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TA的每日心情 开心 2016-11-7 00:15
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[LV.3]偶尔看看II
一 基于均值生成函数时间序列预测算法程序
5 N5 ~/ k. c+ U) U a2 T 1. predict_fun.m为主程序;5 l. j' V4 i! W P8 _; N2 w
2. timeseries.m和 serie**pan.m为调用的子程序
$ J# l/ Y$ n$ ~! p* S$ z0 P- K, a
" V& z# o* a8 s' z+ B. Y+ L function ima_pre=predict_fun(b,step)
$ H5 e( I; M$ W % main program invokes timeseries.m and serie**pan.m
' Y5 Q$ `7 s; S1 k % input parameters:
$ G5 Y$ |5 ~6 E% X( R7 |7 ? % b-------the training data (vector);/ L K* Q# T5 I$ O3 [3 ?* f
% step----number of prediction data;* ^! g6 @6 S/ R% L) Z8 l# {8 V8 }
% output parameters:
6 J5 f9 F+ G( k6 r" m2 ` % ima_pre---the prediction data(vector);* q* R/ V5 ]3 r" _' {
old_b=b;' M4 ^( I% W& j6 o5 r# F' |/ A8 H
mean_b=sum(old_b)/length(old_b);
4 ?# x& R1 b: E- @; j$ E std_b=std(old_b);
, Z* _5 w! ]) D; I: i9 @. C6 n' } old_b=(old_b-mean_b)/std_b;
3 R4 E, w2 Y# L5 L; m$ e1 c( F [f,x]=timeseries(old_b);4 m0 Z2 C3 I6 c6 p* x0 u5 l7 r% \
old_f2=serie**pan(old_b,step);
6 P1 d* R$ V0 d7 W' F- x( R % f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;) Z0 g9 n4 G0 e! D6 t; x7 y) r6 o0 ~
R=corrcoef(f);
+ r. U0 T7 e* A6 e [eigvector eigroot]=eig(R);
( L* S) [3 L' z2 ^6 W! P( \ eigroot=diag(eigroot);, O2 K, Q* I' Z+ n: P, l5 ]) Z
a=eigroot(end:-1:1);
) C9 u- ?$ H! v; x: k4 W vector=eigvector(:,end:-1:1);
! T9 ^ u) U7 X Devote=a./sum(a);
; f; Z5 T( v& {3 Y Devotem=cumsum(Devote);; x9 l: c' s3 \
m=find(Devotem>=0.995);
$ p' k% Q4 @9 ]: E9 E; ` m=m(1);
n7 M! r% C7 t7 @3 H3 {1 x6 F% { V1=f*eigvector';
! ]+ }& d% B' k: K" @+ C V=V1(:,1:m);5 |( T$ \ R" x5 \* _2 O" k6 R
% old_b=old_b;
5 a* y; O* J% ^4 w: N/ Y, a old_fai=inv(V'*V)*V'*old_b;$ e) ?- `' L" `; _! {/ e
eigvector=eigvector(1:m,1:m);
& G* O$ y5 r9 r fai=eigvector*old_fai;& i& o+ q4 l J# ~
f2=old_f2(:,1:m);" D7 p3 ~6 K1 f
predictvalue=f2*fai;
B+ d5 k: s, G O3 v: K9 M ima_pre=std_b*predictvalue+mean_b;' b8 B' l& U) Y$ |
M3 x* {% p$ b8 Z% [! Q' p* V 1.子函数: timeseries.m 7 H. q2 F2 q8 |, b7 f) G$ T( {
% timeseries program%
" R e6 {5 g* y- E2 O# D' W) b % this program is used to generate mean value matrix f; N' V0 N' [4 p7 V U9 `
function [f,x]=timeseries(data) % e' ^' Y8 q3 U7 V6 q
% data--------the input sequence (vector);
& p7 e- P+ _6 W# e$ D % f------mean value matrix f;
0 j% n7 q, t* l4 S3 C" o n=length(data);
3 T: p8 |* ]' I& o2 W: T0 f for L=1:n/2
- _2 |% E8 @: j2 O1 M& r nL=floor(n/L);% m" V0 Z! j1 }8 |
for i=1:L, ]5 }, Z( V( y8 w4 l
sum=0;
' _- ]' b) e6 G for j=1:nL u" R5 I* \) ` P# s# r
sum=sum+data(i+(j-1)*L);
5 H d# T# S9 Y/ s9 b end7 C# T- }4 Z, R
x{L,i}=sum/nL;8 \4 i1 Q1 n- T% }# b
end
+ j# b" m3 S! g$ f" X3 I5 k end5 ]" i2 R# T( f
L=n/2;: v! j3 L" f, r# G; ^/ ?4 x0 H0 L
f=zeros(n,L);: ~/ E, N. F ~8 g# M8 ?
for i=1:L
' f- T* O% F& d7 J/ { rep=floor(n/i);
2 M6 @6 Q, w* v3 P" @; V res=mod(n,i);
; A: V" J2 k# @' g b=[x{i,1:i}];b=b';$ K# H4 {; ?; e# ?
f(1:rep*i,i)=repmat(b,rep,1);' E) b; o/ }5 W
if res~=0
: ^5 [" n. @0 o5 X: k$ F! l c=rep*i+1:n;
8 @2 }1 D! H0 [! a f(rep*i+1:end,i)=b(1:length(c));; o" N6 s% C$ v3 S- }0 `5 D) E
end8 k2 P) \9 R; }- s' O6 h
end; b/ Q" \5 O$ C) V0 ?
