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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
[( U) |; `8 ~4 u* K- }" y1. predict_fun.m为主程序;2 W% }- s% x4 c7 @3 a1 @$ m
2. timeseries.m和 serie**pan.m为调用的子程序
s2 |" K/ ]. A9 z* z" Y4 i0 ] Q1 n- w( U# _: b9 o, @, U
function ima_pre=predict_fun(b,step), `& k: c: T7 Y3 P8 r4 M: k
% main program invokes timeseries.m and serie**pan.m4 \2 {8 \( V X) L* y. f4 s4 ?
% input parameters:
" H5 K' H% c3 v$ E1 Z% b-------the training data (vector);
" h% ]% d8 p6 B% step----number of prediction data;
, R- _ a; U0 G7 i9 N% output parameters:
7 M$ M% P( d2 M4 J: b/ w% ima_pre---the prediction data(vector);
+ p+ ~6 j. v* sold_b=b;
' ?) f0 [( z( c" i$ a3 mmean_b=sum(old_b)/length(old_b);
1 }/ M/ E: n% `$ ~! w' |std_b=std(old_b);$ v/ t) V2 g6 c6 r( ?: E
old_b=(old_b-mean_b)/std_b;' l! i! k, V# m, d5 H1 _
[f,x]=timeseries(old_b);$ a O& G7 G3 h
old_f2=serie**pan(old_b,step);5 [' F) G2 z8 [' \- B9 G5 ^4 O
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;
6 @* E4 n+ d: u+ AR=corrcoef(f);
! ~) C1 w" `# n- ]/ r[eigvector eigroot]=eig(R);, U+ P# o, w. G; ]2 B
eigroot=diag(eigroot);( ?1 v$ l/ _' O- w) d( {# j4 A
a=eigroot(end:-1:1);+ B f6 L2 I8 r3 R$ m" H4 ~" ?
vector=eigvector(:,end:-1:1);% V3 j& {) g( j c5 i( I# l& C
Devote=a./sum(a);2 a- u2 X: g. s4 ?* f# \+ b* I4 h
Devotem=cumsum(Devote);
0 p/ d, n6 T1 p8 L' M7 B$ Nm=find(Devotem>=0.995);3 T. K1 A8 [9 l0 z/ \$ A
m=m(1);
0 r; W' D3 S( g8 gV1=f*eigvector';
& n! u: ]8 W3 {7 i* dV=V1(:,1:m);
6 B' \5 M5 `1 p) |! f3 V3 g% old_b=old_b;
4 p# s, f7 G5 n) ~old_fai=inv(V'*V)*V'*old_b;% T( l2 ?. ?% J/ n6 z w
eigvector=eigvector(1:m,1:m);
) d3 q! H) y5 {! T* e9 j) wfai=eigvector*old_fai;
+ l2 a' Y7 R( {1 f/ A5 k5 _, B5 if2=old_f2(:,1:m);: h; j7 f5 I9 w* c9 P3 m3 [$ E% z2 E. T
predictvalue=f2*fai;! O0 Y1 W% ]) B, r }( J. I6 [
ima_pre=std_b*predictvalue+mean_b;! S& F3 }! }0 k% Z0 x3 O
5 C9 d* U! ?, |1 x1.子函数: timeseries.m
6 B, K4 y b4 E" H; u) i% timeseries program%% s- I: r$ |9 P/ {7 X* j
% this program is used to generate mean value matrix f;
% {: @. G3 `" T! vfunction [f,x]=timeseries(data) ' Z5 `) X1 o- T$ Y u/ ^
% data--------the input sequence (vector);, P& ~- o. D( h. H: {- @
% f------mean value matrix f;" z8 x& u( o" P. F% X
n=length(data);
/ M5 h0 g; |5 F" F6 c3 Gfor L=1:n/2) `( u6 B1 O6 f# q' }9 A
nL=floor(n/L);
q. ]! i5 m- s6 _, ^+ E for i=1:L
$ |7 f8 X: m* A: J& @ sum=0;
; ]+ U8 D+ X" U- K4 f- | for j=1:nL3 m% J7 {/ d( ] A
sum=sum+data(i+(j-1)*L);9 ^1 p( H3 l& l, H8 b) [5 l
end \% f v" K3 J( @
x{L,i}=sum/nL;
6 x& L/ P k2 y end
# A* M r- i6 F/ w$ l$ v3 zend
7 S& P2 P" B5 |$ D( qL=n/2;
* K# K9 P3 q: H6 r" `5 g( Of=zeros(n,L);& V7 r7 p3 X* @" D0 T' F1 r
for i=1:L
6 Q" n4 g4 ]( h! i \( x, r rep=floor(n/i);
& ~# M% B( P9 I {8 D* m res=mod(n,i);( l3 A3 \% n3 b+ Y4 F# G. h
b=[x{i,1:i}];b=b';
5 O4 g( c4 }/ R, w f(1:rep*i,i)=repmat(b,rep,1);% \/ t; H `; M/ S9 k
if res~=0) T: c# d) C2 G! n/ l( S( C
c=rep*i+1:n;) s5 \5 s8 i4 j( b, k
f(rep*i+1:end,i)=b(1:length(c));" i* D) Z0 N* s2 |# A
end7 Q$ K5 b9 g3 L1 ^" [. Z0 W5 l
end- r( d6 d* d# C @( E) D4 k
) P# e3 Z0 W3 Y( ^: q# |
% serie**pan.m+ q! g3 C$ p: n& s' y& w
% the program is used to generate the prediction matrix f; ( d' T! A# p1 r k* u
function f=serie**pan(data,step);
( w, `" Z* `5 C, s%data---- the input sequence (vector) {7 T6 J: h9 F# W+ e2 m: P
% setp---- the prediction number;
/ C% i( B, g* l' B8 p; ^3 u% c: r, qn=length(data);& k/ K$ Z# n1 ~# K- q0 h
for L=1:n/2
