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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
5 e) H% m4 k3 c* Z1 I7 D1. predict_fun.m为主程序;
( M% N5 n& ^7 p f" w6 B) t) N2. timeseries.m和 serie**pan.m为调用的子程序8 m& j" E) [+ [1 _( g
: r9 {; v1 o9 H+ e4 A3 yfunction ima_pre=predict_fun(b,step)
C0 S s! f$ \% main program invokes timeseries.m and serie**pan.m
, d, h4 I% i7 n7 ?0 M- v9 e% input parameters:- V( O4 k) N" R K
% b-------the training data (vector);! w% ?1 s- z8 M6 T' i1 B* _5 c% S
% step----number of prediction data;
3 A& _ V C+ W% output parameters:0 ~ m* D7 {& h5 m; C7 G% J3 x
% ima_pre---the prediction data(vector);/ Y# ]6 \$ _. X8 L/ t% t9 W$ W
old_b=b; e' I# W2 F& u
mean_b=sum(old_b)/length(old_b);
X' A% N$ n! ostd_b=std(old_b);
0 h- C$ y5 R) P. _2 g0 n* U- gold_b=(old_b-mean_b)/std_b;: Z2 K' O/ @) D+ f/ k& V" k
[f,x]=timeseries(old_b);" C6 ]2 q) f H
old_f2=serie**pan(old_b,step);
7 g3 q/ `0 D+ K6 _( U% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;' c! x$ w! p* r9 w/ w
R=corrcoef(f);
8 h6 L0 S- U9 Z3 W# m" V: @6 K4 ~[eigvector eigroot]=eig(R);
. x7 o! e1 [+ s: K9 k/ T( Z( Qeigroot=diag(eigroot);9 ]! ]+ o' }2 R' c; o& J: h
a=eigroot(end:-1:1);
& u- ^* z4 G% c' }& p& T9 Yvector=eigvector(:,end:-1:1);; Q6 [/ \0 G; f# g$ [
Devote=a./sum(a);+ L% |9 Q M1 ^% n
Devotem=cumsum(Devote); ^) e. G# L* j# T& a& \" y
m=find(Devotem>=0.995);
7 G% |8 h z, a' [' [% j ~m=m(1);( y1 p6 y0 _( O3 u5 n+ g/ W
V1=f*eigvector';
+ Z% [; b0 h. s$ OV=V1(:,1:m);8 q* x' \% d. i$ p2 {# W% l
% old_b=old_b;
0 T7 Y4 m& Z. B6 `old_fai=inv(V'*V)*V'*old_b;) g, t0 O3 A& ` y' t! @* T# C
eigvector=eigvector(1:m,1:m);4 V j1 s0 K3 V0 ?1 P; C" f0 _
fai=eigvector*old_fai;
9 y2 b K) m$ s/ Sf2=old_f2(:,1:m);
+ S0 |7 B; i, C. Dpredictvalue=f2*fai;
$ `/ q* q8 ~3 |7 B( Eima_pre=std_b*predictvalue+mean_b;& g. \& U$ h D; o/ t
+ J) y0 S0 a- m9 T/ B; `1.子函数: timeseries.m 2 v# `* I& Q! O& k& j7 S/ |
% timeseries program%
! ]1 v! Z% L9 q0 L+ W/ p% this program is used to generate mean value matrix f;
& c. S" x/ W) l: Sfunction [f,x]=timeseries(data) * u7 x1 h+ u( t& k. L
% data--------the input sequence (vector);- |( b$ C9 o; @
% f------mean value matrix f;
8 |+ G u+ M4 ?n=length(data);! z# V1 h! W# j& U. T& ]; K8 w
for L=1:n/2+ E: K, k6 c( {( G+ H& O
nL=floor(n/L);
( g; W% L0 @0 Q- ^: V* r. e for i=1:L6 T2 o$ Q( B: X; G
sum=0;
, ]3 f; a- Z D4 |" }2 b& g9 Y' h for j=1:nL' a* b+ H- ]3 e. D& F0 d
sum=sum+data(i+(j-1)*L);
. S4 A$ r: i, }& \# c" t; G' e end
0 ]' G5 P& \! X% r, w# y x{L,i}=sum/nL;
9 o, W! U; {$ E1 q$ \- U end
* X9 I; V" w, X0 T- i; A/ `6 gend4 q8 o& a: g0 [: m
L=n/2;' Z }/ n8 C3 l0 M
f=zeros(n,L);, o$ p1 [" h$ R9 L
for i=1:L3 @7 {2 I7 m6 i; ]+ b+ q- {
rep=floor(n/i);
6 t; E% L, p2 A2 S- f5 ~ res=mod(n,i);& Y, |. b. G g \9 {
b=[x{i,1:i}];b=b';
5 i* k" ~' H$ r" n f(1:rep*i,i)=repmat(b,rep,1);2 D5 q; r5 k# f; w% t$ e
if res~=09 Q( ^$ _* h# G
c=rep*i+1:n;
# S3 p# g2 S. a R0 V+ H' Y f(rep*i+1:end,i)=b(1:length(c));
' @% y- g; p7 y( h A end1 g9 L) A% r6 v: _, o3 B8 C" |% H
end
7 _3 t9 F Q7 J' K; N' c" E: n
4 Z5 d$ m0 p8 r3 c: Y5 r' e1 X% serie**pan.m5 r6 n6 u# {* C, W g
% the program is used to generate the prediction matrix f;
8 o0 @* B, y8 w( t' {) h# a5 Afunction f=serie**pan(data,step);
! s8 S- e$ Z0 [; n* ?$ C%data---- the input sequence (vector)
, @( _( {& j! z4 K% setp---- the prediction number;
% z# C0 H! @$ fn=length(data);
3 I6 }( }$ Z8 `) y5 A- Efor L=1:n/2& v3 m9 e+ x" Y+ }" p% b
nL=floor(n/L);
9 w3 o5 h" i! j1 V( z+ S7 j5 e: | for i=1:L
# e6 I2 i, L/ s sum=0;
$ J! i* C) K h( P for j=1:nL
1 g$ v$ @ p3 L" B; A+ O sum=sum+data(i+(j-1)*L);
7 P- f4 l9 `8 K/ y end7 S" z' d6 L7 D/ ?+ O" Y3 j
x{L,i}=sum/nL;
) T" S0 Q S8 P8 i, v) r end- h6 E" M! G; k
end
' T0 F# {) q5 @; dL=n/2;! z. L' _2 z9 J7 M! a7 h' Q
f=zeros(n+step,L);
: k8 Y5 g5 {) |) X. ^for i=1:L6 l% b8 w3 P" \
rep=floor((n+step)/i);
8 Y( K4 T# c2 N* a5 S7 _ [5 y. l res=mod(n+step,i);
$ z+ u: s3 ^2 K b=[x{i,1:i}];b=b';
' s/ D, Z. `- u+ Y7 E f(1:rep*i,i)=repmat(b,rep,1);
% G/ e% i' F: E. e I8 Y if res~=0" J8 i2 J, T) g- @" |
c=rep*i+1:n+step;
" @+ k# v- E2 p$ z- F/ m f(rep*i+1:end,i)=b(1:length(c));
) G- O9 `) A( D3 T3 I. x end
$ P- F: f. Q* R2 |, u2 |; V+ ?end( S6 H* _* b4 ]$ |3 W
! ~# ]% G, r2 Y6 [二 最短路Dijkstra算法& p6 ]/ M& f: F3 q, t! X
% dijkstra algorithm code program%
$ M$ G& _3 Z( m0 e% W! G% the shortest path length algorithm
' Y1 {; o) G% g O1 H7 [function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)
+ L/ P$ d' L0 y* B" H% Input parameters:0 w* Z: g0 l/ y8 p2 y9 g
% Input_weight-------the input node weight!
