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升级   48.42% TA的每日心情 | 开心 2016-11-7 00:15 |
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签到天数: 7 天 [LV.3]偶尔看看II
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一 基于均值生成函数时间序列预测算法程序
; j+ b: A3 {$ j& {1. predict_fun.m为主程序;
4 N: J3 [) ]5 b& _" {. L3 `# c. H2. timeseries.m和 serie**pan.m为调用的子程序% x4 U- t( ]% l. s: s8 {: I- K# s
' Q1 m. }2 [0 S+ x @function ima_pre=predict_fun(b,step)
6 c0 G+ R6 r5 e9 D+ x% main program invokes timeseries.m and serie**pan.m
5 p( z+ S: {6 T7 M% input parameters:$ y( {' A, e! v/ _- N; o* F0 W
% b-------the training data (vector);+ v+ x2 X0 O; B7 r G
% step----number of prediction data;! P! H# H8 @! P( w- m8 m5 k! H
% output parameters:
8 u" V, J J6 j& I5 i% ima_pre---the prediction data(vector);9 ~: x+ k( [: D9 j4 A
old_b=b;
- T& f3 w# U. }mean_b=sum(old_b)/length(old_b);
: F+ ?! ?! D' N" @3 ^+ M# astd_b=std(old_b);
4 ~# R- @, l5 W2 K+ hold_b=(old_b-mean_b)/std_b;/ m! u/ y, N! Y @
[f,x]=timeseries(old_b);
' _& y: _ |( m5 J& }: iold_f2=serie**pan(old_b,step);
% _% d1 d0 N7 n1 {% \ J" ~* q% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;0 }( I- |2 t* W$ B$ l
R=corrcoef(f);* K! k: a) v; J5 C1 s& [
[eigvector eigroot]=eig(R);, c! p: z' |- H# C3 U9 u! r n
eigroot=diag(eigroot);
* c$ E8 F D6 Q2 ^a=eigroot(end:-1:1);
' q4 I3 F5 o/ \; j! bvector=eigvector(:,end:-1:1);
1 M N0 g+ \2 e# S$ RDevote=a./sum(a);5 l6 T" s; r4 [" m" M+ L$ j% N4 w
Devotem=cumsum(Devote);
' q9 v1 H& h* G+ o9 sm=find(Devotem>=0.995);
. n( I, p3 A' e+ A- I" Y' W6 xm=m(1);
- Q: ]# ~2 A _) z0 PV1=f*eigvector';
+ ?7 K" Y2 n& CV=V1(:,1:m);2 r5 n7 e9 w- v, |4 O1 l
% old_b=old_b;" O" Y% {* Z+ x# d& H3 n. x
old_fai=inv(V'*V)*V'*old_b;
7 D; W% `) w0 }( x0 a3 }) feigvector=eigvector(1:m,1:m);
3 I# ?5 P+ i5 g M0 W6 ]& Gfai=eigvector*old_fai;! f; Q9 ]3 [5 Q) U+ D/ C
f2=old_f2(:,1:m);6 C @9 {/ A$ r8 O- }
predictvalue=f2*fai; ^& t% f) Y) ?( G5 b' r" @) n4 _
ima_pre=std_b*predictvalue+mean_b;6 |$ y/ g' w9 K+ q" X6 V! u- m# o
- C2 N1 ?+ {9 r! c
1.子函数: timeseries.m
1 N6 `9 T0 ~% P7 T. ]5 ~% timeseries program%
) d# _) A1 _! D6 `% this program is used to generate mean value matrix f;5 P3 E& p/ t. n
function [f,x]=timeseries(data) . Y; U5 f4 v5 }" s
% data--------the input sequence (vector);% c/ h8 T+ j, D3 e# D* k' Z, d
% f------mean value matrix f;% |' R+ n2 B' G3 p$ S1 p3 W
n=length(data); d4 z# J! f5 H# v) W+ L
for L=1:n/2
: T. Q' }: F* C' B* E nL=floor(n/L);+ B/ D! P b% V3 }# x( C
for i=1:L7 N7 \$ P# B! l, J
sum=0;
' b9 f" G1 O4 M \3 I1 q for j=1:nL' u i5 y$ ^) X9 [* R' g# K
sum=sum+data(i+(j-1)*L);5 @1 B2 A) V ^2 R0 U. _6 X+ U
end
. N0 n" M. o5 j8 V2 B( e x{L,i}=sum/nL;
5 w+ ^6 S! c+ C* _6 Y- S' H end- W$ P$ ] G" E% E3 U3 b& \
end
, M% V7 B( Q; N5 ], G5 }L=n/2;
; b5 u4 c7 N" j" { H1 A W2 `f=zeros(n,L);8 a) B; X( c0 l) ?
