 s7 o: A& G0 L3 i/ f Trace=zeros(eranum,length(bits)+1);- a8 g* E; `1 c( A3 E
i=1;
/ ~8 ]9 k2 b1 v% E: c) I while i<=eranum, L1 s: E4 E4 `0 ^3 B
for j=1:m
4 b% T+ k" Y$ ]) b value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度* q( [" H, K' T/ D
end: }1 l5 y1 H* [4 F1 V$ [* g( {
[MaxValue,Index]=max(value);6 J) j& D+ ^0 @" n) \0 v* n
BestPop(i,:)=Pop(Index,:);
2 n0 L& V, Y3 Q) A! w B- g Trace(i,1)=MaxValue;
# Z- f5 \, ]; \$ y Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);8 j: k' o) p' j+ z9 w8 E V
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择- o J" A6 y( O$ @
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));. t4 h3 Z5 t7 b' F5 X6 f
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率: _/ a0 ^1 t9 F/ Z9 c0 J# A# w
%round(unidrnd(eranum-i)/eranum)
" Q7 t- j ?' | [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
3 [5 D( D) b" i2 V* y8 z, G3 q [InversionPop]=Inversion(MutationPop,pInversion);%倒位
* u0 Q/ y. q- e# {4 Y' M Pop=InversionPop;%更新
# F) B& f# D. N4 U7 B) z; c3 ` pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); ( r; M7 J+ y8 v |- d
%随着种群向前进化,逐步增大变异率至1/2交叉率
3 X* d; J/ X2 q9 W3 {+ d: o p(i)=pMutation;; |) U2 c% ~! M
i=i+1;/ ^4 ^! N/ \4 L4 ?7 Z) |2 M) R
end& m& J, c6 @, T. E4 a
t=1:eranum;
4 y9 | X; Y+ P& \* Y, S; } plot(t,Trace(:,1)');) D) c/ G! f# P7 W" A
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* B" ~/ V& \
[MaxFval,I]=max(Trace(:,1));$ e) K0 l: C2 b" X4 T
X=Trace(I,(2:length(bits)+1));( K4 ~; m) f& E0 ^% T! r m
hold on; plot(I,MaxFval,'*');
2 Q6 o, n; ]7 O8 E% d text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
, W+ T; i7 z$ L* B) P. B: ?7 u 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,:)));
6 E T( R R |8 n5 J6 l disp(str1);* n( p0 w9 J8 V! @# t
%figure(2);plot(t,p);%绘制变异值增大过程
, n) i2 Q" W0 g9 ?+ N( K( O T2=clock;* {. j# W, w" Y% I
elapsed_time=T2-T1;
. c8 A' o" Q: {) l2 N$ @& C if elapsed_time(6)<0: C0 Z* F: v) b" R* P
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;/ n0 n9 X4 j3 B$ f' k' ~
end- X% ^* E: b7 R
if elapsed_time(5)<0
?) k0 a9 E. g! c elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;" s/ j. _4 {' W. v) r$ n) F( r. N
end %像这种程序当然不考虑运行上小时啦
" h) N: D7 } K( g" _5 h 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));8 ?" v* p4 B" B2 r( m+ V# d
disp(str2);/ g1 Q% c$ K& o7 c$ K% _
: U; I% s) |8 g. x7 Q9 B) E ' S) ^) _& h& n, a0 A
%初始化种群
: z1 J x4 O ] %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
2 x" }4 C; W Y, Y6 p# \ function [initpop]=InitPopGray(popsize,bits)! G+ B5 z4 {) y1 f3 b) \4 d* a
len=sum(bits);
4 e0 |" }8 Q) N% O initpop=zeros(popsize,len);%The whole zero encoding individual5 ^ ^, w8 H6 X8 J& z/ S9 l
