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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) B! A& |0 ^$ ~, W" y$ k
1. predict_fun.m为主程序;) G9 t4 f- @6 Q/ I9 T
2. timeseries.m和 serie**pan.m为调用的子程序7 V6 {; X7 M5 G: m& j9 B
* ]7 G* ]* C4 |* Q2 l% I5 S3 H
function ima_pre=predict_fun(b,step)
3 S+ `5 o6 \+ i, n# i. p1 P, ~% main program invokes timeseries.m and serie**pan.m
2 l- M- b& H* Z% q3 ~' M% input parameters:* ^! x l5 g7 B: @6 C- W q
% b-------the training data (vector);
% d2 W# k! V! v1 [- m* N9 w/ S* p+ p% step----number of prediction data;
) ~( R0 Y4 r: n- b. v% output parameters:
/ I M5 `, d( T% ima_pre---the prediction data(vector);" l9 u0 G" n% U, G( W6 |( J9 ?
old_b=b;: n. Z3 ?4 h2 g6 s- \ l; h
mean_b=sum(old_b)/length(old_b);
, O {) y, D% g8 g9 J% O; l$ @std_b=std(old_b);" q, j) ], v9 q$ w! s1 g
old_b=(old_b-mean_b)/std_b;! W% n: G8 O, }$ Z$ Z7 `0 f
[f,x]=timeseries(old_b);4 A3 C$ A5 |- j6 ~4 S& t" s" J
old_f2=serie**pan(old_b,step);9 F( f# w+ R7 _% \
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;
7 S/ Z; g8 H' b* t( q, `) hR=corrcoef(f);
# X8 b$ i8 L2 K! W1 G6 x8 d5 l. h! ^[eigvector eigroot]=eig(R);
: o0 r& ?: i5 O5 ieigroot=diag(eigroot);
7 p# ~7 A+ l) Ka=eigroot(end:-1:1);- D3 M- A) c+ I/ L# r
vector=eigvector(:,end:-1:1);& o5 o6 o4 j7 k/ ?5 g: D
Devote=a./sum(a);4 o X5 U' x: Q4 U' x, ]
Devotem=cumsum(Devote);
* _! l: U8 ]- F8 ?* ~+ r& w5 Fm=find(Devotem>=0.995);
! A& T- y4 I& O0 B9 d0 `0 Z: Km=m(1);
8 R1 S U0 u: B5 N( _V1=f*eigvector';1 l* B; R! _) e( `" Y/ g/ }
V=V1(:,1:m);) ]$ R" I# G* m% O' i) n
% old_b=old_b;# Z) ]% n$ w, f$ E5 j) h0 u
old_fai=inv(V'*V)*V'*old_b;- b* ^6 b/ @, C: K; `5 T3 S( \" q( K
eigvector=eigvector(1:m,1:m);
P H" f- Z2 A4 D# @' ]# T. g) X Afai=eigvector*old_fai; F" `/ R7 m9 _5 y$ c
f2=old_f2(:,1:m);
. ?- e! b! i& {; [1 {predictvalue=f2*fai;
! P: F' k O# w0 R' Wima_pre=std_b*predictvalue+mean_b;5 R5 F, d% L* q5 v7 |
5 `6 r0 F( R' Y6 f; w1.子函数: timeseries.m
" }' P& m9 H+ I0 C% timeseries program%
+ u" V( a+ f) M/ n! T8 }0 B" n% this program is used to generate mean value matrix f;! B6 G. K( P: ^) [
function [f,x]=timeseries(data) ( F$ @- h& G9 Y! H
% data--------the input sequence (vector);& z& j" h5 w8 d$ _ K
% f------mean value matrix f;: i) w: r9 O0 p- N' V% O+ h
n=length(data);8 q" _" Y7 U5 H5 z( W
for L=1:n/2" P7 w# l J1 S. j# l
nL=floor(n/L);+ r# m' X' g6 G3 p( K+ }
for i=1:L" N. e2 L3 A* ?- W6 {5 D
sum=0;
) W5 r# [+ B" d* g$ ]) p for j=1:nL
7 G3 A! e3 ?7 T+ s9 s sum=sum+data(i+(j-1)*L);6 R1 @& |! o- r- B2 B* a
end
! G" U2 e5 s/ G+ K ]9 K# `' ?3 D- R x{L,i}=sum/nL;& r/ d: l- j, h5 K9 p* `& E3 E
end2 F7 m) y9 N& C9 ?" N# _& T
end) j5 t% x1 J9 Q& e3 A7 `* b
L=n/2;
/ b$ `5 @( W- p) Mf=zeros(n,L);+ U" [( D! `* g/ R4 z4 o; T
for i=1:L
4 H0 U+ t2 J/ R+ }1 ]9 C' P rep=floor(n/i);3 X# ^/ j7 ^* D9 w& x
res=mod(n,i);
6 ?7 j! Q! Q9 {, K# Z b=[x{i,1:i}];b=b';
4 e9 n6 b4 I' H2 `. c% l f(1:rep*i,i)=repmat(b,rep,1);
0 d6 q5 `# u- l3 P9 J `: h) H if res~=0
. C8 n! ]2 w' ^0 `( r4 z% Q- X c=rep*i+1:n;) B. l5 j, D! b' @
f(rep*i+1:end,i)=b(1:length(c));6 J# r. \0 t) f2 {
end1 i( ]( M" z. ]8 i
end1 |8 T- [0 N& J2 G7 \4 O& b% ^
# f4 F6 P D: P: c
% serie**pan.m
5 F$ J1 u M/ W' }% the program is used to generate the prediction matrix f;
# T) G- l- U* c. z6 yfunction f=serie**pan(data,step);
& D0 u. i% H& z%data---- the input sequence (vector)
2 s6 N& O$ v$ g! |% E4 j% z% setp---- the prediction number;
/ m3 W2 x- Y( N: J, }8 O$ Wn=length(data);
% H( ^2 I2 h$ x) [, D, Y4 Rfor L=1:n/2
+ `* ^4 m! C. u# p nL=floor(n/L);, y3 Y# i& \. w. E+ v
for i=1:L
/ E- p5 j* A9 L1 d3 a3 t/ h sum=0;
/ l7 q A& Z( ~. g$ v( X" @$ r; @. e, O' C5 p for j=1:nL
) Y" q1 l- M2 q1 P f: \1 K sum=sum+data(i+(j-1)*L);5 ?0 ~$ `2 F* z2 q% h7 Z: u/ h
end
9 O6 W3 n4 g# j7 S! P x{L,i}=sum/nL;8 V6 E# n8 B& G7 o/ ?& k8 I' i) S7 n3 z7 F
end( @' _) i2 Y6 c7 \" s; n
end2 s( l1 ~, R0 s9 _
L=n/2;
7 [' o/ X2 F+ [( z" [/ U* [f=zeros(n+step,L);( j- J$ c0 Y- ~; C
for i=1:L
1 q' h: a9 E4 S5 M& m rep=floor((n+step)/i);
, i9 N: s; R F! F. y res=mod(n+step,i);
1 T( @4 m2 s: \ b=[x{i,1:i}];b=b';3 ]" V( S' i0 @
f(1:rep*i,i)=repmat(b,rep,1);
( F4 X9 w8 r7 j if res~=0
4 E6 J8 J9 u: S' D/ J# t c=rep*i+1:n+step;7 u# A B1 H7 ]' S6 `
f(rep*i+1:end,i)=b(1:length(c));' N6 V, u- P9 }; f
end! f- K) B( S& V$ {8 c8 K7 u. w. E
end2 z1 `) l7 o& @! `
* Z) H3 N- P8 z; L二 最短路Dijkstra算法
; R4 ?- L0 y! u( c+ T% dijkstra algorithm code program%
$ e' }2 b: b8 E& O# q, k1 l% the shortest path length algorithm
g( i% r) t# A9 Z, f% rfunction [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)- S. L0 _; G. R$ f' q2 O' [9 y! ?