" N) O% Z/ @. B: X# q. K8 e& x
% serie**pan.m, B& x9 T, @' @) |0 W/ G2 \% A
% the program is used to generate the prediction matrix f;
+ x, d" b# H# u* ^3 }: |4 t function f=serie**pan(data,step);/ g+ D& a: \; ?% ?' W) r8 w
%data---- the input sequence (vector)0 {$ k5 b! Z/ G0 ~; D u6 o# K4 X
% setp---- the prediction number;
. ^$ @- n# k; b! { S; u n=length(data);
1 C# s+ T4 m4 D$ u for L=1:n/2
t( O) A8 y4 u& r nL=floor(n/L);0 k) p6 D7 k# C# l% r/ W1 k
for i=1:L0 Y% U/ j- e. S$ w4 O9 C' w
sum=0;! E; W# |$ h2 [3 P! j
for j=1:nL
$ V1 Y: S" J7 Q, i0 b sum=sum+data(i+(j-1)*L);
5 B3 S9 u; G6 Q/ V5 u end
, L5 p- x' h7 s6 P \1 E x{L,i}=sum/nL;
+ z" W% X: J3 b- _3 k( G2 p end
# ~% G6 r3 h& Q) B0 D% X7 N end
1 ]: H. d N$ D L=n/2;
0 ^) O8 Q; ~9 y) I f=zeros(n+step,L);# K, D& K1 _8 i6 I
for i=1:L' Q5 X: Y9 w$ u* t- t
rep=floor((n+step)/i);) O+ p5 L* o9 K; W+ `
res=mod(n+step,i);9 Z' C! k# U: }, C. N5 s
b=[x{i,1:i}];b=b';
( `" w( k6 @1 D% n f(1:rep*i,i)=repmat(b,rep,1);& }. v b; l0 Z% m' n0 L
if res~=0" p* e6 y8 i7 s2 V n
c=rep*i+1:n+step;+ `- L' B1 q" [4 ]0 k
f(rep*i+1:end,i)=b(1:length(c));7 \5 l$ b. l7 C( j) p" }3 P; }
end
" |: N7 X& t/ u6 \4 y end
4 p7 H" n0 A( Y! K8 t3 O
+ g4 |: e+ {* K' h: P 二 最短路Dijkstra算法
X7 V. F; M- G0 M; u# b) N/ k* X8 q % dijkstra algorithm code program%
4 Z0 n7 @' X! T % the shortest path length algorithm
& x6 C! x q u. O function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)6 b, r" x7 x% N# \
% Input parameters:/ X; y8 R# J5 B
% Input_weight-------the input node weight!" {& p1 i# v% ^
% start--------the start node number;# a0 m5 ^$ q+ J) a+ v9 \6 l, d; }% K
% endpoint------the end node number;
8 m8 Q" Y! q5 b; y$ T+ l, f/ Q# x % Output parameters:7 @# m. b- J8 b$ b2 O+ B
% path-----the shortest lenght path from the start node to end node;( C8 U6 G# z5 d2 z8 z
% short_distance------the distance of the shortest lenght path from the. V. H0 v* |% g3 x3 I
% start node to end node.
9 _* g4 S3 E1 e, L! a* o [row,col]=size(Input_weight);0 F2 C$ X( k. A0 A4 Y
- y6 L! d$ l5 O %input detection) U! d* f' @( \
if row~=col
1 }" G9 X$ k! ^: y8 o3 r# R error('input matrix is not a square matrix,input error ' );
1 k) @% `. S M" z. T1 h! M end, [0 X) i' {3 N- P. @0 Q+ b8 ]' [
if endpoint>row
. m B* P: { @ error('input parameter endpoint exceed the maximal point number');
$ t! g% F" r' Y+ p3 i; s8 n end( L/ a) b! J i3 g$ K
$ h; t- v- ?. R- L; Q
%initialization
6 Q3 M. B/ S' c9 L s_path=[start];
6 a0 c: c* ~" [% F distance=inf*ones(1,row);distance(start)=0;/ ~2 ]5 q# u# o0 [2 E$ j( w
flag(start)=start;temp=start;
% P( E. b9 o! f$ \# w 7 x X' K8 U3 L2 ` `
while length(s_path)<row
* l- j) L; X6 E6 _, x9 q6 l: v pos=find(Input_weight(temp, : )~=inf);
! `1 c9 s" o( }; Q1 g o3 s5 J for i=1:length(pos)
' @' \% x- A2 a7 F& R1 |$ I$ B if (length(find(s_path==pos(i)))==0)& K# E3 l3 P, X, w# E
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
7 J% g* p/ C2 K6 b distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
~, f, y# [/ h7 k flag(pos(i))=temp;
) ]% s) a" C+ n* J. M end
! T$ C, f9 G1 ]7 Y& z# ] end: D; a' ^3 w* A7 [8 A# R6 ]' B
k=inf;
/ E4 {+ W; c, D for i=1:row
: Y+ R8 B& q$ s8 B if (length(find(s_path==i))==0)&(k>distance(i))
1 `: t1 @. ]- n* N/ m% G k=distance(i);
% V1 S4 P, y3 `/ h+ `; Q temp_2=i;
5 X7 N& K' r1 { end
2 H$ o7 m: Q( I6 T8 B3 h end
* I, r& `( a9 d0 F/ C s_path=[s_path,temp_2];
$ i& j. f5 I: z7 P8 ?6 H4 W% Q/ G temp=temp_2;
+ v/ p0 [4 s' g7 O9 l0 B- ~8 j& D end
9 d3 Y D' E( ~0 S 9 `* w; h) O8 n) x
%output the result
" M9 @2 E; I, @1 y l6 I path(1)=endpoint;
9 H! I9 n) a9 E# }$ P0 c i=1;8 o: T9 u8 l- T: f
while path(i)~=start
8 F! ~/ k1 {8 F path(i+1)=flag(path(i));
! i ]# D) Z3 J M7 i/ _6 D/ y i=i+1;) a; w* Z2 J2 y) |/ F
end
; m! _& q3 J, B3 T0 _7 N5 q4 f path(i)=start;' X9 T5 b7 p! ~2 f
path=path(end:-1:1);" m' ]# l0 t1 Y d/ s
short_distance=distance(endpoint);1 p) W! k3 q3 ?, V& K
三 绘制差分方程的映射分叉图7 [) R, ?+ e3 G5 o) J1 U
! {2 k- g8 k% H6 X" A- ~- R function fork1(a); 4 k2 f9 ^$ f' P8 n! R5 k3 k# m$ }
! A1 P) I0 w {' u9 s
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图; o E6 _' _: h
% Example:
1 y6 P& A7 ?' e) H% ]% N % fork1([0,2]); # V9 m( t" c: _" h
N=300; % 取样点数 8 U3 J' Z; J8 M! B' _
A=linspace(a(1),a(2),N);
