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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! `8 ?1 @' x& n
1. predict_fun.m为主程序;0 Z8 \' d5 X+ c g7 ^, ^5 U
2. timeseries.m和 serie**pan.m为调用的子程序) g$ P- y+ c4 u- d1 Q: r% d
0 \% o' |. {8 L9 I9 e7 p function ima_pre=predict_fun(b,step)
- Y5 ~5 j3 P3 i+ a# t4 w % main program invokes timeseries.m and serie**pan.m
7 i/ P# `- w7 t' z: k % input parameters:
( g/ K8 z( o* r( z/ E1 m % b-------the training data (vector);8 ?, H8 |% S! h7 F% y. q$ b
% step----number of prediction data;/ B8 l. X3 `3 {$ W
% output parameters:9 \6 l0 g d k! k
% ima_pre---the prediction data(vector);
3 e& c- ^( o9 F" ]5 }% Y8 i old_b=b;( e# i0 f/ `& S. N
mean_b=sum(old_b)/length(old_b);
6 M& f2 c& K0 }+ R: {! w std_b=std(old_b);4 m6 j# \" ?. o' A
old_b=(old_b-mean_b)/std_b;/ P' w9 r% v1 N( b+ I
[f,x]=timeseries(old_b);9 W1 L- A( @" A4 X. |# k) o( h+ d9 u! k
old_f2=serie**pan(old_b,step);0 ~/ L0 P# |' F/ i0 Q! r" v) b
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;% l a4 @' O$ F; L" a, V: F
R=corrcoef(f);& E5 ^+ e5 M m4 W9 R
[eigvector eigroot]=eig(R);
6 y; I: a! l# o, B% |( K eigroot=diag(eigroot);
( T. \" ]% i) g a=eigroot(end:-1:1);
/ ^8 J" Z' P/ t8 z; j8 l/ C' ~ vector=eigvector(:,end:-1:1);
( Y& T3 r9 \0 Y Devote=a./sum(a);
; m j. b, U. u, X Devotem=cumsum(Devote);+ i* ^& d1 W2 ^9 m' A% T1 V/ B
m=find(Devotem>=0.995);
' ]3 [+ [* \6 y0 D H m=m(1);
, ^( n$ ~2 w9 s" A0 e0 E3 ^" c" ^ V1=f*eigvector';
2 j, t D' @3 S3 M' S# _ V=V1(:,1:m);
2 B4 B3 `9 ^; R- k % old_b=old_b;; S! t) T+ ^: c. k- `. H
old_fai=inv(V'*V)*V'*old_b;
$ J9 |+ F3 X8 @ eigvector=eigvector(1:m,1:m);7 p8 {/ w5 D% Q
fai=eigvector*old_fai;
5 `4 g9 j/ Q0 r9 ]* h f2=old_f2(:,1:m);5 q+ @" J+ d: Q$ ]1 J9 O
predictvalue=f2*fai;# [* {) t: N) X1 f1 [
ima_pre=std_b*predictvalue+mean_b;7 I4 r% l9 x9 C0 V# N5 e: r
* h8 D! k9 E! w0 }9 X
1.子函数: timeseries.m 6 d5 f# }* z2 j- k
% timeseries program%) N, |' C. v: i3 z! z% o1 j
% this program is used to generate mean value matrix f;8 A J! {" F! L3 r& s. J8 Y4 s' _
function [f,x]=timeseries(data)
7 }" f' m2 R9 p % data--------the input sequence (vector);
/ }+ c+ X7 f3 F. [0 q % f------mean value matrix f;
7 T" ^$ U: h/ X9 y. f7 T n=length(data);
% v4 }2 b: `4 q+ _$ W+ S" K for L=1:n/29 T: h6 Y9 f! h0 E- S p9 n
nL=floor(n/L);6 b2 f+ G5 B( }- t g# z) j0 c( j
for i=1:L% q. T) M1 x/ q) [9 w5 x! z4 B
sum=0;3 H X! O9 a( A& G+ B h
for j=1:nL
' Z, \' k. o5 ?* t$ n, _ sum=sum+data(i+(j-1)*L);
0 D' v! P) ~4 m3 x" ^& z- ] end: O# b; e4 n$ Z9 d
x{L,i}=sum/nL;
0 u$ K( c2 X7 K' t* k end, X. M4 B3 t0 M2 [) n
end- @7 Y h/ U! ?# D( Q, ~$ _/ _
L=n/2;
# w0 m( V& y9 s; y7 \2 _ f=zeros(n,L);7 |% _! q) p6 I; F/ h
for i=1:L
1 w( V" r9 r& B9 i. M/ E0 u, P- E rep=floor(n/i);8 N. x, L9 d) b4 f& D
res=mod(n,i);. R' q/ u' U& ^% e% L, e7 X/ K3 J$ }
b=[x{i,1:i}];b=b';# R9 J) K& H; m+ T9 a+ J
f(1:rep*i,i)=repmat(b,rep,1);
( C4 K l# Q/ x/ q+ p" Y/ p/ K/ p if res~=04 P; G% j9 D1 j; z
c=rep*i+1:n;5 {3 @0 W) U1 q5 a; `4 d# ^' s
f(rep*i+1:end,i)=b(1:length(c));
9 ^+ _5 T5 [; E: W end# V r8 C$ B5 k8 X i8 P) W- |
end
5 j. }$ q& f( j i6 `
% j8 N' W: e# J( T. Z4 q% Y % serie**pan.m! x+ P1 X: t3 D. C# }
% the program is used to generate the prediction matrix f; * j1 K1 D3 a m1 \8 S
function f=serie**pan(data,step); d$ W$ B& O* u% n8 [9 n c- d+ W( Q' J
%data---- the input sequence (vector)
- K; S5 f. |" s % setp---- the prediction number;% I% a5 V: x. O* d2 L- A+ E& b7 B
n=length(data);9 L( m6 `9 ~5 l* ?