% Input parameters:: _/ J7 d3 u; G5 g$ W
% Input_weight-------the input node weight!
5 n4 S- m* t5 q* x% start--------the start node number;
) ?3 D2 Y( Y3 \3 C# n6 O7 T% endpoint------the end node number;7 }4 w- M1 L& _8 n
% Output parameters:1 `4 h2 H8 H) ?. A* ~6 u( G
% path-----the shortest lenght path from the start node to end node;
: F5 h- z: d. G- M% short_distance------the distance of the shortest lenght path from the
1 _0 o D4 h4 |1 h' c5 H% start node to end node.- ~1 H! E' l5 X% _& X
[row,col]=size(Input_weight);
A5 V* ~: N1 y ~3 g5 v n: o% W
%input detection0 `; t3 M: e- Y/ X
if row~=col2 H5 x5 O& c1 {$ G5 j: S# h7 f
error('input matrix is not a square matrix,input error ' );0 V c0 D; h3 {# ?/ B+ }6 f
end. ^9 ~7 x" Y7 v4 g% m
if endpoint>row1 ^) \' J* V2 A- {6 X, X3 q
error('input parameter endpoint exceed the maximal point number');
: f! f4 y1 h/ a: Nend$ S) a. ~6 X, l% L+ b+ P
! ?9 O- s2 x- H; \0 [%initialization
& I, q. W" Y$ b- R Y' {$ n9 Fs_path=[start];
/ I% Y$ q1 C& e* b! ]& W; _2 mdistance=inf*ones(1,row);distance(start)=0;
. a8 z: t* f/ A* N) }flag(start)=start;temp=start;
5 q: X ?5 R6 @- H: C& S7 W- z( V" c0 q$ Z. ]5 _/ ^3 I6 k5 `* N" S
while length(s_path)<row
% m3 E5 S9 w4 F9 D) [ pos=find(Input_weight(temp, : )~=inf);, m K$ M( }! r, V b1 W4 e
for i=1:length(pos)1 l, C" W3 x: E ^
if (length(find(s_path==pos(i)))==0)&1 C+ x4 S( G# M w* V
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
" W$ {& p8 w6 i8 }: z, n" l distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));4 m& q5 ~! I- x" p P" z
flag(pos(i))=temp;* e+ k9 U9 \9 \$ x/ \
end. \2 S! X$ ~8 H' x* L4 T" _1 C/ l1 v8 b. u
end) f6 r {1 E9 f3 U7 X! ?
k=inf;
9 G/ D& p7 p. I0 `, b, E0 l for i=1:row5 x- J* z- |3 T0 C, u
if (length(find(s_path==i))==0)&(k>distance(i))
E% ]# h! t5 R% E, b k=distance(i);
3 m: v! d' C, C; B3 K" } temp_2=i;
3 L4 G: |+ P9 Z- X- `9 G/ |7 X4 [ end
6 R1 F7 Y4 f( R9 V! O1 V7 Y end5 l% g$ F8 t& \& k6 z9 g; p
s_path=[s_path,temp_2];( Q+ ]- H$ o$ ~' K8 n
temp=temp_2;' u" ^+ z" ?7 I9 e \8 |
end) j0 ~& N! ^- q& ~& b$ y* d
) [( q D. Y( P
%output the result( K# x2 n3 T& ^" J$ X, a
path(1)=endpoint;
5 V! s# s) p4 J3 T' x. Fi=1;
, i- Y" k6 e X F+ I1 \while path(i)~=start& q: _" R. `+ |. L/ x) l3 H; }
path(i+1)=flag(path(i));! U0 }- V& t% @$ e/ k% M
i=i+1;
! u. a% R3 t' A/ \6 \# _; cend; a* T! J% s# T# |9 ^+ |7 \
path(i)=start;5 X8 C! G) b: W
path=path(end:-1:1);
- m: K1 N q) d- o9 C8 @short_distance=distance(endpoint);
% y: L+ ~# E3 d2 ^8 Q8 f/ b三 绘制差分方程的映射分叉图) R1 ^7 A* `6 ~+ v8 {4 C- x
* k6 S% A) p$ r! ifunction fork1(a);
9 Q- F9 u- Q0 v& ^+ O5 u/ K* d! {0 _8 @* W7 D1 P; \
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
2 g, Y6 c* ^6 I; l& K# `6 H% Example: 3 G( P0 ]) B; \; @7 c a
% fork1([0,2]); ! M9 R( R- m) w, }9 k
N=300; % 取样点数
; j( \7 p' [6 b) `A=linspace(a(1),a(2),N);
" R) v; a! t# R; X ?% ?& H; lstarx=0.9;
# h2 h/ N1 `+ v4 lZ=[];9 n8 i% D0 |/ u: E
h=waitbar(0,'please wait');m=1;
, P1 D* O+ S) q9 }* Lfor ap=A;
1 w+ h; `6 m) K1 [" Q x=starx; ( q4 |! ?3 p9 p/ H `
for k=1:50; , e: M5 t4 h' W1 R
x=1-ap*x^2;
# @: r; A5 h# J end , _, l0 H- x! D" K
for k=1:201;
5 J) I9 B% @2 i5 A4 w x=1-ap*x^2; . j* O1 [) m( `+ n
Z=[Z,ap-x*i]; K0 O0 n( ~% e0 k( s, F7 y0 g
end
% S0 n }" i' G/ s" i9 n' p. R* o waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);& |; m3 v' W+ v
m=m+1;
k) y# f. w9 d2 S, Mend
1 M* t+ f0 U3 P9 {$ \delete(h);
! L3 U8 V% m6 H* |plot(Z,'.','markersize',2) " E# M9 Y4 l* Y
xlim(a);) `4 c) x" p) y2 S& z
8 a( V4 ~9 k1 G. o四 最短路算法------floyd算法
% \! z% `9 ^+ h" w8 {# F7 gfunction ShortPath_floyd(w,start,terminal) % t: R# I$ b. T
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;1 ~* T$ ~% }; M8 f5 \
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];+ d9 [! i( [* ^6 O$ ^/ D" T5 b7 K/ T
%start-----the start node;