for i=1:L
9 E8 P: l5 k6 s h' T6 c rep=floor(n/i);9 Y# w2 M7 t5 i, b# ]" D3 ]" J
res=mod(n,i);6 c8 m Y/ E+ L5 X+ i4 ^
b=[x{i,1:i}];b=b'; q% r5 J2 a; _& k
f(1:rep*i,i)=repmat(b,rep,1);
" ^0 o6 ^/ r# a/ C* M% l: G5 w if res~=0
3 @0 v. R8 W" ]6 w: Z8 A% V c=rep*i+1:n;6 P9 l2 c; P! ^; A. d+ J
f(rep*i+1:end,i)=b(1:length(c));" h% Q* i9 _! |
end
) _# p, v: w; w, {0 ?+ _! J1 C# Yend9 Y O! u3 ~+ m2 P/ Y0 P
( j/ \4 M! {, C0 ^1 J
% serie**pan.m
! m4 x- F& t( j% z6 a% the program is used to generate the prediction matrix f;
9 R2 i& `; m5 O) cfunction f=serie**pan(data,step);% {- `7 f9 V( Z4 Z( k0 x* {" M8 D3 W
%data---- the input sequence (vector)# t- z0 }& J, K2 A$ Y* X2 ]
% setp---- the prediction number;2 Q$ E, y; b, D7 n
n=length(data);
& f% E5 U; s' q# J7 g( {- W' L1 b. ?for L=1:n/2
7 s0 I3 P/ f9 _8 [( _ nL=floor(n/L);: c4 i- v# l' N# v
for i=1:L( Q, B% m' v" e; Y* C$ p$ V' F
sum=0; t$ E! J" a. p8 P6 S
for j=1:nL
1 u# k4 x, i; d) P sum=sum+data(i+(j-1)*L);* [+ U+ l; i! |3 w: E9 i
end
, T5 J5 H) q0 n3 A x{L,i}=sum/nL;3 ?& ^8 U+ W! X4 y# B: ~) n
end
0 h$ w* q0 n, ^1 ?9 p; r1 [' S* e" K% Nend3 u/ n. b/ @3 v- m* T
L=n/2;
3 p- {2 e3 w% B. l) `4 p- Gf=zeros(n+step,L);
4 f2 @' A5 H' ]6 xfor i=1:L
5 c! ^ Q+ ~6 | rep=floor((n+step)/i);' P" h a6 u- @" m
res=mod(n+step,i);1 O9 h0 j" W. b3 U8 h2 [
b=[x{i,1:i}];b=b';
, f* \8 D. W; J9 I f(1:rep*i,i)=repmat(b,rep,1);0 G' a' P# L: a2 ^, n( Y
if res~=0) U, Q6 N: n9 @3 J+ H
c=rep*i+1:n+step;
/ P& t! p) E' [ f(rep*i+1:end,i)=b(1:length(c));
1 k! O" Y- t- C+ _, J* s9 o end/ I* I) ?. l3 {2 y
end
2 n, E6 ? x8 p3 M
" a I/ r8 `! q" Z+ ~, m二 最短路Dijkstra算法. m" `8 b: j5 j: C
% dijkstra algorithm code program%
% |/ P8 {' C! E- T$ h% the shortest path length algorithm. `1 Y- S' y4 T; R
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)3 i( O! j4 n; ?$ b8 h: G
% Input parameters:
% _7 K, S0 K% a/ z$ L% Input_weight-------the input node weight!
* [2 I- V0 ~) q3 \% start--------the start node number;& ^9 D8 `) {- H5 Z
% endpoint------the end node number;* W _! g9 N# L$ M& B2 r0 w
% Output parameters:
8 J/ F ]" \: O% path-----the shortest lenght path from the start node to end node;* n4 F9 c0 S) U2 w
% short_distance------the distance of the shortest lenght path from the
; u% t3 f; d( n) D' j% start node to end node.
, O4 s, c& E* Y[row,col]=size(Input_weight);
* m4 n# \# @. _" Q
2 O1 y9 x% I; s: ]7 s; J%input detection; v% `% ~: n$ E
if row~=col
! e' ?/ s3 I" e( B7 i9 d3 D# A error('input matrix is not a square matrix,input error ' );5 C5 O' W0 C% ~" {) c! `5 B
end
! U% ]& q' R7 H+ x8 iif endpoint>row
- a. n0 Z: v# F9 f! r( X error('input parameter endpoint exceed the maximal point number');
: S6 D# D' R, a% _$ |end+ ^; v5 Y# u' t$ h( [
. J- x2 n& ~5 |2 g, V: L }" H%initialization
/ o1 K: Z+ q: O$ \, [0 ps_path=[start];
0 n9 U4 N0 B& p3 t- r8 h2 qdistance=inf*ones(1,row);distance(start)=0;
1 I7 Z4 i/ n" n- k0 fflag(start)=start;temp=start;
# B5 B" c- r, U g6 Y% X9 ?; t7 D# x' j* x d. P3 x6 N
while length(s_path)<row& _* ^7 F, T$ Q+ a% H/ K5 l
pos=find(Input_weight(temp, : )~=inf);, _: m3 Q) G D# o+ X
for i=1:length(pos)( B! B- ]* ~/ Y: B% n
if (length(find(s_path==pos(i)))==0)&/ `/ l; c: a1 Z4 o
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
1 h" O& @; j" F- P: M7 a* e' @ distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));( o$ j, H8 [0 X: Y i% {( d n1 |
flag(pos(i))=temp;
" O+ |3 b2 b0 k7 c2 g1 }" O end9 m2 s+ o2 [/ g$ [0 I" O9 R% b
end
/ w4 L% ]0 T1 ]/ \$ ?8 p k=inf;
% ]; E4 r* P9 }8 {1 c) w% ^ for i=1:row' z/ z1 c8 a, o3 N5 g1 C
if (length(find(s_path==i))==0)&(k>distance(i))3 x& Y5 }/ v! l% L5 C6 B
k=distance(i);
8 I% E( Y# F* Z7 S6 T8 z temp_2=i;) m7 k. e/ r. `$ U0 T% f* g) t
end5 U, n( v$ u$ V" [6 c, k2 {
end& |3 v8 e% {' {) m% \# _' _) t
s_path=[s_path,temp_2];
. ^% b+ o6 E- m; s g temp=temp_2;4 U, b4 b# q; g% }7 g2 D6 U
end5 [7 v4 C e( l' o
5 Q6 K! v6 P/ z6 V+ }: i
%output the result
1 d- v- R! b; u* l, G' l/ E; P/ bpath(1)=endpoint;
5 Q8 U4 c; M) \' X S% @i=1;% J" h1 m, _& N0 t( g$ m, [& D% x