for L=1:n/28 b0 ?* q5 ]6 F
nL=floor(n/L);
- Z4 L4 U) I* q0 U2 B for i=1:L' m% [2 a* B( T/ n0 t- s
sum=0;2 M8 Y- i% H# X+ i# j- }7 E
for j=1:nL/ G! [. _) t! S
sum=sum+data(i+(j-1)*L);" p# z4 {/ @ M7 x b3 A$ b
end
5 L! U! l4 F0 ^+ x; c/ F5 O x{L,i}=sum/nL;
8 m, [ [: o: {5 _# g& E end" h- B6 r! `% {, J% [/ S- {
end
6 P% a# h5 h6 r L=n/2;
+ K( Q- r. r/ r3 _6 P0 q' x f=zeros(n+step,L);, l! p, @. W, X; T
for i=1:L
- }5 p, W) Z/ q7 W0 ~ rep=floor((n+step)/i);3 y4 |2 s0 B, D4 D6 P
res=mod(n+step,i);
+ ]" @: K' @7 v b=[x{i,1:i}];b=b';
8 G7 n: u! r" c6 d$ T) | f(1:rep*i,i)=repmat(b,rep,1);. f) _: s. Q4 M5 A
if res~=06 B- P# C9 r. s: A8 Z
c=rep*i+1:n+step;
/ L8 C/ ]; l3 i, U A f(rep*i+1:end,i)=b(1:length(c));2 a1 @/ V1 T' W3 X3 h+ |7 G& J
end* e1 x! `- v3 b! e$ \( {
end
, ~1 v; D, T' a j4 x4 B; X , k3 a9 N9 o) Q O9 P2 I+ p
二 最短路Dijkstra算法
# l5 z5 ]/ m% W % dijkstra algorithm code program%
# G! u8 A" N. C6 C3 k % the shortest path length algorithm
# Q$ o' a: y6 |, b$ C4 P$ E, d function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)' Y% `, [( O& C! u' |
% Input parameters:* E7 x2 v ]" s, ^
% Input_weight-------the input node weight!
8 ^; Z/ E$ [2 E4 H % start--------the start node number;2 ~2 S. r" {5 ~9 Q$ i
% endpoint------the end node number;8 P; u) x( i0 s
% Output parameters:& }+ ~2 m6 M: X; j- @" E
% path-----the shortest lenght path from the start node to end node;
$ [) Y2 b! o) U5 m % short_distance------the distance of the shortest lenght path from the5 _, M) D/ f! `2 l, `( Q
% start node to end node.& J: t+ g* _& t4 K& V% p
[row,col]=size(Input_weight);
$ J7 L0 U' A2 R" Q8 L) J" _# w
* e+ q: H- p% Z# D %input detection0 {, E" k3 {6 C* r0 I2 A
if row~=col3 r! e! G+ Y" ^- g
error('input matrix is not a square matrix,input error ' );, v7 x! f* e( F( u: w
end
/ u$ V" j* A- H" H# u6 _ if endpoint>row" _' P6 _. J! \! G, }: X4 D7 x! W
error('input parameter endpoint exceed the maximal point number');
; m0 ]$ ~8 C- e, q end
% b1 J- m9 R* f- t0 R6 h( X' p! I
" q' j9 F0 R0 x %initialization
. W k3 B! }, g+ f s_path=[start];
! {3 G) [" q6 H distance=inf*ones(1,row);distance(start)=0;
) \, r9 B: t H6 x+ L flag(start)=start;temp=start;
5 L4 K. @1 W: x; [0 m$ M # x( f- S, @. V1 H
while length(s_path)<row
3 q T2 S% M& W. J0 ~ pos=find(Input_weight(temp, : )~=inf);" f, L4 f9 q y: _+ ?3 e3 C8 r8 P" S
for i=1:length(pos)+ L" E/ m9 j& V: K" x
if (length(find(s_path==pos(i)))==0)&
6 C, c) y' D. _" C( X- T( [ (distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))1 v3 I( a2 }4 l. k m
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));! L, k, [; U, R9 J& X
flag(pos(i))=temp; s; r/ w/ g; M' T1 I
end, c' u7 ]1 F% ^, i- J
end
, V7 }+ A- S) N3 X" P k=inf;
4 z9 }! y1 z) @! [6 r" K; e \ for i=1:row6 U! n+ U4 @0 k& S, m
if (length(find(s_path==i))==0)&(k>distance(i))9 W7 X. G+ r! v3 J' i% C
k=distance(i);" I; P! s$ H) w
temp_2=i;; w0 q6 d! g% H2 x3 q9 f
end
" j7 O7 u; Z7 e- T9 A" K5 ` end7 o4 ^: P$ L" P3 X
s_path=[s_path,temp_2];
V- I$ ~1 N! o4 }) N9 q temp=temp_2;
. w: k' X% n" m- w- B2 U end# e f; u4 o" L* `1 m: S+ r1 z
$ C5 s) `8 a6 f* v; P' ? %output the result
8 E3 c* q. ~* F- i( w path(1)=endpoint;
& F" ?. ^" r. E! Y, d& y i=1;
1 v/ m/ R8 Y! l/ f4 D+ e9 {, {9 a while path(i)~=start/ B0 n9 ~# o( J0 u
path(i+1)=flag(path(i));$ R% D, j5 d' ^+ U0 ?1 G0 R
i=i+1;0 g1 S1 W% V. b
end z. |) f, \3 D$ } C3 k( O5 A
path(i)=start;3 B# b( x0 p: S- N3 F7 Q
path=path(end:-1:1);# i5 p* l* W/ K8 c" `6 n
short_distance=distance(endpoint); }7 D$ U# V& G; z% ^
三 绘制差分方程的映射分叉图
8 }4 G8 @- _ N1 H) a- L- Y9 @
' y6 q: g. K% g/ { function fork1(a);
5 V8 e, ]& Q; r 9 X3 _* x! f: ?% C* l7 ^, P8 `4 _" Z
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
- V3 O8 p: ]1 @; `! p % Example:
! Y# V2 a- U0 {" O % fork1([0,2]);
& V+ B1 k' Z5 p' v c2 J N=300; % 取样点数 - S+ d! Z* W5 D: `; p* O6 C
A=linspace(a(1),a(2),N); . D& C* A; x& `7 y3 V
starx=0.9; / v: p1 P: A% ]( B( o4 F. ^
Z=[];2 {; B0 A8 ` \$ k; q7 W/ G
h=waitbar(0,'please wait');m=1;
' c6 D1 a; Z' i/ \7 p' c! b' w! W u for ap=A; 0 T0 u' M6 m' K! ?