0 ?4 S8 X5 y/ |+ X6 U& w7 p%terminal--------the end node;
+ u5 g/ S$ @! D7 K9 \n=size(w,1);
; D; ?# P4 \' ^+ _! o2 I9 ^[D,path]=floyd1(w);%调用floyd算法程序
& I5 `' N" Z9 }) a* C
6 y7 H1 T8 O* n+ r" g- t/ i: ]%找出任意两点之间的最短路径,并输出: X# O# C+ M! E' L
for i=1:n
" L2 `1 \' A3 V Q3 a% ] for j=1:n
3 x) ~1 S/ G" H, N Min_path(i,j).distance=D(i,j);
3 X- z( d8 l( ^2 h %将i到j的最短路程赋值 Min_path(i,j).distance% F( X2 S) h8 b1 ~: e9 N
%将i到j所经路径赋给Min_path(i,j).path
8 f( v6 i3 \9 r" R2 A f# s/ f" F Min_path(i,j).path(1)=i;
1 z5 [1 [9 @( M; V k=1;
% A7 i; \) {- w: c8 P+ P0 o" N while Min_path(i,j).path(k)~=j
# `& f E4 h$ h4 v# e5 c" r8 v k=k+1;
; X# G9 _' o8 j1 J0 G* i- @$ D' v/ o Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);: E" y: Z4 X5 L
end
; c$ a: i2 s) w3 Y, i end+ Z7 q6 E) J$ V
end
+ {, ?8 [1 j% o" ns=sprintf('任意两点之间的最短路径如下:');
( E$ H* B/ ^" o4 j$ S9 ~disp(s);8 S# Q" y& d0 J* [4 ]0 I$ e
for i=1:n
8 h2 ?2 R; h6 S% E% [0 \ for j=1:n) A/ g' Z, f; S; p( ]3 |, o# z9 n
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...( C' E b8 C: q! K
,i,j,Min_path(i,j).distance);7 r6 D4 ]) Y: N
disp(s);1 ~7 @* B( A2 u ^2 o( E: v
disp(Min_path(i,j).path);* [! J: i2 q; G/ x+ ]9 K% w- }0 z
end& n! C4 Y3 j7 [' k
end
0 q( g8 i: j; x+ E/ j: ~2 r- N3 a) b: i b/ v2 A
%找出在指定从start点到terminal点的最短路径,并输出
) b5 u% ]- ^9 i4 K; Astr1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',..., G" x4 D/ B. s; O, g& W
start,terminal,Min_path(start,terminal).distance);# \& _! n5 t1 A. E* t
disp(str1);* A5 U- L9 |6 f' c* e- S/ A" a
disp(Min_path(start,terminal).path);+ S' f O4 F b4 t! t3 b6 Y
1 R" Y; B" Q7 S% _/ S% p
%Foldy's Algorithm 算法程序
6 D( `; U: E [, S% Lfunction [D,path]=floyd1(a)0 k; q& X( r* b% C: I# s1 T
n=size(a,1);
+ Q4 [" E- s& v4 W5 M% lD=a;path=zeros(n,n);%设置D和path的初值0 }+ r+ _: z9 i9 `5 t" ^
for i=1:n
+ `5 e; s: V: e6 e o( t6 p/ v& ]3 } for j=1:n0 T9 ^$ v& v9 g4 K; Z6 z
if D(i,j)~=inf
4 k5 z+ [- N3 l7 V: i+ o path(i,j)=j;%j是i的后点
. E; H1 `, {* p) k+ c) a+ d end" g2 Q! ~7 Q1 z8 T \2 \
end! {5 D/ w% e/ }6 Q# k r; d; [& V
end
5 ], Q9 U" V8 h, k7 _%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
9 @# Q! R }2 Q _: _( K8 Rfor k=1:n! U+ }/ y+ p2 c$ D8 q/ Z
for i=1:n
' R* F, c1 W7 ?4 U4 n# i! f* F for j=1:n. m" h; r% c& X6 V) k' I
if D(i,k)+D(k,j)<D(i,j)
3 c. ] {5 d3 N j/ f D(i,j)=D(i,k)+D(k,j);%修改长度; \5 A3 @! {$ ]/ [! A
path(i,j)=path(i,k);%修改路径# n! o6 F5 n& s* k, s
end
5 \ M, V1 B8 Y end
) @" l. W8 f4 C- Q7 d& O: { end9 p3 E+ @( C0 a4 _" c4 E" z1 o/ h: ~
end
2 | \. |1 ?0 M+ E) O9 k* |; [* R0 ^, _* O
五 模拟退火算法源程序
- I2 l4 _4 b# B, T7 _function [MinD,BestPath]=MainAneal(CityPosition,pn)
" W: ? g3 r Q# k' o2 r- efunction [MinD,BestPath]=MainAneal2(CityPosition,pn)
* r3 n) ]. l4 ~1 x( C6 I8 @%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' o" t- @7 S* D; K0 }' ~7 H
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
, G7 G: ^! { R& R% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...' B4 ^7 g# Q0 @# q! R; }* j
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...+ e+ C: o+ |. W5 `1 Z
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
8 x0 M: H# q. u4 A, T1 T% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
& G! U e) i |, U8 j v9 ^& V$ F9 R/ I2 i4 a& ~& v
%T0=clock( x' |! k# w! r5 E7 s* J! G
global path p2 D;
, v9 E; y2 B/ T9 o" p[m,n]=size(CityPosition);5 O2 z o* t1 h# R- z' j1 Z5 o
%生成初始解空间,这样可以比逐步分配空间运行快一些
4 [2 n* \* z3 ]5 H' rTracePath=zeros(1e3,m);
4 R7 K5 c! j, B. p: tDistance=inf*zeros(1,1e3);
\$ B. y1 g& P& I& Z- N& V( q \9 U) E6 O3 S1 i( w
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...1 Y5 O* F. B' S3 S) [
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );; W2 p6 `3 W, ^) ^) j2 |" z
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)" K' d: ^8 y! D+ s5 a5 l
for i=1:pn# }0 H5 V/ V* `; k# C! l0 W: u# u
path(i,:)=randperm(m);%构造一个初始可行解! S7 h3 p4 D# D* d
end