0 `0 \6 c; F" E6 D5 \% start--------the start node number;
: M4 s+ |8 M" m& [% endpoint------the end node number;/ a6 W; T+ E; ^1 i( U
% Output parameters:4 U9 w& e0 j( j) B1 _* B
% path-----the shortest lenght path from the start node to end node;3 ]! i2 P0 ^# w1 U" i
% short_distance------the distance of the shortest lenght path from the2 O, r! R8 x1 C9 N0 ?' H( i. {7 z
% start node to end node.( T$ H# ^( ?% \" I! h: I$ j
[row,col]=size(Input_weight);* o T8 R( [4 z
) T$ \. h4 u4 I%input detection1 @& [$ U* P* K3 S8 E( ~% u- v$ o
if row~=col
! d( h6 g0 `6 C error('input matrix is not a square matrix,input error ' );8 x8 t+ F- |; }" p4 ~( ?/ K
end
: s0 T5 F0 L; \) d6 r6 cif endpoint>row2 n3 W4 c! I% j) A' w: h. Q
error('input parameter endpoint exceed the maximal point number');
7 }1 D! i$ m0 d( `end
# ?- j* }" M" M& G. d. g. d
. o$ F8 _% Q( B2 s%initialization
* s4 ^- @4 o- {1 W2 Ds_path=[start];
- F8 d1 G* R8 Y5 u" z Jdistance=inf*ones(1,row);distance(start)=0;) V; ~$ N7 l! [# E( t8 a
flag(start)=start;temp=start;
1 S: o6 U1 W x. t" R
3 `$ t, ?( T, u* n7 Xwhile length(s_path)<row
/ V- j( ~, Y: i/ g- B& |4 U' X5 C pos=find(Input_weight(temp, : )~=inf);
9 N/ u$ h2 b+ g for i=1:length(pos)
1 I$ a- [7 j) e" @/ U) j if (length(find(s_path==pos(i)))==0)&7 f1 `# r) u9 x' [; g
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))1 w( G) e9 E4 D+ J' o
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));0 C* u% K' L! I. j0 o% E/ _8 |: X
flag(pos(i))=temp;3 ]$ ^+ x Q) q6 u4 S
end; M) n, s8 B5 g3 T/ c: `* e
end% A+ a5 m1 K; {9 J O
k=inf;
* _0 B4 {( i( |$ `8 V& M: e! w) F$ p for i=1:row9 B9 X# ]* S: [, d" s
if (length(find(s_path==i))==0)&(k>distance(i))
: |! A% n( o. o* K: J3 O k=distance(i);/ [$ Y4 t- M. Z$ C: V
temp_2=i;# O! t# ]0 m M
end
1 l( t, W# N( W' p end9 I/ @! O5 u0 a* N: t
s_path=[s_path,temp_2];* u6 f- X/ `- H; \% O
temp=temp_2;
' v3 z' _: G( @) j! h8 @$ Tend8 g3 n7 z0 X, R: E( ]) l
* O: B9 Q. z! S& I; ^# ~%output the result
a: h3 H1 {8 s# M* D1 A; k7 L4 P3 Wpath(1)=endpoint;
Q& x4 X% x1 Z4 Q$ Fi=1;
5 g( c: u2 q, Y( I. ]0 [5 Owhile path(i)~=start+ L ?7 w0 U5 i& i
path(i+1)=flag(path(i));, \$ P4 s; Y- I% |8 h
i=i+1;8 s, Y: P+ B5 A" T: @7 g5 [# [; f
end
% ^' l/ y7 y/ X6 h- {8 O3 hpath(i)=start;# s* I0 l+ I+ A/ f& O3 O+ a/ V
path=path(end:-1:1);/ ?5 ?; ^6 d+ c' Z
short_distance=distance(endpoint);
" ?% {# ]% K/ S. @三 绘制差分方程的映射分叉图& S4 ?( P8 U$ c" \: w- {
) y. l4 r, n- Z* g: ?function fork1(a); 7 R' z+ N1 C. I% s3 ~
) B0 q! z! C* N2 {/ U& P: h/ d
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
! a* i: h/ p i1 b% q% Example: , x6 P0 y9 j& m1 k; k( H g
% fork1([0,2]);
; p9 f1 i/ o. ?% j( ZN=300; % 取样点数 " S/ ?1 c9 U1 }- O p$ D
A=linspace(a(1),a(2),N); 9 b! S* | p/ ]& i" ~' G) b- f
starx=0.9; ! Y' ^" J2 K, {8 _/ [9 q8 ]- @
Z=[];
3 R% ^+ K8 Q3 D+ \h=waitbar(0,'please wait');m=1;
( ~! w2 ~4 |( }6 U- ^! x; X; Kfor ap=A; ' Y' X' Q: a5 n- n8 t7 j! ?