while path(i)~=start& W1 |. F8 I# F/ f
path(i+1)=flag(path(i));
! u ^# w2 K L0 T; H i=i+1;, e% [ P) D4 W4 ]( t1 P ]
end! z/ L& `- e( f" M6 Z! D* }. K
path(i)=start;
) y. y5 [# r. W* Epath=path(end:-1:1);
/ [/ n' s$ F# W/ f$ J2 ~3 zshort_distance=distance(endpoint);8 R; x+ B, g' K- X1 c
三 绘制差分方程的映射分叉图! s5 x2 T6 u8 [6 U( e0 @) T3 J5 ] r
% y$ [2 h! u0 m8 b) ?, r5 O
function fork1(a);
- f: q$ |: g# s4 o8 P T# P2 C* d! \- s9 ~$ a
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
, A/ u* l- h# s, X7 D8 C1 e% Example: ) a: h; z+ |( {. p$ V9 }$ O/ \. ~2 Y
% fork1([0,2]); 8 O6 `, e- M; F4 u; V0 a
N=300; % 取样点数
4 b/ X9 l8 ^3 W. mA=linspace(a(1),a(2),N); 4 P9 b1 [. r5 R: t; R5 r4 N
starx=0.9; ( f; d1 {% k: K: ~+ d% i2 ~
Z=[];. G0 G% {( Q( [& S3 i1 S1 u0 T
h=waitbar(0,'please wait');m=1;. [1 x9 s. D. b
for ap=A; ; E# Y) z3 d; w& B: \
x=starx;
) U& T7 W7 p) a for k=1:50;
7 E% ]( [! |7 W( Y7 h x=1-ap*x^2; ! K6 J4 P8 U$ p. g% I
end 0 x: U! N! h, ]7 v5 v) D
for k=1:201;
2 W2 m/ n1 c% w M x=1-ap*x^2; ' v, M6 @8 X: D4 {
Z=[Z,ap-x*i];
' H5 y6 A; N* g8 T6 z# X W end
5 S+ ~2 `. ?: n6 R; x: Y. G7 z waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);9 K6 K3 |' b2 j. M" s' }$ F
m=m+1;1 d( a8 D c5 ^+ T$ Q J- b' a
end
4 d( K2 ~. V, N4 c$ Zdelete(h);
2 t. a( o3 z: H: R, iplot(Z,'.','markersize',2)
& K* j8 u' z2 B0 Uxlim(a);* D8 r7 \3 n2 ^! h+ \7 q. J. X) _
/ T- x0 @! b0 E; Q四 最短路算法------floyd算法$ y8 P* ^1 C0 | j5 ^7 z
function ShortPath_floyd(w,start,terminal)
1 R- y0 k5 I8 K- p%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
- A2 q: p2 H& @. E+ v9 D%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
7 I1 Y7 Y ~; _" f5 ]7 T; s0 d%start-----the start node;/ _# F! N( q" Q/ A9 \: p
%terminal--------the end node; 5 p* Y z' ~1 t; w; ^" q
n=size(w,1);8 Q2 g% I0 ]* D8 H, y4 [
[D,path]=floyd1(w);%调用floyd算法程序
7 d+ Q- w' }3 D
( @; P j$ n9 p: t" G6 E%找出任意两点之间的最短路径,并输出* l3 u! p) k0 f% P/ w% R
for i=1:n/ [; R1 l( q. q) C2 ?' O" ?7 x
for j=1:n
: e2 T, Z" C( B# G0 ~# V' s% v Min_path(i,j).distance=D(i,j);' v( ]. G1 P* m0 H' h" O# r0 G' _
%将i到j的最短路程赋值 Min_path(i,j).distance
, d A$ g8 Z0 d7 ~' c# r/ W( W* K %将i到j所经路径赋给Min_path(i,j).path
* g! r% A' a5 K0 b. J9 Q G) C Min_path(i,j).path(1)=i;& G) K& H% Z4 e @# Y1 [
k=1;
D+ Z- k4 _% {" T( } while Min_path(i,j).path(k)~=j
' D% Z) A/ d7 N" { k=k+1;" _" l+ H/ y- o. H+ q, D9 C
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
' _! q6 P- ~$ {5 f end
& J. _# V+ L- T+ K% N- a) ? c end
5 j6 @9 s2 d9 o9 F1 Lend: \6 Z4 @* a- p+ l- h! Y9 {/ c+ f
s=sprintf('任意两点之间的最短路径如下:');. J$ H# K: C! d9 i( A' g5 j
disp(s);
: [6 F- g" G& {for i=1:n, n2 C1 Z+ e/ h
for j=1:n
; }* k/ L& [6 X# p s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...1 r8 W! Z6 _! q" U- L# y" N- [
,i,j,Min_path(i,j).distance);. d# K+ _4 R7 g& f
disp(s);
4 A8 s3 G: ]2 a4 s% |' l! m9 l disp(Min_path(i,j).path);
: c* L" K! }: ~& F5 `5 Q end% I8 {# Q6 f( V k! d' T( J
end
) [% Q6 H0 S8 y6 k9 W' s8 V3 T! j. A; G; x
%找出在指定从start点到terminal点的最短路径,并输出
& E. S0 B3 V$ C$ ^6 v `: m2 R5 q: ]str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...* `7 s9 G1 Z z% M7 F
start,terminal,Min_path(start,terminal).distance);- c5 l0 W" s8 }: o
disp(str1);1 J' U& u1 h" H, k* L) e7 `
disp(Min_path(start,terminal).path);
6 ?% e% b/ T9 Q$ K, z; ]" l0 Y6 o! `. C; l* P% M
%Foldy's Algorithm 算法程序7 i7 p0 @ }, L, _( d$ P
function [D,path]=floyd1(a)4 G: {# z( E0 i) t1 Z/ \
n=size(a,1);
2 `/ V4 l& }2 J6 Z1 ID=a;path=zeros(n,n);%设置D和path的初值
+ a3 D! W' d% l; Dfor i=1:n
; `! }9 L) X( D for j=1:n8 z# m; n- T( i: h1 j
if D(i,j)~=inf
+ |2 t# I7 t; [- U, R* z+ | path(i,j)=j;%j是i的后点
/ J, ]% p' d/ D B; ~0 m- e end" b0 `8 ^- P, G
end
* _8 ?# y& P0 [" Jend2 J+ e+ \# V5 z% }0 u) o
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
+ Q, q, E/ S/ Z8 Mfor k=1:n
, B3 ~- G; k" S! J) ?. ~$ d/ V8 p for i=1:n1 u4 N6 Y7 Z- R0 x# j4 ^$ Y
for j=1:n
5 s% A. I; z: T% ~+ p. o if D(i,k)+D(k,j)<D(i,j) J+ `! a N4 `" f: v
D(i,j)=D(i,k)+D(k,j);%修改长度
( V* W0 V4 `( I8 d/ b path(i,j)=path(i,k);%修改路径- D9 g9 |( ?' T9 d, J$ y& h; R3 Q5 ~
end) x* Q$ _% g# U. s+ l