# T9 _0 Q5 T1 [9 et=zeros(1,pn);
( }) z5 A# n, Zp2=zeros(1,m);* J. I" j, v' S6 Z( H& R
5 v6 [% a/ |" {+ A& u& _
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
$ V0 C/ q- X0 Y' e) Q X" Dm_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=' ) ;+ z( n2 F q5 g z& K
%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! x3 X" t8 y%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
4 S {- I% F, [& O%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0 s- s; D% Q/ _+ J" d% |1 ?6 N
%会收到到比较好的效果
$ f+ l% L/ A& I
- }8 ^- Q' k2 k) L0 ^T=1e5;
; R) K0 x6 o, y+ ZN=1;* ^* u/ i7 O. N5 Z
tau=1e-5;%input('请输入最低温度tau=' );% j& ]3 y9 m# V& l
%nn=ceil(log10(tau/T)/log10(0.9));
_% l) e, B! vwhile T>=tau%&m_num<m_max 0 R1 Z& c- |: d' J4 E
iter_num=1;%某固定温度下迭代计数器
8 n! Z8 h' x- i% ^; y6 j- j m_num=1;%某固定温度下目标函数值连续未改进次数计算器
' M4 L' m3 D( }/ v0 X %iter_max=100;
1 h) _9 O0 k9 {, G) |% O %m_max=10;%ceil(10+0.5*nn-0.3*N);
9 X) g+ {& P0 i! `3 S while m_num<m_max&iter_num<iter_max& \! v' v1 B& E5 F
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:; r5 O4 e8 o9 K, B ^
%用任意启发式算法在path的领域N(path)中找出新的更优解6 q& t* V+ `7 |, Z; \, u |
for i=1:pn4 c% v3 T2 d6 |6 h
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);, {& s$ G0 g* N w
%计算一次行遍所有城市的总路程
D1 U& r, T5 a x5 y1 K" H [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线2 d' }7 q2 s/ j
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
$ P; D; T3 x& ^/ I8 O( C# W end1 _2 K; v, H( J0 e! V
%Len1/ Z1 R: l2 s! f6 `# I* v. r
%Len2
7 `9 p9 m9 u2 t) H) n" o1 E %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand, o4 Z) |/ [" z! M% q I
R=rand(1,pn);9 \, i% A8 H5 {1 _5 h) h) P: q
%Len2-Len1<t|exp((Len1-Len2)/(T))>R
" G* G0 P, j/ \ if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)' x; C" A! O+ h/ h+ t( V
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );8 ?% K: Q) @2 p' j2 M5 t
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));! [# h8 |- g5 W. d" P
[TempMinD,TempIndex]=min(Len1);% e. D) W9 _) N% N" P. L6 p
%TempMinD: S0 o% c# b1 I2 _
TracePath(N,: )=path(TempIndex,: );
4 Y" {. f$ C* j8 { Distance(N,: )=TempMinD;8 }2 p `/ v, m0 w
N=N+1;
) |: x" T, r" w4 F$ S' T %T=T*0.9
( M5 b2 I& T5 B e" O3 P+ C m_num=0;
- f: H1 q+ Z4 d7 i$ I else
- }6 P- S6 q! [4 X8 {6 v' S3 N7 j m_num=m_num+1;
2 J% S) o0 [: B1 S! D3 n end
3 S6 @% g! t8 }# I iter_num=iter_num+1;
& n& }; m; @5 W# h6 S7 k end% U; V; t+ g1 x; [; {8 k$ e
T=T*0.9
2 W3 l5 I) |! W! h7 f%m_num,iter_num,N
" ~2 _$ L+ ~; ?: U# Zend
) t( |6 n- W* X4 {2 y; Q3 P. Q[MinD,Index]=min(Distance);
' t$ h: F5 }* hBestPath=TracePath(Index,: );- H" m3 ]0 K% A7 X1 t$ @) R) E
disp(MinD)1 p; m: W$ t: P- ]3 F7 E5 X# B
%T1=clock
% u3 D9 d- P/ t) ~. z0 g" g
2 h3 n+ b3 T3 k 0 [* h. o& A; j* T
%更新路线子程序 , V/ `! i n3 Q$ d; {7 _. S5 G9 i
function [p2]=ChangePath2(p1,CityNum)
/ [* F0 Q! T8 J: r. i2 [$ yglobal p2;
& J4 }% \% u7 P6 Y9 U: _8 `while(1)
6 N3 i* i2 x0 i( t! g9 L+ l R=unidrnd(CityNum,1,2);2 a3 t _! Y, x I- T0 y
if abs(R(1)-R(2))>1/ M4 u0 n9 a$ p9 c7 R
break;
[; p9 ^ J% [7 P2 j% G5 K end" O. t i* @# ^: a$ @, V9 e+ D: }
end
6 h; J! i, s% p) w9 C) }R=unidrnd(CityNum,1,2);
! H+ X O) q" K' o& b9 e+ `+ H7 GI=R(1);J=R(2);
$ C$ Y5 H, B4 G' k6 c0 p%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
: O p( h5 U& \: j3 I; S1 A/ v%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
4 h6 _" ^# y C) l* Qif I<J4 \4 v" o6 {# ?1 Z/ ^/ w
p2(1:I)=p1(1:I);
) v$ u$ m( ?/ c p2(I+1:J)=p1(J:-1:I+1);& i& h& `6 m& F7 g$ d: v j, _; |
p2(J+1:CityNum)=p1(J+1:CityNum);
3 Q- r9 R* E& K4 Zelse
: F$ x0 |6 u* r$ o, n; T p2(1:J)=p1(1:J);
; b& F9 s) n& T; d4 t/ i p2(J+1:I)=p1(I:-1:J+1);
9 z `! K. N3 y q3 Q p2(I+1:CityNum)=p1(I+1:CityNum);
; `! t1 d& c) p+ b& Gend; O i. p4 M* U) f# E
: _' g$ A8 N6 Q7 x" A
六 遗传 算 法程序:1 o1 E$ ]9 `6 n
说明: 为遗传算法的主程序; 采用二进制Gray编码,采用基于轮盘赌法的非线性排名选择, 均匀交叉,变异操作,而且还引入了倒位操作!