x=starx;
$ m' L) G7 P( m( f for k=1:50;
( b7 e+ a6 K/ K* J! l8 U x=1-ap*x^2;
* [" b+ K6 s9 B. B+ W M, _( w% V end
; \' z0 y1 R: M/ [' ` for k=1:201; 3 G6 T& ?. W6 D3 @- k
x=1-ap*x^2;
- l& g3 [! Y2 ^' ?0 v3 b4 t; ? Z=[Z,ap-x*i];
9 {9 P! z) `8 h1 I1 h5 J end ; H& k5 O% ~$ f0 `& Y
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);1 J9 ]7 O; R E
m=m+1;1 d/ b3 {- z. J3 D; D
end . q* p: S6 c+ f/ ~- v: m+ V
delete(h);9 M0 F% f# E2 j3 e* m
plot(Z,'.','markersize',2) ) \" W9 i7 Z' F, |( H
xlim(a);, l( I, \' U3 \; S j
; f+ S' q: n" c" i四 最短路算法------floyd算法6 [; e7 w, E$ i d6 g% G
function ShortPath_floyd(w,start,terminal)
" v: K" I; I5 G%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
* F5 l, m; u% J$ X( O" c8 `$ h+ L%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
% w) c/ O. f1 b%start-----the start node;0 `8 l: V: R- n2 I
%terminal--------the end node;
4 B6 \9 X3 X0 A, |( s5 On=size(w,1);$ T4 T! H' \+ A7 z8 c2 n; q* J7 Z A6 T
[D,path]=floyd1(w);%调用floyd算法程序
2 O8 X* X( k6 |1 k# }, i2 O& }, ^2 z: n/ @% V
%找出任意两点之间的最短路径,并输出
4 [* n& {% E' t) x% kfor i=1:n
0 e& ]9 b5 I: J( ?8 F F- Y1 A for j=1:n
6 ?+ v# o% q' q- f+ ~% ^ Min_path(i,j).distance=D(i,j);( Y) \1 p2 K* ?( g/ y1 j0 n
%将i到j的最短路程赋值 Min_path(i,j).distance
5 F+ Y) }& b4 L5 { %将i到j所经路径赋给Min_path(i,j).path
$ p9 }- \) p+ i* `& D* S J! X- H Min_path(i,j).path(1)=i;) O5 p2 h. v1 R3 [* _" [; \
k=1;
3 s5 v+ g- c- g" f( m0 b/ ~( O9 V while Min_path(i,j).path(k)~=j
# j7 {: @; Y. k$ i& @3 y! X6 @ k=k+1; r( q4 B/ `# T% H8 [) f2 }5 S) l
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);7 t+ x- O$ d; x1 g) Y, q- C, J
end4 z' i. `6 K, S0 L
end/ S3 \ v( x6 s9 G4 M' u4 j3 T
end
& S& p/ S4 F+ ?2 J1 ]s=sprintf('任意两点之间的最短路径如下:');' I7 H+ J c/ f
disp(s);0 u, ^3 y, y: q% Q$ u; N
for i=1:n- v; T/ j/ b' s. N! w' |( @3 b9 O
for j=1:n
( ^5 a" h0 T# ? s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...% T) P+ z8 }* O$ A
,i,j,Min_path(i,j).distance);/ [, J) b) y+ g6 m4 _6 \: K$ W+ O* Y
disp(s);0 T( n$ K7 D) Y4 A4 {6 ^) M! x
disp(Min_path(i,j).path);
! h' X0 n1 u3 W) n. H/ U end
4 {. ?: _# b8 ?1 u" S% Vend0 u, C4 K, x& b2 ~& b% i; I
% v1 E/ D+ b0 p! b, l3 {5 F%找出在指定从start点到terminal点的最短路径,并输出
) [) Y# \; T7 F9 _str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',.../ C6 P- @5 W( w2 C9 a
start,terminal,Min_path(start,terminal).distance);$ Y& o( K& M) @+ F; C5 ?
disp(str1);
5 W: {2 ^: U4 S8 @# wdisp(Min_path(start,terminal).path); I8 `- [7 v9 O) ]! G% u* ^
! d+ W0 K" y, [4 s* o3 _5 R
%Foldy's Algorithm 算法程序
( s/ S" y# A1 x8 S- r% a* G2 pfunction [D,path]=floyd1(a)
9 w# y9 y/ J3 { Dn=size(a,1);& X6 g) b, z8 c3 Q- K; f# Z
D=a;path=zeros(n,n);%设置D和path的初值
, }: q6 f- q. I2 C1 {for i=1:n
# h- u) }9 y T5 l8 i, i: Z( B for j=1:n4 d Y8 S$ T" C( j4 h+ v; L+ f
if D(i,j)~=inf+ ^, Y2 b+ O3 C; q2 E1 `
path(i,j)=j;%j是i的后点/ @& x/ @1 G y& s* N4 U$ m' w
end/ S4 k3 x& ^* X8 z# _) e. T# R
end
9 ~* P' o( L# z" \- p+ Y. gend- b- k+ _( |: [6 L
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
0 n( Z5 f5 |- w0 T+ w: y; qfor k=1:n
+ |8 I; p( U) O! { for i=1:n3 u0 ?% v1 G( i/ Q6 E
for j=1:n! P; i/ X1 i- z L' M
if D(i,k)+D(k,j)<D(i,j)
1 L6 ?: U: L0 C# B# s- `' d( f& W5 a D(i,j)=D(i,k)+D(k,j);%修改长度$ b, v4 O5 s! n _- o
path(i,j)=path(i,k);%修改路径
. S5 n* J% o* E' V A: A, r end S6 O h5 v" O2 d
end/ J! }, Z6 K3 d ?
