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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# u6 ~9 m+ U9 x4 {) m( l, F
1. predict_fun.m为主程序;
' V$ J' X; M1 n: I$ U3 [2. timeseries.m和 serie**pan.m为调用的子程序
, i! y% E+ }. k9 \
, W& K ]% {6 _7 e; }, ^% `+ k; P# Gfunction ima_pre=predict_fun(b,step). b* Y. q5 P! E% t* c4 {2 d2 C. i
% main program invokes timeseries.m and serie**pan.m
( l# u. S4 R- k# k% input parameters:
/ v$ y+ h2 Z2 b; l2 n5 N+ O) G% b-------the training data (vector);9 W; [$ J- h8 @* ?( ?( v
% step----number of prediction data;1 e! u+ }- n; B t1 f7 I9 ^
% output parameters:: [' F5 f4 ^ r3 k U1 H
% ima_pre---the prediction data(vector);
3 I, Q- N* ^, j6 Iold_b=b;
- q; n* r* T' O2 Fmean_b=sum(old_b)/length(old_b);
& I4 h6 R! X8 h6 ~8 ystd_b=std(old_b);
* @( ~5 D. W% zold_b=(old_b-mean_b)/std_b;; w! n2 x9 v, X
[f,x]=timeseries(old_b);
m' R h# v% _: bold_f2=serie**pan(old_b,step);1 ^$ ^5 Y5 V4 @
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;# v( ~) Q, H0 I8 W7 J& h" E
R=corrcoef(f);
4 \2 J% n$ P" N& p+ ][eigvector eigroot]=eig(R);
1 Q2 x* R- I! q7 Ieigroot=diag(eigroot);
4 L4 ]( {$ v2 E& q$ ?a=eigroot(end:-1:1);
. w! H3 `+ Z9 E& U8 S! v7 Ivector=eigvector(:,end:-1:1);- w" X7 x- v4 F; o7 q
Devote=a./sum(a); F; B. k. M$ {3 B9 e2 ?% l% V
Devotem=cumsum(Devote);) y" Z# B. t9 A8 E. Z _& _, |
m=find(Devotem>=0.995);
) C- y: _$ A# c& sm=m(1);
0 `+ x9 ?! d( ]. U: }& R CV1=f*eigvector';
' ~- a& C8 v& G6 `V=V1(:,1:m);
) \0 {# O0 w( H2 u. A% old_b=old_b;+ A7 e5 A8 U$ m; N: t7 ^3 t1 q
old_fai=inv(V'*V)*V'*old_b;
/ ]- F: @% @ z7 j/ Z3 Q. ceigvector=eigvector(1:m,1:m);
4 w- T* r8 j7 Y, i+ `fai=eigvector*old_fai;
9 m: p! P7 Z" a5 T: ]& F' B v3 _f2=old_f2(:,1:m);$ _; G# O- U- S
predictvalue=f2*fai;# o$ m7 q1 x$ W% ]3 }
ima_pre=std_b*predictvalue+mean_b;* o6 _( N- ?9 G6 a# D, ]
1 J2 v/ f* b, ]9 c4 D1 K1.子函数: timeseries.m ) I, f5 ?/ g# A8 x: c+ z& I
% timeseries program%
A. [- Y) b9 w$ ]" h% this program is used to generate mean value matrix f;
/ ^. [! b, @/ |/ c. e$ Qfunction [f,x]=timeseries(data) . L, k/ B O8 y$ o0 r
% data--------the input sequence (vector);
+ N8 Y. p: W8 T; t' H" H% f------mean value matrix f;
) \. s9 s5 c, E6 u! yn=length(data);
+ S. }3 Y9 T& q" T5 N) x" Yfor L=1:n/20 L! v B. ]' c7 q5 D! I# Q
nL=floor(n/L);2 [% n2 C8 \- ~3 u* c
for i=1:L
/ @8 I% d3 H: K" @3 l5 {$ L sum=0;
# W* B8 _3 j( D8 s" n$ o2 C, H' ^8 E for j=1:nL
2 ^% {+ p* c8 }5 T/ s+ M sum=sum+data(i+(j-1)*L);6 I$ V l/ x0 t# \. f
end
, g- M' U8 J A1 i x{L,i}=sum/nL;
3 r0 |$ b! M m$ X3 k( a) X end7 \# i' o- B6 S6 h3 n
end
s' M/ V& A5 k4 Q. eL=n/2;
1 r4 ^" @" v) J8 C- X1 S& ff=zeros(n,L);
# X7 u9 N& e+ H, E- }5 yfor i=1:L* c& Y( v' @& I- O
rep=floor(n/i);
3 `+ M a$ Q: P6 g) a! z res=mod(n,i);$ a9 M4 s+ p4 o' S) |
b=[x{i,1:i}];b=b';, Y& J1 q* T: W0 D; ~! c
f(1:rep*i,i)=repmat(b,rep,1);
! T) Y4 r* F0 l! }+ Y if res~=0& p7 d) s3 J$ |
c=rep*i+1:n;9 u. | O+ ?# `1 X
f(rep*i+1:end,i)=b(1:length(c));
. Y J2 Z1 m( J) I, [4 }+ @ end3 ~) M0 U* R0 w7 b) @& @" v
end
- C: s+ s, m1 i9 h' C2 L! p1 N/ B7 E1 G- L" K. V- X$ F2 W
% serie**pan.m
# [# _2 Q' x& n% the program is used to generate the prediction matrix f; 5 U1 |2 ]8 ^( G
function f=serie**pan(data,step);
+ A9 X4 n7 o ^%data---- the input sequence (vector)6 j) ^, H# f& c6 M+ ?0 a& @
% setp---- the prediction number;
0 X( v% N' B$ }3 z2 Dn=length(data);+ z9 ~( N" t$ F c' m9 ]
for L=1:n/2
4 W' j" B" p+ `( f nL=floor(n/L);% J& k' R$ m# O
for i=1:L6 g+ n$ W9 E/ O; a) i8 v I
sum=0;- |' N9 g, V2 ]& C6 f6 O- J
for j=1:nL
( t+ v- g/ z7 }, [( [. I sum=sum+data(i+(j-1)*L);
4 j1 n, X. h8 z" @ end
1 R. Y) N6 }$ F! q8 B: P: L x{L,i}=sum/nL;
- w* R. P! X4 i: j end
$ R6 O2 Y; F$ r( O: h6 Uend
, w9 l7 S, `5 l6 I4 tL=n/2;4 S2 a( g9 m/ x; m c7 B6 V, F1 Y
f=zeros(n+step,L);
# {6 P* Q! z0 e, f7 w, b! nfor i=1:L
3 t6 K# @0 _' o( T- F6 G rep=floor((n+step)/i);0 _- j7 j4 @- _+ ?