* @; d- @5 }# v5 s) ` nL=floor(n/L);
) _4 [" E. `- Z1 ]1 j0 p for i=1:L( X' `4 b& i! a$ J" }5 T
sum=0;! G2 N- v, d* l2 ^
for j=1:nL
0 M1 t% u [* X {2 R1 Y. U J sum=sum+data(i+(j-1)*L);4 S. [" ]/ q. f+ E0 b8 A
end- P: n* o! w6 Y9 i. s
x{L,i}=sum/nL;
8 q; C$ g X* r( ^7 L5 C end( T( G4 U3 Z, f
end
4 J5 z7 {2 y. G7 F0 [8 ?L=n/2;
, e% N1 Z+ \& |f=zeros(n+step,L);
! }! \, d1 Z# a6 e( w6 _* Efor i=1:L6 W% Y2 \0 Q! p. P
rep=floor((n+step)/i);
; E& z" J! p& [9 O res=mod(n+step,i);9 G" a4 n. b: t+ N. G* g
b=[x{i,1:i}];b=b';1 ^: a( H& B' x8 K
f(1:rep*i,i)=repmat(b,rep,1);% Q2 p7 r' N; }! M
if res~=0
]' s9 N3 u. P5 j6 h, | c=rep*i+1:n+step;3 J: c+ @# ~9 |7 {; p
f(rep*i+1:end,i)=b(1:length(c));
+ W/ S0 x# _# \/ `/ ` end4 t/ i0 d$ ]+ p9 h
end) @8 N% B9 X0 e
0 H5 \* B2 j3 g
二 最短路Dijkstra算法
6 C7 E( @* G* l% dijkstra algorithm code program%
0 `) k+ g) X2 F, k( ?$ n. b9 f# T% the shortest path length algorithm! ^, i7 i' D9 ^1 s( ]- X+ g7 y
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint); W* {6 z& _, `; c
% Input parameters:: J7 M- E) d" W7 ^6 E
% Input_weight-------the input node weight!3 z5 S3 v) \: b3 ^' Z8 X; l
% start--------the start node number;
8 t( V, b1 Q4 I4 o$ p4 t! q% endpoint------the end node number;3 t0 \% N' J/ `7 }* u. C
% Output parameters:
& [( T3 r8 [, ~4 }2 i3 ~% path-----the shortest lenght path from the start node to end node;
5 Y% e% r& v: I* A- V$ D+ s1 Z, k1 ?% short_distance------the distance of the shortest lenght path from the. s% ~ ~) |8 {) N& Q) u
% start node to end node.
: E' `: t5 @) b% M, I% z" k[row,col]=size(Input_weight);
1 J+ r2 I" N) Q& [3 z$ U! ?# h3 m3 X+ X: \+ c! h8 j5 w, x/ c7 ], e
%input detection; n! _" z- {7 V
if row~=col) i0 F- p, }9 W5 ~' i
error('input matrix is not a square matrix,input error ' );- N+ d3 x1 Q0 Y& R
end
' ^3 |! R3 `% p* m. M7 _, lif endpoint>row
3 E7 W* ^4 n: e& B; Q+ @2 K error('input parameter endpoint exceed the maximal point number');! A' [7 T/ h$ L- K
end |/ y3 o# f6 q/ A% y
, M' e3 [$ s( ?( E%initialization
: a+ `/ W/ R# ds_path=[start];
0 Z' g' u! _4 X- W; W# Zdistance=inf*ones(1,row);distance(start)=0;' D- _! r! m( q. } Z: F- _4 h
flag(start)=start;temp=start;
2 p& |% I6 _8 J7 E8 u, p
# c. ]! N" G! h" Xwhile length(s_path)<row
$ ]6 s" P4 H. C8 u$ ^. W pos=find(Input_weight(temp, : )~=inf);
" [, q* x2 a" j8 J s3 x# e for i=1:length(pos)
: t' a! |1 ?" n! j6 N if (length(find(s_path==pos(i)))==0)&
' ^$ c. B$ W, X) {) P( Q(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))% l8 {; d4 Z7 }% U' K" Y+ p1 }
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
2 X3 d. X+ H" C7 D! a; g. ~, V flag(pos(i))=temp;
' p7 {7 A# u2 T4 B1 b, O end
3 F+ u1 i+ Y+ m' s ]9 V# P8 I9 t; Y end
5 |, B8 W& \- B, U6 @/ T k=inf;) g% |* I( v/ o# i% r
for i=1:row: y: ?# {' w& T% c; H; ^1 @# ^6 d
if (length(find(s_path==i))==0)&(k>distance(i))
& F* O' i" p: Y k=distance(i);, w+ B5 h) U- P$ Q/ H7 q
temp_2=i;2 ~! I. G: n( @1 e5 z
end1 W6 p8 S2 O# k6 G7 d% K
end
, {$ j! A6 t6 l- y4 a* A7 H# ^# z s_path=[s_path,temp_2];
3 |' u: N4 G3 R% x( L' ?8 a temp=temp_2;; L, e0 x+ I- S8 ~7 P
end
9 G$ @7 L; ?. V& F4 L. w2 \+ L9 Y0 q' M/ U* e3 Y X, H" {$ y
%output the result2 O) n. u$ G+ @! R# k- z
path(1)=endpoint;( f% _' ~6 u0 M3 B( i, \
i=1;- _- A; O" S9 h
while path(i)~=start' d5 h) s7 G7 o* ]+ z3 _% V
path(i+1)=flag(path(i));6 y. ~- U3 Z0 y+ L+ o, e) d( y: ]
i=i+1;
. d0 i7 ^, s, y1 G; z. Xend
# _& ^& b5 R) t Q5 F/ V6 q0 s) G$ ppath(i)=start;
# {, h; m7 X0 J; Zpath=path(end:-1:1);
7 Q1 ] P4 k' H; }1 Qshort_distance=distance(endpoint);9 p/ E9 e4 G8 Z/ I$ t5 N