' G* W1 `, I" E/ A% V
+ D& r3 f, g1 N& Efunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
7 b" o. T9 I; ^- e; R% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
3 `3 h. R5 `( k2 u& M5 S, O% Finds a maximum of a function of several variables.: P, K8 V8 ~$ E2 C
% fmaxga solves problems of the form:
) n' F4 L `. x( h, X8 h! ?% max F(X) subject to: LB <= X <= UB 7 @$ a, j+ u9 r! T6 S
% BestPop - 最优的群体即为最优的染色体群* _: p ?( Z0 U( Q3 J) j
% Trace - 最佳染色体所对应的目标函数值
& k' W, P4 c, J& q5 Q% FUN - 目标函数
+ C4 s d) u8 ^9 R% LB - 自变量下限5 u* f6 o8 O1 \) v2 _: X: t) k
% UB - 自变量上限
% I6 z. E9 ]5 g% eranum - 种群的代数,取100--1000(默认200)
( j( l' E1 r. {" ~5 M5 g0 \! _% popsize - 每一代种群的规模;此可取50--200(默认100)3 a4 Z( \8 E5 W7 m+ r3 r
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)7 W6 ~7 P3 I/ c/ N) M8 C8 f
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
/ ^% s( ]9 U3 ^6 T- Y. w3 C7 u% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2), @: A, g, B5 K5 @9 [% b% R/ t$ K
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编; B" `0 P- m3 w: F1 a! x. i
%码,option(2)设定求解精度(默认1e-4)
! j) ?* S Q0 U%
2 f4 K4 g' `& J- ~+ I% ------------------------------------------------------------------------, b$ t) ^5 w* Z1 v4 [2 a! A6 E& G3 H
$ z4 m, u, _9 S/ d5 S- m- y+ ~T1=clock;# b- ~0 Z3 i* s4 c4 s5 X
if nargin<3, error('FMAXGA requires at least three input arguments'); end* o) u, D4 L7 M' P& e9 @0 g
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end9 l" M7 i1 l% t2 N7 M) g
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
/ T2 q' m# j$ m/ @) Bif nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
& t7 f; n$ v/ H z. ^! ^if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end5 ?, U/ F0 W; V- O0 g3 ^9 h
if nargin==7, pInversion=0.15;options=[0 1e-4];end
4 M7 y3 @# g S" u* }2 aif find((LB-UB)>0)
, A/ Q2 r. r- h( O- G" \ error('数据输入错误,请重新输入(LB<UB):');' x$ O2 k* ?. P4 Q- y1 L+ o6 v" c+ D# Y6 k
end
# C* W) v6 n7 b, O/ T0 ^s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
# Z, ?. c" V% B1 N7 Xdisp(s);
_! L2 i& y4 e0 q( T# @5 K2 n9 ?6 S$ V" J2 y$ ]
global m n NewPop children1 children2 VarNum1 q3 ~& ]" K- p7 F
# U5 `3 s8 g0 _/ J, e6 m) q
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);8 G/ |$ `6 j$ ^9 N/ A
precision=options(2);%由求解精度确定二进制编码长度
% r6 ]: Z) q* [9 ?1 e7 g+ Zbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间7 y8 ?( `3 j8 f( [% q" F
[Pop]=InitPopGray(popsize,bits);%初始化种群
% ]8 w. c6 U5 g( D: J$ f9 M[m,n]=size(Pop);
6 W& p- C0 T% I( w9 T$ Q$ @NewPop=zeros(m,n);
9 W( }5 l! L% `children1=zeros(1,n);2 H3 a. f2 ]" w$ s) Q6 W$ o1 n
children2=zeros(1,n);
% w3 `% M; k& N u, G/ apm0=pMutation;
8 w+ {' n& {( K, s0 C( TBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace" w6 e3 Q" X4 j4 ~ E3 g
Trace=zeros(eranum,length(bits)+1);
7 n. `4 W8 h% K B- ]% ]9 E1 [i=1;2 @4 [0 \, o" ~9 r# M3 _7 F/ c
while i<=eranum
6 h9 L3 f; o; d: t8 s for j=1:m
F& j. j9 [, L3 _' ]! \! b" J value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度# E) _* ~+ B! {# ^4 j& R' F
end
/ d K% N2 P* c1 e [MaxValue,Index]=max(value);
# b0 F! Q# ] B' C' W+ @ BestPop(i,:)=Pop(Index,:);# n5 `$ n$ ~5 k W5 j9 e
Trace(i,1)=MaxValue;/ t( i" b8 e. }. E
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);% A4 c& U9 V% T- G3 o3 e# \
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
# d8 e7 i) J2 H# g' \! g[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));) | p3 i2 \) Q4 x7 g# K }3 G
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率 v2 a; u- {* P3 S+ Z
%round(unidrnd(eranum-i)/eranum)
1 J7 n) }) C* f [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
2 ^& V& \" K% E! G( { [InversionPop]=Inversion(MutationPop,pInversion);%倒位: d' z m% k' e# @7 X
Pop=InversionPop;%更新. a, {/ Z6 v9 T# ?2 {, ~% X
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); 3 k4 t0 W& r" V6 b( H+ K
%随着种群向前进化,逐步增大变异率至1/2交叉率1 U* P# c# m% v7 F6 M6 P