res=mod(n+step,i);7 h% B, Z& M3 j' V0 [/ @0 `* V9 L- t
b=[x{i,1:i}];b=b';9 x$ ]% _4 J: P# m( `0 `
f(1:rep*i,i)=repmat(b,rep,1);' h3 G! Q3 @2 `( G9 q# X
if res~=0
0 D$ {7 K1 N; Y c=rep*i+1:n+step;
2 h" X, |2 _( j j% o5 W f(rep*i+1:end,i)=b(1:length(c));. V2 d! U8 m) n: ~; }' ^( L8 t: _
end
2 p+ C) q/ { f! n, H2 G T& Dend
5 u0 A) [' E% W" t! I1 E! E" u9 x& A1 U& x d
二 最短路Dijkstra算法
6 ?* R# t3 s" V2 l; y3 a% dijkstra algorithm code program%- B+ f. P; O& X* N
% the shortest path length algorithm( `9 j. m$ i" |3 _( F& x
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)5 h) Q/ ?" H- R% \( u3 i+ h |
% Input parameters:# K5 q ~8 p0 t# X4 N; d, A
% Input_weight-------the input node weight!% ^; \' b$ L" }0 ?
% start--------the start node number;
2 d" T, w' G- r8 W0 F; ?% endpoint------the end node number;/ _& D7 {$ H% M5 b% _
% Output parameters:
- ?9 g; B6 K% J, ~% path-----the shortest lenght path from the start node to end node;$ [5 y0 N% Q" H4 q; [
% short_distance------the distance of the shortest lenght path from the: E8 X% u2 N9 z: q6 B5 B
% start node to end node.* u3 c+ }& H% C( f* T
[row,col]=size(Input_weight);% o; J& a' o2 `( }
4 I$ P; X e$ }, I Q* C& s; h, a2 @%input detection* }- E# b1 h) I+ r% v+ V; T
if row~=col
8 m. u, ~5 C9 ]3 f error('input matrix is not a square matrix,input error ' );
) {% Q* d$ Z% e5 hend, ^, `$ @5 Q1 z& n* k- B
if endpoint>row$ h, ~% ?2 K3 H; B `
error('input parameter endpoint exceed the maximal point number');1 N2 l' C9 y( P4 l
end. u, @; n- ?7 f
1 F( u2 q- j; b) g' F# a
%initialization
- P, V6 b: d% Y6 ?8 z* P9 H0 f7 Ks_path=[start];
' W# }: Q9 }! j7 n8 w0 q* tdistance=inf*ones(1,row);distance(start)=0;+ `- o& P) T1 d5 P
flag(start)=start;temp=start;
4 d( r& \7 f2 h1 _3 T$ a- n
( ]8 _( d6 b: ^" V# F2 ?while length(s_path)<row
" p$ z+ A5 {+ \3 n, p/ e, f$ w( C pos=find(Input_weight(temp, : )~=inf);
2 K, V% S& P# h4 ^; L for i=1:length(pos)
' r; L5 I0 l3 R1 g) ] if (length(find(s_path==pos(i)))==0)&
6 s% @) o: r7 b# Q' @(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i)))). H- f$ z* p/ r; d; R
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
2 W- M! U, n5 G: o0 G flag(pos(i))=temp;
# m v1 |0 ~- V; _ end
$ S3 s3 v3 S2 ^. n) p: B end& K1 K; P. ]9 D2 Z& d
k=inf;
: C: J1 @8 h) H& s% M; O: h0 ^8 e for i=1:row
6 K& ~" O; c$ S5 j! D- g1 W if (length(find(s_path==i))==0)&(k>distance(i))
: n; g0 D& N7 d! O4 T k=distance(i);- N/ Q9 a. o; I
temp_2=i;8 |" j# t9 W; X5 m) m
end
! Z4 N+ p2 R* G end) z: l. s) h3 d" H5 f& N6 U
s_path=[s_path,temp_2];; h& y2 k1 C5 `& |3 K& q9 u2 X& l; w
temp=temp_2;/ B3 M3 a* P; A3 j1 [
end$ z9 u$ f* p# `$ u, M7 @$ f
( K; I! W2 Q4 e' o+ g3 B* y1 l
%output the result0 D- ?' _) S9 v* D
path(1)=endpoint;9 n/ \3 m" x! f( W: {
i=1;3 W0 {# L/ f" G8 V" h
while path(i)~=start* C& ^! \/ }; R5 ~: n# S* L7 X) R' {
path(i+1)=flag(path(i));
4 C* F; L1 H: d3 t; E ]. [ i=i+1;/ R; ^! U1 J( ~! ^# U* J5 ^
end3 N0 K& a& d4 V5 g# I! w; K( Z1 u
path(i)=start;
5 l$ I1 P9 P1 ^8 q3 b0 }; rpath=path(end:-1:1);! {3 n+ l& s+ m7 Y# v$ Z4 K
short_distance=distance(endpoint);
7 t: Z" f! m" P& R三 绘制差分方程的映射分叉图* Y: z c$ N9 U2 G! Y5 g
" J3 V0 q, `& t" N0 u5 v
function fork1(a); : p" g+ I, z1 c0 S8 d3 V
, A( v- w$ x! ` }% W% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
5 { p# J% H1 M; x% Example: 0 N& o% @7 x9 |$ c( A
% fork1([0,2]);
# q5 I2 O# ^& u; B1 ~+ X& bN=300; % 取样点数
# T" J+ M: `# z) n7 cA=linspace(a(1),a(2),N);
+ x3 p O: C% M' l0 O2 pstarx=0.9;
: N, j$ I- t CZ=[];' y6 c* o/ ^6 D1 m! U3 h
h=waitbar(0,'please wait');m=1;
" n0 c! m0 `4 L- n5 Kfor ap=A; 7 y8 l9 T; O- o% Y7 n" h6 y8 R" m
x=starx; : \5 Z0 R1 O3 k8 h- t) n7 M# d+ r
for k=1:50;
+ | Y( N0 l0 @ x=1-ap*x^2;
4 Q i2 O9 T- N$ ?0 I end 4 ]% t' i. E, U$ F
for k=1:201; # A& r1 y8 V( a
x=1-ap*x^2;
3 N( Y% l) Z& w9 |5 h: g( |% M* C* a& J Z=[Z,ap-x*i]; : | G/ t6 i( v" _$ m8 X+ x
end ' B$ a0 ^+ Y: W- _) ^8 m
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);1 | f1 P" O# t1 _3 G9 F( j
m=m+1;
0 ~$ V; S! }* h4 o& P" Zend
* C- p! I7 R2 o, o& X; Kdelete(h);
+ w. m+ Q# d6 r+ }6 N9 oplot(Z,'.','markersize',2)
: R, c' `: H+ [8 p3 P1 wxlim(a);$ X; Y/ k3 B1 L
" s/ U/ O' m$ \0 |8 ]- f# l