end
! }3 a1 S: S; oend! b# v7 Y* W0 v
* M8 m9 L- G$ f$ {+ N1 k. D/ Y
五 模拟退火算法源程序
8 Z% O5 Q0 |: E, y$ d6 ufunction [MinD,BestPath]=MainAneal(CityPosition,pn)
0 s2 O7 ~* J) ]function [MinD,BestPath]=MainAneal2(CityPosition,pn)
" V0 z0 i& a O( c5 K%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
4 h. e! B( \0 e3 i- I" ]3 t2 H) w%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
* `* `, S$ J3 ]4 i8 L' i" p% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
3 ?" p# y, R* c* h+ I* B% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
3 c% \9 x' f# [7 v. o$ h% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...- x$ a3 A* q$ F, P8 u3 ?* Q
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
8 D1 Q3 ^$ E$ T3 s$ d- U6 C) n
4 B; C7 V6 P0 ]% q4 v%T0=clock
- j) a1 c, S, e. l6 I: Fglobal path p2 D;& _, y, v! B* R1 z* P g. J) r
[m,n]=size(CityPosition);
% \; J3 Z* j K# M! B: J%生成初始解空间,这样可以比逐步分配空间运行快一些
* b' g ? U. X, a8 q) ~, tTracePath=zeros(1e3,m);, \5 R& m, t% |7 ]# W. `& c
Distance=inf*zeros(1,1e3);
9 b( T) R) K/ k+ G' V; X
' r' u4 p: D/ sD = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +..., ]! x8 o4 X+ Y# p0 G
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
% d3 h! T. ? _%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
! ~' L( q+ j, Qfor i=1:pn
/ O0 i8 v `8 j4 o* f ~ path(i,:)=randperm(m);%构造一个初始可行解. v3 I! E* G$ \" e9 A# q X
end
# n* l9 S$ e( Vt=zeros(1,pn);
& k3 ?( m5 @. p( J: z5 A0 [p2=zeros(1,m);
K1 L+ }& A2 O8 ?9 g0 T+ d) p4 ]. {8 p1 z4 o
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );0 {( ~. d' u. Y$ U1 k6 M
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=' ) ;
# a3 u9 m4 {% ^%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/ U% |3 c9 H k4 o: ]: K/ {
%而随着降温的进行新解被吸收的概率逐渐减少,又难以跳出局限2 s" e; a. b) e$ y, 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( [ T5 B. K3 H N: P9 e
%会收到到比较好的效果
4 l6 f* S0 Q: Q9 _/ h
, F% k7 E' B8 K8 W) JT=1e5;$ J u2 N& f1 `4 c
N=1;+ |& i, q8 H$ E
tau=1e-5;%input('请输入最低温度tau=' );
9 H$ f* y1 x2 Q8 i! a%nn=ceil(log10(tau/T)/log10(0.9));
; S7 S4 V X3 @4 o. d7 q1 }( x' [9 ?while T>=tau%&m_num<m_max
2 n8 d0 q+ T9 W* d$ _, Q5 S: d iter_num=1;%某固定温度下迭代计数器
/ V6 V; B- b* ] m_num=1;%某固定温度下目标函数值连续未改进次数计算器$ o/ ]! K' {, p5 H7 q
%iter_max=100;
0 R% C2 P( h7 f0 m* B V+ C %m_max=10;%ceil(10+0.5*nn-0.3*N);
5 G5 L% U: h( W* h- K while m_num<m_max&iter_num<iter_max9 k) q2 O p1 ~& M
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:8 R' c. s, X+ n5 G
%用任意启发式算法在path的领域N(path)中找出新的更优解# H' ?# o. O0 D9 }9 o7 Y7 o
for i=1:pn
9 E- B9 M$ y$ e( J9 B Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
! V9 l. L, |7 U' B& F8 x" ^%计算一次行遍所有城市的总路程
5 C- l+ U. U; z0 [5 I [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
, P8 O) q& \/ W/ M Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
/ n) l! i3 I, v: ]4 i end
. B5 i$ J# q7 e/ l0 P %Len1 `4 i! \' Y. j1 b5 o' N8 p% s* ]# r
%Len2 _& l2 q' v& Z! p& G0 d
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand/ l1 R% y( k& ]6 V. m
R=rand(1,pn);1 j) j' p4 h# g2 i. E" V
%Len2-Len1<t|exp((Len1-Len2)/(T))>R5 w" q2 {2 Z6 O5 O- z
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
" q) i5 R4 D. r/ g6 d2 P path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
3 w- |" ^' ^5 S, O) M1 {9 E2 N2 d Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));6 W5 Q3 W0 s4 c9 M& E) O
[TempMinD,TempIndex]=min(Len1);
1 r1 q# @& b r9 n# X, V %TempMinD0 l- c- B3 [$ D; c
TracePath(N,: )=path(TempIndex,: );& P% E/ s! l# K$ u
Distance(N,: )=TempMinD;
, ]2 \. @6 i6 ]- A; k% W. S# L N=N+1;. V, ?* i; b* K
%T=T*0.97 W+ { L% @6 r( P+ x' x
m_num=0;
: X/ x: _) Q# X/ b9 z8 Y c2 i else
( a; r) @3 Y* J( x9 ^5 T m_num=m_num+1;0 Q, ]" j3 V4 R9 c
end
; w8 u" ~+ o. D" r& e iter_num=iter_num+1;
( R: I0 g: D0 r T* a; F end
# f; X9 A3 q7 m+ ~) z T=T*0.9- `6 C5 n7 k# G3 \* t
%m_num,iter_num,N) J0 J! m6 g t6 }! H6 U, T
end * ]( C& z' X5 Z
[MinD,Index]=min(Distance); V% Y+ V9 h7 b: e# u/ D
BestPath=TracePath(Index,: );
+ U3 L/ Q4 _+ X0 J/ Cdisp(MinD)
9 M7 ~5 ^2 i+ t& e%T1=clock/ y& ^! [( c0 ~8 c9 t
, d1 Z% u1 N0 r* ^ O6 W & R4 @6 ~5 v! U7 _. X/ e
%更新路线子程序
: u, I7 d) t, ]9 o3 Z4 A& z% Kfunction [p2]=ChangePath2(p1,CityNum)
i) U. {( n5 c8 }8 ^. zglobal p2;5 m, h) ?9 A. E0 @1 _2 Y4 @
while(1)3 n! a4 U+ T5 J8 c1 l+ N
R=unidrnd(CityNum,1,2);" |5 e. E% C9 s, o9 {
if abs(R(1)-R(2))>1+ T& i+ n s+ _6 y+ M+ Q
break;5 O% w! y$ m: ^" g: p5 W. b# g
end/ v) m9 f0 Z( F& d
end
0 b2 Z7 c- d0 R5 F) C7 tR=unidrnd(CityNum,1,2);
8 [6 g$ i7 y7 `3 J6 lI=R(1);J=R(2);1 f* z, u8 t5 o) d* k$ d
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
0 N& M9 v/ Q2 E+ X b%len2=D(p(I),p(I+1))+D(p(J),p(J+1));9 H4 Q" @: m. c- g6 }
if I<J7 _3 A. _. n5 e8 a4 X, M, P
p2(1:I)=p1(1:I);
5 c4 H& y9 q' z8 y8 q% m p2(I+1:J)=p1(J:-1:I+1);
+ M" p0 P0 m: F. A( i p2(J+1:CityNum)=p1(J+1:CityNum);; s. _5 H9 b" E
else( f6 g: [9 t( b K+ f) N
p2(1:J)=p1(1:J);& k0 R. J9 A7 P
p2(J+1:I)=p1(I:-1:J+1);" J* ?6 c% z+ L9 @4 M) D# J& \, Z
p2(I+1:CityNum)=p1(I+1:CityNum);+ o2 J8 o' B) g
end
8 `( W @! v9 r, D" ?