for i=2:popsize-1* c4 i+ g) G3 }" H# Y, k9 |+ j; W
pop=round(rand(1,len));
' _) {& G. @5 y pop=mod(([0 pop]+[pop 0]),2);
2 W4 _4 [, T8 {9 K %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
% O7 P# r6 m8 t" B3 X %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
' [ s7 l# \* W) O3 x+ r7 [ initpop(i,:)=pop(1:end-1);6 L. ]6 P9 [5 U' ^3 R
end- B1 l S8 L9 p0 Y
initpop(popsize,:)=ones(1,len);%The whole one encoding individual" X" d6 Z5 D6 z( Y; v- Q+ [' a
%解码+ x$ w1 l" r6 ^, K1 R; {$ b
4 j5 P# z0 Y7 z# U4 v. v3 D3 @ function [fval] = b2f(bval,bounds,bits)
4 g( @9 c1 q" F% j$ S: ^, M % fval - 表征各变量的十进制数
. u R) ^3 \! {% P % bval - 表征各变量的二进制编码串
7 C; a, ?- F4 u" j( U0 [ % bounds - 各变量的取值范围
" w7 d: Q$ F) B3 L( \8 B % bits - 各变量的二进制编码长度
: L7 z4 j7 _- [) x scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
3 N8 K) x: y6 | numV=size(bounds,1);
/ F' ]1 ]. w7 \( f cs=[0 cumsum(bits)];
! b1 n+ }, F/ p for i=1:numV, w: E! r/ W; j. F7 F: U7 n0 Z
a=bval((cs(i)+1):cs(i+1));1 v3 j8 U: F& J2 B' p
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);# a+ J c+ z5 h9 o: ?4 {" [+ n
end; H* m5 g8 ~' z4 i* C5 S; L
%选择操作# w$ O/ s- N/ u+ F
%采用基于轮盘赌法的非线性排名选择) P0 V& t% l$ S8 ?
%各个体成员按适应值从大到小分配选择概率:
z: D: ~/ H# v6 p) } %P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=19 U2 P, ^* O( F0 g4 f" d! g; j
6 X v! O8 o4 u* d' w# o F' A function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
, D9 d5 _, a4 F+ K global m n0 `. A% @+ u8 d7 F
selectpop=zeros(m,n);! l& _+ E' {( x# p& S+ F
fit=zeros(m,1);
& W" Z* S& s7 Z% X1 t for i=1:m
' H; i# I1 q( {) x6 G6 T: B fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据' R! F! N8 ~; i/ o9 B$ G' x3 w3 W
end
0 |6 x9 |9 l! V a/ o, J2 e* I selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
& Q; ] N% E; s: R; G7 T* d8 ` q=max(selectprob);%选择最优的概率
$ a. {8 s O' ]1 D g+ i x=zeros(m,2);
" y9 ]' `* [ ?& U" A x(:,1)=[m:-1:1]';: f/ w: E) _- Q% s
[y x(:,2)]=sort(selectprob);
* E% l2 O$ J, e2 ` r=q/(1-(1-q)^m);%标准分布基值
N3 A9 p8 D: |: C+ g) x( ]" i; Q newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
2 P; L! H o9 P" k6 e# y0 V& z newfit=cumsum(newfit);%计算各选择概率之和
5 J3 z; ^3 {7 _* V% Q ~ rNums=sort(rand(m,1));: w" N/ K7 P8 S) v
fitIn=1;newIn=1;- V( @- N+ P! P/ c. Q8 M6 V, Z3 c/ U
while newIn<=m
! ~* o$ W2 x- m( N& B. { if rNums(newIn)<newfit(fitIn)
8 x5 h% H- Z' R' ]) C% ~) [ t selectpop(newIn,:)=pop(fitIn,:);
7 {2 `5 M0 f+ n7 ? newIn=newIn+1;
4 u* m$ H# X4 N* F else0 \, ~& a: M" R) J) G* H( ~! r
fitIn=fitIn+1;
% z% u5 D f* f0 C7 u& p end& s# {# }2 l6 h4 d
end$ f6 W* h8 O3 |3 q$ E8 b6 N
%交叉操作. Y T) Z: M3 P7 ?