四 最短路算法------floyd算法
6 m; M5 S2 n! ~- |" i) q0 F7 Pfunction ShortPath_floyd(w,start,terminal) & Z7 Y" ~1 b' f- ]/ W
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;8 w7 T+ V/ u9 o) T3 v5 U
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
' x% {) j7 H/ G1 Z- C. y* P%start-----the start node;
$ r- T; h1 R4 Z' ?' r t%terminal--------the end node; - b6 @% o: z6 ~0 m
n=size(w,1);, y9 S/ U( i, C
[D,path]=floyd1(w);%调用floyd算法程序# t: _9 P9 R" X% P" T. L
- X' X. u4 L3 L3 W4 t2 ^+ W7 `4 M# g%找出任意两点之间的最短路径,并输出5 ~* H0 k) Z( s7 }
for i=1:n
$ ~' w! r( R) C( x+ m1 \9 O! c X5 u for j=1:n5 W9 \, `+ S; Q
Min_path(i,j).distance=D(i,j);
- i c) a6 Y$ W' ]! u %将i到j的最短路程赋值 Min_path(i,j).distance; T0 I7 B& M, Q) l. U. v, V
%将i到j所经路径赋给Min_path(i,j).path' x# m! s0 c/ t$ j( G& G& F! g
Min_path(i,j).path(1)=i;( {6 E, w& Z+ X1 V2 a
k=1;/ a3 `# D* a! E; a
while Min_path(i,j).path(k)~=j
1 s8 B+ W, i9 W6 g! z' X. c k=k+1;" t" n: R0 |" i- d. p
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);2 _* r- W, z" k. H; _% F& _
end
; R" Y$ N8 l0 X& {% Y$ l end2 t6 _/ g# H9 ?) ^+ J
end7 o6 g0 J- {3 N
s=sprintf('任意两点之间的最短路径如下:');
/ j; F) Y$ @" T. |( \( Fdisp(s);. U0 F) m0 X& y- ?- k. F! l* x& p
for i=1:n
1 M& F8 @3 c% y1 z q; S$ }& \; v) S for j=1:n7 y$ y% o+ a1 z- [6 T' Y! z
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
/ [. l& n9 w0 f; `9 u ,i,j,Min_path(i,j).distance);8 u' s& @' y0 j9 `. Q) X7 j
disp(s);& b& |. @+ n c5 }& `8 l
disp(Min_path(i,j).path);+ u: r2 W( S- B
end
7 b5 A4 ]9 t' v4 p5 Dend. A+ ? w% r( E, U
& R3 Y$ p! Y! J; s( }9 I%找出在指定从start点到terminal点的最短路径,并输出
* `4 C8 `+ }5 A/ U3 R/ ystr1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...2 E# l6 W3 h! f5 s( w
start,terminal,Min_path(start,terminal).distance);5 G4 T. [$ P4 s$ }' w _' F
disp(str1);! K) O& E$ z! t% b5 O1 P! o
disp(Min_path(start,terminal).path); k- W. O+ s# k: h. t4 U* y0 K/ r; N
: L v% ~' h/ F8 f$ g%Foldy's Algorithm 算法程序
1 u$ G& O) y% g! i$ C. n0 B' ofunction [D,path]=floyd1(a); J$ ^0 [+ f1 t; M' x/ [
n=size(a,1);# S, ~% y `0 F# m9 b u
D=a;path=zeros(n,n);%设置D和path的初值5 G1 A* S; e6 b5 u$ B. ?+ v
for i=1:n
3 n5 R, x- W) _! O5 |7 Z) G for j=1:n
+ G# f: U m- p) E3 S+ N if D(i,j)~=inf1 B1 B% \' y- _0 P4 N- z7 H
path(i,j)=j;%j是i的后点
6 ?3 B ~$ Q. o3 D7 j9 H' F& } end p, h8 ], L0 r5 d' l! i: l/ A; A
end/ L& u; l% s) L- t% [
end
% W+ U5 z# o3 h; z/ h%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
9 B+ h$ N& V6 [' W! k, \for k=1:n0 u7 e( g. y' a/ r0 W
for i=1:n* U# i/ A4 b+ @( ]1 ^
for j=1:n
& p$ D. ^- [% q) ]: N& C% O if D(i,k)+D(k,j)<D(i,j)
y: B$ v/ \ W2 g" o1 ]" p4 K1 u& V D(i,j)=D(i,k)+D(k,j);%修改长度
: x4 n! p& Z! i$ y, h) s path(i,j)=path(i,k);%修改路径( n: v, r9 T0 o5 {# g8 B; h
end
" G8 C X) m6 M. e( h, i' y- @ end/ d; N3 v1 ~ {6 Q8 M: j+ L
end
' K" d4 t$ M' }7 c% qend
+ |- j0 X6 X: H, u/ q' ?/ Z. N! l0 C6 U4 N4 {, }. X8 i
五 模拟退火算法源程序& `; ^( O* `; y9 J2 e
function [MinD,BestPath]=MainAneal(CityPosition,pn)1 K" T6 t$ U; J/ @8 h' n7 ~* V
function [MinD,BestPath]=MainAneal2(CityPosition,pn)
4 s& q# b9 m; [% g( }%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
) F/ h2 _9 L' F( H%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...& M/ W5 d/ p8 B2 n* B
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
* U: b- M$ r$ W+ S1 X% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
2 ~) Y8 s3 o D( y% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
+ T. S9 n! H; z8 o* d9 L. ~% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
3 \8 u# s# N' J: b" {/ m! ~
) w6 {8 C1 I) \; c0 n%T0=clock/ K0 K( i6 Z0 H$ D
global path p2 D;
1 l2 D, X- J8 z Q+ |" z[m,n]=size(CityPosition);
2 w8 L2 z5 |$ H7 T* `; P8 O- u# _%生成初始解空间,这样可以比逐步分配空间运行快一些( Y3 D: U1 R# q) {) W
TracePath=zeros(1e3,m);& u. Q0 R H$ n
Distance=inf*zeros(1,1e3);
0 x1 N0 e2 y/ P9 C( r
! d2 L6 c5 { ?0 @$ q: X$ {7 JD = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +..., i! j0 q- Y2 C; Y# J; m) K" n0 y! m
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );( v% x2 `: J1 V' \2 F: J0 h( w) C1 D
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)* V$ |+ f0 c8 y% @7 P @
for i=1:pn( ?# S6 e, Y; |+ a! Q& j
path(i,:)=randperm(m);%构造一个初始可行解3 ]( S5 T4 P' l+ @