. Z. _) R% i, q& C六 遗传 算 法程序:: K# G9 C ]5 e0 m+ n
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!
) S" B. [- |( q/ [, Y' P6 W5 c$ H& A' ~1 X- M% M. W$ e+ m
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options). ?6 E# F* H t- n5 q( l, s' K& G
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
6 Y; @2 A$ ^" i/ F7 B% Finds a maximum of a function of several variables.) ]- _! G% x- X; c7 x3 q* {
% fmaxga solves problems of the form:
0 v1 H" x' f' c0 {% max F(X) subject to: LB <= X <= UB 6 A c- Y+ y5 x7 D8 s& C
% BestPop - 最优的群体即为最优的染色体群
4 K- k1 K6 ~6 e' W! y7 f" I% Trace - 最佳染色体所对应的目标函数值$ Z" J' M7 o( a4 E- P1 w
% FUN - 目标函数
1 r; H5 q/ y6 |% LB - 自变量下限
% K d5 Y g" c- q- n% UB - 自变量上限
3 g, E1 C# G3 G# Z7 i% eranum - 种群的代数,取100--1000(默认200)9 g y) o" i: z, {# w
% popsize - 每一代种群的规模;此可取50--200(默认100)
' V0 W2 d/ [6 `3 ~2 h' M% i& ^. U. T% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
! d( l. b6 w* @7 N% O% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1): N& A9 y; [4 @1 L W' H6 ~! B, }
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2): z) P, b2 a! I& R8 ?9 p/ ^
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
9 c% P$ x% P% j! ^%码,option(2)设定求解精度(默认1e-4)6 J# z$ {- v& b( S& n
%, _6 i" W- H4 E1 x: a9 G8 Q4 ?
% ------------------------------------------------------------------------
" w ]& x+ h; b: J/ K4 ^; X" _/ R, o
T1=clock;1 t0 Y$ B% v1 s/ X: D! e* j
if nargin<3, error('FMAXGA requires at least three input arguments'); end% o+ y# [* z- l, y! f: E% b% @, A
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end# _2 R/ r4 f7 u6 R% a$ h
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
1 {" C! F) \ Bif nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
c: _3 k8 X9 M- A# n: rif nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end; C9 o+ s1 w( n
if nargin==7, pInversion=0.15;options=[0 1e-4];end
; j4 l2 b2 L. }3 t' ~if find((LB-UB)>0); X; }/ Q# @& S$ P0 }: ]
error('数据输入错误,请重新输入(LB<UB):');( \% k5 |1 k# u
end/ F( a' u: o$ ?5 u' y
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
1 _# r+ L) @2 [* u; hdisp(s);
3 H7 m2 T4 A4 T/ e, V3 X. u- X( g' T: D u. d7 V
global m n NewPop children1 children2 VarNum
. @1 g' H/ f) |& D/ g& A
, z8 x! H% K3 t; Y' j- @% Bbounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
$ [1 k- C6 q/ @1 e# }- Z7 ?precision=options(2);%由求解精度确定二进制编码长度
. F4 p& u7 T1 @% Fbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间- x! K! @7 k( D& Q U% z
[Pop]=InitPopGray(popsize,bits);%初始化种群
9 x9 b6 o) h3 B* ~1 J# t[m,n]=size(Pop);
" g8 y, G [2 YNewPop=zeros(m,n);3 O; a0 E9 m3 H
children1=zeros(1,n);9 S& ~- U0 V2 _" q% p
children2=zeros(1,n);# s; }9 ~; p9 A9 N9 C% G* a& k
pm0=pMutation;/ y7 {, A) H: E
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace9 @2 O( b; N/ `& _; W
Trace=zeros(eranum,length(bits)+1);
; c! d+ N. C9 g+ v3 gi=1;
& L8 l% K, O+ D# x$ b* x0 K" Owhile i<=eranum
+ p* _9 v' m8 A7 K for j=1:m' \: f1 ]6 N. V
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度- \5 u; x7 a1 A3 s* B. g
end3 a/ y& B/ ^# |( f0 q2 [* x! k+ T; x
[MaxValue,Index]=max(value);
4 U9 o% `: ^5 H BestPop(i,:)=Pop(Index,:);
: U2 s; w1 j8 E# q Trace(i,1)=MaxValue;2 x2 W& ^0 d. ^& x" d: }0 K5 i
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);; e6 x4 {3 O1 y h1 Q, V
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择# u1 T: s" i) n; V# K8 @
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));2 x# S$ K2 T2 R8 m8 v
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
5 d. y5 S! n, {6 P1 G; t3 } %round(unidrnd(eranum-i)/eranum)
, x" {6 G4 P1 {5 e. ] k* S [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异9 E! v& r. F/ A5 H( E2 \ Y) t% {
[InversionPop]=Inversion(MutationPop,pInversion);%倒位
1 |9 e6 B$ e+ I- I4 o Pop=InversionPop;%更新" p# z( H: N) C! e+ m
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); ) g ]* {6 O2 E$ s