x=starx;
6 R2 B; m: |1 n1 ?: e9 F, A for k=1:50; . d+ P* c% K. \) I! @
x=1-ap*x^2;
% ~& v8 ~8 O3 z- z! Q end
$ a( {/ ~* j3 B* G. Z for k=1:201; 5 h3 P& J6 w/ F% J% K! i' c
x=1-ap*x^2;
" ~9 Y8 S0 P6 P; s0 Y+ s Z=[Z,ap-x*i];
8 k4 W& A: O% b$ L% Z# R! T6 b end 7 W4 D1 t! x: C4 X* Y. c$ y
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);( R. F9 l, U+ _% N/ ^, M4 s8 J
m=m+1;
6 P* \1 j- e# u% ?3 [ end y7 g- c0 M/ s( _* u. w0 D
delete(h);) t" j8 R5 s I/ O) C
plot(Z,'.','markersize',2) 4 l6 k& O. [( t. t
xlim(a);
1 W6 T4 [; Q3 L) T" j0 w) |! h
9 d/ I2 P7 @+ k 四 最短路算法------floyd算法' a3 O, T6 `! Q/ U8 a$ L
function ShortPath_floyd(w,start,terminal)
0 r$ S* ~3 p6 _8 b, n %w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;1 n( O; G" O$ L# o4 ], Y
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
3 x3 N) U+ i3 m/ U/ E %start-----the start node;1 m" _8 d6 c! s p8 @: o
%terminal--------the end node; 0 U2 Y0 h3 C9 \- n) T) c
n=size(w,1);* f6 B w" g. c& @. Y; c
[D,path]=floyd1(w);%调用floyd算法程序
* n# ^5 _1 W' t | # v A" f; x( j: Q/ y
%找出任意两点之间的最短路径,并输出% }( |# f& D# j
for i=1:n' m/ J+ R E" C$ q# h$ j: u" H: S1 h7 s
for j=1:n8 X! _' G4 D( D1 p. c
Min_path(i,j).distance=D(i,j);6 ~. S" x: s$ C5 w) b
%将i到j的最短路程赋值 Min_path(i,j).distance. |' k* _! _. O4 a: m1 _- g
%将i到j所经路径赋给Min_path(i,j).path
4 k. i, \" R+ ~% D* [+ j( x; {: o Min_path(i,j).path(1)=i;- I; e5 k1 A: H& i5 q
k=1;
7 M v8 Y# B; P) j% ~( u0 ]/ y1 K while Min_path(i,j).path(k)~=j
}, T B' Y7 W/ P6 j k=k+1;# S; G: Z3 `) X' R; W
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
3 E) e% ~$ o: ? end
8 K5 o. r/ g U) \; d end
' f" K" r$ } D3 v$ u, d# X( Q end
' b+ n8 _* G* P9 u/ e1 b5 t; Z6 \ s=sprintf('任意两点之间的最短路径如下:');3 L; S9 I2 m; a5 \3 O+ g
disp(s);8 R, A) {! {4 R; P/ _
for i=1:n& ~9 @* g' @6 I4 z: S: P# ^
for j=1:n
3 l6 n6 G- Y7 F s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
! u: r& O. g B6 S. `( r# ~0 H+ u3 O ,i,j,Min_path(i,j).distance);6 P3 y% y" n4 X9 |/ r# w
disp(s);
* ^2 i# Q% r; g. B- w disp(Min_path(i,j).path);* _3 n& y# V/ s8 [& M0 e
end3 a9 ?+ P% O7 w% L' b# G
end% S' q# r! p; I& f1 w \" P) k: \
" B5 g6 c" t, q %找出在指定从start点到terminal点的最短路径,并输出" b1 A: g0 m- ^0 o
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...0 I! i" T* d4 I
start,terminal,Min_path(start,terminal).distance);: h* O; H+ M9 g; s7 \
disp(str1);
8 W7 m# W3 ?) P* ]) s0 A' H disp(Min_path(start,terminal).path);3 B4 T3 j/ N/ w' e
& d0 {8 {, e1 l. ]* m9 R9 t %Foldy's Algorithm 算法程序
- m# a: i1 r$ G( Y function [D,path]=floyd1(a)
3 p8 h5 d! Q4 _3 h4 a4 Z n=size(a,1);
( T9 x6 X$ H* Q' | D=a;path=zeros(n,n);%设置D和path的初值4 [7 K5 F9 ~! z& j( r, f" e; z
for i=1:n& v$ E/ Z- R3 H i' a& Q" b! `
for j=1:n
6 O* }/ d) J# d* G0 L( q if D(i,j)~=inf) D/ V/ F) z [! @+ K/ |; p
path(i,j)=j;%j是i的后点
; u: |. A& x" [* s" K" O5 D end
: V2 k1 S$ U! V, W! m8 n `% i; ]( m5 P end
0 ~3 L( q2 m$ _3 c7 O2 q! P4 S end" `8 M9 y: Z6 l( a6 |
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
# p. B' A4 }2 J: B6 t) z) { for k=1:n
4 v$ v9 b* R8 v* m, r) \ for i=1:n9 V9 B4 F; z- L
for j=1:n7 I0 \( l6 o% ]9 o
if D(i,k)+D(k,j)<D(i,j)
9 O% a, R+ { ]& B+ L" u0 G7 n D(i,j)=D(i,k)+D(k,j);%修改长度
1 W1 A0 \' |. [ d# E path(i,j)=path(i,k);%修改路径, h8 Q p" s5 l
end: W8 h( K4 L- d* s* H9 _- U
end
0 C: q* I; k. k. o; k end
0 x' ?$ {1 e6 s3 E end4 Z9 V+ l4 G. z# ?