end: N6 ]1 `. g' Y% ]( e" {
end
2 s' L" T: }2 e0 bend
% K' Z; ]0 C0 N) ~) b; l' Y( `' ^
五 模拟退火算法源程序
0 y" i6 W; e6 l5 M! \function [MinD,BestPath]=MainAneal(CityPosition,pn); x( z/ k4 ~" T( e9 J1 o
function [MinD,BestPath]=MainAneal2(CityPosition,pn)* g" ]! b# P. i1 O1 f
%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) @& M- ^7 N _2 R2 D) }
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...9 H2 o1 p( p5 Z1 B3 n
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
" l+ e$ @" Y m y, ^7 d$ \% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
' N+ z: j; l4 H% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
& X4 K5 f: E) W& M9 e, U2 Z% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];% F7 q* w6 m3 t
" ^8 h) H4 [2 F
%T0=clock7 L# @! n7 n# t( h! Q1 F7 n/ U
global path p2 D;
- g# [% v4 A! w6 ]2 v: {, V[m,n]=size(CityPosition);
( x- b8 u9 S- g( g%生成初始解空间,这样可以比逐步分配空间运行快一些4 X+ O: U/ z! _2 p! k
TracePath=zeros(1e3,m);! B2 Y1 J7 H3 y! A
Distance=inf*zeros(1,1e3);+ ~0 p: U/ _) u5 X2 K
- ^# a$ Y4 ^& v$ _6 E, ]2 F+ KD = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
$ ^ X4 L) O4 x9 I5 g( l% C (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
, u8 f# R7 f0 [7 V( B6 G& I7 Y%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
* n0 p5 B4 y+ C( lfor i=1:pn
% J. y# k9 ~& J$ W6 p; r; X path(i,:)=randperm(m);%构造一个初始可行解" f+ T5 X5 V4 S+ D- K* \
end5 ?3 v% a; X; \" W$ }6 K* ]3 W
t=zeros(1,pn);
; W& w/ ?4 C$ o6 T8 u8 I& w6 I0 Vp2=zeros(1,m);
o- g; I( H8 E' B( C5 k, I, ]+ K9 Z5 k- T7 x9 a" K
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
$ f+ J5 U. M( q0 ?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=' ) ;6 [$ b6 q* ? I3 r
%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4 `" ?; c- q; r! N
%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
; k) v Z! d, ~8 u: j% K%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
. v8 e9 m" m2 I- s%会收到到比较好的效果/ U+ Q, o3 ~' C/ d( A( F0 p
; p5 H! C( R ?) DT=1e5;
R# L, T8 K) _, b9 aN=1;
' R0 f; F+ Z& `: ]: d9 J8 dtau=1e-5;%input('请输入最低温度tau=' );
1 z/ P) s: `$ Z& ~1 y4 a- [%nn=ceil(log10(tau/T)/log10(0.9));
" m( D, X9 H0 O3 V, Z! p% Ywhile T>=tau%&m_num<m_max
" \! v' ?6 I! z% C% T+ V iter_num=1;%某固定温度下迭代计数器
2 ^; H& N, U4 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
$ c6 [9 l7 {: ]. @# ]; B %iter_max=100;) N; L+ H. W8 r8 G/ l8 h7 \. p: Y
%m_max=10;%ceil(10+0.5*nn-0.3*N);0 M# D4 M S8 O( Q# I
while m_num<m_max&iter_num<iter_max
; [1 V% J. K3 v/ f; P# `0 r %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
3 B1 p& D: I4 Q1 l %用任意启发式算法在path的领域N(path)中找出新的更优解7 O$ {% n6 }* L
for i=1:pn
- D3 n; ]: h" ~3 Q6 L Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
$ ]& J, x: A5 C%计算一次行遍所有城市的总路程
. v5 `; J6 f, B [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
4 l7 c% p) b: T' I1 E; j8 M5 E9 p Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
2 m- @. q. I6 t+ } end
9 Z& u8 G1 E$ _9 |8 } %Len1
# w3 O9 i5 d8 o1 } %Len2
2 ]+ d3 J) j" d7 e! R %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
+ y9 x& R4 }; `" E _$ ^( j R=rand(1,pn);: [! T) h) C7 l9 r$ _0 P
%Len2-Len1<t|exp((Len1-Len2)/(T))>R
7 s, g: w9 ]5 |- | if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
7 r6 X: e1 U1 P; L# j path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
; g0 \3 J; H4 }1 @ Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));0 Y, c" }# U7 ^% y! t' o3 I3 A
[TempMinD,TempIndex]=min(Len1);
' `" z8 g1 z+ K& R, g: Y5 K9 w %TempMinD
! j- F3 ]) K: T- s F; ~ TracePath(N,: )=path(TempIndex,: );+ u+ C+ ]$ ~; w1 k
Distance(N,: )=TempMinD;( }; y+ [5 r7 ]% U
N=N+1;3 P% h2 K2 B9 k6 S9 V' H1 c
%T=T*0.9
+ w" M$ @/ ]5 N m_num=0;
, p+ b: x, V7 z5 |, a else
, \4 B6 g) o+ U/ N/ n m_num=m_num+1;% t& u! M! ]# Z% _
end
! F. R7 P8 b/ t# S, z& K iter_num=iter_num+1;- Y. `8 ^6 g, B- P
end
, X/ w! q# h" B0 N6 s9 o B7 E T=T*0.9
4 V9 _, G8 c' Y) X8 U: M+ K( \, J%m_num,iter_num,N1 i. _2 r6 N/ x/ d
end
% H+ j1 Z; Z* t0 N1 K5 P[MinD,Index]=min(Distance);
/ V- P, h1 P( J# y I# WBestPath=TracePath(Index,: );