end; w& d5 W+ W: h( T: E
t=zeros(1,pn); t. e+ J& F$ {7 b7 s
p2=zeros(1,m);- [' ?9 w. T8 P b. q/ {- m
) G' F7 w- e- B# I, t: m6 _
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
. {4 `/ h+ @: E6 S% ], d6 J' Nm_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=' ) ;
8 E* {- c9 j @) d2 E% j2 v# `%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9 k9 z5 W( ]$ J# e
%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
X( Q; v9 l' i _5 W%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
9 [- u& m0 w0 h/ Z4 a%会收到到比较好的效果
( j9 y% T6 I$ l3 Y _/ l0 W; k; e1 O6 g# a* @! {# `4 @( f( t1 x
T=1e5; v7 t9 q5 ]0 A( f9 ^7 ~
N=1;
0 ~6 n+ o0 b, @6 B, S* `0 i* d$ N1 Vtau=1e-5;%input('请输入最低温度tau=' );
/ l( { @ N# i/ Y5 S; a! ^%nn=ceil(log10(tau/T)/log10(0.9));
+ y- ?; V# ^$ z. Q8 z$ D+ Kwhile T>=tau%&m_num<m_max
4 i! l3 G* d( d, v& y0 S iter_num=1;%某固定温度下迭代计数器
; C m: `' g( H b7 Y- E2 R m_num=1;%某固定温度下目标函数值连续未改进次数计算器8 q. G5 H& ?6 R% y4 q, [
%iter_max=100;
/ T) C" I# t, v0 w( M; d H/ H! P %m_max=10;%ceil(10+0.5*nn-0.3*N);
. M% F* Y( W N1 @- x while m_num<m_max&iter_num<iter_max D+ z! s8 T O2 `
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
3 w: V" y% f7 t% T+ v; {$ f %用任意启发式算法在path的领域N(path)中找出新的更优解
: @# Q9 H( f8 _$ c+ p for i=1:pn
1 j5 j/ `4 g" o7 Y$ j Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);, n) v0 U& u7 f$ z H: `. X
%计算一次行遍所有城市的总路程 ) q3 L1 r Z' L- B2 v4 v
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线1 {4 s) t- P' H" 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))]);
2 u+ m8 v0 B; k1 m! Z4 f9 {. r0 b% h end
, T, ?. T5 r) y& G7 v %Len19 x6 j: @8 B, y3 J9 k
%Len2' ?0 \9 Y: ]5 u, {: U' B/ Z
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
/ v) ]2 D9 H1 q+ ~: s1 ~ R=rand(1,pn);
- s8 r; X$ k; G" Q %Len2-Len1<t|exp((Len1-Len2)/(T))>R! y6 G9 t w6 S# B p
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0) M3 A: N. B* \1 B' M
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
6 Z/ `8 G8 N6 _( q3 ?! Y5 X Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
' @ ]( T$ o! ] } [TempMinD,TempIndex]=min(Len1);; H8 m: B6 T# J, O5 z/ R
%TempMinD5 a6 ?) { d% T8 e0 Q
TracePath(N,: )=path(TempIndex,: );1 L: s4 \1 q8 Z5 }& A% g
Distance(N,: )=TempMinD;
$ K8 z6 T/ T7 ]& P* q6 L N=N+1;6 h: ?9 c4 r; f3 e
%T=T*0.9- f* r4 F+ ~- w3 V' v
m_num=0;- Z) L6 @- h" Y+ D0 j" g8 c# g
else, a, z( N k6 ~7 B% a
m_num=m_num+1;1 q. B* ~$ E4 G
end( [* Z; x5 c( u0 w% Q6 @& Z, T
iter_num=iter_num+1;
/ c; r8 i4 Y# W7 T$ ]- K end5 t0 L6 J' u) _ Z/ t" C
T=T*0.9% H: K3 [( v) z& P% D7 N# B/ t
%m_num,iter_num,N1 y" x A5 ~, c! A5 _' R
end * M0 D- @! i: v8 k( j( e( w
[MinD,Index]=min(Distance);
& Q! }, f+ g# y3 E5 ?BestPath=TracePath(Index,: );
0 z) Z3 @ A: K1 f Pdisp(MinD)
5 x1 Y. ]* c! ], ?# n& s9 y3 q%T1=clock
% o- J# M+ R) j( U) V' h 6 s j( O+ _6 n7 b/ X
, }2 t( a3 l5 t6 e5 l' V
%更新路线子程序
! u' f3 M1 [- y4 s) l$ Dfunction [p2]=ChangePath2(p1,CityNum)# j) i c0 w u0 P% B- F$ e
global p2;& o/ c5 Y ~3 \( O1 k. |
while(1)/ S- T" @5 ]# t/ F/ ~
R=unidrnd(CityNum,1,2);
. F% A. f1 N& W* y7 | if abs(R(1)-R(2))>13 b* x" n4 C7 b5 }3 L1 D
break;% j+ ^# v1 o) s+ v w% y1 H
end
2 f$ z& w9 n$ D# o* t0 _6 G0 P# cend; _3 A; }' q3 t1 S, J9 K
R=unidrnd(CityNum,1,2);9 P$ R# A! Q1 E
I=R(1);J=R(2);7 a- t& i- O# ^1 _7 i. e8 A
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
, g) c* U. Z7 ^4 b, O$ c%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
. f3 B3 a2 X$ ^9 g- Dif I<J
* Z8 k" a; ?; u p2(1:I)=p1(1:I);; |' o# {7 c1 A! w- x3 o/ C+ h4 u1 b' m% |
p2(I+1:J)=p1(J:-1:I+1);3 g9 D4 n8 x5 \
p2(J+1:CityNum)=p1(J+1:CityNum);
u' C* G# ~3 f5 R$ }3 Lelse
+ o' f+ _+ Z5 o8 X7 L3 T# U; i p2(1:J)=p1(1:J);4 ?' h4 g u( H
p2(J+1:I)=p1(I:-1:J+1);) E3 w; C# V+ J6 l; S( `
p2(I+1:CityNum)=p1(I+1:CityNum);
1 ]+ }; C2 L# ]4 p1 nend
+ g% e0 ^, m" |$ q. p( K' x
1 ^1 c( J( H6 p/ U& S2 `六 遗传 算 法程序:
5 `, N( l. A5 s! w0 G 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!1 ^7 E; S2 ~+ p& m) n
- p% X, K0 f% t2 Qfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)- ?2 O) I# V% B) M
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
) ]0 u7 x% _3 K v& A$ ^; t% Finds a maximum of a function of several variables.