( b& o7 O- ^- w/ {- {* } 五 模拟退火算法源程序0 t! ^8 E5 I/ ^: O# }+ w: Y+ }& s
function [MinD,BestPath]=MainAneal(CityPosition,pn)
$ s$ c( g' n! Q+ W function [MinD,BestPath]=MainAneal2(CityPosition,pn)
. f7 B+ c9 P/ w/ }5 M% b) s: v$ z M %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9 Y9 _1 B5 I3 M
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...: k7 A- c! w; v8 t
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...9 c/ M, a/ G# @+ b: Z/ g
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
! V1 ^: q; E6 G; c2 o; p' E8 D % 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...2 W$ @% Q5 {* m
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
' T% q! |) ^9 r0 C& L0 R ; X. D: ?1 i, f5 d
%T0=clock
; B* Y6 S! R# u P$ D0 M; _+ G global path p2 D;6 U% {, X4 W! ~& F
[m,n]=size(CityPosition);' M& n+ g9 ~# ?+ N
%生成初始解空间,这样可以比逐步分配空间运行快一些
* J& }4 U: z9 z! T5 o8 x5 t TracePath=zeros(1e3,m);
* S: V! V# g# Z8 q \; M Distance=inf*zeros(1,1e3);. C2 P% G+ {! |6 }! Q5 w
# m, O G6 u: e4 I4 N$ c M. }
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...: F+ W$ A. H- Y. }% |: p
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
& l1 u4 |% d6 e6 z& \, | %将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵). y, ^7 ~2 Y; t6 B" q" _: q
for i=1:pn: v' N/ M! T8 H% K4 {9 S9 x ~
path(i,:)=randperm(m);%构造一个初始可行解
! h- l, U6 j' ?9 X& Z end$ j( X2 J. v& |3 K8 @
t=zeros(1,pn);
w4 [5 }7 M X# ^ p2=zeros(1,m);
4 a" l# }- {8 N0 j$ ?' Q" Y6 t+ r
( S$ Q% T1 g9 m' { iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );4 m) }4 x4 D* R, F- e2 `
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=' ) ;* _3 i: F' R8 G5 A* V- X0 ?! t# I
%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
( }' H% n% ~" S- W) Q# | %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
5 B/ @( F$ c# e5 g9 s; v3 S %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
4 x9 _ o2 o- ~! P: J" Z" j4 @6 u* | %会收到到比较好的效果
' z: g" O, b0 }* D7 a8 i( e; c * R [" N/ A+ l
T=1e5;
7 X7 E7 h, b% ? N=1;
) P) ]8 ~( A2 \' u. x0 D tau=1e-5;%input('请输入最低温度tau=' );- f0 { F3 |/ `5 w m
%nn=ceil(log10(tau/T)/log10(0.9));( z+ U$ f0 B$ P% i5 s/ c+ F: S) R" E# K
while T>=tau%&m_num<m_max
5 s3 m2 ?+ I {; M iter_num=1;%某固定温度下迭代计数器! A- b; }5 ?+ `$ d
m_num=1;%某固定温度下目标函数值连续未改进次数计算器4 r% e ~# Q' Q5 b Z5 A
%iter_max=100;6 v- e5 u5 o: @( K! |+ } G9 v/ E
%m_max=10;%ceil(10+0.5*nn-0.3*N);# D+ e0 U% l' s% Y
while m_num<m_max&iter_num<iter_max
0 \+ Q' k9 J* t# n' I+ D: D* L( S %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
5 [( d" t/ G; C6 C4 O* j& j0 D5 p %用任意启发式算法在path的领域N(path)中找出新的更优解& r5 [3 D. ^2 P3 {3 I# n
for i=1:pn; z( W' B3 q7 {- Z4 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))]);
: ~- g" t/ h. i %计算一次行遍所有城市的总路程
2 P6 O! F( l6 [7 l. Y [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
" F6 h& l" _; ^( ^* } 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 X, ]. U2 @6 `7 } end
) a) I3 q& D- d2 A %Len1
3 |& l. i; h: F6 Y) V4 ]9 o %Len2
5 c H+ `1 T/ Y! i. A, P& ]. D' e %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand# q4 V# L5 ?* a2 k: p
R=rand(1,pn);) b: R7 Z4 [) O
%Len2-Len1<t|exp((Len1-Len2)/(T))>R# p2 l$ y9 k) U3 n6 ^
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0). Q0 S; A+ O+ e
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : ); N1 S% p! [5 ]3 ]! K8 D
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));( o, q/ ]: B, L2 E# H) Y+ V6 a, T) u
[TempMinD,TempIndex]=min(Len1);5 @: G, A; g* F- D! f
%TempMinD
8 b1 f4 H5 b2 D5 s TracePath(N,: )=path(TempIndex,: );
5 B0 o4 d9 E+ h+ y Distance(N,: )=TempMinD;
; _6 X1 M8 l- Q( Q2 Z4 H N=N+1;
% J7 m" ^+ o$ b %T=T*0.90 k) f0 F. s7 e
m_num=0;
9 H; B5 c1 n% I3 M/ l9 K else
: C- r4 i% T2 O- ^1 {9 w m_num=m_num+1;
6 `8 g4 t1 R6 ~9 S; _8 | end7 W8 f$ i& O4 _# w
iter_num=iter_num+1;
% F* `7 n- q" j5 x, f end
8 j" }; s. [( G9 n T=T*0.9* r- H$ p3 b' L, H
%m_num,iter_num,N; ^) ]& s- |& c% @1 V4 [
end
* j: R' }% ~& I' ^& l9 ?" q3 d [MinD,Index]=min(Distance);9 g) g. B, {2 G- U5 i2 k
BestPath=TracePath(Index,: );6 S0 v1 t o. `8 j, ?