( b3 [6 T. o: h/ c starx=0.9; 6 N9 U/ D$ `$ F5 }, k3 Y! K
Z=[];
5 x; K1 c& Y9 a$ e9 t' Z7 t h=waitbar(0,'please wait');m=1; X9 X" m, m8 ]
for ap=A; 6 z1 V. b2 `" V+ N5 ?( `
x=starx; ( ]) t% o2 _0 j! T5 v
for k=1:50; % A% i- ^( c- L, }7 ~0 K
x=1-ap*x^2;
k* e7 Y( |0 A% [ end
9 C* J* O1 J* V K% K, @' I W( u for k=1:201;
& \& [+ E# m! T: v5 J" X x=1-ap*x^2;
6 u6 W* |( u" y& l- |8 ]/ M' Q Z=[Z,ap-x*i]; a& n9 x9 W3 K! c" a. q' w
end 4 j( g+ y; ?& K. c W" x" q
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);" S, [1 L5 D0 @8 O
m=m+1;
2 s" B# ]) Y7 x end
x0 @1 u" @) }7 H% s delete(h);
$ S2 W( H! \; o! n' p3 B6 |6 N plot(Z,'.','markersize',2) $ e0 K7 d( [2 h% V' E
xlim(a);/ o9 b: z- A4 u8 |7 ]1 D; j. o. u
5 S4 G+ P$ ~' y7 `1 R6 X: @. E3 g
四 最短路算法------floyd算法) S7 p" C5 T* v' H: O
function ShortPath_floyd(w,start,terminal)
) H1 e' P+ A- h2 m" i0 d %w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;0 R7 k6 |, Y8 K$ I) y
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];* J# c+ Q, [, K, K. m( U
%start-----the start node;
% c) b+ G! Z; L/ i %terminal--------the end node;
B. V1 R+ L% K$ ^' h n=size(w,1);
( _! `6 c4 S7 g [D,path]=floyd1(w);%调用floyd算法程序
3 H* `) T2 N' @$ X0 \ : M* E! `. g% q7 X
%找出任意两点之间的最短路径,并输出* ?' ]( u; [1 b/ N9 ~
for i=1:n( x8 _ j! A: [
for j=1:n
* V8 ~" D7 K! Z9 e4 j+ b Min_path(i,j).distance=D(i,j);' s+ G" ? h0 E, c# Z
%将i到j的最短路程赋值 Min_path(i,j).distance. p/ v/ I- j0 I9 x) z; o
%将i到j所经路径赋给Min_path(i,j).path
) G: C+ x7 ^& K: W! n$ e( f Min_path(i,j).path(1)=i;
: }( Q$ T7 \6 ]5 m& s, T9 F k=1;
7 _8 x4 D g& P5 l* c' ? while Min_path(i,j).path(k)~=j
% |6 @% y9 P* y1 v; a, Z K, o% p k=k+1;
9 L; p8 S& f3 C9 C$ r Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j); L6 M' t' H! D" r" @" Z, E
end
; G" x. d4 X3 I# K7 k end
# q, [- Q; g9 i% N% } end
0 t6 X/ G* ^9 H7 T1 l s=sprintf('任意两点之间的最短路径如下:');
" v1 v& f% P( n$ e! z: l disp(s);
% C2 O: d8 C7 t, |8 s: T) | for i=1:n
G) L& q" P1 @' j3 G for j=1:n
, _0 R1 h4 M+ H$ Y1 H% z s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...& K8 Q7 ^, _) \) C& T( Y
,i,j,Min_path(i,j).distance);
$ E. e* o% t2 p0 J( H4 g disp(s);
, b: p2 P9 L2 H7 m( U disp(Min_path(i,j).path);/ K% U! x4 k7 G) ]" P' O
end
# _# {" I7 U# W1 y* f( H end
. V' E5 T7 u( {; k8 \. V + @6 G8 _/ h/ T' B
%找出在指定从start点到terminal点的最短路径,并输出' i/ `* O) ^$ }3 q
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
1 S! U& Q: t9 T1 P+ L, } start,terminal,Min_path(start,terminal).distance);
0 ~4 b& Q* T. t2 O disp(str1);+ z, c8 {) h/ o6 f* d
disp(Min_path(start,terminal).path);1 _0 {& m* D+ c3 T) E2 T
5 ]* {/ m0 H- W' m& t3 q %Foldy's Algorithm 算法程序7 V; \; N+ t& y5 w# k7 J
function [D,path]=floyd1(a)
, g2 U2 R! x7 W! x- ~; t n=size(a,1);5 |' j0 \7 Z# s* r- M, \; v
D=a;path=zeros(n,n);%设置D和path的初值
! A; M5 z& z8 _; P) o" R for i=1:n
" X# y; C) B) z5 z8 w7 c% E5 ] for j=1:n, `& h- s, p$ j* i) l' ~
if D(i,j)~=inf$ t) N. G) `& Z/ |# `
path(i,j)=j;%j是i的后点) q1 P& B- h! F) f
end8 n Z9 h8 T5 f
end2 q( z+ e5 l1 g; G& s! y: V |
end
5 h& o/ w( M6 n6 J. S% [) m r9 s %做n次迭代,每次迭代都更新D(i,j)和path(i,j)2 b. W1 V9 Y1 G: N
for k=1:n5 @+ c( i4 s$ J0 I2 ^9 U8 I! ^
for i=1:n
! d: s7 _3 M0 D7 B& Q N/ e for j=1:n, a1 f8 h5 ]3 Y E: }% o
if D(i,k)+D(k,j)<D(i,j)- o* E7 V Y# d* R
D(i,j)=D(i,k)+D(k,j);%修改长度
7 B S4 `- {8 I- ~6 U" i% w- P$ z D) R' y path(i,j)=path(i,k);%修改路径
: x% B% W7 C) E1 I2 P( l d end
+ W' c/ l3 j8 o end
* I4 B# o4 C) R/ b/ ]" h end
! _* f3 [7 r0 k, a& W! _ end1 V( b$ F# r# x, t
2 b) O( w$ Z# L5 _' ^0 ~/ @3 Q
五 模拟退火算法源程序
( t0 B* ?: O3 d function [MinD,BestPath]=MainAneal(CityPosition,pn)* k. |1 }9 z& |; Q" B4 C1 q
function [MinD,BestPath]=MainAneal2(CityPosition,pn) ~: e ~$ p4 ]9 X- @! B
%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! D" W& X) k5 a! t7 ~% t
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
( P# v& S; v! {2 s+ Y m f6 J6 P: O % 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
, t R5 \" b" z% i$ b % 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...7 P8 \1 O: j$ D) u/ |9 n7 F2 o
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...: G" x& e* H9 Y9 q" D
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
6 U8 N4 o. K/ f( h8 F! G2 u ; U8 ~" Q) M) t* j3 p
%T0=clock