! K, s% ]4 g% j: m6 K0 i% fmaxga solves problems of the form: - ?! S, r8 f0 b8 L$ z5 U$ o
% max F(X) subject to: LB <= X <= UB
$ q! }, Q$ h, R3 m% ~5 T! q: Y% BestPop - 最优的群体即为最优的染色体群! M: y0 R5 f, e4 V
% Trace - 最佳染色体所对应的目标函数值
$ l# s( G3 Q2 C ]5 h0 a% FUN - 目标函数* Q; h8 E% C, l O. v8 B% j( ?6 Q) S
% LB - 自变量下限
$ v* C |- b! o% R* Z; ^% UB - 自变量上限9 O6 Y- G+ A! v, q8 c
% eranum - 种群的代数,取100--1000(默认200)+ e# a) {; @7 |8 ^& ?
% popsize - 每一代种群的规模;此可取50--200(默认100)& h/ ^( ]/ i7 |! T
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)2 i5 ~- M$ i- B c+ s; s/ i5 f
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
) G% b2 [! Y7 `" H! Q3 k& `+ |% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
" A8 Y6 \( G3 c W/ j% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
2 f1 K+ I! _ X- q& M%码,option(2)设定求解精度(默认1e-4)5 q2 p+ n& Q; I6 k8 K
%% G8 Y- |+ @! @, i; L
% ------------------------------------------------------------------------
; p4 q8 E6 w* L l6 \; j8 d! B7 q! H# w4 _' f
T1=clock;
. p' w5 u6 L; u: hif nargin<3, error('FMAXGA requires at least three input arguments'); end
5 k" I5 P7 \; ^( Gif nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
A; {7 Q' j; E. ^" |: V# }if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
; p' o) Q, v4 P o+ uif nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end) x" m7 U9 w5 a4 H2 a
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end5 Z$ L8 b9 {& x; H+ Q
if nargin==7, pInversion=0.15;options=[0 1e-4];end
, n* F0 Y' P8 L3 z; X& b. pif find((LB-UB)>0)6 Z, `8 O4 s9 t) E! K
error('数据输入错误,请重新输入(LB<UB):');* G) {2 a4 Y5 B& q3 U f
end7 F5 B* J' f- k& @
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
$ @" C9 a1 w' u8 adisp(s);: K4 D( a/ Y) c1 r7 J7 U
) x! K9 @; U- {! L4 } z
global m n NewPop children1 children2 VarNum8 k3 G+ {* G3 E
1 h6 w( r. Z$ t9 ^! S# E6 E% Ubounds=[LB;UB]';bits=[];VarNum=size(bounds,1);' X. H5 j" T/ s" w& i, S) ]
precision=options(2);%由求解精度确定二进制编码长度: P# D! b: ?( q- T: `% l8 v! R" A
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
# k C1 u7 h s7 Y2 k {1 M[Pop]=InitPopGray(popsize,bits);%初始化种群
, v( d1 i e/ w% g7 A. F[m,n]=size(Pop);
- _' r0 ? i3 K* XNewPop=zeros(m,n);9 H7 h; S7 U' ]
children1=zeros(1,n);7 W4 ]; e# Q4 R4 m$ W
children2=zeros(1,n);
( w% R: t8 s' B, W9 t8 Spm0=pMutation;
. \4 @* R9 l' ^+ w: M0 ]BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace. t- M+ k5 a: b% ]3 Q& I( y
Trace=zeros(eranum,length(bits)+1);
$ n) Q1 I$ Q6 ^! \) [i=1;
5 p4 T( B( V! D5 f* ?while i<=eranum. D x U6 b" ^4 r6 k8 q
for j=1:m) ?7 y" ^7 W. e, y6 A" G& J' T# n
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
1 M4 s* r2 D$ t end5 w$ g- p$ A" m' k
[MaxValue,Index]=max(value);' d6 w; R. |8 s
BestPop(i,:)=Pop(Index,:);3 G0 |: x/ C; e S4 g
Trace(i,1)=MaxValue;
- I3 O, V" K' {. T$ Y' M Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
! H' j- T' A: u; e# C8 c. l [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择$ A9 D. p- O( i2 O% s4 p2 D9 a
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
9 r2 k" A3 |, L# ?: J% Q%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
8 n* m8 m8 w9 v# e %round(unidrnd(eranum-i)/eranum)
C+ z! k: g! H6 |4 } [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异0 i+ I- B! \( X1 @' _: H3 x
[InversionPop]=Inversion(MutationPop,pInversion);%倒位
! l' Q) u6 Z2 H/ a. R. k Pop=InversionPop;%更新: Y% E( W# i6 `3 l: }2 U
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); * [% \% c! d G8 {; ~
%随着种群向前进化,逐步增大变异率至1/2交叉率2 q- e5 e$ r- t3 V- ~
p(i)=pMutation;
X" G+ S& l2 T7 v i=i+1;
9 Z4 h# B! Q+ O5 p( @- pend, o; N f8 w. E$ p2 O
t=1:eranum;
4 n" e3 ]+ d* T, b6 ~% kplot(t,Trace(:,1)');
. l# `( B! j0 V! p' 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)');
7 U# ^; k3 i% a6 X1 P[MaxFval,I]=max(Trace(:,1));- [. ?9 }2 s: S
X=Trace(I,(2:length(bits)+1));
1 I3 e$ Q) U$ t8 u* \. uhold on; plot(I,MaxFval,'*');6 Z0 W6 k3 ~8 u1 \4 V' B
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
) N( Z: Z$ C/ I! M3 estr1=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,:)));
4 c; y, K/ E( H# udisp(str1);
2 d+ O. v/ m1 {3 y, v/ S+ R& L+ s%figure(2);plot(t,p);%绘制变异值增大过程$ t, W) {6 x" p; z' |1 ?