function [NewPop]=CrossOver(OldPop,pCross,opts)
! m- v( p0 F% G %OldPop为父代种群,pcross为交叉概率* v w, E) M5 C8 f
global m n NewPop 5 B# C9 n$ [ ?0 l
r=rand(1,m);: g$ E% h" l& I( M; @$ J
y1=find(r<pCross);
2 ]- K6 n' G3 _; ]5 _ y2=find(r>=pCross);
4 ?; @% f& w5 _3 S. q# {' r len=length(y1);
8 r$ t" p n8 I# a: X& f$ J 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
0 r" W4 V. Y6 _- q" n y2(length(y2)+1)=y1(len);
3 H( v* @* s3 P" e) ` y1(len)=[];/ Q G; B+ x1 a
end9 O. }6 z, X! A0 j" W( R D
if length(y1)>=2
( {! m$ F% K* R& L% d2 x for i=0:2:length(y1)-2
* F/ U& S: Y% c( }2 x0 N2 R4 D1 V- X if opts==05 Z8 S3 v- v! [; f! t+ c
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));5 P8 z' o- v. W) D4 S: d$ e
else
\# ~$ ?, A# t* G* k# {; q4 y& h [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
: e2 p& g4 t/ r# H# j end: m$ }* |. d1 ]: ~) m; {3 T+ H
end
3 K& i# B% W: ^ end
+ T9 T; N% [5 f8 G1 X NewPop(y2,:)=OldPop(y2,:);
# c5 S' E2 H! H' |& Z, l0 }( G) r- v
d* x# b9 S6 l %采用均匀交叉 9 { {" ]- R4 A% v- }3 X8 T# l
function [children1,children2]=EqualCrossOver(parent1,parent2); t) N% r2 R5 L* ]0 a$ u. u
1 a' |/ D5 n# C; J7 i, j4 Y3 D
global n children1 children2 % y& x/ C# ^' W8 D
hidecode=round(rand(1,n));%随机生成掩码
6 \3 S0 {" z/ a crossposition=find(hidecode==1);- e7 k, O; x" M \+ Q$ C- R$ u
holdposition=find(hidecode==0);" b6 w9 d9 b, d) A/ ]
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
* h) A* X: O9 W1 u) B4 f+ B$ L& n children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
8 C8 j) e# O, U8 A children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因" A0 n- r# e6 N
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因* m! v/ y+ z! ]" e
9 u1 E9 F$ J' _; f' ?8 k6 C
%采用多点交叉,交叉点数由变量数决定. A' }( H9 f6 V; ~- N8 G3 D6 W) V! \
% \- N2 i: \0 `
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)
' x$ F G. M) H0 w" Z7 S/ r - Z% M8 \4 _- I5 K2 \
global n Children1 Children2 VarNum
/ D7 l7 x& R3 H, P Children1=Parent1;
- X, V- E+ R5 U' Q Children2=Parent2;, i. L2 P/ l. Q7 c1 [( M; s
Points=sort(unidrnd(n,1,2*VarNum));
, C0 N, X/ T% k for i=1:VarNum
n( K, f; @& o9 Q9 F2 J1 s Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
5 U' G; q% }: ]5 W: z5 n+ A Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
7 L8 h& `( J: K# `7 l3 g; c4 ~ end$ h/ P3 Z: Z+ ]- {' m
0 L6 K6 K5 \3 I; F( x' Y
%变异操作
3 E6 B0 q9 I. |7 j function [NewPop]=Mutation(OldPop,pMutation,VarNum)
, ^, U' o: J- G' M9 ?% N
d |/ I% @! x: X% ?2 o% }1 P( P global m n NewPop