1 L8 R- |2 @3 X3 V) mdisp(MinD)% o F6 j5 v ]7 o6 I
%T1=clock8 g2 P' b- J H H! h/ {9 T6 X
- k, Q6 y7 |+ p o/ n8 s
# d, o5 i% U& y5 e" ?( E" P, @ e6 ?
%更新路线子程序 ( s! b: O5 u ]" G( X* B
function [p2]=ChangePath2(p1,CityNum)
: g( s$ K0 z& `& Y9 N# \& \global p2;7 P& W2 e: y+ f) _
while(1)4 t& C- d( A! z) @5 z* }
R=unidrnd(CityNum,1,2);
% M7 o) Z$ @+ Z/ j1 }- v if abs(R(1)-R(2))>1
! F: |6 w4 Z/ q9 v. \2 P break;
& `& N9 R" D5 l3 @1 `- S l1 D; d% } end
% l! B" G! z& ]1 y0 Jend, o! R7 p6 d/ R( U6 h, K. t* V( F
R=unidrnd(CityNum,1,2);
; F; k* z" A8 D/ m. oI=R(1);J=R(2);
8 G" h; P3 a# x4 v/ g" `%len1=D(p(I),p(J))+D(p(I+1),p(J+1)); K* [: `1 _5 H2 v5 j
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
. c- O/ `; Q J2 t! T5 w, eif I<J
. R2 F% F9 H: c& I2 E$ | p2(1:I)=p1(1:I);
* d. x6 t" ` D) f p2(I+1:J)=p1(J:-1:I+1);
j; E- G" d' }: O9 x7 e1 Y p2(J+1:CityNum)=p1(J+1:CityNum);
7 G: D/ k/ }% P0 o( g( Zelse$ ]7 E+ m6 D! e9 j6 s- [
p2(1:J)=p1(1:J);
" E5 G! j/ L) C* D5 f p2(J+1:I)=p1(I:-1:J+1);
@( A+ p6 i/ o" \$ \ q7 c* c p2(I+1:CityNum)=p1(I+1:CityNum);" v5 X- X9 q1 D2 Q( `/ s6 O
end5 \) q- T) y7 d, {* G" w( I
4 T# q" s9 _' ~6 `六 遗传 算 法程序:
4 w( t/ `3 n0 G4 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!
/ U& \! w- l i" K4 e- w9 c Y- O
) N3 j3 s: U( i6 j% h+ g" p1 ffunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)) r( X* l! D! B+ c
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
* ]0 e$ Y* l, T' H2 }' F0 _% Finds a maximum of a function of several variables.' I# C% U- B, p, E& b& {
% fmaxga solves problems of the form:
2 t i7 B# O' T1 B, E# r% max F(X) subject to: LB <= X <= UB / G. l; S* i- Y3 J$ N$ ?7 I
% BestPop - 最优的群体即为最优的染色体群- M6 ?& N3 R- a: Q) }4 D+ w9 G
% Trace - 最佳染色体所对应的目标函数值3 b7 r$ ~+ V, v& |7 P- y/ |: `( Q
% FUN - 目标函数
S4 i- M2 _& }% LB - 自变量下限3 y A9 t& ^- x( L* U8 b2 w
% UB - 自变量上限4 u$ i) y* v# v5 X: _
% eranum - 种群的代数,取100--1000(默认200)
7 {* I5 @2 V' D! `% C% popsize - 每一代种群的规模;此可取50--200(默认100)& [6 \( ?% R! h" D+ i5 s( f5 R
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
1 Z5 V. u$ K; L# }7 l3 G: O% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
+ q) @. m: e! J5 w% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)7 \! K7 ^( @9 k+ C( {& W
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
# m$ W# b7 B7 v; D%码,option(2)设定求解精度(默认1e-4)
+ g6 Y7 u. O" T, _3 Z%/ R) D* r" G! B4 k E
% ------------------------------------------------------------------------
6 T0 B2 F# s |' M# r5 x) i( {" Y; w2 f8 p7 R
T1=clock;" M# z' y- j4 e. d; ^
if nargin<3, error('FMAXGA requires at least three input arguments'); end
! Z. N S$ E+ V+ G( k$ yif nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end; l2 T7 H& @$ O3 h% }2 `
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
- ?' ]" l$ @/ Eif nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end4 V3 @: T& t. ]4 p A( Y$ c
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end9 F9 r. J$ r5 _7 A# N
if nargin==7, pInversion=0.15;options=[0 1e-4];end
( f& F% M4 x# l1 }if find((LB-UB)>0)! a4 [4 F$ x; m6 ^' h$ E
error('数据输入错误,请重新输入(LB<UB):');( [& b) q. b/ _- A4 o+ E
end/ i5 I5 J& T) Z8 \& t6 X5 @
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
9 m& N% ~( y9 U/ J+ l* qdisp(s);
$ \" i. i0 `+ s, [2 h9 d- i5 p1 ~/ H4 w4 j
global m n NewPop children1 children2 VarNum. c. z/ S( G- n8 R& F
2 ~1 `+ M+ d) i, {8 Q. T. p8 cbounds=[LB;UB]';bits=[];VarNum=size(bounds,1);" T, _+ e$ \- [1 o9 q2 R( U
precision=options(2);%由求解精度确定二进制编码长度' E6 b2 z* B9 u' h/ R* ~; w9 I
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间1 T) q# O% U( k# l* _/ P0 [) r
[Pop]=InitPopGray(popsize,bits);%初始化种群; N: r, A9 a" m
[m,n]=size(Pop);
y* h* G8 E$ k% PNewPop=zeros(m,n);
$ l5 p* B* ?3 h O! R' Vchildren1=zeros(1,n);
- k% x; {: L3 q1 I ochildren2=zeros(1,n);
: b0 O% O0 h: Opm0=pMutation;
$ Z: u1 }# U9 g) Y8 zBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
' l& T" X2 q6 N1 y- X2 \' `! DTrace=zeros(eranum,length(bits)+1);' X- W5 F/ ^) o. @( k5 _% P% e* W
i=1;
3 r" \$ ]6 T# }' J4 s8 Fwhile i<=eranum
# X$ l: ?. @0 h for j=1:m
$ w- d; b/ \5 l. x value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度/ g2 c& D I% ?' x' @& n
end: |# R: K( G$ b: f' D1 |! M
[MaxValue,Index]=max(value);; V4 I9 j$ b% K2 t
BestPop(i,:)=Pop(Index,:);: `7 m- s4 T' i) h
Trace(i,1)=MaxValue;
3 C$ q6 v$ r, j Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
; U+ T3 S! U4 N. B- {* d- k [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择6 l1 W6 t! A/ o' s z' _. X/ t
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
% R! p) k' Y7 `, {) z! o%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率- s( W( T, O( \' F7 c; c$ E
%round(unidrnd(eranum-i)/eranum)& Y7 _- k7 B7 ?