8 z; r' s" ]- I1 V! G& b global path p2 D;1 q! w A! ]7 y3 O
[m,n]=size(CityPosition);
) Q) n. a; Q5 C4 v1 ^" `2 \- f %生成初始解空间,这样可以比逐步分配空间运行快一些' T! g9 \" n2 N1 e8 F }
TracePath=zeros(1e3,m);4 Z; k, H w( G2 b% F
Distance=inf*zeros(1,1e3);
6 m' Y8 n2 P; ~9 w! `! d
" p) U* K/ T# ? D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
# E) |. y/ H* q, V) v (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );! X$ q' Q* ^! k! r/ Y, `
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
' y& [8 d6 p! f+ a2 t for i=1:pn9 B5 }% q# p: s. G+ \( f
path(i,:)=randperm(m);%构造一个初始可行解
5 l5 ?0 o( }5 ~. W* ]8 C end
( A \7 o& {1 j# g0 }4 C t=zeros(1,pn);! S9 h# Y' j' k. A5 j
p2=zeros(1,m);2 R5 T6 N9 J% [8 c1 K; C
! C- p. [2 |* T, X: N iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );% S+ F! y7 T3 K4 A ~* z
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=' ) ;; b' `/ B Q! ] d
%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
' w& H6 P/ W1 N1 K" M: e9 p %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 b6 o! a2 n# i6 a %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
( I$ Q# a( s6 u %会收到到比较好的效果' V4 R! b. C$ j |
2 N, l' {8 p7 T* g4 d* M T=1e5;" |/ ]* m6 D& b/ Z% Q4 Y
N=1;% O* `9 d' D0 H) i$ b Z4 |6 H
tau=1e-5;%input('请输入最低温度tau=' );( S7 s4 \4 k& D+ g& z5 s; Y
%nn=ceil(log10(tau/T)/log10(0.9));
/ g( E3 c+ i, A& ^4 c$ t0 P0 j while T>=tau%&m_num<m_max
$ v- j( v4 D3 @5 o8 U9 R7 y iter_num=1;%某固定温度下迭代计数器
$ Y& ^( |9 Y8 q* R0 ] a m_num=1;%某固定温度下目标函数值连续未改进次数计算器
# ?( d( Q6 i$ @" ?9 o9 u4 ~$ @6 O %iter_max=100;# H S* H' g- F+ v1 b! L
%m_max=10;%ceil(10+0.5*nn-0.3*N);, V5 N6 w7 J% C0 T0 f
while m_num<m_max&iter_num<iter_max9 {0 C" R T* j# W$ `
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
( ]1 y7 T$ ?: w2 \" u %用任意启发式算法在path的领域N(path)中找出新的更优解
$ l( @$ U o% l0 R& { `# Q for i=1:pn" r4 r7 Y! F: W2 q/ z) R( Q* T
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);, Q' }+ V! k% L2 b
%计算一次行遍所有城市的总路程
3 q; O- f! O6 }! \+ L5 } [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线: e$ }8 Y# ^$ \# i2 F, Z5 v
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);$ g" G3 Q# M" T% k
end
# ^- x! D/ |' F; e %Len1
" z1 L% G( _1 }& n %Len2
- u# ^ g: n# r) P: w5 G9 p: R %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand! u7 F' Q0 I/ A/ v% n
R=rand(1,pn);
5 {; e- z$ B" c. t %Len2-Len1<t|exp((Len1-Len2)/(T))>R$ ^- P8 ?4 D; X: _' Y
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
0 o7 ]' B3 S7 ?8 x% w0 P9 N/ [" { path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
( G6 x2 ^5 `4 Q Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));; d9 Q6 }6 f% L
[TempMinD,TempIndex]=min(Len1);
1 ?8 M/ q; `+ ]8 H; J %TempMinD6 @* ~ t" N% ^" P5 ^) S9 Z u
TracePath(N,: )=path(TempIndex,: );2 N+ q! U1 N- J# y( i! g) v! T }
Distance(N,: )=TempMinD;
$ _3 I/ I4 W2 s N=N+1;2 E1 v1 Y5 t! J0 t }$ X% b
%T=T*0.9
+ B( }& J' D; {9 Z: G m_num=0;
6 k1 H* F: ?& a \: N else$ J* N* l8 |' ^; Z: ?3 m3 Y
m_num=m_num+1;
7 Z4 f7 [& J5 ]2 o end
. |" A/ l/ f0 z6 f- I/ ~) r iter_num=iter_num+1;
+ Z- B; ^* K+ r' p5 d9 z end, `7 S/ ~6 Z; b8 P: Z1 n5 D
T=T*0.9! S6 e7 @, v; M. B- |% X
%m_num,iter_num,N! B; i: a$ k# g& P) e% ^
end
$ ]3 G' A% B0 X# j2 r! B; q8 r [MinD,Index]=min(Distance);/ M) u! S7 B/ z- j
BestPath=TracePath(Index,: ); f/ J# v) W' a) m' M
disp(MinD)
6 O) P, d+ P. g %T1=clock$ ^& h3 S/ n7 k4 w2 R' c: G
: n F$ S V0 @* y8 O, Y
( Z# U& `7 ~5 |; l5 b5 o %更新路线子程序
k; i o+ T" h: N6 O c8 | function [p2]=ChangePath2(p1,CityNum)
; y: N5 t9 Y; K+ a+ z global p2;
* M; C7 `# P% v9 H8 y1 j, L$ k5 L7 X while(1)7 g3 ], X9 ~ @ |/ L+ C6 j
R=unidrnd(CityNum,1,2);% v( N6 U s6 _5 l
if abs(R(1)-R(2))>1$ p; E/ ]/ m' N4 {! ?5 Q- B$ P
break;
9 M! o5 N, Q" a# d2 _1 n end/ t. ]/ o% N$ v3 X! a0 d; }& q x
end
. `9 |. o% B! V8 r R=unidrnd(CityNum,1,2);
% \1 \$ h ?, z N9 K, z% A I=R(1);J=R(2);3 v: t# N. `$ e- z8 g9 ]
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
! R) V. o& S+ A( e. m% m4 ~ %len2=D(p(I),p(I+1))+D(p(J),p(J+1));
; [( b' n, e! O! x if I<J
9 Z: a0 h: c# |2 R: H4 g p2(1:I)=p1(1:I);
9 v- r' Z+ r! C/ v" L, e p2(I+1:J)=p1(J:-1:I+1);
' t( y" c$ H" U- d y p6 V p2(J+1:CityNum)=p1(J+1:CityNum);4 h7 {4 i8 `0 U/ f3 t4 h9 R
else
" D6 j& }" j! E! w p2(1:J)=p1(1:J);) E( A# D2 z! l* ~' t0 ?