disp(MinD)
, [3 H, _9 K' ]& S5 B# Y %T1=clock
0 r0 M6 Y! n5 y7 L' Q- } * ], B" H i, T) @/ [
- a% Y) s# J* X %更新路线子程序 6 C0 f" U& N) X4 ~* m4 O# _
function [p2]=ChangePath2(p1,CityNum)- \! h6 n: Q1 M+ T# w' t
global p2;7 v7 `' @) q& _/ X' z8 J
while(1)% Q& _; u5 e& _ J/ {" j' t; j
R=unidrnd(CityNum,1,2);% v! W5 [. N9 n
if abs(R(1)-R(2))>1, n! A& j7 J: v
break;. p2 K. s$ x2 L! f
end7 j; b; t' e# \$ q; C
end
6 g% U/ d) Q* P/ B1 c R=unidrnd(CityNum,1,2);8 i4 {' ^% o; Y/ H3 q! u
I=R(1);J=R(2);
. |$ j! L6 k& i/ G# p0 H& V3 l %len1=D(p(I),p(J))+D(p(I+1),p(J+1));
* b. f, N0 e6 O: V( R %len2=D(p(I),p(I+1))+D(p(J),p(J+1));
0 O( E: S; u9 d if I<J
7 U, V7 i* V" ~8 H5 W6 P p2(1:I)=p1(1:I);# M0 b0 P9 j% \% Q' b
p2(I+1:J)=p1(J:-1:I+1);
0 e" e' Z% Z9 B1 u p2(J+1:CityNum)=p1(J+1:CityNum);5 G7 @* O# u. X: h& J& ?$ X4 ], U- L
else
4 @7 E" _+ [% k' M6 v6 h p2(1:J)=p1(1:J);
, n$ Y: Z/ Q- r$ r a0 U p2(J+1:I)=p1(I:-1:J+1);; K/ }: O, t0 Y9 G
p2(I+1:CityNum)=p1(I+1:CityNum);
! n, _5 X7 s1 Y0 y3 Q# l. \ end( v4 _, n. e& R o+ C* H2 h: l
7 [, _+ Q' A3 e- b 六 遗传 算 法程序:. G9 F M; a7 [" ^
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!
# T8 k: G3 _" k' \6 H: ?9 B \
0 _ P! ]- B& M( ] function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options); j; f" {/ j! b! G7 N" S
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) + Z: X7 k6 V6 }$ Y( i7 @# x
% Finds a maximum of a function of several variables.
2 e" j, q0 h; w( u* G+ Z' Z % fmaxga solves problems of the form: $ d: n! q. J' l. ~. E( Q
% max F(X) subject to: LB <= X <= UB
! M& _9 h0 @ ?$ c- T % BestPop - 最优的群体即为最优的染色体群9 U3 Q+ `2 X( q2 w# e- J
% Trace - 最佳染色体所对应的目标函数值
7 f7 H: d1 w1 K3 j3 Q. V& q % FUN - 目标函数: [" y# G% Z+ f& N( a' R" k
% LB - 自变量下限. u3 \" c! w0 _' I
% UB - 自变量上限
: M; T, F1 H6 N/ ? % eranum - 种群的代数,取100--1000(默认200). B& j1 v& Y4 u$ G
% popsize - 每一代种群的规模;此可取50--200(默认100)0 f0 D7 v: x# A8 z. a6 K
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)/ I& R" y* |, b
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)$ ?9 D7 r5 k" n% Y3 F4 |2 b" L
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
2 q( }+ q9 c/ v % options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
7 h# @: n- y1 S0 W; q) V %码,option(2)设定求解精度(默认1e-4)
0 M$ N3 n4 \4 _5 V9 N) y e %
, A2 c V& Z, x% J7 G& X % ------------------------------------------------------------------------
8 A! j, c) r4 h 8 @0 s1 x1 [4 z: z& _* D
T1=clock;" U! H1 l* X% b4 l9 l7 ~# X
if nargin<3, error('FMAXGA requires at least three input arguments'); end$ a C6 a0 d+ i6 ]* O/ t
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
; `2 L1 W5 O" }9 v, d7 R0 n if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end+ I; W% t: K0 Y: l# ^4 r8 ^
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end0 z! `( n ~/ A7 N6 t
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
; ?+ h" k& P' c! o if nargin==7, pInversion=0.15;options=[0 1e-4];end
' `; n: d- c/ t, N$ M8 n if find((LB-UB)>0): y" R& G1 o0 B9 J, D# N& D5 d+ |
error('数据输入错误,请重新输入(LB<UB):');4 ]# {) p; m+ O/ M
end
% q. E9 i5 c" S* i, n$ z7 T" A s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
' H! Y$ |: v1 U# Q disp(s);
; u G J; M) {$ {2 @. Z
$ T0 @4 H8 V2 I8 M" O" P8 v2 [ global m n NewPop children1 children2 VarNum3 [% g# Y- F# m
; x+ t8 d0 V" |2 a7 O bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
! K {5 J0 N" R6 b# x precision=options(2);%由求解精度确定二进制编码长度# _8 x2 L- q% L7 j
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间1 H( }% O/ d/ Q% n
[Pop]=InitPopGray(popsize,bits);%初始化种群
! |/ z h. |& ]( d2 R* v" F [m,n]=size(Pop);
) P( y6 n, M) y f, t& f NewPop=zeros(m,n);& W q, s& _( A
children1=zeros(1,n);" U* }$ I" D8 k2 q5 D
children2=zeros(1,n);
. d( L, F, m. K0 c% l/ i5 s pm0=pMutation;/ s0 ?4 ]: M5 I9 X$ D
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
& F0 p6 f/ c( D. x1 Z Trace=zeros(eranum,length(bits)+1);
$ T3 d1 k, P; [& Q. w/ | i=1;4 @2 S7 U; H$ ~( m' @* T' F# q
while i<=eranum$ U: m1 R/ Q+ W' ?# Q
for j=1:m
' z1 O7 u4 A, y6 j1 Q4 j value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度$ w8 G" }3 }% z
end