%随着种群向前进化,逐步增大变异率至1/2交叉率
- U5 n- F3 b1 A& J' O) q6 V* `$ ^: | p(i)=pMutation;$ u; |, @- o. u2 E0 x6 E" G" J
i=i+1;
; a9 K% X5 B, U. Yend
8 w& ^ z; z) n0 A* Y! y4 Wt=1:eranum;' S- H) F" M) B0 e/ L7 ^ n5 ^- V
plot(t,Trace(:,1)');& o" ]' Q/ {; A4 t
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)');2 l' ?" \, r# @* t3 j ~7 {
[MaxFval,I]=max(Trace(:,1));% V3 @' _* s, y: l1 w
X=Trace(I,(2:length(bits)+1));
% F6 D9 f3 F+ a0 q# Lhold on; plot(I,MaxFval,'*');% e1 N4 N" g# _
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);5 `6 N6 g* b7 E/ r* e% f$ |
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,:)));
# o* \! U, k, t: R( s8 }* @disp(str1);$ T* J) a* _- |, @
%figure(2);plot(t,p);%绘制变异值增大过程- Q* Z7 Q( I* P, j o S
T2=clock;
/ s+ r6 h6 F6 n3 b5 [$ belapsed_time=T2-T1;% L4 |+ ]0 U( D! h# D
if elapsed_time(6)<0
9 i+ S D# Q0 @$ P. D elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
+ h$ e( C2 _9 f' }7 p: X! Q8 ~end
8 t v5 i c- B! mif elapsed_time(5)<0
( z: y% {( ]) a- N" V+ U" p elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;* n- M, O% k1 k8 ~# Y
end %像这种程序当然不考虑运行上小时啦/ \5 {5 _2 l' a. R8 V k5 B
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));
6 v6 J1 X9 v6 e1 N" rdisp(str2);
( h# G' C! X7 c7 R, j: h* n7 M- S0 P O1 @
5 Q2 [6 l6 E6 `! q1 V. Y%初始化种群
1 v& K6 s* Q' X%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( d! z( e: L4 I, f# [
function [initpop]=InitPopGray(popsize,bits)
% n% x; i7 r4 H. C, l" ]- Elen=sum(bits);
6 L1 P4 F" p! c8 j) minitpop=zeros(popsize,len);%The whole zero encoding individual" [- g+ q5 ~1 P" ?8 V; w8 l; r
for i=2:popsize-1: [0 s$ z2 k. s+ `+ N; H
pop=round(rand(1,len)); L+ O: q9 K, H9 T4 f& |) i
pop=mod(([0 pop]+[pop 0]),2);/ F& L6 }" s. t; Z
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
3 \; t1 j0 L1 N %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)3 C# m8 s z" ~; F, T$ x( b
initpop(i,:)=pop(1:end-1);$ N2 t7 ^8 ]+ b9 V& C
end& x0 b. V% l) }! b0 a
initpop(popsize,:)=ones(1,len);%The whole one encoding individual, R H9 u0 O" R# h+ ]+ n0 O
%解码: j0 {4 ^2 P! }
# D* o+ D% }7 w
function [fval] = b2f(bval,bounds,bits). }% Q' q9 k) [$ S
% fval - 表征各变量的十进制数# K o* e! h& S7 v# v$ H
% bval - 表征各变量的二进制编码串 u1 M4 R4 S" o6 X3 H4 A6 G
% bounds - 各变量的取值范围! b2 {" M. W7 V) o* r* T$ ]& d5 c
% bits - 各变量的二进制编码长度3 d7 {" N2 |' W0 L' t _
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables' z9 A6 ^ u1 x- I% b
numV=size(bounds,1);/ |! z" C: I% w. e# L- \; v
cs=[0 cumsum(bits)];
2 F3 C7 {8 t, c, L$ i* f. Xfor i=1:numV
5 a7 G* A2 v/ o) ] a=bval((cs(i)+1):cs(i+1));
4 _, k: d; h/ L) f$ C& L fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);+ s0 |: {; S4 C4 k+ r- Q6 C# \
end* \6 R! M! z% @6 e2 L) j; o
%选择操作
3 b) _/ @6 w8 c$ J! Y" H%采用基于轮盘赌法的非线性排名选择9 A0 x/ I `; _9 H# V( ^2 A
%各个体成员按适应值从大到小分配选择概率:. \" c/ `. l# b$ I' r C5 b4 Y
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1* A/ K3 N% C7 U4 l
; v# C0 J! S7 ~& h9 N- X( B) hfunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
; K5 Z3 y6 R7 c* E6 M: x" x9 dglobal m n9 l2 c6 c1 u) }! N% Y# s u, U
selectpop=zeros(m,n);
4 G# j/ g# Y# Q7 L1 t$ S- R- Wfit=zeros(m,1);
0 ~: g; k, R- W# ~for i=1:m: L- Y: \. S3 Z$ D
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
9 z' s# _: I* d$ c: c% M. ?end. v; L; G5 ?& R- B6 f: N6 ?" ~
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
- O0 R) X* B* ?+ Aq=max(selectprob);%选择最优的概率
% c" y! t6 ?* A: O+ }3 }, q* Dx=zeros(m,2);1 G! l- X3 P; R
x(:,1)=[m:-1:1]';
4 m) ~# R0 G8 W[y x(:,2)]=sort(selectprob);
* u" Q' H7 s1 e8 L* H; ir=q/(1-(1-q)^m);%标准分布基值
7 g2 v6 g4 p9 F6 enewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率& Z8 j' c- L# I6 C6 T2 M. u8 S7 f
newfit=cumsum(newfit);%计算各选择概率之和) y! P8 o, A' D4 ~* s
rNums=sort(rand(m,1));
1 F0 j: d, ~$ ]- s: RfitIn=1;newIn=1;) q& V" x- x( Z7 [
while newIn<=m: b* i& h9 F. Z" t