p2(J+1:I)=p1(I:-1:J+1);
( V( v! z: Z2 g! v) ` p2(I+1:CityNum)=p1(I+1:CityNum);9 j7 b" w( ~* }* G
end
# e0 F+ g* F, L1 w& F& F% z
9 R: K5 k3 }, C" }5 u 六 遗传 算 法程序:
7 R+ n: Q. d: t, I4 Y& f4 x) Y4 s 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!3 N* h3 A. u# g3 o# ]3 t2 a @7 |- \
! Y+ g! l7 h: D
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)& m0 l3 ?5 c3 R1 P6 ]1 [
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) d" S) g |' q* ~
% Finds a maximum of a function of several variables.
1 U8 t# g, a7 B: O % fmaxga solves problems of the form: : K8 G, F3 p3 {8 }" N2 {0 H3 O
% max F(X) subject to: LB <= X <= UB
/ L0 F0 p7 N; B* I % BestPop - 最优的群体即为最优的染色体群
' x1 a7 r! v8 C: E2 j2 L0 Q % Trace - 最佳染色体所对应的目标函数值3 C6 p6 ~; J" Q1 S+ d) _- O
% FUN - 目标函数! Z) |( R" i- E7 T4 E5 [
% LB - 自变量下限
6 b# f T/ h: J, Y- p* g# h % UB - 自变量上限
$ l/ k3 H+ w8 ^/ Z [/ g/ ~7 r % eranum - 种群的代数,取100--1000(默认200): g" V1 D9 x+ f" U; \: s0 O' o# z! n
% popsize - 每一代种群的规模;此可取50--200(默认100)) @; d8 v& K' N- T- Z
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8): V% z6 K) \2 E6 g
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)/ x7 v* z' L4 ~& o5 U
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)+ E' S+ g6 f- Z5 d( ^
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
& T) J1 R7 P1 A, @7 `* s; m %码,option(2)设定求解精度(默认1e-4)
" ~$ ]" C& u/ Y %
) ?; T# I I* E$ f( j/ } % ------------------------------------------------------------------------3 d, T1 h& y# Q# E/ [1 V/ e( h
6 s# }5 t+ m5 ]9 l, u3 G T1=clock;1 z/ h5 K: G [& j
if nargin<3, error('FMAXGA requires at least three input arguments'); end
) J3 l. y. J1 V% m0 G, O2 N if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end% v& v& u4 {8 U0 m
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
/ F' `) U2 ~5 W" k1 C) F0 E if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end1 ~0 O- W& Q0 |
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end1 l5 G- b+ W8 V
if nargin==7, pInversion=0.15;options=[0 1e-4];end
{$ Z2 n; B) D& G. q# P% ?& O3 |% G if find((LB-UB)>0)
+ v8 k; ~% b5 ]& X error('数据输入错误,请重新输入(LB<UB):');2 U% r* w3 e- {
end
- J) T3 A6 ]3 O8 p( \/ I s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));' d* R6 f3 H4 U* [7 G, y4 M
disp(s);
$ n9 I. n; l0 |7 u# Q9 K$ x% m
; d7 ]/ V* {1 A. i global m n NewPop children1 children2 VarNum
" \* s& A3 v8 M6 Y+ J% [ # E* C3 D7 X# W1 N
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
2 R$ E9 M D. K6 g- W precision=options(2);%由求解精度确定二进制编码长度
' S: q5 N [# g3 L V bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间6 N1 C. v1 `% N) a
[Pop]=InitPopGray(popsize,bits);%初始化种群
4 E0 v" v3 S6 C. M3 | [m,n]=size(Pop);
8 D2 Q( S9 J l3 ~5 I NewPop=zeros(m,n);* [3 V! \* w% N2 [4 a
children1=zeros(1,n);& k; J! N" [3 [! x. g
children2=zeros(1,n);
- Z+ w5 s% M D7 D0 V pm0=pMutation;& {: C0 X3 z! S+ R: [
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace& D Y: D7 t( B. y% l7 S
Trace=zeros(eranum,length(bits)+1);
2 C: u; b* }) c i=1;* Y3 P9 b) c) W7 t2 E/ e; A# D; c
while i<=eranum
$ N- s& H3 @% ^ for j=1:m
T/ A! T9 T) {. n& [3 F value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度/ ~7 l$ x: h+ F" @0 l
end! \+ X4 D* B- x7 F
[MaxValue,Index]=max(value);
; X- ^5 ~5 \8 r# E BestPop(i,:)=Pop(Index,:);$ u( y' J% `9 y' p
Trace(i,1)=MaxValue;
2 o1 N. S8 \7 q; R2 ]9 I/ F$ N Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
) N" K" {/ p; j; s" X9 N1 ^ [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
& a( t' W1 S e2 s2 [/ [+ a7 n4 N [CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
8 c4 K9 e# ^( c4 T %采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
2 U! ~+ B. O( r9 j# Z8 O3 f %round(unidrnd(eranum-i)/eranum)
$ w' _& V1 X3 I [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
4 ]7 f- n. b# }3 E& L [InversionPop]=Inversion(MutationPop,pInversion);%倒位
- z$ Y# O& m; O Pop=InversionPop;%更新" } J% W4 f) W. F( U5 D" W" |+ s
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
7 ~' U+ ]& ]3 B1 |# G+ e6 H0 w %随着种群向前进化,逐步增大变异率至1/2交叉率9 l! V; u% [0 M4 ?4 @( q7 g4 _# O' ?9 F
p(i)=pMutation;9 ~( x; V: F$ f7 C) \+ B
i=i+1;
: a/ I2 H$ g, F9 Z end _6 J- a z& `" I0 Q1 y/ O
t=1:eranum;8 Y) @& P; |/ J+ ]
plot(t,Trace(:,1)');