三 绘制差分方程的映射分叉图/ r9 q/ |0 Y. ~, j9 j m
6 E5 Z- i) o/ e4 n7 u% _# Jfunction fork1(a);
' Y5 m! q" \/ i; T1 o
8 I9 e" Q. h3 }; J: o6 g% 绘制x_(n+1)=1-a*x^2_n映射的分叉图0 V0 E f# O: i W# V
% Example: . K/ @- L2 X' V1 A! |* k% X* W: S
% fork1([0,2]);
) B9 p5 ?, p7 }- e7 B! p/ rN=300; % 取样点数 2 X. ?* z4 {2 I0 f( }- J* c, J
A=linspace(a(1),a(2),N);
5 [6 K6 ^; I$ T; W. o% Z" estarx=0.9;
8 o& b3 `/ M1 LZ=[];
% ^ L, e8 [( K1 wh=waitbar(0,'please wait');m=1;9 B! w) z) J! L% X0 e @0 y
for ap=A;
' C/ d! e4 O; y* z# r4 x/ I; F x=starx; , G8 V; }' I, J
for k=1:50;
, U( T' o5 z b) a0 k1 R x=1-ap*x^2; ! d+ g5 @# I, _. o7 R# I
end [* o) k$ }- z- T: p
for k=1:201;
# H8 ]. x! Y& d/ \3 I0 ^ x=1-ap*x^2; & J' \# n% O# F7 M* \% Q! V
Z=[Z,ap-x*i];
( o" X+ D% A1 l' z; V3 \' {$ ] end
) o: T F" g6 C waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);& `0 p1 G& q7 y2 ]
m=m+1;9 k$ p4 ]+ U y3 _' j# O' _. z( r& P
end ' ?9 U( e+ z% @; v( A6 B; @$ U
delete(h);! f; z0 ~; C) g8 U M: w* F
plot(Z,'.','markersize',2) # I* W0 D$ R! n) H; B# L8 m
xlim(a);& U5 @7 t. L. x* s$ I
0 h1 n- R; x: r G% [: P四 最短路算法------floyd算法7 n8 H E/ V. S G; F O6 E0 H# _
function ShortPath_floyd(w,start,terminal)
! U( A# j5 c; N$ U& d' H%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
: _; s1 Z) [, `) T$ m%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];, o: x* h) ]6 H7 C+ o
%start-----the start node;: L( i; a! Q7 t5 [6 @
%terminal--------the end node;
: Q3 P( \; B9 t" O& e. `4 dn=size(w,1);
7 D+ e; N0 K( d$ w% i& ][D,path]=floyd1(w);%调用floyd算法程序
( p; `/ ~ W3 P; k2 E3 f
. k9 E, ]0 M* \5 H% Q+ u4 t) [%找出任意两点之间的最短路径,并输出
& f- a! G8 }0 U+ D! Gfor i=1:n
. ?: z& n' a1 d) g2 N! T+ [7 N! x. M for j=1:n) t$ g) o: D8 j
Min_path(i,j).distance=D(i,j);
7 e% P5 D( ~& m& k$ Z3 H7 @3 ] %将i到j的最短路程赋值 Min_path(i,j).distance
! l& Z4 w# C+ }3 @ \ %将i到j所经路径赋给Min_path(i,j).path) Q- A1 ~2 r# T# M( k! B7 r) y, y9 T; Y
Min_path(i,j).path(1)=i;, M3 E. F3 Z7 Y. s
k=1;* S; q' e' o5 C5 g7 j
while Min_path(i,j).path(k)~=j$ p) M6 e8 X$ f1 {+ V3 D+ S
k=k+1;0 @2 X* v+ C2 V- E$ U( a% r
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
1 p& g; R, Z5 i. G* J! O5 B end/ L5 v! {: J) |4 |+ u- d: ]
end
- Q% t2 Y6 F9 G& x7 u9 D/ k! xend
! m: f* s6 o# B5 j8 v9 J. V6 l7 Gs=sprintf('任意两点之间的最短路径如下:');
7 S; U- _- w- p7 d( p/ Y8 ?. Zdisp(s);; E1 n) L7 g6 h5 k, \0 |! A
for i=1:n) G: @# }5 O9 X/ p3 f' i+ ~- K
for j=1:n- a6 \3 u _2 ?8 E/ f
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
7 J4 W. v! h0 H$ Z ,i,j,Min_path(i,j).distance);% ]/ m; _$ z0 T- m6 ]" i. ]
disp(s);/ _' |4 u; Y# X+ O
disp(Min_path(i,j).path);; |4 F" e& k! D1 R) |$ O9 I
end/ K/ ?& n* V! H2 \, x6 h$ r
end8 ]' d1 K( T9 a! b
& f; ~' C/ e0 ?2 A3 f3 \%找出在指定从start点到terminal点的最短路径,并输出8 j5 Q% G T8 Y. }
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
. o& b$ @% @3 [5 L start,terminal,Min_path(start,terminal).distance);
; J8 h7 v1 x' I% h" U) j+ Ndisp(str1);! C5 x- Y a: S0 c' v4 S/ p) C
disp(Min_path(start,terminal).path);
8 d$ g! M7 i* e X# \
F/ y' n, L/ o3 W0 Q" j) T%Foldy's Algorithm 算法程序: e' i# N% W( _& @2 i4 |
function [D,path]=floyd1(a)5 m3 V( T* _6 a
n=size(a,1);) `! R$ W Z o" o! j
D=a;path=zeros(n,n);%设置D和path的初值
. N+ o, @- n8 z. |9 o$ Cfor i=1:n H/ B2 W, ^2 K& w! H
for j=1:n) T% Z3 w/ ~8 `: v- U- \# a
if D(i,j)~=inf9 E* m- D0 B6 i! n
path(i,j)=j;%j是i的后点 s4 ?) J2 r$ i" u
end
; M) D3 c D) n) Z3 ^$ L1 o6 j end& c( u' d% _6 R. v
end