T2=clock;4 k! }" P# `0 H1 b
elapsed_time=T2-T1;
" D7 h/ q. K' c2 i% uif elapsed_time(6)<0. ?) ?+ M9 ~) Y+ [! Q
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
& \0 e. w2 h' T+ Fend* F. F& j( H8 @6 j! O& c; s# v/ j, D* P
if elapsed_time(5)<02 a* a5 A4 j3 T+ `( M7 f
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
( l, T+ \8 L: T6 b: tend %像这种程序当然不考虑运行上小时啦4 c- J6 V% q. N* d
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));$ M; `+ p! U/ V1 V, }
disp(str2);
3 K z! i2 \8 ]# L9 ]/ H
, y& _( v; N9 b5 \, E9 n8 I7 ]" }) H+ k, N, [% ?2 n
%初始化种群1 O, p2 p, O! D( X+ b8 ^ V, y
%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
8 J* q. j6 z: x- ~+ d2 Sfunction [initpop]=InitPopGray(popsize,bits)
3 \& T; ]8 T; e0 P; y8 D' Vlen=sum(bits);: D" V2 ~% a6 P/ X, i* u
initpop=zeros(popsize,len);%The whole zero encoding individual7 ]" X% c; R. @# _5 a+ q+ U+ }# O
for i=2:popsize-18 w+ [3 h7 T) H
pop=round(rand(1,len));
3 P3 z3 j/ e9 [3 R" w+ g pop=mod(([0 pop]+[pop 0]),2);, ~ ]9 D/ @8 q2 e! ~
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)5 w1 e- Q- o8 Y. E0 w7 w) |
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
7 w/ `1 n# g, K* X( R initpop(i,:)=pop(1:end-1);3 H) H: I4 A; p E! {: n6 _# t& x' P8 E/ P
end
# i& k9 H9 V8 ?8 Vinitpop(popsize,:)=ones(1,len);%The whole one encoding individual3 o" B$ |: | s/ S' S
%解码
+ G0 A; f$ L8 [" k% k/ u* J- H: q# }$ {6 [, }
function [fval] = b2f(bval,bounds,bits)
( D9 ]/ {# v# x0 f% fval - 表征各变量的十进制数 l: w- Q4 s2 g h/ |4 H& X
% bval - 表征各变量的二进制编码串3 j* P2 E# }/ b/ d! d
% bounds - 各变量的取值范围
: \* z+ Q, f$ D e% bits - 各变量的二进制编码长度
" ~ I7 {: e9 b* U& U1 _% i2 Iscale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
$ N9 H$ W! J; L* U3 |+ snumV=size(bounds,1);
" B9 U8 x* @$ ]/ } M& Bcs=[0 cumsum(bits)];
" w: _' L8 s$ gfor i=1:numV2 b. _0 ?9 e& ]& j
a=bval((cs(i)+1):cs(i+1));
) k1 ]) p+ s# _5 q) ]6 j fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
: H% e5 k* z4 I+ v/ ?end
2 v; Z# S! s9 p, i%选择操作
; x. K9 p4 k( Y0 m2 W%采用基于轮盘赌法的非线性排名选择1 Z8 v/ Y S, A/ R
%各个体成员按适应值从大到小分配选择概率:9 t& |- y; D# B+ Z% j. O+ B
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=11 B9 ?7 t9 k: ?+ [% k$ x
1 B3 U2 O6 u2 m/ S3 {function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
2 w/ @' _) ?+ K H5 J2 vglobal m n
9 {! r7 H6 {; L o1 W& jselectpop=zeros(m,n);
* y( f6 V, n8 H) U3 Ifit=zeros(m,1);
) x5 P) G8 ? O4 |) ifor i=1:m5 C5 g( ^. n. x# L8 H" o
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
( x# p r; S4 k# ^0 Z" _4 @end; z) e% l& @ f
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
1 z0 ^; w Y6 s$ Kq=max(selectprob);%选择最优的概率
+ o4 ?* R0 U" d* t: Mx=zeros(m,2);8 j% a( r5 x0 J, e) O/ [1 L9 s
x(:,1)=[m:-1:1]';: U5 b* Q( _5 ^1 r" o9 I2 D
[y x(:,2)]=sort(selectprob);
* [: L% n/ n' U+ Ar=q/(1-(1-q)^m);%标准分布基值
9 b% W6 `3 _, ]5 e2 ?/ Ynewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
! }! d% y# R+ D' @# Ynewfit=cumsum(newfit);%计算各选择概率之和
4 @( L4 ~; K! d2 q' Z' QrNums=sort(rand(m,1));
* O- _0 s# C3 w8 r6 AfitIn=1;newIn=1;% {: i* q1 G V) K5 ^
while newIn<=m
0 @7 ~. h5 H& S0 c if rNums(newIn)<newfit(fitIn)
) i- `2 K' h2 b, D8 Q) T2 N selectpop(newIn,:)=pop(fitIn,:);% m2 @5 K( l6 Q- t1 u/ M7 K
newIn=newIn+1;- K: ` O* I) Z3 G3 M, p Z( r* H
else' \6 y/ \. y+ J: w3 [: V
fitIn=fitIn+1;9 X( N, o! y$ C% y1 r
end1 E: ?5 ?# R. t
end7 c3 w/ U* `: ^; D
%交叉操作
! m4 D7 z$ x9 R- {8 Y5 M) b5 P7 u. _function [NewPop]=CrossOver(OldPop,pCross,opts)
2 r+ i: [& k$ J) W7 n%OldPop为父代种群,pcross为交叉概率
# v1 e; K2 s4 z( H2 `global m n NewPop `# g4 c. b% T0 x
r=rand(1,m);! W% i! Z$ v/ d' z* i( J