Y/ n) n% s+ S 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)');
! G/ i' D( Y" E; N" o) }# _ [MaxFval,I]=max(Trace(:,1));+ ~ | u7 @$ E& V" A+ ]6 k; k
X=Trace(I,(2:length(bits)+1));
# S& Z" D2 m5 a; l8 j, d* L hold on; plot(I,MaxFval,'*');! m c: p2 D4 N8 s0 n) S
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
7 Q2 t8 c7 s. R% j$ [ str1=sprintf('进化到 %d 代 ,自变量为 %s 时,得本次求解的最优值 %f\n对应染色体是:%s',I,num2str(X),MaxFval,num2str(BestPop(I,:)));# K8 o7 y/ I3 l0 o+ r0 L
disp(str1);2 `! ?$ O* e; ?/ t
%figure(2);plot(t,p);%绘制变异值增大过程" O/ J( j# q1 `; f+ b/ ?! I
T2=clock;8 i9 a9 T3 N1 B: d a( w/ R3 c3 o
elapsed_time=T2-T1;
$ I7 j( r1 E& n" h6 t& Z# w2 i# S if elapsed_time(6)<0
/ k& D' S. Q# y- k elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
$ A) d/ ^2 u G4 b# B- I/ R! Z end
$ J1 P" Y; r" ~1 L if elapsed_time(5)<02 ^7 \' Q3 z0 L* A
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;- o; N+ t' |. w u9 |) z8 ] V! D' C
end %像这种程序当然不考虑运行上小时啦; j( R# J1 t* P, I* c/ m
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));" ^7 C5 v! l) J$ x
disp(str2);$ q% g+ b& K: n: K \9 ]/ X# h
3 m' `9 { k" E* R& w+ h# G; l
( g' q# j, W( d! X+ p %初始化种群: ?$ e( G& l( S, g f8 u% ]. V
%采用二进制Gray编码,其目的是为了克服二进制编码的Hamming悬崖缺点
! }2 X5 D2 F1 o- M$ N$ l) L: j4 A" E function [initpop]=InitPopGray(popsize,bits)
# l" ] K" X- A: Q7 R3 V len=sum(bits);% `$ ?, B, X" t1 b
initpop=zeros(popsize,len);%The whole zero encoding individual) q1 S& n# n8 Z2 B7 Y; g* d+ A6 y
for i=2:popsize-1
5 t# V6 D% `" S, \' R4 j( D1 j( @: E pop=round(rand(1,len));
1 x V3 {( l) n3 }4 U8 y/ p( p, \ pop=mod(([0 pop]+[pop 0]),2);
$ p+ G# v2 Q8 m5 N. z& V' G# A %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)+ w2 m' A4 }$ K B1 e) I' Q/ h
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
( i, K$ L2 v( G initpop(i,:)=pop(1:end-1);
+ j, B' `. @! U/ |8 W q& R5 Q end
" |( p, P3 c+ S! u3 l! ^ initpop(popsize,:)=ones(1,len);%The whole one encoding individual
, k1 K' h9 C( X$ `9 ] %解码
, f3 S3 Q; P7 ~
# Q/ c3 t* q; b' K function [fval] = b2f(bval,bounds,bits)
& k V+ d0 N, N% I/ T* N; F( n1 O) Z % fval - 表征各变量的十进制数
- P1 k' _' e) E$ h5 j % bval - 表征各变量的二进制编码串
9 A- Z# a9 D7 e, Y b1 z" M% Z % bounds - 各变量的取值范围
9 ~1 L6 F3 t: K# [2 X0 w T % bits - 各变量的二进制编码长度
* j6 U1 w$ f! H scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
; x1 S+ Y' P# w( s& P numV=size(bounds,1);5 }6 ]1 Y+ ^, F$ L' Z; O9 z; x
cs=[0 cumsum(bits)];
& T2 x0 d+ B6 \& j! t' o# _ for i=1:numV# {! S5 A8 G' f: B+ L
a=bval((cs(i)+1):cs(i+1));
( j4 M% f7 s& A _/ R. f$ P" G fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
6 V" I2 p& s' Q! W2 j0 s4 i( ?" B end7 j& r# z+ L4 | W* B+ ~4 ]
%选择操作
; L" B, @( r) @3 f/ k* ] Q. J# U %采用基于轮盘赌法的非线性排名选择
! b6 @; I+ h2 V! { %各个体成员按适应值从大到小分配选择概率:
. Y+ ]7 [+ |7 E7 g8 N& t. f %P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1
0 |) \2 ^ l g ; l- n, m( a1 }5 c0 t; m
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)$ k4 r& |- R1 C) \7 J2 b1 S
global m n
3 m3 ^; v) x3 H# c9 }! P, e selectpop=zeros(m,n);# \& L E/ E, O6 P: X. j) ~
fit=zeros(m,1);
) G5 g. Q/ ^% J2 g) d9 o- c for i=1:m
% J4 N# m h) L# u fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
2 w5 x' w. ], c end8 [+ b. j" h7 f' ?; _, I* q
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1) R( q) E7 m6 o1 o" F7 l6 V
q=max(selectprob);%选择最优的概率
) Y) q7 O% v4 G' u. R x=zeros(m,2);( q/ i* z- K/ U# d
x(:,1)=[m:-1:1]';& _# \) j$ H. c3 |' X
[y x(:,2)]=sort(selectprob);
( e \3 q1 A% K& m3 N/ E r=q/(1-(1-q)^m);%标准分布基值
# L9 z0 y g) l$ o7 K8 E7 ] newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
/ g% R, g, q1 \* D* x newfit=cumsum(newfit);%计算各选择概率之和
( w4 h+ o: `1 r2 {- N, p$ A" U0 C rNums=sort(rand(m,1));/ [, g5 f9 T! L- R4 X
fitIn=1;newIn=1;; `2 ^8 ?' U9 o% C6 w
while newIn<=m9 g0 Q" w6 z9 p( C6 c
if rNums(newIn)<newfit(fitIn)* V9 k. b) D: p- {: x# Z* d4 H
selectpop(newIn,:)=pop(fitIn,:);" S) Z0 w9 f I
newIn=newIn+1;
, Z# O! ?" N3 r/ o1 w8 L6 S else
# b6 i% I! u. g0 n0 E1 k fitIn=fitIn+1;2 Y8 M" p! Y7 X. j1 g
end' O" K" a$ H# r4 M9 M9 D
end* e* F+ I2 H& P% i! b; [( Q
%交叉操作) v% b5 v/ T7 A% `& {0 g6 f
function [NewPop]=CrossOver(OldPop,pCross,opts)
. a( R) F3 k; s" R6 ` %OldPop为父代种群,pcross为交叉概率
- R5 I0 y1 B3 [- F global m n NewPop . D9 P& r) p3 N, V/ K3 ?