1 d, [/ l- S! G%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
6 Z0 @$ l3 Q3 r! b5 F& Gfor k=1:n$ ]: U3 y$ W# w1 R0 ~
for i=1:n
. _9 y4 f# V/ e1 q, |& P for j=1:n
- A, R. I0 p& e: ^- N1 e( h! c if D(i,k)+D(k,j)<D(i,j)8 q! h# Q0 b6 E1 D6 p
D(i,j)=D(i,k)+D(k,j);%修改长度
( Q7 ?( m+ ~7 n6 } path(i,j)=path(i,k);%修改路径
# C- I4 V0 _& j( o4 x end. b. v" H; V: ]- P# v
end
! ?" w% t+ q, g8 A( Y, w end
4 C, N: J! B: {' A) \5 Y1 qend
# q3 u- ]9 K I2 F$ f' d+ E' J
$ ?2 {' g4 Y# e+ n( [: O+ ?五 模拟退火算法源程序
; g3 E8 x: C3 a4 Tfunction [MinD,BestPath]=MainAneal(CityPosition,pn)7 x, }: m/ ^6 c# H/ _1 x
function [MinD,BestPath]=MainAneal2(CityPosition,pn)" i" Z9 @/ w. C
%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
0 J0 R; g2 S. I. k6 O%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
) z2 x, w) E/ U/ t% I5 B% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...) ]1 J3 ^4 F( r0 ?& j- T* s: X
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
, V* A* y/ o& p5 y% q+ f+ M% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
8 q( c4 ?: P, V% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];4 _& f* J1 t- P5 z v
) G# N4 d( {/ V
%T0=clock& d8 o5 y. Q, U' n4 m3 e0 V$ m" d
global path p2 D;
$ ~$ W4 Q, v/ g3 c9 `' T3 o2 y[m,n]=size(CityPosition);- J+ l9 l5 u+ `0 V( s
%生成初始解空间,这样可以比逐步分配空间运行快一些. G! {5 c P- ?% K) o5 {4 F
TracePath=zeros(1e3,m);; S0 X' A; A$ Z- l
Distance=inf*zeros(1,1e3);
3 x I: r& m' a. i2 ~! D9 ^6 E7 V6 J2 V: d7 Q4 w" I8 d
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...8 y M( o. ?8 O+ S, S0 ]
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
' T' T8 k2 z. ?. H- _& m9 |: v# O%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)% B9 Y& S7 `; y9 \- n
for i=1:pn# w& {$ B1 ^3 {: C. X, h
path(i,:)=randperm(m);%构造一个初始可行解% D/ ^7 _% A: r* D( m: m
end1 }6 M( p0 C; f; ^5 T4 Z
t=zeros(1,pn);
* [7 L- Y7 ~7 X8 q7 [p2=zeros(1,m);
$ I. g6 v$ w2 y) G2 g9 ?" y/ L8 m: ?+ {% M. T6 k. T
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );1 a [7 B. U5 C
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=' ) ;
$ S9 J1 B# l$ f7 e%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
! N- U& G1 p7 b6 |%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$ s/ b; E. s6 D
%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1 T7 D( b5 l% O3 G
%会收到到比较好的效果, H; C: i; V, p! r" N
# U# I8 Y. o' T- n1 c
T=1e5;
8 y) V3 {$ O p+ F+ AN=1;( J8 [( [' _) Z" F
tau=1e-5;%input('请输入最低温度tau=' );
! d0 t# z2 o0 W8 c2 X%nn=ceil(log10(tau/T)/log10(0.9));
' {. Y+ m) w) |8 z: X9 F! ^* `" Swhile T>=tau%&m_num<m_max 7 H0 z* L* E/ C& p1 I3 K# K5 N7 }
iter_num=1;%某固定温度下迭代计数器
y4 s* O2 Q/ }* | m_num=1;%某固定温度下目标函数值连续未改进次数计算器
) B9 [; Q3 b6 D" Q$ i) ?; D %iter_max=100;
& A; A2 J- H& h( N, s0 ^ %m_max=10;%ceil(10+0.5*nn-0.3*N);
+ R. y$ Q f( @0 s: j# _7 J9 `" K" h while m_num<m_max&iter_num<iter_max7 E$ |3 v: ~. T8 _ r/ o
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:& G0 `. r4 l6 `# I0 _
%用任意启发式算法在path的领域N(path)中找出新的更优解
5 U& K4 n3 H9 P5 m9 `! a9 Q0 e8 w! G for i=1:pn
: u8 O* l5 \- X! w C l3 s# u4 n Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
% j6 a' p& J8 G' I& [6 S$ W( L%计算一次行遍所有城市的总路程 3 |2 ^8 |2 D) c$ G& a7 o3 U
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线4 R* l+ U# _8 A, ]
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);4 g& Z" R& f* W8 v" T
end8 N1 p/ ?% Q7 ]% N% p$ j" f+ w
%Len14 ?9 w7 z: W( t1 V3 g3 j3 B5 j
%Len2
7 w! u3 t4 l- i; i %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand9 w& {, [6 v, @; ^% ?* I% ?