7 G" Z7 q H+ t1 {) q; I0 b [MaxValue,Index]=max(value);9 ?5 c3 V! _& s
BestPop(i,:)=Pop(Index,:);" Q5 |6 Q6 A, u# h
Trace(i,1)=MaxValue;
6 x, ]6 G# u# U Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
' I5 x `' ?- D4 K! ~: l3 N8 I$ | [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择/ d; h0 z+ p& Q7 c& A. g: s
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
: q$ D. l& p: d& S" u. \ %采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率) r6 ]5 f( \, |
%round(unidrnd(eranum-i)/eranum)! ~! t* C; }2 U+ f" n9 o! O
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异% _/ Z& U. X- ^' W
[InversionPop]=Inversion(MutationPop,pInversion);%倒位
. ~1 U& S, v, p% U0 g( o0 p0 O2 H+ g Pop=InversionPop;%更新6 k; k1 F4 P! d, ?6 ?; t
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); & \- _3 Q9 k: P2 a+ P
%随着种群向前进化,逐步增大变异率至1/2交叉率
# K4 L7 e9 Z9 T p(i)=pMutation;
/ P' y- _' x6 j5 a8 }/ u i=i+1;" E0 a# a; c1 D8 e2 f% V
end9 |7 j* f: |& n Z: t) y* F5 r
t=1:eranum;2 s0 e0 n G6 Y* M% x- F( ^
plot(t,Trace(:,1)');
0 m5 ]9 D2 e8 U5 y 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)');6 }" R/ t4 j) l) ~+ ]. F
[MaxFval,I]=max(Trace(:,1));
$ H: u' i; U0 p7 g# x% n X=Trace(I,(2:length(bits)+1));
- M- J1 j9 @2 @' [& y U hold on; plot(I,MaxFval,'*');
2 p+ |8 z& W6 U- }0 C0 Q text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);. ?8 _$ z* F4 j
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,:)));
. }% Y; U: {8 c9 c8 t! G4 F disp(str1);
7 y8 y% E6 g# R, b' p& R5 k/ v %figure(2);plot(t,p);%绘制变异值增大过程
) j( P, B5 ?# u9 K# K% o T2=clock;
# o6 V p( Q+ @& M elapsed_time=T2-T1;) Q6 t4 X" P5 t) a, g8 m" ]( h. U
if elapsed_time(6)<0
1 F; ?. s% t1 R elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
; V1 G3 }0 h7 E6 f w5 }5 h7 S end, A) Y9 f/ t1 {: `+ i; O$ w1 U
if elapsed_time(5)<0$ }2 @; j' E2 Z: T: A& h
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;; j8 A8 [( C4 x w. a
end %像这种程序当然不考虑运行上小时啦6 g V5 \+ T( S
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));+ A }+ u( q" C0 F0 Q, b9 Q
disp(str2);
, r" z, L. @& Q' j $ j) c6 D( b2 J1 ^5 ^
$ g+ t U( J& b7 \8 n$ ?" S1 P
%初始化种群
+ s" Y4 D3 B- F* i/ ~ %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
" u$ t; E8 @: _' S7 v5 P5 c function [initpop]=InitPopGray(popsize,bits)8 R5 D$ u- P- t$ ?( r# P
len=sum(bits);; b- I" |6 n! |1 `7 M
initpop=zeros(popsize,len);%The whole zero encoding individual
5 y" Z2 z) |9 a3 C for i=2:popsize-14 l# l# j9 e6 D4 h% }
pop=round(rand(1,len));1 ?8 P+ a" L t' ~( c- D
pop=mod(([0 pop]+[pop 0]),2);
6 I x0 y# h$ d- l0 Z" d% k. _/ W %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2); {+ I, v$ p; O! y4 a8 M* [
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
7 \% N: R, t# ?' w2 X3 }2 A; { initpop(i,:)=pop(1:end-1);
; Q0 q# e5 X! t$ _ end
9 h4 i( P7 `! r- Y4 w( A initpop(popsize,:)=ones(1,len);%The whole one encoding individual8 T, P' a/ e: V& N
%解码
0 J9 a1 b# [0 y( T , b \/ X7 }$ d) x
function [fval] = b2f(bval,bounds,bits)
, k/ Q; R9 y4 t# b( Q1 Y; R# A9 e % fval - 表征各变量的十进制数3 ~ A* Z. ~' P9 |) E. u3 i9 E
% bval - 表征各变量的二进制编码串
7 t& X; u9 ?! o0 ?, u3 J% A$ Q % bounds - 各变量的取值范围* r% @8 X, W0 t1 s, f
% bits - 各变量的二进制编码长度, t4 C _" J- u; ^* B2 E M
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
H7 K* u8 [2 L. c numV=size(bounds,1);7 X' l k3 X, I5 O
cs=[0 cumsum(bits)]; , d# E' c) d7 T$ f, B
for i=1:numV
: z; L: u# J( @2 p7 a1 M" O a=bval((cs(i)+1):cs(i+1));# B7 D [! x+ X. M2 M3 W
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);& H; E! s2 v% V8 V# f/ p
end# l! | J( b# E" w
%选择操作" v- _: n+ ]( r. @9 w4 z
%采用基于轮盘赌法的非线性排名选择
2 A/ k) x& q6 g g0 u9 g" j" f4 C' `- P %各个体成员按适应值从大到小分配选择概率:. Z4 R; K$ @. R" q! W3 h% Z D4 m
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1
/ W2 `, A" J& t6 Y# m/ o
# k& t( g6 v% c2 t function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)$ U7 W! z9 t- V( ?4 N/ B
global m n" q% f! n. l5 _
selectpop=zeros(m,n);
, ~7 N( [: E0 m fit=zeros(m,1);0 U6 G4 r0 r8 n0 L, }
for i=1:m
) `$ c5 T8 S k' z fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据& A6 x3 S8 g+ a2 G
end1 N5 L9 z' C% \9 O2 V" z