r=rand(1,m);
- }. }1 O) [. Z7 o4 k6 D; P0 } y1=find(r<pCross);- l% F9 G2 X) g/ q8 j; T/ h1 {
y2=find(r>=pCross);- ]- [4 ~& M1 I0 A4 I
len=length(y1);
1 x' M: J4 S, X7 b7 O7 L 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& t& Q" o; L0 N$ g) Y5 T
y2(length(y2)+1)=y1(len); C: P) M1 Y6 Z7 e9 t
y1(len)=[];
3 i3 k) D% w1 \& z4 x0 F; b end& r8 M. g$ O3 F. @# }
if length(y1)>=2. n& i I. s5 [. x& z! Y+ G1 I
for i=0:2:length(y1)-2
. J$ A; Y/ b4 g( f" }; T' D if opts==0+ q5 C! M" m; ?9 o- t- W
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));$ e% e! A: h% C5 |& u+ {
else
# d( P/ u) h& G1 E: \9 ` [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));" r! ? N4 u, v: j' n0 |! q9 Z
end9 U! k' [" b& ~* n+ r- h
end 5 u4 M5 q( J* t0 E* A" O1 U; p
end+ F4 P9 b, e/ X( Y( ?
NewPop(y2,:)=OldPop(y2,:); _5 \4 |; }3 Y1 |9 Z
3 q7 s: N8 L4 I' u; ~" Z %采用均匀交叉
0 E& S7 z, y4 n! K: e7 ~ function [children1,children2]=EqualCrossOver(parent1,parent2); h2 ^ }- S7 f# k
- i) a: C3 d$ R! i global n children1 children2 t( L4 x: T) @' c8 L. e5 W
hidecode=round(rand(1,n));%随机生成掩码& `1 u9 {7 Y$ N. j6 k
crossposition=find(hidecode==1);
d4 O7 e! Z( N: n% ]4 X1 z holdposition=find(hidecode==0);
2 Q) {7 c- g' ~7 m1 P' H children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
) }1 n! k8 p: z0 [% ^ children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因9 K% h# A2 K1 f- t
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
/ o; w, |8 P+ q$ L children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因/ l' _. M) A; [ t' |* |
& @2 |9 b- ~3 I6 z; i H %采用多点交叉,交叉点数由变量数决定
3 y/ q! g# s8 b1 u% z D5 _1 b5 M; { ~6 x- ?$ l- O% M* `
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)
8 d! Z" O+ V& U* T2 B 2 ~0 Q$ m# X: W5 l& d! q* j; a$ P2 m
global n Children1 Children2 VarNum
+ m2 R6 w( [( \ t Children1=Parent1;" A8 M0 n: M, ]% L
Children2=Parent2;
) K8 e; W. k; Q. a: p Points=sort(unidrnd(n,1,2*VarNum));, n) i. Y3 t( }# ~, O3 k
for i=1:VarNum
3 b9 _. {! o) h0 ?1 d+ o+ G" C1 j Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
% n& p" v4 l8 {+ g) {9 A5 o" I3 Z* i Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
* m' ~7 f+ Z; |0 ~1 o" f end
( Z4 d2 y) l' |
8 |( q, M6 ^ S0 {" V$ x %变异操作5 b4 L0 u# W D x1 c
function [NewPop]=Mutation(OldPop,pMutation,VarNum)
3 D2 h# ~' N* J7 y; y/ A' k& M# e * W. h* q, d7 [4 X' {
global m n NewPop
) L# a' H# _+ c r=rand(1,m);
9 q. D2 J$ W: N" X1 z" c; N* v position=find(r<=pMutation); ?6 G8 e' b \
len=length(position);- \; c6 D) C2 A+ s
if len>=1" ]1 [( `; o& K Q
for i=1:len
" q4 H9 N# I6 ^, t+ l- B k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
3 g' C# m# _+ l9 j, W8 f# H# q( E: L for j=1:length(k)
' o: Q7 ^- ]+ a if OldPop(position(i),k(j))==1
( d% @ o; E1 x( }. I- W' w: F OldPop(position(i),k(j))=0;7 a9 Y6 i3 `% }/ e: w' O" ~+ |3 P
else
2 L+ ?8 F$ f' i, D3 d3 g OldPop(position(i),k(j))=1;
. g0 a" F, K1 z, n' i end- u. T+ x4 [8 P& ~) M/ K* Y# ?3 M7 U
end6 F& n! P6 o, h. v/ Y2 l6 y3 L
end* b6 T- S& v9 _) w, }; d" r
end
% q- \4 h" P1 E; _ NewPop=OldPop;
! Y8 h+ q; j6 u( N4 _2 y
$ i! |- i3 Y; N; J- x0 _ %倒位操作
- n. d8 B. Y& H* v% X
. I6 }7 N+ ^& ~ function [NewPop]=Inversion(OldPop,pInversion)' Y: l; w( ]6 ~- s: U2 b9 x6 B9 M; Y
# }- S+ C( T h+ D: p8 w global m n NewPop# D0 i8 J6 f6 j0 r$ T
NewPop=OldPop;! f) u7 N/ _9 h5 W: E
r=rand(1,m);6 H2 ^! a4 M6 e
PopIn=find(r<=pInversion);( k" Y9 N. a3 \" r* ]( U* \: w$ N$ l
len=length(PopIn);
# M2 B2 O4 ]- n- h0 o5 Q( q if len>=1
9 _% Z) Z9 s; r$ V: L0 M for i=1:len
& E8 |7 C% o2 P0 R0 G d=sort(unidrnd(n,1,2));- _' X" o; `4 S
if d(1)~=1&d(2)~=n