p(i)=pMutation;
4 S3 R) P" b$ V* e l+ i9 n: ` i=i+1; y' ?. l: i& j# [4 s) P
end9 p, a* v2 b& H0 n# g" h6 d* w5 a
t=1:eranum;
g4 B6 }6 b( d U1 o+ Vplot(t,Trace(:,1)');
2 |$ e# _5 @8 P7 rtitle('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)');5 n) s: p L r6 e
[MaxFval,I]=max(Trace(:,1));0 ]: L2 e+ g# V
X=Trace(I,(2:length(bits)+1));* K4 i+ j7 ?( o( Y! a
hold on; plot(I,MaxFval,'*');+ Y5 U' n, ]0 r2 e% t4 |
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
8 K1 F& @& o h- a4 @2 K4 v$ Hstr1=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,:))); g( g0 i: \7 l. l. A8 W8 h
disp(str1);& v& ~- x( L+ ]9 O l2 t
%figure(2);plot(t,p);%绘制变异值增大过程
) c2 O+ @- \' g! n$ JT2=clock;4 x% u4 ~: u2 l! T0 w, j
elapsed_time=T2-T1;. u2 c o0 k3 ~
if elapsed_time(6)<0
2 [$ c# g0 X9 o3 p+ ^ elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
2 q2 o4 P* o% xend+ W7 F' o% | X: e
if elapsed_time(5)<0
- J- |9 X) d% l+ d) ? elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1; S( d8 N& k+ c; r+ R6 x0 i. U. G! w
end %像这种程序当然不考虑运行上小时啦# T# M# P/ f0 q
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));0 a- l! \6 X& [6 E/ K- ?0 f
disp(str2);$ X0 s. |3 G0 t) t0 P2 T
/ Q* [. k+ d3 u$ c$ R. Q
6 y; j9 l0 n$ {, P! B
%初始化种群
! D' S( h2 u0 w+ `%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 I6 V& y, [) L- c! J1 J1 O! l' A
function [initpop]=InitPopGray(popsize,bits)& i1 h/ i* j" N# A$ [/ g0 M
len=sum(bits);
# a7 s8 F$ Q1 q) Zinitpop=zeros(popsize,len);%The whole zero encoding individual7 o2 T ~- {* J% z3 |4 e( X9 M1 `
for i=2:popsize-1$ V6 [* c4 @, ^2 a/ q g J
pop=round(rand(1,len));: y7 P. V5 ?' s
pop=mod(([0 pop]+[pop 0]),2);4 A) b* H( F" \" _# S2 T
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
/ C7 Z/ Z* u$ i% V* @/ F% @ %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n): y- Q$ i* k. P( n
initpop(i,:)=pop(1:end-1);9 \- |! o, }+ O( T+ @& r
end
C! g/ z1 G6 y" yinitpop(popsize,:)=ones(1,len);%The whole one encoding individual! Z, ~" A$ F/ o2 P; I. S
%解码
5 ?' B' D/ g: {1 i/ t4 c
) B- R/ E& Y! L& D! @function [fval] = b2f(bval,bounds,bits)" \$ Z. Y3 |' s8 d8 j+ ~1 S
% fval - 表征各变量的十进制数
1 k; c" d8 `$ a0 O4 g% bval - 表征各变量的二进制编码串
- i$ p* M8 T% H' i- n* ~( V2 T% bounds - 各变量的取值范围
. W7 p( r& o2 j" ~5 h3 X% bits - 各变量的二进制编码长度 e6 J& B& u3 I# V
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
$ M+ c7 e) e( i0 T- @numV=size(bounds,1);8 `8 k- L& \; r% e
cs=[0 cumsum(bits)];
! z3 H$ H2 a* xfor i=1:numV
0 ]) ?1 r& ?% ~# d5 l a=bval((cs(i)+1):cs(i+1));) G8 q; \/ J3 M- e j
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);8 Z7 v6 L4 C" ]6 ~7 ~5 O1 d4 x; E
end
k5 C! l% B a" g4 Z* ?%选择操作
4 ]; c9 V A0 w; {5 j/ {' L8 s%采用基于轮盘赌法的非线性排名选择
1 \1 \* j3 e9 { A* S) K%各个体成员按适应值从大到小分配选择概率:
* r* P1 x' n6 }%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1
0 P7 `: d8 y- u8 O0 o0 T2 h' j" m
2 n% ?. H! y# j8 k) F) B3 Ifunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
?7 b' C4 N# A" `8 \global m n( H& e, Q# a& L0 r) H
selectpop=zeros(m,n);/ U: m' f( A' j u6 ?. |4 P4 M: @7 j
fit=zeros(m,1);
- U: ~3 M! m, U, z* Kfor i=1:m7 A; S0 v$ r1 O; Y* [
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据& \- n( L: i$ ?* z4 p$ ]3 C
end/ o+ l2 U9 A/ f! x* L; G
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)$ T1 B0 m) j2 M) T. [' r% h
q=max(selectprob);%选择最优的概率
5 G- G3 m$ R. l7 p7 d4 Vx=zeros(m,2);* X7 ^- @% p: u' O$ s
x(:,1)=[m:-1:1]';
% Q# X+ ?9 f' T5 p" a4 Z8 A n' z: G[y x(:,2)]=sort(selectprob);6 v2 A. ~6 g) P8 J' a# d
r=q/(1-(1-q)^m);%标准分布基值
* t; X, L: C2 q$ A2 m8 |newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
, T" y+ X7 z% J& X7 h6 t$ v% Jnewfit=cumsum(newfit);%计算各选择概率之和) j- e9 T0 ?# A0 z9 l
rNums=sort(rand(m,1));
' y% F& k4 g% t4 A0 c u J# @% GfitIn=1;newIn=1;
0 ?, \% F0 U' |" i% `while newIn<=m
3 m: v; A1 @& h/ ] if rNums(newIn)<newfit(fitIn)8 Q$ u# |( w6 G4 u