y1=find(r<pCross);. o0 w- Q. K8 E3 g }. P
y2=find(r>=pCross);
5 V' [4 w5 C( O. Z5 p Plen=length(y1);9 @" j% [" H+ A7 w; d/ Z
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. x) w, g) c5 R6 C
y2(length(y2)+1)=y1(len);3 U) u; x9 m- i3 Z' [: G! |. C
y1(len)=[];: p! }6 |& k+ [
end
}2 ~. ?( I1 e$ cif length(y1)>=2
" A& T) _6 l$ b0 y for i=0:2:length(y1)-2
7 U; t L) \$ v- q/ h8 t7 e8 d4 d. B if opts==0
! |1 z$ A+ I0 @8 {" F" y [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));- \/ l$ K: Q5 k" r+ _
else0 i* P2 H( A( |
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
7 x4 ?2 V* C& ] | end! x& e: t9 ]: ~! v; `( [! {
end ! d2 N! ?, N8 r7 P) n; P
end
! B, v: f3 Q$ G1 LNewPop(y2,:)=OldPop(y2,:);
2 v! c4 J4 x) Q% {. t! g/ B; \
6 E- `3 ?+ \% i%采用均匀交叉 * C: o7 v. r8 Z9 f" X2 d
function [children1,children2]=EqualCrossOver(parent1,parent2)8 M: C) B0 g% ~7 l Z. z
5 H) L1 \; m" v7 t- oglobal n children1 children2 / h, f; Y# }3 U: r# ^# ]: k' B" Y6 L& p. ~
hidecode=round(rand(1,n));%随机生成掩码
5 G/ O0 n6 }4 i& Zcrossposition=find(hidecode==1);1 v% A j( W2 k
holdposition=find(hidecode==0);
3 Q8 j# z4 p7 }* r1 A' mchildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因 j' H' L3 `( Y: n
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
- G* ]/ Q) k2 l) g+ n" \5 Bchildren2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
$ U" c6 i. N* Y: ~children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因& {: A# I3 M S+ X1 s* V- M
/ x8 E& w: b* c* [+ y) e H% W%采用多点交叉,交叉点数由变量数决定
9 v/ T" U+ r* B7 R( l
8 T6 U+ U. |5 R& g7 k1 d- Gfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)6 l3 D5 R0 y2 L% R9 \
$ p0 T; t: b2 a
global n Children1 Children2 VarNum
$ H4 Q! S$ o' B7 @Children1=Parent1;
* N2 G# @0 @# p4 \Children2=Parent2;
9 w9 Q+ Q/ _+ \4 r$ |Points=sort(unidrnd(n,1,2*VarNum));
# W9 P: v- ~+ Q @ B8 nfor i=1:VarNum
3 o5 y- ?( b; @2 ^) h; N. B) N+ c Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
; Q! [) f! ]; s0 [( s. D Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));& E2 i+ M( l; Y( ^7 p/ \: m. N
end
4 |8 y U" ?8 E+ ~$ D* |. J* r* n' O) F0 M# q; P( |
%变异操作* c; q' j9 k T" k3 k- E2 g( S
function [NewPop]=Mutation(OldPop,pMutation,VarNum)
D8 J$ t2 h+ F4 a) U, X' b- T) ~) H# ~
' W8 q4 m1 [, X9 o2 `1 j0 W- O( uglobal m n NewPop
% u6 A: I% T4 A: i) L n, Vr=rand(1,m);
; c; q5 I7 b+ S# }6 }/ Kposition=find(r<=pMutation);" N2 q# ?2 x0 ~" V" G
len=length(position);: N3 A' o) T2 f: J
if len>=1
( n. B ~7 t7 m j for i=1:len
; R0 c5 J% ?) ]. _0 M k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
0 T; c! ~7 u9 W; w for j=1:length(k)
; |) S" |; k& h C) b+ i: T# Y: W if OldPop(position(i),k(j))==1
9 J7 I" O* d/ P& x OldPop(position(i),k(j))=0;
! v* Z1 Q' W3 U& V c6 K! D else* X( R" a* M3 ?+ [7 A! b9 T
OldPop(position(i),k(j))=1;
+ d) ^5 D$ V7 X* U% ~# m end
$ H; f7 G! l/ R- H end. a" a5 {/ I8 Z, {5 `7 D
end
7 I( P9 r, ]! ^3 K9 d% Tend
! B# o- L6 g0 Z5 ]2 f5 C+ C8 mNewPop=OldPop;& P1 Y" P4 U1 n- M
# U3 h5 L( A* ?# M
%倒位操作, p6 |& z/ x8 A: H+ O, S
( Y+ D( m1 u" ~/ W& W4 \function [NewPop]=Inversion(OldPop,pInversion)
* E( i0 I0 c* A6 s% D' _+ `9 B( g: `
global m n NewPop
+ k8 |6 K% D5 s" |: zNewPop=OldPop;
' N9 O8 ^& V9 i" Y! \r=rand(1,m);
8 v) X: |6 ]7 `3 @- vPopIn=find(r<=pInversion);! V' C: y' M- J8 u5 _8 ]% x6 z! ?+ Y
len=length(PopIn);* J3 f" Z* C: d8 m% `. ~& `
if len>=19 ^' I+ o# y4 C$ M/ Q) u
for i=1:len
: b3 v- s! E7 d- F5 ]3 l d=sort(unidrnd(n,1,2));0 \! q% V0 b+ }6 Z
if d(1)~=1&d(2)~=n
* U# x7 Z1 E5 e- q NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
5 K5 `9 J; z! h: h NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));! D) j: E, c, ^0 F0 ]+ c0 [