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)0 z: ?4 f' s a: |4 e4 X6 V7 i
q=max(selectprob);%选择最优的概率
9 C) X# N- N) j4 X- ^2 E x=zeros(m,2);8 i/ m# L2 a+ z4 G5 X8 x
x(:,1)=[m:-1:1]';
6 H$ P# B0 J1 R [y x(:,2)]=sort(selectprob);8 z% h1 S! M# A! m- x
r=q/(1-(1-q)^m);%标准分布基值; t9 D5 }; g \
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率" H* y1 l- d' L
newfit=cumsum(newfit);%计算各选择概率之和
# k/ c$ ?0 R# ^5 S( S2 n rNums=sort(rand(m,1));
; e* D' D, x P" t7 m4 | fitIn=1;newIn=1;1 Z$ @( D* Q2 p9 J$ T% R+ f5 v
while newIn<=m
. s2 Y% |- B, h! \ if rNums(newIn)<newfit(fitIn)
. p! {: {' _8 m* T selectpop(newIn,:)=pop(fitIn,:);
# b" m, I; Y; H4 B% _ newIn=newIn+1;
3 O& ~9 @0 M. E. m- V( @ else
6 H8 E( q+ i+ l( R fitIn=fitIn+1;
* c3 H1 g0 C9 @$ G7 f* H end' j! B% M5 a9 J7 O" X/ ]
end0 A/ f$ ^, M- }5 @7 [9 ^/ L
%交叉操作
! ?. _' i, {! c7 G: Y function [NewPop]=CrossOver(OldPop,pCross,opts)
; q! \; S: I$ G6 c8 M %OldPop为父代种群,pcross为交叉概率8 q$ m1 U) N5 F8 }2 A+ f
global m n NewPop 2 F. E) [( ^: y o& [
r=rand(1,m);
; t0 T0 G6 e7 h/ h5 |2 @ y1=find(r<pCross);
' ^6 [2 c+ o$ `" g7 e9 M y2=find(r>=pCross);) I0 M9 V) O0 ]3 K9 w0 I
len=length(y1);
* `" ~# I7 W h5 D0 I+ N 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
+ I% T9 d! |2 p- s; I! y. A8 V y2(length(y2)+1)=y1(len); N! H6 D. d2 ]/ y' ?9 l% b
y1(len)=[];$ P. E8 [ }0 j& b+ ^; H
end
) K4 |0 a n, X* x- `, n if length(y1)>=2* R. t. j( ~0 w0 _. y4 q. ^1 T* w
for i=0:2:length(y1)-2
( a9 T7 Y- u9 @0 } if opts==09 D# r2 [+ R W( P9 f
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
! N2 \$ Y% p( Z, u* x else4 [0 g2 V& s2 {) _( `6 g- s' L
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
+ k+ h$ s8 g \- L, n end- e% B4 P1 e* q' G$ |* x4 ^5 b
end " B% I! U* {' r% j# u/ H
end
7 [7 b, F) l3 r NewPop(y2,:)=OldPop(y2,:);8 n$ M2 Y5 n$ a* }# e. c: E" }' @# e
) v Z0 P2 Y1 ~* |6 h- M: U$ d& ?" l %采用均匀交叉
' U1 P J1 k! v5 D function [children1,children2]=EqualCrossOver(parent1,parent2)# S Z: Z5 k" x
* |7 V1 a& {) [ global n children1 children2 8 M: T1 e+ N% x
hidecode=round(rand(1,n));%随机生成掩码
$ Q. O% x: O7 E7 I crossposition=find(hidecode==1);
! R1 z! s# u! |. c F1 `2 w holdposition=find(hidecode==0);
2 }" K/ Y: m7 |. L9 g7 n, w z/ v children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
7 N8 B% G0 c3 d/ V( h! Q children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因4 n9 f2 t: E: | @0 M* A) Z
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
+ r- P; J3 I* I; Z: i/ t+ u children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因6 ?* T8 f; F. t! u
$ x. O8 m; I2 p %采用多点交叉,交叉点数由变量数决定
+ h. n/ N: S8 Q0 N% ?3 E / ]7 C* |* i2 u' s# ]3 w; e y
function [Children1,Children2]=MultiPointCross(Parent1,Parent2); D& W, P! M! h5 M2 {
; ] v3 \! u+ i
global n Children1 Children2 VarNum
- V! G1 p5 C/ V0 }: @- Y( a9 K, I Children1=Parent1;2 \( d9 h4 |8 a. W
Children2=Parent2;
& E; G3 L3 W& c( v' r8 e" } Points=sort(unidrnd(n,1,2*VarNum));
" u& H# U) g( m- c for i=1:VarNum
; k1 |$ O B5 A' R' l7 p& q. L Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
. `; j/ Y; A% K& L s( l) G Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
; y: ^6 n9 C% ~0 B" m) k \ end
S, d7 B7 C5 h/ [) u2 p! j
2 m( b& ]3 b+ E0 k" i0 L f %变异操作
9 J4 y$ [8 N1 S+ ] function [NewPop]=Mutation(OldPop,pMutation,VarNum)+ N) ~3 B% V$ T+ f5 v
; f5 ?7 B- u. { o* { global m n NewPop
) w4 q0 b) x1 X# D& Y% Y+ k r=rand(1,m);' T& }! u- i) |! e
position=find(r<=pMutation);% D7 o2 B; U! t
len=length(position);
/ r8 H9 J7 {0 A# E$ c if len>=1
! d4 H* f/ \$ c7 `. k for i=1:len
( [4 D$ u+ s& U) ?6 } k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
& ~2 Z$ T: P# v1 X% F for j=1:length(k)
# @0 ^6 u& F8 y3 Q if OldPop(position(i),k(j))==13 c. Y; w' i. ~$ y# v' {8 R
OldPop(position(i),k(j))=0;
2 a9 s, d5 Y) S9 n1 e/ [ else
+ s, T" O2 T: Z5 F( v OldPop(position(i),k(j))=1;
) ~! E* x" _& B9 m" b' Q end$ H2 b3 i* P0 g
end
# ]/ a8 V V0 ?7 n! e end( ]( I$ S$ C& a4 v. T" J1 x
end
: P6 i( p9 I' ^ NewPop=OldPop;
! J' I- g' Q4 l
+ U @6 x% ^/ U5 x %倒位操作 s& s5 T% e& |1 i7 @3 f0 B