R=rand(1,pn);, j2 U7 ?7 X1 |2 r1 f7 r; C% r- W5 N h
%Len2-Len1<t|exp((Len1-Len2)/(T))>R+ H/ b% G) X) {, q6 `
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
- s9 A3 H u8 A path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );, J& `* _! h% R4 d) H9 L
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
# {$ Q# Y5 z" E6 e3 T [TempMinD,TempIndex]=min(Len1);$ y- U- R2 P$ B* a
%TempMinD
* N4 ?' X3 r O TracePath(N,: )=path(TempIndex,: );8 o% I& _9 W6 A: d( T- j
Distance(N,: )=TempMinD;* @4 V E) o' ?. x k( F( d) @
N=N+1;5 y. R/ `& ~8 G1 S6 J
%T=T*0.95 J1 w3 |/ n) I& H
m_num=0;
+ ^* x$ n% w" O' `2 R; h% q# l else
5 ]7 R1 _) @% Q7 c" ~ m_num=m_num+1;8 b" k7 Z& `( ~- ?! ]
end1 `) R) _2 k, ^* {: K
iter_num=iter_num+1;) R/ b3 @0 q! \- E/ t: y
end- G' ]& h2 k$ C+ O% ^
T=T*0.9
- h: V! j) |4 a- @0 F8 }%m_num,iter_num,N7 I! H. p6 g" _8 [5 L; a8 F- m5 ?$ S
end
, e9 x9 r& I' v' h C[MinD,Index]=min(Distance);6 [% P, C; x) v) k' S# M+ G- V2 ^+ L: ^
BestPath=TracePath(Index,: );2 {, O/ U/ Q7 C3 F$ K
disp(MinD)
" m; ^. Z i* S%T1=clock( C* b0 [* r# x# o
2 |! z+ i# x8 |% [ @
) ]- X3 g/ z7 G7 L1 X6 j%更新路线子程序 & r/ Z6 v0 E [+ d1 k8 p6 A
function [p2]=ChangePath2(p1,CityNum): R% W1 \4 R# n0 C0 V* D
global p2;* F5 t- U1 y! N/ a# m! h, r
while(1)& T5 N6 y) G' Y# O. e8 ~. t
R=unidrnd(CityNum,1,2);
' K6 G! r$ J( H4 n1 t if abs(R(1)-R(2))>1" c0 c9 D% F# C6 Q* P! e4 E Z- c
break;0 G; p1 q* x- H$ H8 a$ s
end
" L' {0 z& o& qend
- j, a- C" u8 O+ r; \R=unidrnd(CityNum,1,2);
; d6 p9 ?4 M# ZI=R(1);J=R(2);
8 s0 V) E4 c. R: B%len1=D(p(I),p(J))+D(p(I+1),p(J+1));4 g' x5 n& q% `, h, \ f5 `
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
9 x( F# i$ h$ m- h. e$ m. yif I<J8 X+ _: N0 K" j' q) [
p2(1:I)=p1(1:I);
4 b; D6 E5 k0 l( w& p: z p2(I+1:J)=p1(J:-1:I+1);
+ i H5 _( e5 c p2(J+1:CityNum)=p1(J+1:CityNum);
9 K% b0 [3 K, Aelse5 M, @1 m: ? ^6 D9 X
p2(1:J)=p1(1:J);
. f! X. {7 E F0 }( }. d p2(J+1:I)=p1(I:-1:J+1);
1 B, V& T7 b/ T1 i1 j$ [ p2(I+1:CityNum)=p1(I+1:CityNum);
- V0 J! i! `5 A7 b" Z' }( V8 t8 Gend
/ ?1 T8 w: J) I5 t/ g% N I6 u
4 H* @$ K" n9 b& _六 遗传 算 法程序:
& ^' f7 b, X7 _ 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!' A8 ?* U' {3 F4 \/ s! F
' N* n- u3 [% M: T5 N
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options): [1 y& R# N6 c0 \6 U
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) ' K. F+ U0 ?; D8 k$ N! I
% Finds a maximum of a function of several variables.. q2 U& K& S2 h, s& [
% fmaxga solves problems of the form: * K, a% R; I' ?( u" Z
% max F(X) subject to: LB <= X <= UB
7 u, }: V3 [1 L4 E/ G, y) t/ O: g% BestPop - 最优的群体即为最优的染色体群7 K: Z E" H( g
% Trace - 最佳染色体所对应的目标函数值
) Z: w9 Z) Y9 O% FUN - 目标函数
6 n( d/ e# ?: ]% LB - 自变量下限
" c6 Q: M3 p3 e% UB - 自变量上限
) r( M; E+ h O$ p# n% eranum - 种群的代数,取100--1000(默认200)
6 r# _6 G8 Q6 [/ E% popsize - 每一代种群的规模;此可取50--200(默认100)* a! `5 f. x+ u x4 @5 Y
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
! i8 o8 e+ X3 g2 o8 v% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)1 [* Y4 [% s9 z) r* z2 F3 _
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
2 D% x$ ?# Q. Z/ o% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
4 Z$ I) W5 @- P%码,option(2)设定求解精度(默认1e-4)
$ ]$ ^' D6 j8 y9 _%
( n5 v" g; ?- n5 P2 ~- A. k% ------------------------------------------------------------------------
( ]5 T- l* S: M6 |7 h3 x, v7 |2 t" S/ d# g
T1=clock;
/ _* d7 v; z6 Z3 \- B! x6 zif nargin<3, error('FMAXGA requires at least three input arguments'); end4 r5 z- F5 f, b/ s1 f7 l0 o# \
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
$ Z! n; Z* f3 m1 m; D8 O9 Pif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end) W/ Z6 N& E9 Q( p2 k f/ j7 g
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end& [# I) ^8 ^2 H) a+ T. w2 c
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
/ ~ y7 ]: F, f0 Gif nargin==7, pInversion=0.15;options=[0 1e-4];end4 r" H! k7 D9 q& p: y, c
if find((LB-UB)>0)
# @1 I, Q& R3 J error('数据输入错误,请重新输入(LB<UB):');
- p5 Q- M8 l; a5 i7 X% E T( Uend
) T0 B0 g' L1 z' B( J, ns=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
" I8 W ^9 I" p8 e1 wdisp(s);0 S3 p4 ~' c; m# z8 U2 T
- t' E3 L" I- b& l0 Y2 q( u$ {global m n NewPop children1 children2 VarNum% V7 x9 X7 i+ z4 e+ a6 M