selectpop(newIn,:)=pop(fitIn,:);
8 V% t! B3 ^3 ~6 Z& F) C: | newIn=newIn+1;
) J2 Q; q5 b. `/ x/ S( p6 B else7 _& a. {3 x" n) o! Z+ d
fitIn=fitIn+1;, [7 V( P3 t6 z
end
! q. l7 B- y6 J- B$ G3 Z" |5 yend: t! l' T5 c0 m; r/ R2 r- f; E
%交叉操作6 \' Z2 W) |* [5 b) d3 K" f/ Z
function [NewPop]=CrossOver(OldPop,pCross,opts)
3 j+ y8 J) U7 @& F; X%OldPop为父代种群,pcross为交叉概率
) |- r0 J/ t, K" H1 o: oglobal m n NewPop 9 A8 K! `, v- S' x4 O, {
r=rand(1,m);
4 B5 m, Y1 Y& O' @% ry1=find(r<pCross);
* L9 Q8 u$ y3 l% oy2=find(r>=pCross);9 \' H0 J2 p6 e5 a
len=length(y1);
: k9 k. P& D* B1 X- Y3 Fif 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
$ U5 l# `& l8 W% x, R4 P1 n8 y y2(length(y2)+1)=y1(len);" `# R! }2 _: _
y1(len)=[];
6 ~! y6 ?6 V' l: q+ Bend
8 }" g! O9 \- j- ]4 G. k3 p. Yif length(y1)>=2
* Y5 w# ~9 S" a, R9 I( @ for i=0:2:length(y1)-2
9 g3 O! s$ ]6 M6 M* m7 | if opts==07 n7 z b% |+ H/ Q: r: q; A+ N4 E( ?, t+ p
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));% |& K6 O5 s$ P6 d
else3 s! v( A; ]5 H' k7 I
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
/ v- {. K5 F1 b end" f" C- v3 z' T
end " z) m' w" t+ _! ~& }3 b0 M1 V
end
: ?! V% j9 }% o! N/ O4 DNewPop(y2,:)=OldPop(y2,:);# Y4 F2 [( X* d' s" \- @; t
. e% u6 b4 @2 q5 i; J; o6 y& k7 q
%采用均匀交叉 $ ?& |- h9 M& [4 W, _
function [children1,children2]=EqualCrossOver(parent1,parent2)- W: @, F6 F# M) S
% E6 _! I1 s8 Jglobal n children1 children2
) D# ~- O3 C) O, Ahidecode=round(rand(1,n));%随机生成掩码
* L5 L0 i6 ~; E Ecrossposition=find(hidecode==1);- {! V' [6 j. q, g" U5 l/ C# _ Y" n& |
holdposition=find(hidecode==0);
. d/ |- |! _+ A& uchildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
7 P/ m2 X# ~+ |. R, Q+ _1 a8 m! K# wchildren1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
8 F& A3 [! R: @8 \! {0 g9 Nchildren2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因: I7 K# I- U9 c. o) w6 k f
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
$ C3 U9 j Z5 ?7 r+ B7 d) f c6 A1 P7 z/ W6 x
%采用多点交叉,交叉点数由变量数决定
) x6 E3 r3 F0 K, R j1 |, e& }
+ Y4 k, Y! S; e/ Ffunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)
, x" y. ]/ d& N3 a& o: ]0 |9 X- l! N6 ^- }) y
global n Children1 Children2 VarNum' e' T1 c9 u& F4 S
Children1=Parent1;
% }9 Y( t6 l/ x3 W2 {. }& ]# AChildren2=Parent2;) N: U7 ]! {6 @+ J' R
Points=sort(unidrnd(n,1,2*VarNum));
) T1 b% Y0 Y5 i7 V9 }6 _; Wfor i=1:VarNum
: F: u* H" M2 O8 h2 ?4 I- {; N' \! v* f Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
) c8 F2 t8 D. O' b1 B! T# m7 M" ]# ] Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
. S7 g+ R( Y: Z) }5 q4 u4 oend
! _( h1 \5 o2 D$ { T( r" z
5 _0 ?" S: l7 \; A, }%变异操作
2 l: f8 E* l" L1 s7 F1 z5 @8 h) v6 g8 s$ Zfunction [NewPop]=Mutation(OldPop,pMutation,VarNum)
; p N. l: e- c' U$ u J
! y! F4 x/ u6 Y8 @# oglobal m n NewPop5 Y- P! k, C+ `$ x- h4 P8 p+ a( _4 ?3 {1 z
r=rand(1,m);
9 O9 h. j, a y F7 j: n$ lposition=find(r<=pMutation);# p$ O2 X* v o. z0 \' J
len=length(position);9 L7 p9 J3 u( S" b$ D
if len>=13 S3 s6 y- E. j+ a9 t* h6 e, K
for i=1:len" k( R S; F$ O+ X' Q" G- U. t6 j
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点 I3 v+ a6 \2 W; O; h! Q
for j=1:length(k)
c* ^& t* H1 Z! A0 Q) e+ V if OldPop(position(i),k(j))==1
+ i; s/ Y# F& \4 P" k5 {+ k& | OldPop(position(i),k(j))=0;7 J4 D- a( _9 \, M+ R6 M9 d
else+ b. _/ S: k9 s8 |! F" k/ f+ r3 C! c
OldPop(position(i),k(j))=1;
8 {6 k0 E- B9 \2 I$ P6 F end
: C# S. F# e8 Q end: m9 e8 [: {( D3 ]# O- w
end
9 b, H2 s R8 f( l5 L3 Jend
, d$ x; i0 K+ V1 Z+ L: YNewPop=OldPop;4 h6 Y, J( p9 {
* U, ? a' m U6 U$ I5 y$ e7 M0 O
%倒位操作1 q2 {# E$ N- D( ^
4 O h" S5 u+ n; i3 b6 @8 \
function [NewPop]=Inversion(OldPop,pInversion)+ g: c5 G. z8 R: H
2 x. }) V& r, f% L7 Y* Dglobal m n NewPop2 n% D- h$ _$ |3 a: B; H% S
NewPop=OldPop;
" {7 O3 z6 ^* q% g; u2 Gr=rand(1,m);
- a: E& {! s5 p# O" F& I VPopIn=find(r<=pInversion);
) T% {9 {# ^# z, A9 H+ {len=length(PopIn);