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
# n7 S" U6 K# }6 w8 P" y! ]: S0 @! c end* O+ _' `+ s6 _- E
end
0 {. ]; k& \9 j* j8 Dend
1 n, ^8 C1 Y- s: @9 S; H2 @# I4 N5 F7 m
七 径向基神经网络训练程序
9 m* p7 E( J5 L6 e
n3 o* ~# q1 lclear all;
/ `- R" o) U& b; Rclc;& T" L) `4 x- W9 [
%newrb 建立一个径向基函数神经网络! [9 I+ d: |5 B+ c9 `9 t5 j" Q- \
p=0:0.1:1; %输入矢量
. i. v1 a. W9 Tt=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量8 r: Z: |( G7 u' X1 o8 u
goal=0.01; %误差0 P( Q* h6 w k0 X; m; e1 K
sp=1; %扩展常数' Y/ K/ I, }3 [. ^! ^. d T9 R h
mn=100;%神经元的最多个数
+ g- o0 C% g$ h0 s4 Ndf=1; %训练过程的显示频率" I# d0 K2 K2 w2 U0 c4 E
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
; e/ J5 v& I6 @& K% V& Y$ P9 v% [net,tr]=train(net,p); %调用traingdm算法训练网络
' n! p i6 Y6 F0 t* Q! |/ Q%对网络进行仿真,并绘制样本数据和网络输出图形
! `$ m% C2 z" b8 K* qA=sim(net,p);
9 u0 u h% F" v. X2 U qE=t-A;
2 d' ]4 y5 L" z h0 u7 tsse=sse(E);
6 \! z8 \" j; I5 b0 Q: ]8 K- O Jfigure; . H- C. U# r2 q9 `" J3 q2 d
plot(p,t,'r-+',p,A,'b-*');: |2 J1 W% o* M2 a
legend('输入数据曲线','训练输出曲线');
9 I* m/ i( P3 ?echo off
) h, _* v* [; |/ k5 M. f7 c
& N- ~, l/ R# e7 n5 R3 x说明:newrb函数本来 在创建新的网络的时候就进行了训练!( t4 r3 l, d8 ~) j% M7 U
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,( D& l. U- p8 T
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!2 J2 a/ d' J! U! N! I
2 i; b9 B! D5 D& ]
: T B) Y! x( U% Z2 d; O; u训练结果显示:
5 d' F1 d! q6 [0 f/ g- MNEWRB, neurons = 0, SSE = 5.0973
7 f* r1 M$ Z! }- V H) F+ ?NEWRB, neurons = 2, SSE = 4.87139* s7 \* C8 z5 n& e0 v
NEWRB, neurons = 3, SSE = 3.61176, O4 X4 `3 @( |3 R1 c
NEWRB, neurons = 4, SSE = 3.4875% v) u/ y. H! R4 D N1 x4 Z
NEWRB, neurons = 5, SSE = 0.534217) z2 r4 E* [* t- y) f- c5 v- S$ D
NEWRB, neurons = 6, SSE = 0.51785
v! y" H* n) P" r, oNEWRB, neurons = 7, SSE = 0.434259" D6 R! Y7 p# ^
NEWRB, neurons = 8, SSE = 0.341518
; B/ u3 O* D5 Q: R! vNEWRB, neurons = 9, SSE = 0.341519
7 O, y- y# [) b2 FNEWRB, neurons = 10, SSE = 0.00257832
s& @( w2 v- W( j/ m5 Q1 l( H P
9 P5 r! P/ g0 p" e- F' G! o八 删除当前路径下所有的带后缀.asv的文件5 A3 W& [6 ^+ a j8 q( x1 j) V. Y
说明:该程序具有很好的移植性,用户可以根据自己地; f( M( g0 s1 z/ A. c' @! Q
要求修改程序,删除不同后缀类型的文件! 0 _+ A X% D2 {0 P
function delete_asv(bpath) 0 _4 H2 d5 g+ P9 L0 J
%If bpath is not specified,it lists all the asv files in the current
9 G' o/ d- G8 |) @%directory and will delete all the file with asv q$ J2 g Y" e; X# Z
% Example:
1 B! X" W' D! G/ l6 s: V% delete_asv('*.asv') will delete the file with name *.asv;
o# s2 @+ F- w5 @0 f# \) M) ^% delete_asv will delete all the file with .asv.% B1 |, ~% E3 L7 Z# s8 u4 z3 g( s
9 {% r2 H; O5 z& d+ i3 I. O. Gif nargin < 1
' y1 i$ G) t& a8 r7 ^%list all the asv file in the current directory2 _& W% M; K" \( P p+ q- j$ s
files=dir('*.asv');" F6 |0 q4 z* o6 x6 V
else
8 m& c+ y' ^( M6 l% find the exact file in the path of bpath
$ ~0 }9 P- `5 ~* S/ g8 l [pathstr,name] = fileparts(bpath);
+ Z. m% _/ W1 [! A if exist(bpath,'dir')- j- W) E; U- Q# B9 Q
name = [name '\*'];4 j2 D! P$ g8 j2 }# L. }3 V
end4 D7 n$ }' i! n; ^' }" b
ext = '.asv';0 i/ H5 v' N6 f5 l" A
files=dir(fullfile(pathstr,[name ext]));
- {; {. o) z z5 [* S3 ~end
9 R6 C+ Q- w: q# C/ z3 n# C
7 k; g- U5 f1 u6 [) _ cif ~isempty(files)
1 Y+ U/ l# C- H! c& ?$ o for i=1:size(files,1)
k, }" ^! Q8 X. J5 h* ]; v5 j" U title=files(i).name;' y9 I9 _) ]$ J4 g4 R" N
delete(title);
/ @3 W) l5 N- ^( z1 i% g end
& ^; O# ~/ x- q6 A4 ~4 Qend4 X. q% i5 n g% Z
6 ~* _* o0 u0 B. Y8 x% L) {% R! ^
+ L1 R8 ^! t/ ]4 J$ h7 D同样也可以在Matlab的窗口设置中取消保存.asv文件!
e6 Z* N; B! n4 {# g; L: m* \& P9 c |
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