1 r* G- s x/ [ d3 m, B' gbounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
$ T6 u3 N$ l) r+ U' A/ N4 {, {: Hprecision=options(2);%由求解精度确定二进制编码长度. b0 K. Y8 |& u ~% ~$ t1 k* _4 V
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
& i, `' H7 s. C[Pop]=InitPopGray(popsize,bits);%初始化种群
; P5 m) `, q& v/ Q. O3 Q* t[m,n]=size(Pop);
`$ E% g* c4 p$ ENewPop=zeros(m,n);/ k7 S2 W i& }, Z, t/ @4 V k
children1=zeros(1,n);
( Z- u/ B( @9 X& dchildren2=zeros(1,n);, F. X6 R* l- M4 B
pm0=pMutation;2 Y0 p) e1 r* E. c
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
2 L5 a& v) D0 ^% `) uTrace=zeros(eranum,length(bits)+1);3 `8 y( l, N( [& s" c
i=1;
8 `) n) z6 o( k) R" U& S: nwhile i<=eranum# }0 A4 \$ S! K3 u- h7 g- P# H/ H' F
for j=1:m' X4 ^. ?0 w' k/ j
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
8 w& J O: N' H* N s end/ A" v) e* m" r' k2 C
[MaxValue,Index]=max(value);
& y0 f& T7 G0 i% y" F+ |7 a BestPop(i,:)=Pop(Index,:);" A, h& o- E0 U( Z: F3 J* h
Trace(i,1)=MaxValue;
* O2 O, ^7 F8 q: d) ] Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);5 J* g7 i& K# Y6 D, g( \; D' [1 l3 h; B, ~
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
) F0 R1 n$ k; m8 Z* P1 E( h i[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));+ B. U1 [: {& a: D2 t
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率, b. I+ N3 s3 v, n; h' W5 t8 ~
%round(unidrnd(eranum-i)/eranum)) N5 H2 c5 R( T1 ^; T( Q
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
, _2 V2 }/ r8 ?1 J; r: p { [InversionPop]=Inversion(MutationPop,pInversion);%倒位
1 |- j( Z. w+ C( B j! t3 T Pop=InversionPop;%更新, H E: q3 N r& F5 ~- ~- [3 J: V
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); ( n. t) O" J, ?$ s0 Y7 ?' L. B
%随着种群向前进化,逐步增大变异率至1/2交叉率: @# G* A+ M, w( [* K0 f
p(i)=pMutation;! B j: D) U6 `. M
i=i+1;+ i! c. U3 k4 b: z* E
end6 ]8 Y6 ~/ w5 Q8 y% m+ M9 X; Y: F4 l
t=1:eranum;
( X: i3 c# G, Lplot(t,Trace(:,1)');7 X$ Q% ?6 E; \6 K/ A" 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)');
, y5 ?0 @6 l% g" M8 ?[MaxFval,I]=max(Trace(:,1));
% D, ~' e5 \) U" x D+ gX=Trace(I,(2:length(bits)+1));' L4 N1 a5 E) q) x- U( |5 N
hold on; plot(I,MaxFval,'*');8 }) C) ]. ~9 V( u5 {6 d
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
+ [, @4 R) j7 u# M/ Y. Q. zstr1=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,:)));2 Y h2 w5 o& O% U# ^# w8 Y
disp(str1);" e9 l1 J+ N" S c) T
%figure(2);plot(t,p);%绘制变异值增大过程+ b% i4 d- G0 x
T2=clock;
, X U4 J5 l; {" Qelapsed_time=T2-T1;) l" r, k! B/ R9 a0 g$ H
if elapsed_time(6)<0
. _, U# B& `" G2 x& B! [ n elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
' m( L6 ?7 B7 \- m( N4 |: fend
3 b1 j( q- [; ?. w2 Bif elapsed_time(5)<0
7 }) p3 F/ A. U/ g, B" `( j% j elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
5 }2 m( I8 E# B0 D9 O0 bend %像这种程序当然不考虑运行上小时啦
) }4 P( M) ] [- z" hstr2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));
+ \4 \8 d: Q/ }% I1 jdisp(str2);
6 t4 z5 y8 m& E4 J& o' ^
$ u& {2 Y5 o8 J' K9 D- v+ g3 E3 N* \" i
%初始化种群
. Z5 D# S% ]! c7 B* f. c- S9 U%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
$ B1 u4 ~0 j6 Q. G& F, F4 nfunction [initpop]=InitPopGray(popsize,bits)3 k0 y7 I7 X( y7 L1 i- a& V0 m# P6 ]
len=sum(bits);1 U! o# J% ]) L; U2 h1 ^& o" Z
initpop=zeros(popsize,len);%The whole zero encoding individual/ E! ~( z- j( |! A, W1 I8 D
for i=2:popsize-1" q: x9 L) V }$ y1 t* D7 E
pop=round(rand(1,len));
C1 P0 k' O9 y# _+ l pop=mod(([0 pop]+[pop 0]),2);# _: K. K. M) E- v( ~1 m
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
* s: T+ s) ^/ `5 M1 D7 F+ ?4 g %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)8 x( |% n6 w! ~. R3 c$ S
initpop(i,:)=pop(1:end-1);( Q2 i }9 N! Y6 f5 Y
end. i5 G' z: c3 |4 k* K: V
initpop(popsize,:)=ones(1,len);%The whole one encoding individual
) H; v3 v- q" N% C) n2 [( ?%解码4 _4 m/ O$ R" i, Y, _+ `( X- d. b
" n4 G! c8 T- I3 u# u9 m& A
function [fval] = b2f(bval,bounds,bits)% s2 l, i% ~8 ]
% fval - 表征各变量的十进制数$ l) z: `7 I9 J2 O
% bval - 表征各变量的二进制编码串
% g6 r4 B8 H% s5 ~9 \. [8 ~% bounds - 各变量的取值范围$ Z0 V( `1 B1 f7 x0 f; c0 j
% bits - 各变量的二进制编码长度% Y; m1 l9 Q R
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
9 O$ ]7 ]! s; V8 P# Q% x- W3 [numV=size(bounds,1);: r) Y& x; G# S. T; N