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
* G7 H% x$ ~2 L1 B8 J; [6 p [InversionPop]=Inversion(MutationPop,pInversion);%倒位 P5 @% M+ E, C
Pop=InversionPop;%更新: x. X# R: j1 v) R9 a- [
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
3 P6 A, c" o* w4 Q5 Q1 E( J5 d%随着种群向前进化,逐步增大变异率至1/2交叉率4 p1 N& | u1 p+ |& \
p(i)=pMutation;
$ K! w6 L# {3 z6 {7 a7 B i=i+1;# C4 q3 k4 f( z" Z
end7 k4 f$ i) {+ O$ ?; B- `
t=1:eranum;
+ s- R3 I2 h+ c$ e; Z( r/ \plot(t,Trace(:,1)');9 r% ?' k- X* d/ w( j0 T5 @5 I
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)');9 ^/ a# }0 U' }2 r
[MaxFval,I]=max(Trace(:,1));( T0 w- g1 b# T
X=Trace(I,(2:length(bits)+1));8 n1 n& N' q) ^7 M
hold on; plot(I,MaxFval,'*');. x3 z% q, z" n4 e
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);+ ?! r+ y, @* _8 A* c
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,:)));& B4 n/ ~) w3 ^& s$ ~( O9 L1 h
disp(str1);
+ v" c5 O8 } e' O( E%figure(2);plot(t,p);%绘制变异值增大过程
* V4 n2 D8 A9 w/ D, D6 P9 w7 RT2=clock;1 b8 X( D# C3 l. [5 U
elapsed_time=T2-T1;
% T& `' O* Z$ Mif elapsed_time(6)<0
9 Q; o, w& b, Y b8 {0 z elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;% p. d J0 l6 o; |2 G* j) V/ w9 {
end
; F4 V9 V, w+ h( V! Sif elapsed_time(5)<0
V( y* W/ O5 P" G elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;: }. I$ t* `# m$ e5 G) u B
end %像这种程序当然不考虑运行上小时啦8 M1 K' e# _3 J# m6 \- i
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));+ o2 {8 \6 e, _0 f: g ~1 j
disp(str2);
5 n/ M9 k: H; u
5 h- [+ _) f Z# L4 n
; L! }6 S. Y5 S4 m) |! ]%初始化种群
. N$ M: Q9 W8 t%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
6 c4 `4 ]/ y' s9 P! hfunction [initpop]=InitPopGray(popsize,bits)3 K9 u! i/ o D Q' u
len=sum(bits);
m7 @: v% ~$ j; n5 e3 u! A/ kinitpop=zeros(popsize,len);%The whole zero encoding individual' F7 e& [9 O9 P6 A' X2 u* T
for i=2:popsize-1
% _: G. w* {5 T9 Q1 v/ c pop=round(rand(1,len));+ {1 Z+ S* o/ m' y7 X
pop=mod(([0 pop]+[pop 0]),2);
- B. V% m% X" w* ]. i %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)- w$ c, X" i1 T9 w- ~6 H
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)5 v* ]" `* h5 F
initpop(i,:)=pop(1:end-1);
; n2 f ?8 r) a& L2 m- K7 aend; I9 u s. @9 s. b, M: d
initpop(popsize,:)=ones(1,len);%The whole one encoding individual
' L* \5 ?! Y1 W' B* @ `%解码
0 Z7 x3 F. k& Q: {- p& T- |& g8 d: t+ A) Z( _
function [fval] = b2f(bval,bounds,bits)* t# G8 `# Y) R" c; n
% fval - 表征各变量的十进制数
' s4 t0 l& P ^) H3 c% bval - 表征各变量的二进制编码串
! E9 x, R/ V3 I+ s; w% bounds - 各变量的取值范围7 O# G4 k& }+ h n
% bits - 各变量的二进制编码长度- ]; D" v f$ \& g; _1 c- U/ G
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
: S; B# C9 F% D8 ~+ PnumV=size(bounds,1);
) L- @0 h7 m) [8 h: n7 jcs=[0 cumsum(bits)];
+ ^, V; Z2 p/ wfor i=1:numV
2 h/ j2 N. L! j% m7 k a=bval((cs(i)+1):cs(i+1));0 w- \! @, g9 q. Y
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);% e* h4 q' _8 ]$ \7 e
end% q k4 |" I; ^
%选择操作
" l1 K8 a& a' _( ^- \%采用基于轮盘赌法的非线性排名选择
8 i$ ]: g- \# W! K%各个体成员按适应值从大到小分配选择概率:
) R* b- L( W* h: ^1 N%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=13 W( o b; }( t6 n2 x, W* l2 ]2 k6 E
- b- |0 n+ \5 B( e- O8 s
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
: l7 E: f- w7 N6 I2 ^0 I+ Zglobal m n
5 L8 |7 f* b" e0 R4 J& ^selectpop=zeros(m,n);1 h; O! E% j4 P+ x7 @/ H% ^
fit=zeros(m,1);
3 ]% f1 P: U5 f( \7 v5 Ufor i=1:m
/ [: u; f. m3 u. k fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据! n5 X# F5 B! Y" u& T# b( G
end- |8 d) D+ ~0 O. H9 a+ K$ D
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
, A+ X: p6 Z) x! z v. A, xq=max(selectprob);%选择最优的概率" a9 T7 ?4 ^6 `' j. L K
x=zeros(m,2);$ i. S8 m! p' ~) Y
x(:,1)=[m:-1:1]';* \# n. u3 E3 d
[y x(:,2)]=sort(selectprob);
) y- e- q8 v) O- H4 W5 [r=q/(1-(1-q)^m);%标准分布基值
: L7 Y) a [. w4 H+ [! |/ j; N! p8 _newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
- s- Q, m# a3 `; u, e. cnewfit=cumsum(newfit);%计算各选择概率之和
. i7 [7 }2 @9 O ]; y, orNums=sort(rand(m,1));- R- }5 e$ H: g/ | g9 B# d' P3 N
fitIn=1;newIn=1;
" e3 h, R$ [2 u* Vwhile newIn<=m
5 W# ` _ d- @) g) c if rNums(newIn)<newfit(fitIn)
& K! b5 i( Q* L7 x selectpop(newIn,:)=pop(fitIn,:);
/ A4 I, ~3 L* q, Y" g @( K% D newIn=newIn+1;
* X7 F' T; f% K* C else9 N. y D. V3 o2 @
fitIn=fitIn+1; C" D5 k% B+ e/ J* p
end
1 ~5 `% P+ W. B4 c( E5 fend: K7 p" z0 Z9 c1 u
%交叉操作5 ?9 E7 j% _8 s: S/ E ~
function [NewPop]=CrossOver(OldPop,pCross,opts)( d; s8 P3 J2 `- I+ A* y$ ?