8 l% X: L: S6 z0 Rif len>=1( p V& ^7 F6 j; ` X/ p n
for i=1:len) R' a# a* ]7 L
d=sort(unidrnd(n,1,2));
" U5 s0 j* d9 U9 T if d(1)~=1&d(2)~=n# f$ F0 _% T/ g9 Q* `' i" f: K
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
- Z* J& X; Z/ z5 K NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1)); m% T" }7 T* o, i
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
, u5 p9 @. Z3 C4 E' i! H$ u end x- m6 B% B& x
end8 G: y+ R; s* k; k' Y: x! ?' C
end/ U& z! r+ T* u& L+ R- } Z" Z5 E
; Q8 y8 |6 {6 p: u' q$ ~1 x
七 径向基神经网络训练程序9 i0 F& Q. G; Y+ C/ G# h1 i" w
; _: G# U, ]- G9 T- j( Aclear all;
/ D: ]1 [* ]5 S# eclc;( u- v @; g5 G* X: f" Y& d6 u
%newrb 建立一个径向基函数神经网络8 {% P, @% P, q. k7 b
p=0:0.1:1; %输入矢量' K& j7 d; r2 e
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
) R- F* ?2 Z4 u: fgoal=0.01; %误差
. t; F$ l9 r: Z- s* N# Q' Zsp=1; %扩展常数3 B) x3 H/ F+ ~* P c6 \
mn=100;%神经元的最多个数
0 ^1 ?8 W' x& {df=1; %训练过程的显示频率
* I5 x$ o0 g: W2 U; a, i[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络1 o5 B1 _9 v3 k8 K, p8 }
% [net,tr]=train(net,p); %调用traingdm算法训练网络1 g1 e( w1 ~/ v( R: B1 q
%对网络进行仿真,并绘制样本数据和网络输出图形
' N. j5 |! W& l5 j+ wA=sim(net,p);1 {( F w$ c$ X7 L
E=t-A;
" Z. E4 N; N W. s- L0 {sse=sse(E);
! v3 Z& Z- Q. D9 Y8 }figure;
8 k" f" ?/ _- s3 X0 p+ [! @3 Tplot(p,t,'r-+',p,A,'b-*');
: \; q: z$ s- O5 A! M3 ylegend('输入数据曲线','训练输出曲线');/ v, g& m( ^5 H% @' h) b
echo off % X- m+ l+ g2 s" A& H7 d
/ E @9 l4 G* W+ n
说明:newrb函数本来 在创建新的网络的时候就进行了训练!
; d# ?7 x) ]5 Q( A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,
4 W* Y% i+ a1 A3 U1 y% B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! `7 M0 T) g1 T( q z# c* G
9 @7 y+ U' E! m) E
) e: n4 U' V& h: d训练结果显示:5 b- i# W% @& ^/ {- J
NEWRB, neurons = 0, SSE = 5.0973; l+ x* x, S& w7 Q4 A" f' H3 P
NEWRB, neurons = 2, SSE = 4.87139$ S8 v! a# r; k n' t/ s: s. E
NEWRB, neurons = 3, SSE = 3.61176/ O; n9 v3 k" U, M
NEWRB, neurons = 4, SSE = 3.4875
* ?5 ^8 ~; }7 [" I2 zNEWRB, neurons = 5, SSE = 0.534217
1 S! B1 a) p9 e& `, W+ k% `NEWRB, neurons = 6, SSE = 0.51785. R: S6 }% n7 n5 W
NEWRB, neurons = 7, SSE = 0.434259
) l5 I6 G5 Y' k8 ?NEWRB, neurons = 8, SSE = 0.341518
7 ?- p0 M! |4 t+ Y2 K7 mNEWRB, neurons = 9, SSE = 0.341519
0 Y4 k" U0 |, t+ V) d4 N" X8 fNEWRB, neurons = 10, SSE = 0.00257832& Z; R" M1 \2 {) R& ]3 f
* @. [1 k0 w9 k- N7 y八 删除当前路径下所有的带后缀.asv的文件
* {8 r- O7 T# |/ e$ K说明:该程序具有很好的移植性,用户可以根据自己地1 X' Z! j/ W# z9 r2 S$ O
要求修改程序,删除不同后缀类型的文件! & ?, l8 j& g5 ^5 Z2 q& t9 J4 C+ p! q1 c
function delete_asv(bpath)
) X$ i4 b8 K# t%If bpath is not specified,it lists all the asv files in the current
: @5 |9 i+ J6 y3 l4 \4 x$ M%directory and will delete all the file with asv 4 U9 T7 w- Z. t
% Example:
* J! T8 H+ Q+ J9 j; C0 g$ j1 o2 }. ?% delete_asv('*.asv') will delete the file with name *.asv;
& Q5 k5 L) S2 \1 o" F) A0 e$ h, U- k% delete_asv will delete all the file with .asv.
' i$ Y; @' }7 i: r) F* f( r5 D- Y. \
if nargin < 1
\5 u9 a" K5 c" ^' @8 Z%list all the asv file in the current directory
2 y. c9 o! R: T files=dir('*.asv');
2 u' X2 w5 Y0 Q2 h' Y: I" uelse
) o+ t6 E; j0 y: h H% find the exact file in the path of bpath
; ?7 X5 D6 q* O! k [pathstr,name] = fileparts(bpath);9 c+ u8 {( ]- I) R
if exist(bpath,'dir')
) N/ j. @( D5 t/ I* v' ~# f# R name = [name '\*'];/ [8 C& k9 L. i0 F( g3 O
end% I* i. R8 G5 S( o8 f
ext = '.asv';; ~0 P& i3 Z0 O y# x; y
files=dir(fullfile(pathstr,[name ext]));/ b1 x! D" }+ i) I/ J5 ^3 `3 Y. n
end
q- n% b3 ?5 y+ \' @4 i! Q) J- {/ Z# i9 ]3 B) O& _' O) j
if ~isempty(files)
( o" l% t- O f for i=1:size(files,1)
6 I' w" L4 L* ]# J6 V9 e5 |9 i% Z title=files(i).name;/ x/ @5 _- J+ _; o
delete(title);
0 L: b6 @! F, ^* `, A: u( K5 h end
+ o( i* g) y3 j; ^0 x. D9 pend
& p& Z4 S4 E8 r1 u( j
- C' v- i: V: Y. {
- b/ B2 e7 t2 v9 i5 R同样也可以在Matlab的窗口设置中取消保存.asv文件!" I5 X, N- J5 H* I2 \* q
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