cs=[0 cumsum(bits)];
% g* {5 j2 X. P7 \8 Y) afor i=1:numV
, ?1 ^3 k% V4 x a=bval((cs(i)+1):cs(i+1));9 r" r: h0 F" d6 V- G. z: V
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);/ [6 N. N! T% z+ m* y. n3 y6 t- y
end
! c! a" y" W+ ]. @%选择操作5 L. Q. B8 @8 b, o5 T; {. L
%采用基于轮盘赌法的非线性排名选择; U1 E# f; J& P' d2 s( s1 v
%各个体成员按适应值从大到小分配选择概率:, B. `4 X+ B; @1 X5 K1 ]
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1
1 H1 @/ L6 l9 H8 \( s* _2 x: K; [4 I0 D9 B5 U
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
6 @0 ~! }2 J! u( r6 e- s; z# w, K eglobal m n" m! U; ?$ `+ S" I
selectpop=zeros(m,n);- `5 k- n3 H& V5 v( s8 B% m8 R. m
fit=zeros(m,1);' A1 j) B: z/ d' g6 T- E
for i=1:m2 m8 R% I* w; P% z# J% A2 F
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
- R* ]1 U3 \' qend4 \# h# E+ u& W8 U2 }9 c
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
/ t \# v/ r# a5 Xq=max(selectprob);%选择最优的概率* s4 W3 t5 t9 s# B! N$ b
x=zeros(m,2);
% a7 h! r$ R( ~: Y7 D: H! W7 ix(:,1)=[m:-1:1]';
' g2 n4 ]/ E# ^' I v[y x(:,2)]=sort(selectprob);
1 F+ a$ ^% y, E% B: x/ [, A& B; vr=q/(1-(1-q)^m);%标准分布基值
! i6 ^+ M- z- o: M: [/ z# _newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率# d8 L6 O- W$ T& ~0 j
newfit=cumsum(newfit);%计算各选择概率之和1 s* C* e8 L1 R% |- Q/ e
rNums=sort(rand(m,1));$ H$ s' Q! j; G7 O8 j: k
fitIn=1;newIn=1;4 ]6 ]# p* p) z; S- ^
while newIn<=m
& S- F+ l! [/ I3 s$ r if rNums(newIn)<newfit(fitIn)
9 x5 G; `& W6 X: F/ r5 q selectpop(newIn,:)=pop(fitIn,:);2 ?0 z* ]+ f( R
newIn=newIn+1;
! z" O# @: [, D else, W/ r' X; `8 A P' e- g1 ~ g/ G
fitIn=fitIn+1;6 |- J+ j) O6 l$ [( C
end/ _: [" a* X7 t5 i( V8 w
end9 R% Y' A4 u- \0 P z T- }
%交叉操作
. O! }- A0 V) e8 p4 c# @function [NewPop]=CrossOver(OldPop,pCross,opts)
' n t3 ]: q5 U%OldPop为父代种群,pcross为交叉概率8 ^ ]& s; c& V3 a% Q( B4 c
global m n NewPop
M; y% ?& ]. e7 b1 g4 W" O$ wr=rand(1,m);
7 _7 `% B- _8 z- x" j0 [; m+ }: Ny1=find(r<pCross);5 D% i; V4 e* M# F- o0 c
y2=find(r>=pCross);
, N2 C4 k" h) d! V" P! t4 |( x6 z. ]len=length(y1);
" Y4 ~: ~) p$ N& h$ 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
5 W8 e" ^: n; A) J; v! |( o7 K2 W" c9 q y2(length(y2)+1)=y1(len);
* U. z! u2 ]+ i/ Y y1(len)=[];% x/ W1 \5 a7 e$ w7 ]* `+ L
end
, q* D6 J; v* i2 B: p0 ^if length(y1)>=2, U/ x6 M4 e) {, P8 [) d' R
for i=0:2:length(y1)-2
8 n/ q1 y+ g! u if opts==0
+ I i# J" M" ]1 R% M [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));! e- ^5 X' l1 z: @5 r0 c
else
+ x2 ?( ?8 n* J$ n, j1 p$ E7 @ [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
- a6 r7 T5 M! N, k0 M# {6 D end3 U m' k- a8 V0 Y6 g( q& U5 e4 r
end 4 o( s# C( `& w4 W
end5 _. [0 B" `7 k- x4 u b
NewPop(y2,:)=OldPop(y2,:);
& g( g, ~+ \$ ~5 C; X# K
$ |. r/ g+ `( E4 ^! ~%采用均匀交叉 + x6 T0 J& G( {
function [children1,children2]=EqualCrossOver(parent1,parent2)$ R9 `) o9 X3 {/ P: _
4 T8 L3 ]* k$ f/ [
global n children1 children2 9 g% [! o! s! C( Z/ _, G6 D
hidecode=round(rand(1,n));%随机生成掩码
2 i, [4 [% ^: ocrossposition=find(hidecode==1);
( [# Z; C2 G0 choldposition=find(hidecode==0);
# D4 G2 \* ~0 s+ O# ^+ echildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
# ~6 O; b; ], ]+ }" r0 R" ^ ^children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因' ]" ]4 c" d0 I( V
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因" K, R* ~. s7 p$ X; J
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因% S6 H7 p% G. V1 a3 t+ k
) g/ M6 f$ h# Q% ^/ o%采用多点交叉,交叉点数由变量数决定
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, W9 D; K7 Z1 Ffunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)
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global n Children1 Children2 VarNum+ D; t6 C c2 ~2 o2 K2 p/ f
Children1=Parent1;
, D* H( s* L0 N* KChildren2=Parent2;7 }# g( P g1 w. i
Points=sort(unidrnd(n,1,2*VarNum));
% O& U Q& @. L8 @& [for i=1:VarNum$ d c# W* [' |
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
& q1 E; E. n8 \8 X- ]9 W3 p Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
, r' E2 a, n7 oend
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%变异操作
0 L9 H7 ^ {/ {+ s8 M8 a5 ifunction [NewPop]=Mutation(OldPop,pMutation,VarNum)! X; O, \- J. Y$ I( k1 t
: n1 I: t3 ^8 P& c/ A2 y9 p2 uglobal m n NewPop! Q0 z4 F6 a5 f* H
r=rand(1,m);1 n1 [0 k! ]# g1 D4 s1 n! ?