$ i7 Y7 s9 K3 R' @. E r=rand(1,m);
3 A) k: x) c6 \. \& _1 F position=find(r<=pMutation); x P( b1 o" | p
len=length(position);
3 u* j* W& u: a if len>=1
. J+ {6 N4 d8 ^5 E$ k) ] for i=1:len
+ D2 ]# n3 M: u7 c# Z1 ^) d k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点1 J- K* X6 c7 }
for j=1:length(k)
5 g# ~) D1 t- W6 o; G" C+ n7 E if OldPop(position(i),k(j))==1' y6 ?7 y$ v5 V! N. |$ n0 e
OldPop(position(i),k(j))=0;' c/ ?/ t) c# W1 h* k
else
b, i( V0 c7 D9 [2 K7 D+ T OldPop(position(i),k(j))=1;
U( B p" G F" W% T* L end
$ g, a& v! q( r8 ^0 V c9 Y end
2 K! H! q9 K. d7 o end
! v6 F3 M+ Y* N end+ z8 _; }- t# E9 l2 o: @. L
NewPop=OldPop;$ i1 i9 y9 _( n4 k- u
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%倒位操作3 v5 |9 S6 x* @4 @# h- U
- k" m ~8 B1 x1 b; X. ^
function [NewPop]=Inversion(OldPop,pInversion)4 D6 f, _: w9 r$ z9 O) |
. S" r- ^: v- t- C! C8 J- { global m n NewPop
5 {4 Y3 [# p9 o5 o! J1 G1 r' l) T NewPop=OldPop;
$ q: \0 R5 u8 h& \2 J2 a. ^8 f9 S) M r=rand(1,m);; M* l g% {# G0 J, H: p
PopIn=find(r<=pInversion);
1 ]+ _/ s* n8 z1 u- n' @ len=length(PopIn);, W: m5 s3 ^" `( S: }& ^1 p8 Y
if len>=1! k; Y# D- k+ [
for i=1:len6 \6 l; |# g# c, s9 j
d=sort(unidrnd(n,1,2));- O6 O' U0 z/ m# F. _+ Z
if d(1)~=1&d(2)~=n
: T4 A% \4 a2 D: S NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
6 a: b4 P8 p6 q( h NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));7 D, X9 \8 c# l; N9 h
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
) Q8 K3 c4 q# V end
; K P& g/ |- a/ d& _4 n% ? end
' X& O5 ?: V9 O end& d6 t. |% u+ _, S6 c3 m/ {
0 Y$ u: W: v) D B5 J% ?! R
七 径向基神经网络训练程序
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7 E0 ^" T* A) ] clear all;" H8 _8 _! _$ c) U6 ~4 U" e
clc;& d+ j7 ~- y; k* v! F
%newrb 建立一个径向基函数神经网络
# A' Y2 W( e* K" \/ U- E) G p=0:0.1:1; %输入矢量. P# X4 }# s6 V M: B2 i q( h7 ~
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
. g! V6 z" l- l goal=0.01; %误差4 O. Y! }9 T7 m; \- Y
sp=1; %扩展常数
& {/ ~" b9 N$ y' {( u mn=100;%神经元的最多个数
; j( X+ K0 q' D4 U. ]& R! i df=1; %训练过程的显示频率
4 v7 D5 f1 Q+ F/ b& f9 [ [net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
; i& y, w( u2 h/ s7 J$ ~- z* J, A: ~" u % [net,tr]=train(net,p); %调用traingdm算法训练网络
6 @& `9 ~1 g& a7 P/ a %对网络进行仿真,并绘制样本数据和网络输出图形% H5 ^% _3 }; \. M# O2 A
A=sim(net,p);( ]% c8 Q. L5 I+ J' c5 K9 F" v5 R
E=t-A; R9 z& _$ e' Y2 d1 ] d$ Y
sse=sse(E);. l* `/ c/ K: b. e
figure; " W9 c& B5 Q! q% A6 b
plot(p,t,'r-+',p,A,'b-*');
6 N8 l) A, I8 V legend('输入数据曲线','训练输出曲线');