if rNums(newIn)<newfit(fitIn)( y- _% R% v4 V9 _
selectpop(newIn,:)=pop(fitIn,:);
( f1 t. c$ @+ m5 D' P+ L newIn=newIn+1;
' [. X @) _/ e0 E; G. u else+ z, Y6 H: i! V2 a& Y& }5 D# |
fitIn=fitIn+1;
5 q u/ W: D; I. I- i end k5 ]) s I$ ?" _1 v6 Y: L
end) H2 [/ S! w' M
%交叉操作6 W0 a2 m% B7 N; N& k6 j
function [NewPop]=CrossOver(OldPop,pCross,opts)
- ^+ i. ~# \5 S% R2 ^%OldPop为父代种群,pcross为交叉概率$ g( p4 I C. B; R, b: O
global m n NewPop
4 v0 C$ ]& E2 ?; Gr=rand(1,m);
$ f( d# P( {8 J7 j/ V' R- _y1=find(r<pCross);
1 F1 B8 x* P# b% Zy2=find(r>=pCross);8 _* ^* y$ q% l! V
len=length(y1);
: ? d/ ~* X0 P* i1 R4 `" pif 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
o3 X) |# j; R7 p- X+ t y2(length(y2)+1)=y1(len);
8 k+ N. s' v1 Q7 ^9 a$ `1 W! Z y1(len)=[];
q2 L4 ~/ s) Pend1 Z i: H9 S' M! }
if length(y1)>=2
1 |/ n" P* ~; q0 K+ A/ ^& d1 w& W" t for i=0:2:length(y1)-23 ]/ [& \( S/ T4 q) D7 \. ~
if opts==0- {; X5 I5 o# |. Y: F
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
i( H. Y( C) [8 ^4 i else
3 r; ?2 X/ r# } | [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));2 Q7 w/ q7 R2 Y- u
end9 c) H/ c0 Q( t; y$ A/ D' q
end
4 }$ W- o( P- S7 qend
* [+ f: E) U7 B# ]& o4 R2 C! t0 A9 oNewPop(y2,:)=OldPop(y2,:);0 O; }6 [& t2 ]/ T* w$ C
$ g( o0 r2 f; v%采用均匀交叉
7 M" `+ U+ X0 _$ t) `3 _" gfunction [children1,children2]=EqualCrossOver(parent1,parent2)8 l3 X5 r1 G& y0 k, {
6 A+ s7 ~9 { u2 x7 h, R k, W
global n children1 children2
- i7 j4 h O$ X) phidecode=round(rand(1,n));%随机生成掩码" }" c4 P4 d5 Q$ K1 L' O
crossposition=find(hidecode==1);: r$ K4 f' |/ W% B. |5 {! @4 b' e
holdposition=find(hidecode==0);
% z# Q; \ r0 d Mchildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因" Q/ Y0 Y1 {: d: y3 W
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因0 P! u$ G7 y! N7 Q
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
1 j9 l) P, c# J. l1 Echildren2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
: E3 r0 e6 a' {( @0 f& i) T8 g0 S9 R7 O5 Y4 h
%采用多点交叉,交叉点数由变量数决定
$ N0 V( \( o: x# E! B* C
* `! L! r8 t( _2 u' Z" H) x7 Jfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)
% U% {/ i( x* f- x3 T/ {7 |* ^
9 S8 P' d- E/ `global n Children1 Children2 VarNum2 [$ ?% @. r4 G& W, ~3 m
Children1=Parent1;
" v/ o0 }9 c9 i2 X* k$ cChildren2=Parent2;2 q5 e4 K1 r( J6 L! P% |: t
Points=sort(unidrnd(n,1,2*VarNum));5 n( l# z' |1 }7 p& M" T) A
for i=1:VarNum4 ^ L9 r3 s/ K' w
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
( h' |- J( y: O \6 B g& }) { Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));1 x0 U# H8 `* e" @5 z1 T, F' p4 \
end
9 @3 t7 K6 J, _9 b u' k& t, {5 F. C6 G: n& P- Y; \4 L: r0 N
%变异操作
, e. ^& ?" V+ u5 e) `$ Gfunction [NewPop]=Mutation(OldPop,pMutation,VarNum)
( }' |. b# _: H+ T$ C7 A+ Q- U2 M* [- r O! i9 ^$ A6 p' P
global m n NewPop" f2 Z1 z6 G9 |8 e/ t. s, T
r=rand(1,m);8 Z5 J# h, q: P3 t% D, z
position=find(r<=pMutation);# y9 C$ t' h" t" ~# ^/ e5 o, B+ V
len=length(position);7 c! i8 a9 x: k: `9 r7 Y( G2 L
if len>=1
: N9 ? w6 [4 v) X8 K0 B for i=1:len
! t9 d9 }* I Z k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
+ t) H1 n) B! |) L+ C t1 s) F% N for j=1:length(k); r4 k8 ~5 o. ]4 E0 ~ t
if OldPop(position(i),k(j))==1 Z" @6 b; U, J0 Y' V" Z
OldPop(position(i),k(j))=0;0 R. H& `' L, |- `3 R
else
& e& s' u7 K" W* y7 x OldPop(position(i),k(j))=1;
: M+ R. t5 H" f7 V1 Z3 h5 M end
: W! R" C- m# z end2 K, ~% q- e j( B7 ^2 S
end+ \) A0 y; F5 J' H$ \! P
end2 l# R8 L) \+ Z3 E5 d i, u& D* {
NewPop=OldPop;
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, A3 C2 b5 ]( N9 S%倒位操作2 x- {7 n! t$ G; V. j
: }" F# s( R6 `- N" d. Tfunction [NewPop]=Inversion(OldPop,pInversion)5 C& E K6 q v* o# q* z1 w
+ I8 @. E: \2 A2 W# l4 e8 F4 M; P
global m n NewPop: w8 B7 }( t/ P! l% E3 Y
NewPop=OldPop;4 H! G+ j+ [8 F+ l2 ]0 o; {6 ~
r=rand(1,m);
# E$ A+ ~8 R, KPopIn=find(r<=pInversion);+ |! L* l5 u1 B* N& f! q6 {, L# L
len=length(PopIn);