# Z- e3 Q1 ?$ G0 V6 D4 I9 E( Q function [NewPop]=Inversion(OldPop,pInversion)+ N, V- F; s5 R
: Y2 V: y, [, v" {5 p' I! W global m n NewPop
" B* R2 [4 _$ _; {, s0 y NewPop=OldPop;; H0 m4 b9 Y3 p3 ^# p9 ]6 A
r=rand(1,m);
% ]8 p5 A* B8 U) M" G PopIn=find(r<=pInversion);- G, c. l U- @; @
len=length(PopIn);, m5 C: ~2 W' @( G+ U, j* @+ C8 u
if len>=16 w& P4 c" K1 U
for i=1:len
9 r1 S1 {" g2 _* m0 _8 b1 b d=sort(unidrnd(n,1,2));
2 O/ S; g: U" W6 n) e- l+ P if d(1)~=1&d(2)~=n, u" w9 @; Q( H* r' {
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1); A5 T9 E. ?! B9 O) Y T
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));& j* l& J3 k N, R
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
" P1 @4 y0 K/ ]4 ]! j7 f end1 J/ T; P( G& Y; K9 `$ b/ A G, X
end
& I i( _9 D9 h* F6 D end
" U6 p2 r- W7 n" z; B8 a" L - I4 x) T# \7 R" T8 z+ s
七 径向基神经网络训练程序; S3 c o* }; `/ D9 k! k
6 T$ \- ^5 _ z+ A' P: ] clear all;
) ~! J, @& ~+ [ clc;
* A+ q8 q5 D) G* w6 o %newrb 建立一个径向基函数神经网络
I( _8 U# S. U p=0:0.1:1; %输入矢量
* n9 ?+ Y5 P4 M t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量) m: s7 {, X F1 e
goal=0.01; %误差: E1 |8 k3 x( ^. Q, a7 G- q4 D4 a9 _
sp=1; %扩展常数
1 R% \ X8 @! y* f& {* A M5 S2 B mn=100;%神经元的最多个数
; G1 ]( c4 J1 ]+ ]& v' O: U df=1; %训练过程的显示频率
" ` J0 u/ X: B; i6 n: d8 N [net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
$ x. q) d4 i# C$ Y! t# } % [net,tr]=train(net,p); %调用traingdm算法训练网络
% ?7 u$ H8 w" B- O2 ] %对网络进行仿真,并绘制样本数据和网络输出图形2 h& v) X& `) A9 P3 r
A=sim(net,p);! k# K, P4 p6 G0 @' Z; e- u
E=t-A;$ j" n3 {- C7 j4 k
sse=sse(E);
" c# }$ V( S5 h" _% h8 F figure;
$ ?2 n' \- U0 l6 [" H plot(p,t,'r-+',p,A,'b-*');
1 e' C- q8 g: i) V legend('输入数据曲线','训练输出曲线');
. i7 G; G# [% B; J0 z3 W) M: a echo off ; W+ o( ]0 ^' P6 i& ?( i; X
B2 D; u5 o* h8 ], c5 o8 ~9 e 说明:newrb函数本来 在创建新的网络的时候就进行了训练!- d; C, o+ Y* s, ^/ x) M# L1 b
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,
5 C f, P: Q, p1 {+ L4 C 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!) P2 H; @+ \: T9 n
, W9 S' ~7 o; }, H6 {/ `( e. a8 u
}/ D, h) Z; k8 Y }
训练结果显示:
7 @, f' q7 l7 N6 o% ?7 j. h4 f: }* W NEWRB, neurons = 0, SSE = 5.0973) d, I1 k9 ]( n$ Z! r. e
NEWRB, neurons = 2, SSE = 4.87139
, y3 @, U- _5 N1 {' c& L NEWRB, neurons = 3, SSE = 3.61176
2 v( F' V2 u5 A/ S$ \7 s; i i6 [ NEWRB, neurons = 4, SSE = 3.4875
7 @7 p8 d! I1 O( Y NEWRB, neurons = 5, SSE = 0.534217
6 ^: _+ B: b+ x* F; L" U3 e! T8 } NEWRB, neurons = 6, SSE = 0.517851 P/ _0 ` |8 t( D8 @5 S& |
NEWRB, neurons = 7, SSE = 0.4342591 Y* A! R! o5 _$ J
NEWRB, neurons = 8, SSE = 0.3415181 L! K# E% C& b
NEWRB, neurons = 9, SSE = 0.341519
- W/ l5 ]2 g) Q) ] NEWRB, neurons = 10, SSE = 0.00257832% i8 f% d c/ S0 v1 a
: a8 I2 E- q' P 八 删除当前路径下所有的带后缀.asv的文件
' q/ R& M# h3 q- m( ? 说明:该程序具有很好的移植性,用户可以根据自己地- ~0 w$ I! [5 E: p
要求修改程序,删除不同后缀类型的文件! ! @% k Q/ [; Y! o9 ]2 J* N
function delete_asv(bpath)
& p$ p+ J) u$ L5 i: `) R %If bpath is not specified,it lists all the asv files in the current
\" A+ ?' C5 n0 ?* h8 S0 }1 K+ T) X %directory and will delete all the file with asv
3 A/ p: c. w3 ~3 X& p- k4 B1 P: w % Example:
6 | `8 y9 t* P q % delete_asv('*.asv') will delete the file with name *.asv;
* ?, m* b+ m% o) x2 g % delete_asv will delete all the file with .asv.
* m( q! V L. u5 P- x
+ z! M% z# M h9 G5 q if nargin < 1
1 D8 {! P/ A! ~; N# e. i %list all the asv file in the current directory
% H& K8 C9 f) R+ a" ^# j files=dir('*.asv');3 g5 k2 ^; c7 `0 u
else
8 D, s H; B" G0 ~9 C % find the exact file in the path of bpath
* E, S2 A9 j% X4 \; {: l [pathstr,name] = fileparts(bpath);
f, M4 q; Q4 m9 X" Y, q& ? if exist(bpath,'dir')
) N6 K2 r) s6 B l& Y; ]+ o name = [name '\*'];
1 I9 R% l) b: ~3 H( D1 h. v( W end
) V; G0 ^+ g! z# a- Q ext = '.asv';
7 `# q, W5 {, h; H/ v9 U files=dir(fullfile(pathstr,[name ext]));2 x/ [! a0 |) P) ~' f5 u! o
end
; y( o& G% f. k# m3 f g" a' \4 D
: ^) r7 s3 B$ D- l; j if ~isempty(files)
1 E T. {5 V6 i for i=1:size(files,1)3 B' X" y7 A% x8 v) `* ~
title=files(i).name;' a g3 k: W( M! |
delete(title);% {6 T5 S2 {* _9 V
end
2 X" \, C0 ^ _2 t% [( z end$ X1 B( A) u' z
: \6 ~* \ @+ G2 R+ q
e7 x% [2 j; X9 O/ @% J 同样也可以在Matlab的窗口设置中取消保存.asv文件!2 Q4 l6 m; W* c% q+ I
zan