%OldPop为父代种群,pcross为交叉概率
1 y5 I! O# W3 {% b' P3 B: Qglobal m n NewPop # @( V. ?1 S; T% a
r=rand(1,m);% P( o4 l. k1 I: g6 i. C! b4 ]6 r8 z3 f
y1=find(r<pCross);
$ d5 M! A2 b! E$ ]: s+ [y2=find(r>=pCross);
% @3 d, A7 R; s7 i4 ]- I, m/ b0 Ylen=length(y1);8 g' v1 c8 X! W9 @4 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
/ l0 }, }; @% q4 W& D% x! u y2(length(y2)+1)=y1(len);3 {, @1 e2 h% e" a& i5 I/ M
y1(len)=[];( }' t6 B) Q* O; M3 c/ G$ b( e
end
A% S5 f# z: h/ lif length(y1)>=2
: l) o+ k- g# {' f8 d5 S for i=0:2:length(y1)-2/ N) C" b, i3 X0 ^1 x7 `0 a
if opts==05 e) P9 m U' e- {! W
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));; D4 s0 f5 Y1 f# Y7 o& G4 \7 N
else
2 M7 y ^1 }! |! X* k; q+ Q [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));3 G# ^2 }3 H% }6 Q8 q6 z
end9 K9 F9 c8 I" [. K, X0 k: j
end
9 V( ]5 y, m" M' Yend
: H' ^, @5 h$ Z/ [NewPop(y2,:)=OldPop(y2,:);
0 c d5 `2 p% q+ j3 R6 T/ V# P; h# c0 _
, Q0 q: `' V+ i4 S$ F) w%采用均匀交叉 8 T F. m. t) E1 t
function [children1,children2]=EqualCrossOver(parent1,parent2)
& d* O2 R1 V3 _) ]$ x: R5 U0 h8 V- x! ^4 q
global n children1 children2
- g3 U; s6 x2 g$ hhidecode=round(rand(1,n));%随机生成掩码4 c6 p% \; W# M
crossposition=find(hidecode==1);
' M' w4 B& j% Sholdposition=find(hidecode==0); ?# K5 d* z2 M' d8 q* V2 E
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因5 F9 L) L! H) `& g* M- q% y/ X
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因, c( z5 c! @/ f, m; w
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因/ d$ Q( \% L+ r4 a) H" d- U, D J, f
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
2 c% X3 A6 Z* C0 p% n2 A$ B% `$ N) |3 P8 `/ h4 K1 E7 v' I$ @
%采用多点交叉,交叉点数由变量数决定2 `+ F* y+ m. c1 Q, l, v
; Z" E- `* \7 N6 i& hfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)
7 ^' H' \! n* `7 ~1 D, U4 _
. o( `& Z) O9 B' ]+ o5 e2 S* fglobal n Children1 Children2 VarNum
- f9 W& m) A, b7 aChildren1=Parent1;& Q2 I; Z- _3 b8 U* k! v/ i Z. G
Children2=Parent2;; b% w+ p' }+ y% y ?" s; _- ]
Points=sort(unidrnd(n,1,2*VarNum));
) k& ]2 g% T: H$ Q# v: yfor i=1:VarNum
: l) [4 F9 `1 @$ _: r2 y Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));6 ^. w% B: G7 V" v3 c: W5 e" e2 o
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
* Z) R0 O. G1 J: dend
) a3 \: ^- G6 {9 X, V$ p) k! t8 W: \0 {; X2 [" p7 h
%变异操作
( e% `8 ~" ]/ Xfunction [NewPop]=Mutation(OldPop,pMutation,VarNum)6 W, ^- m6 X" I. k' ~3 ~
5 O7 \0 ^, _' F3 \4 A
global m n NewPop2 j* S1 i3 c) }: s2 b. C
r=rand(1,m);
5 w' V( \# X" d3 X, Q0 fposition=find(r<=pMutation);
( Q9 G, p- J. U; Vlen=length(position);) J/ k. I0 {" d
if len>=1- H X4 U2 F* l' O' D \( i- E
for i=1:len
: E" q8 z# Q. c( e* w1 k j k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
t3 }+ u, Z9 O0 `- X for j=1:length(k)4 i3 A- X3 T* i4 s
if OldPop(position(i),k(j))==1
! X$ R' I5 u; z# m; ?/ {; l OldPop(position(i),k(j))=0;
2 d t0 p; b" b3 Q# W else# w. s$ ` l9 H* E4 X" c
OldPop(position(i),k(j))=1;
! K: f; f$ L6 X end
( y. M3 V! R+ K7 X end
, p; m5 q/ M' P7 @0 b- [: r) l& u end! v! C) P P) j1 p# V7 A* L
end
. r1 T/ ^. `: ]5 ~: tNewPop=OldPop;
! C. b$ T9 S" \* I4 X. f3 V$ o( p8 Q% \; Z) F5 f7 T
%倒位操作& r$ }$ }4 k, F: N) m
* q- s, `$ L$ K: W$ y* h! E$ l2 Hfunction [NewPop]=Inversion(OldPop,pInversion)5 [' V% w& J* `7 ?+ Y
5 t, J2 `2 Y+ b8 l: Iglobal m n NewPop
0 I; P) V# p9 l" e0 wNewPop=OldPop;
' z6 [0 f9 c: w6 _( rr=rand(1,m);
: n! M3 s4 E! E) ?PopIn=find(r<=pInversion);
4 g: k6 o! m% o7 a8 Olen=length(PopIn);
4 N+ z" u' m) gif len>=1
2 Q% O/ k7 [% {- W for i=1:len
3 y$ q( j& C9 s5 w3 ~, Q% r. X8 x d=sort(unidrnd(n,1,2));% W! [ X! U0 [$ {5 X, y
if d(1)~=1&d(2)~=n5 W) x0 Z3 G+ N2 S7 N O