position=find(r<=pMutation);' I) Q& {( g+ I, a' n( O9 N7 U& c
len=length(position);
1 |) \! A! h+ n mif len>=1
- m, Q- R) M! @ for i=1:len, `0 U; t; X, O( ^6 Z
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
5 c U4 D y# b for j=1:length(k)
# C# x7 ]) }% N7 k if OldPop(position(i),k(j))==1 a; |) E& P! t3 R; s3 X$ o
OldPop(position(i),k(j))=0;
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OldPop(position(i),k(j))=1;' B7 o" A% M8 C! x- \' Q8 q1 y
end6 h& o) V) Y7 a5 o
end- _* Y/ ^8 w7 U- f2 U( T" @
end
7 C Z0 |6 \8 `2 V3 Tend( B- } C1 B) W9 G5 Y, @
NewPop=OldPop;
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%倒位操作
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6 C9 \. P0 b2 J1 c0 Gfunction [NewPop]=Inversion(OldPop,pInversion)6 e) J4 n$ D! F# M/ _. `
x, z) r8 J3 w
global m n NewPop5 E- e" ^5 ?- p) l) d. e
NewPop=OldPop;
3 M. A% d& C2 Kr=rand(1,m);
- e. l8 I9 L9 g0 A9 O) DPopIn=find(r<=pInversion);
% P6 j; ] x& l# ~ U! E& Z# |: _( [len=length(PopIn);1 N( e; A2 m& B( N
if len>=1
4 R& ?4 w/ A! @: K for i=1:len0 c$ ~$ @ M7 O& J" `
d=sort(unidrnd(n,1,2));
/ ^6 i1 M. y. m if d(1)~=1&d(2)~=n" y# n2 w- E5 X6 Q2 ~6 R
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1); g1 v: u) B2 i6 N; e( h
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
: q7 Q4 d2 t. @4 x% ] NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
; {$ k! P; v& x. E0 f/ ?4 w: z- ? end: J$ O& c# c- D" ?; N" ^
end
6 h2 z0 p& `! H# ]2 s% a3 M9 C5 `end
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七 径向基神经网络训练程序
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clear all;
3 \" g! f1 |# B0 ^clc;0 v( u8 u9 y' J" D
%newrb 建立一个径向基函数神经网络2 F" Y/ J3 L! g1 U; ^6 H% @. n
p=0:0.1:1; %输入矢量: f9 R! ~5 b# B9 Q; w/ h
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
) x$ S- T/ [3 D* E, b% C7 {, t7 Igoal=0.01; %误差3 T( \4 k5 l6 X. r( |! {) ?
sp=1; %扩展常数7 c. x- \& N" i; _( e4 P }
mn=100;%神经元的最多个数* _4 {7 X$ [3 i/ j/ {
df=1; %训练过程的显示频率 {( D+ U0 n# p/ ]
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络; [0 ?& z' o/ r+ {
% [net,tr]=train(net,p); %调用traingdm算法训练网络
- h$ e$ S8 a( v( Q1 @# _7 X v%对网络进行仿真,并绘制样本数据和网络输出图形
$ m8 |0 E3 k* \' MA=sim(net,p);) q {& {, I6 ?9 B: t. I
E=t-A;
- ~& B, a% {5 \. @! }sse=sse(E);
/ Y: L. ]' @9 h+ z8 Efigure;
3 p. x( F! O+ G! V0 t5 c! mplot(p,t,'r-+',p,A,'b-*');2 d3 V: `# U7 v5 ^/ K9 r" V/ w# O
legend('输入数据曲线','训练输出曲线');
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说明:newrb函数本来 在创建新的网络的时候就进行了训练!
- P1 i* x1 \; i7 X- D. P" x( O每次训练都增加一个神经元,都能最大程度得降低误差,如果未达到精度要求, k' }2 c; @/ ^0 }( [ ]
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!) B' z, V0 z1 Q" @) x
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训练结果显示:
& E9 n- d6 k- `NEWRB, neurons = 0, SSE = 5.0973
/ t% a& q, Q$ [- I% kNEWRB, neurons = 2, SSE = 4.87139
$ ?! I% i {0 v; [6 N$ v6 ]NEWRB, neurons = 3, SSE = 3.61176
' V- P+ A% ?# a, o+ aNEWRB, neurons = 4, SSE = 3.4875
* w2 l1 N- N3 t; p- w+ G3 mNEWRB, neurons = 5, SSE = 0.534217
# _% u: u) b3 N* \% W9 K& ^5 B6 H6 ~NEWRB, neurons = 6, SSE = 0.51785
; o9 N+ G2 N% T4 T4 q* h. QNEWRB, neurons = 7, SSE = 0.4342599 \4 O# c7 b2 [( Q& H
NEWRB, neurons = 8, SSE = 0.341518
) N; Q+ ]5 e) C0 m1 T$ HNEWRB, neurons = 9, SSE = 0.341519
: ^& i/ ]" w+ t! INEWRB, neurons = 10, SSE = 0.00257832# K) g# F* i3 b* |( `
& s- E4 l4 x* K+ P6 b+ C八 删除当前路径下所有的带后缀.asv的文件 z- I* I7 I3 @# S) q4 a3 W
说明:该程序具有很好的移植性,用户可以根据自己地) k* g' c# V3 C" ~# H
要求修改程序,删除不同后缀类型的文件!
/ z0 {; V5 L$ k/ G- V/ i+ D- Lfunction delete_asv(bpath)
^* j' W8 ?& d3 V%If bpath is not specified,it lists all the asv files in the current0 z: L7 g$ b: ?3 B0 m$ ~! }0 f, H
%directory and will delete all the file with asv
! C8 ~/ G) F8 ~* o3 E" O8 |4 W( L9 v% Example:) t: e& [! t/ w6 C1 q- r: p7 M( i
% delete_asv('*.asv') will delete the file with name *.asv;2 k( S4 x3 E0 W% r4 e- n
% delete_asv will delete all the file with .asv.. D8 j, }1 b) y2 U
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if nargin < 1
$ J+ v S( i1 J' d H% W0 Y%list all the asv file in the current directory% J6 L! s2 Y* y+ p
files=dir('*.asv');8 `* h* r, A( W7 ]& Y& j4 Q O1 i
else
$ O5 [, M' V; W: j! E. v% find the exact file in the path of bpath; n5 c- m0 l5 L0 b
[pathstr,name] = fileparts(bpath);( \$ p; Z/ E: Q! J8 A
if exist(bpath,'dir')9 O6 x' |( R- e* x! y' c3 n6 T6 q1 R
name = [name '\*'];. L. z9 M, ]) L3 u6 n$ z
end
7 Z0 q# ?) X& T! Z- M ext = '.asv';
6 y" R2 v2 H/ G+ x- V( s9 d% W files=dir(fullfile(pathstr,[name ext]));
E) ?2 R9 c" |# Gend
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if ~isempty(files)
% ?: F; s, r" Q4 i, r0 q, E% Z for i=1:size(files,1)# M1 ^4 |, d n8 P- J1 m
title=files(i).name;- V$ H, G* g" z9 O
delete(title);
/ e7 u) K& k* j }1 l end
8 m4 w/ ~) {* d1 uend9 ?6 Q# C: Z1 ?! o
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同样也可以在Matlab的窗口设置中取消保存.asv文件!) D8 W5 V! [& K2 r2 Z
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