2 D2 [# P( h& X% Pif len>=1
7 Y. C+ V1 l& ]& {( W" w for i=1:len
7 x E* N& R3 X8 K! R# w# s d=sort(unidrnd(n,1,2));
5 ]& e5 T. s$ ^- u* }4 v7 l if d(1)~=1&d(2)~=n& F7 y$ _8 J) a R {* O
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
) v" |& R3 C: G4 {' a \ V NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));9 e; N' H* ?+ `2 t* z! j* j
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);& K! }: @% u1 _ U
end% Q+ }0 }# r {. V0 L. C
end% R1 d d& }1 `$ W5 b7 f7 s
end5 [! q1 V. Y& E, k# A* R
# @4 r4 L" {- \' m. _& p
七 径向基神经网络训练程序
/ Z6 s! x- E1 y9 m: u6 O( |/ o# H Y: R6 F6 O, L- v" \' O; d0 U
clear all;! i: F' R0 V" C4 ?9 n$ i/ T
clc;
3 z1 x; {4 ]" Z, z+ _%newrb 建立一个径向基函数神经网络. w0 B- X/ H0 g' s6 Z+ L& k) [
p=0:0.1:1; %输入矢量& l3 g$ J% t! l( |; d
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
4 F' c0 ^4 g( A2 Wgoal=0.01; %误差 C& C1 @; L& ~* [% C6 K W
sp=1; %扩展常数
0 o" C" _) x! m* omn=100;%神经元的最多个数
! T4 {5 H& Z% b! jdf=1; %训练过程的显示频率: o1 L0 F9 f' ^( L' f- [
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
) S4 j3 ~6 y) m# \% [net,tr]=train(net,p); %调用traingdm算法训练网络, q5 |! n( }) }5 i
%对网络进行仿真,并绘制样本数据和网络输出图形
L6 x, k- ?6 H1 H0 gA=sim(net,p);
1 J) _$ v& V: fE=t-A;1 [0 G9 Y. p+ u, b
sse=sse(E);; V- s/ S0 N$ i4 y/ X# F
figure; ( r7 X: G& v* [! }. H' O
plot(p,t,'r-+',p,A,'b-*');1 I: R) N; g% m! h. h
legend('输入数据曲线','训练输出曲线');
4 L" a! m4 F8 W+ J/ Vecho off ' O, f0 O& W3 R" C: z9 Z
( k' \7 `# }3 k$ J: {7 h2 [' L% }
说明:newrb函数本来 在创建新的网络的时候就进行了训练!
9 m3 X* s+ o& x) o4 X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,
$ p$ |( h! ?* t, Z q: D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!
" s$ _/ e: \& U6 Y
6 `2 Z" E; q9 R9 U3 l7 \0 i; A
- _$ V1 e: d) \, n训练结果显示:
* H* C2 b2 a2 t) V' uNEWRB, neurons = 0, SSE = 5.0973
0 t! r2 ~. s; {. f# uNEWRB, neurons = 2, SSE = 4.87139
, w5 ^* y, B$ T3 H5 L+ s; xNEWRB, neurons = 3, SSE = 3.61176
) \$ ]1 W1 v9 J) i* DNEWRB, neurons = 4, SSE = 3.4875
" l& g! ~+ u; ?% e: u- H) K9 jNEWRB, neurons = 5, SSE = 0.534217
( e4 e7 _8 t& m: f. qNEWRB, neurons = 6, SSE = 0.51785
+ N! n7 o$ Z$ }. l* i6 MNEWRB, neurons = 7, SSE = 0.434259
5 _4 v' R4 [4 j! @" v. lNEWRB, neurons = 8, SSE = 0.341518
/ n( r) @8 S1 y- X8 FNEWRB, neurons = 9, SSE = 0.341519
; F6 ]- A* b/ d( v" V3 oNEWRB, neurons = 10, SSE = 0.00257832( T5 G8 r/ s2 @. a a
/ h8 @" d* U$ @2 I
八 删除当前路径下所有的带后缀.asv的文件& p9 z1 n# o: ?( K* Q
说明:该程序具有很好的移植性,用户可以根据自己地( u' \9 n: k7 c: }+ v6 T8 r
要求修改程序,删除不同后缀类型的文件!
: k3 K- Q# y7 f/ p2 A, sfunction delete_asv(bpath)
0 D- e6 Q3 t% C2 @%If bpath is not specified,it lists all the asv files in the current( k1 P4 S, p% V
%directory and will delete all the file with asv
8 q" B9 N9 y4 d6 h: [; k% Example:
& o M$ I8 q/ L; c) `8 l1 o! o% delete_asv('*.asv') will delete the file with name *.asv;
* q2 T2 [% u1 `* p# n3 i% delete_asv will delete all the file with .asv.; \: O" r& [6 i* i. y
# F% B) [9 u- r6 l/ `if nargin < 1) E: _4 w4 A9 s- F. D
%list all the asv file in the current directory
" y: V W$ C$ N: V2 Y files=dir('*.asv');
8 Z" v1 K! T2 S1 ?9 A5 Xelse
! j) u3 d1 f$ t2 F' G% find the exact file in the path of bpath2 g7 @- Y" F( `! ?! H
[pathstr,name] = fileparts(bpath);9 y! Q9 A# ]* R# p8 d: i
if exist(bpath,'dir')
2 V5 B$ s4 d% L& Z* l9 \" B2 u name = [name '\*'];
/ D f, S4 l7 a3 M end6 L3 p% o8 \% l# I9 a9 K" v% ~
ext = '.asv';* Z5 d& R* w$ {* H
files=dir(fullfile(pathstr,[name ext]));7 y/ |6 p R9 H: r
end
9 t7 a2 K! W; K/ l0 E6 G- f' G
2 X/ \0 w3 _) Q7 t! [6 N6 Y* Uif ~isempty(files)
: | Y0 h# i2 [) q for i=1:size(files,1)8 Q& }: m1 {5 f8 T
title=files(i).name;5 b) T( X2 X6 V& n) L) U
delete(title);
) l' u' _' r+ ^ end4 D3 \! J5 M& H& b8 R
end7 y( }6 {- s( j6 w9 M$ w! K
# D, l5 j* v- h$ }+ V" A
0 C. | @& ]7 P$ z7 ?3 `
同样也可以在Matlab的窗口设置中取消保存.asv文件!4 \% l, K( j5 C2 J6 r, R
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