9 N# x( [6 `0 w m echo off 6 Y0 v- N* \/ z, a1 U' c
1 B# v( x L; p% Z
说明:newrb函数本来 在创建新的网络的时候就进行了训练!' I3 C, F+ Y, o
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,+ v& C" _, N' D% {8 O1 i6 B
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!. o. T$ b. T( b: \: [; {
/ E' L0 M8 e+ V: a# x2 e- _
' `; l5 Y4 ]" p# F) r 训练结果显示:9 |( w( r* v# D& K
NEWRB, neurons = 0, SSE = 5.09732 P* b( V! t; l6 l7 j9 w" U
NEWRB, neurons = 2, SSE = 4.87139
4 Y8 |3 O0 g" \ NEWRB, neurons = 3, SSE = 3.61176+ i7 E$ n& [ {1 V9 B
NEWRB, neurons = 4, SSE = 3.4875
- q) [0 i$ x- C; L" x. M: E n NEWRB, neurons = 5, SSE = 0.534217
$ H5 H8 M- x6 a/ R& r/ ]$ p6 E NEWRB, neurons = 6, SSE = 0.51785
. a+ `; L" m4 e' j" A& } NEWRB, neurons = 7, SSE = 0.434259
) K# R% ^+ r& f* F8 ? NEWRB, neurons = 8, SSE = 0.3415186 p% B+ \) ]5 b! o1 J' s/ v% }
NEWRB, neurons = 9, SSE = 0.341519& ]9 ~. k4 p, z0 A& U) R. ]) ?
NEWRB, neurons = 10, SSE = 0.00257832# |( P- @9 k& C2 W0 W& f7 |: x
4 p! e5 Y! Q: D. t3 D/ I 八 删除当前路径下所有的带后缀.asv的文件
4 k3 l/ @# C/ M/ ~ 说明:该程序具有很好的移植性,用户可以根据自己地7 D( D' w. K% w
要求修改程序,删除不同后缀类型的文件! ; ]. R8 r7 d0 _# `
function delete_asv(bpath)
, V3 b+ ^; S9 j0 {+ }0 k3 P) E! C %If bpath is not specified,it lists all the asv files in the current
* n/ P' W, B8 c %directory and will delete all the file with asv 6 f. _6 J2 d/ v" f* a$ P" i4 P
% Example:
# S! L) `/ ^' } % delete_asv('*.asv') will delete the file with name *.asv;8 B' Z( k9 { l% A L& M/ Y z: \6 k
% delete_asv will delete all the file with .asv.3 J y7 G: e2 ^( M2 e
* ?1 }* U" {" x1 z) |+ b) k8 K0 [& j; E7 b
if nargin < 1
6 P6 ~, H/ q+ n5 h5 }: x %list all the asv file in the current directory5 b# a# r1 Y- i0 ]1 X6 Q
files=dir('*.asv');
! i8 l8 @- j: v( r) W# d/ m: V else$ |$ h6 J3 m5 Z$ X$ E0 P
% find the exact file in the path of bpath, u5 v9 q/ e; i, q
[pathstr,name] = fileparts(bpath);
& Y9 g& \; m; n7 T" Y" @ if exist(bpath,'dir')
* W: a5 C3 [( a6 u! Y- c6 q name = [name '\*'];
0 u5 E+ f5 }8 L- G I: r+ T1 u end
& R% r- c. i* l+ o9 A ext = '.asv';
. @( _( |! f& j files=dir(fullfile(pathstr,[name ext]));
: J% V( x/ x, R) v r" A end4 V- L' s1 T7 U; C* }; i
4 r5 n" q2 ] Q( c0 b) h# f% [" E if ~isempty(files); |+ L1 q' U3 w- I6 Q l5 j
for i=1:size(files,1)9 l) t$ P- I4 f( L0 x5 ~" `3 E
title=files(i).name;
% y; b; k" g# g* `; x8 z, B delete(title);) c, s/ B y% M- p4 X
end# e( ~% V# D8 v
end
u. f9 X4 {+ c# e/ r ' w4 o) V2 G$ T5 w$ u% s" ~
0 [3 G |# ?* Q- v4 C/ P
同样也可以在Matlab的窗口设置中取消保存.asv文件!
9 H9 a5 o+ f7 n; H1 `2 g
zan