2 t& }+ O* F- `- b( ?3 f! z NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);: m# I3 N- T( w, j' E
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
: q# ]; y, O3 \( [0 n' s NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
9 Y# q; s! ?; s end( c0 _; N0 J" Q5 ^2 q6 ~, m
end
" ^. J, D/ A5 \: [: y' H end1 |/ d% z+ ^! S; V4 R& T
, t8 c4 z. }$ [0 e7 K
七 径向基神经网络训练程序9 g' ]1 `2 U1 P! T
) A9 I3 p# S# R( ~ D7 { clear all;' J# }- Y; Z+ `7 ]6 O, S# r
clc;& V7 P6 E& S9 K0 z$ x# ~
%newrb 建立一个径向基函数神经网络; l" c' _6 X$ s [; d& |
p=0:0.1:1; %输入矢量
; g5 P/ p8 q/ |9 v t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量9 [+ C1 R0 Y. p% P4 R3 ]
goal=0.01; %误差3 v/ c, y8 ]6 O
sp=1; %扩展常数
/ ]2 Z; x: ?' w6 [9 X0 E mn=100;%神经元的最多个数, u# O1 J/ s* H" T0 @
df=1; %训练过程的显示频率
7 R+ v) Z' H5 t9 m h5 C [net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
( @' |4 J: Q8 K % [net,tr]=train(net,p); %调用traingdm算法训练网络
5 k* v& u4 @) b! f7 i3 I %对网络进行仿真,并绘制样本数据和网络输出图形# _- m9 {, o. }3 H0 m! F" s
A=sim(net,p);
/ B8 O# N; e- k E=t-A;
$ i; x' ?6 ~4 f8 i0 P sse=sse(E);. w& a* H6 o e# F6 {( Y& I
figure;
! U; b" T, a4 @6 h4 u# [, a9 L plot(p,t,'r-+',p,A,'b-*');
6 t6 x4 h* [/ K# U: _ legend('输入数据曲线','训练输出曲线');# e; R6 T. ? d) Q
echo off
! Z e/ `" P* b
x5 ?3 L1 g; X 说明:newrb函数本来 在创建新的网络的时候就进行了训练!
. {0 ^ y$ J* o) d1 g0 ^ 每次训练都增加一个神经元,都能最大程度得降低误差,如果未达到精度要求,
1 F$ s) _, {; H8 t- O 那么继续增加神经元,程序终止条件是满足精度要求或者达到最大神经元的数目.关键的一个常数是spread(即散布常数的设置,扩展常数的设置).不能对创建的net调用train函数进行训练!
5 m& q3 p- D% B, i& k7 ^ # j( ?7 G: k: ~* @5 g# K
4 P8 C; o/ z0 b/ A! G2 j0 g( J+ R
训练结果显示:: a0 H/ d1 T& X
NEWRB, neurons = 0, SSE = 5.09730 `1 f5 ?, T$ v3 z% ^8 e9 x- `
NEWRB, neurons = 2, SSE = 4.87139' {; y/ s, o* O0 _. i1 `
NEWRB, neurons = 3, SSE = 3.61176
7 q3 P2 _# q$ g# \ NEWRB, neurons = 4, SSE = 3.48754 Q y9 J+ i: K; h! S: \) i
NEWRB, neurons = 5, SSE = 0.534217; |: p1 _" M, h
NEWRB, neurons = 6, SSE = 0.51785
c$ [3 |* d. H& m% r NEWRB, neurons = 7, SSE = 0.4342593 L5 P8 Z& f6 c, f& k! p; E4 o; l
NEWRB, neurons = 8, SSE = 0.341518
9 {: _7 Q" }: D* Y9 Q# V NEWRB, neurons = 9, SSE = 0.341519' d/ D$ i c, k$ J+ n
NEWRB, neurons = 10, SSE = 0.00257832# a4 t2 e1 ]* H7 t
, w) D) l2 k$ O 八 删除当前路径下所有的带后缀.asv的文件
. f4 K" O4 {% V1 C4 d; Y+ a 说明:该程序具有很好的移植性,用户可以根据自己地
8 i$ J' k U: V+ A' J 要求修改程序,删除不同后缀类型的文件! 5 ^9 I# i1 u4 A/ G* |
function delete_asv(bpath) ! R* i' @6 @8 h1 q
%If bpath is not specified,it lists all the asv files in the current
# ^& Z2 b- O# `+ F %directory and will delete all the file with asv
6 E! ]3 U$ ]) j3 v % Example:
% |! g# J5 J8 N % delete_asv('*.asv') will delete the file with name *.asv;) X( p' y1 {" l! w$ f4 K" ^$ k5 `
% delete_asv will delete all the file with .asv.
+ R. w) l6 u. p/ Z- j7 x1 y. u & m8 u4 Q% S4 W' x* N3 |6 j/ P3 s
if nargin < 1: J. `5 L/ o/ y0 `3 _
%list all the asv file in the current directory
$ {3 y# W* g s" T: l) e files=dir('*.asv');3 P, b0 F: h( ~" Z3 G
else
0 L; ?* p$ A9 [3 t, C % find the exact file in the path of bpath! ?" d2 [; M$ f9 F$ h
[pathstr,name] = fileparts(bpath);, ^9 C+ b \& r, E
if exist(bpath,'dir')' r: \/ m& w* R) p) ~ Z2 n
name = [name '\*'];
( G! E4 T6 x& g7 L" Z+ U end
7 o0 C" l3 P4 e8 j ext = '.asv';6 D* r+ W8 u2 C% m
files=dir(fullfile(pathstr,[name ext]));
$ v( J, a: }, c' p& f1 S$ A end
y6 A$ W; J% P( j( k
( L6 ]8 X% z( X) Z$ C B2 r if ~isempty(files)
. \' e: [5 r' k" Y. z0 Z) o" g$ Q for i=1:size(files,1)
% K" R1 [! r* J. Z2 p5 \& E% h title=files(i).name;
q r, b# ` c/ F) W* ~# h3 k delete(title);/ J3 V0 U5 N6 V4 _
end
' D4 J1 `: ?+ F% c" f7 M) H end& B0 |8 v' e7 ^$ |: p9 Y M, k
' E3 P& a9 \% ?' t+ I, O$ ]
3 W3 o4 N. |& J8 g. r! f# z
同样也可以在Matlab的窗口设置中取消保存.asv文件!
2 C: v M$ A2 H3 p1 V
zan