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);: c; P6 e/ U+ p, d( b6 u6 U e# ]
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));/ F) G& j$ ?1 ^+ Q9 H
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
& B# {4 E1 Z& N, e) V9 f. F2 W end$ u, U# g! g, T
end% Q- Q4 Q, P: N; Q
end
2 D' a$ j6 V) V
6 @' A: D) K8 E/ D七 径向基神经网络训练程序% P. T# p: z/ j; L9 `
# W; y" a! J. A* z
clear all;
( {+ k0 }* J, i5 pclc;, W4 ?+ p+ m9 Z4 f$ K
%newrb 建立一个径向基函数神经网络
4 c- S6 B5 b$ @4 g2 ?p=0:0.1:1; %输入矢量8 D' K7 q8 @6 ~
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量% g$ c3 x& R6 a+ c' {
goal=0.01; %误差
{6 C8 j( ^0 Gsp=1; %扩展常数
3 t- l9 F+ _( L% {( l" }- J7 bmn=100;%神经元的最多个数
- I) u1 @2 y) J% Idf=1; %训练过程的显示频率
4 @7 M; [+ E* r7 v# s[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
" g4 U4 ^. T0 u9 u0 ^+ e; I, c% [net,tr]=train(net,p); %调用traingdm算法训练网络
% C* M/ s; R1 W z& L1 G+ y%对网络进行仿真,并绘制样本数据和网络输出图形
( O% ~' l: c3 M3 L7 d O! J, ?7 BA=sim(net,p);
; X+ F6 p; `8 kE=t-A;& G7 e4 s3 c' }2 j, i+ ^
sse=sse(E);8 L# p) G$ f/ e- R6 A+ a
figure;
# P6 b. H% Q( [7 G9 ^% rplot(p,t,'r-+',p,A,'b-*');
+ h3 Y8 \. R8 a' a: p' w$ p" Z7 Elegend('输入数据曲线','训练输出曲线');
; ~# J: ~: q, D% K5 @7 ~echo off
6 r- b" l. E6 R- P/ g% p- z* z9 `* F1 C
说明:newrb函数本来 在创建新的网络的时候就进行了训练!. @ J3 s$ V8 e
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,
* S) B, ~! K! a1 G# J6 }2 n G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!
# J. w q. p$ E3 R( u; `' b
, }, {0 _1 i% `8 c$ n
* J( Q- [6 \5 Q7 n s- X训练结果显示:1 @! `) [( K; |* \
NEWRB, neurons = 0, SSE = 5.09732 `% p3 X; x3 u4 V1 s/ {* k( g2 H
NEWRB, neurons = 2, SSE = 4.87139
" G/ H. }, O. Y$ [. F/ N$ ^- v( FNEWRB, neurons = 3, SSE = 3.61176) g7 B* ?4 {. |0 Y/ j5 z
NEWRB, neurons = 4, SSE = 3.4875
' k# i; t5 x8 P8 R" F8 }NEWRB, neurons = 5, SSE = 0.534217/ D/ J1 n$ N0 \/ x; @' D# a/ J
NEWRB, neurons = 6, SSE = 0.51785
# c& N" U- r" `% ~( C* SNEWRB, neurons = 7, SSE = 0.434259
. Z, ~. ?" `% f& s Z- gNEWRB, neurons = 8, SSE = 0.341518% A1 N9 e/ Q2 J$ V( x* `$ G
NEWRB, neurons = 9, SSE = 0.341519
% s1 q6 Y8 @' D+ L* A+ [0 fNEWRB, neurons = 10, SSE = 0.00257832
0 w" o. A( S# L6 `2 C4 o
) s- i3 t9 P0 f八 删除当前路径下所有的带后缀.asv的文件; G' k( j$ [) S% X6 p: h2 |
说明:该程序具有很好的移植性,用户可以根据自己地0 ^0 c Y$ n' T; F. \, F
要求修改程序,删除不同后缀类型的文件! 8 {( D+ L) F! G# {0 l, ]4 a+ k0 d
function delete_asv(bpath)
) ^; q! h+ A7 f- F1 Q ^8 p; p%If bpath is not specified,it lists all the asv files in the current
4 x" L2 N( a! V3 Z h) {%directory and will delete all the file with asv # N+ a* _% ~, _
% Example:
) y/ Y' ]# w* i" M% delete_asv('*.asv') will delete the file with name *.asv;$ ~1 H/ l. q% v, i$ Q( S* z; O
% delete_asv will delete all the file with .asv./ `/ c; K( l' q( t9 D
4 e7 e7 t3 C) qif nargin < 1/ E2 b% {+ A6 Y8 b
%list all the asv file in the current directory0 p6 |- ?3 w% @+ w$ O$ p6 K2 U
files=dir('*.asv');
+ e6 [; f0 Z4 o2 |; j! melse
( @1 ]9 Y5 O, p+ F8 t# t' V% find the exact file in the path of bpath
/ Q+ {( y. @+ [/ c# `5 @3 m [pathstr,name] = fileparts(bpath);/ J* R+ H7 M& U1 c; A6 t
if exist(bpath,'dir')9 ]) p1 g V6 E7 ^% j8 S1 x
name = [name '\*'];
2 p/ m5 w: J6 N8 S end# f: o- S/ N3 m0 j; r$ S( T- J' o
ext = '.asv';
' T" ]6 `' r# w# o$ ` files=dir(fullfile(pathstr,[name ext]));( Q( i' W) ?/ ~2 r
end
" P5 X; T* t( ?
0 v0 k/ Q: B, V5 B) fif ~isempty(files)
2 e) @6 }0 j5 u7 f3 U1 g5 @( i for i=1:size(files,1)0 f6 ?* x% |* O9 F
title=files(i).name;& n$ Y8 ^7 T. V2 I* X$ D8 R
delete(title);3 l! x' o9 g' h) @8 w! l6 V! e
end, I8 } s( Z0 ]% i3 v
end8 Q/ W9 s& K6 s( {6 o
" |% l1 e, m+ O4 [
! V* H6 n" W( N; @! }" j" v$ P同样也可以在Matlab的窗口设置中取消保存.asv文件!$ e# C. t6 O |2 B. X2 l' U
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