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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4 z! k4 i2 ^/ m8 T6 x) |
1. predict_fun.m为主程序;
: v4 D' S$ M$ z3 v1 W+ ?4 ^3 Y3 z 2. timeseries.m和 serie**pan.m为调用的子程序* m9 K5 ]9 x! x. V: @3 F& h) D2 G
3 \8 o4 [0 q+ ]9 u5 x1 x m
function ima_pre=predict_fun(b,step)
9 h/ Z3 x( v! i0 o! {3 X % main program invokes timeseries.m and serie**pan.m9 ?1 g* }/ Q/ U) d. R+ V
% input parameters:
- X) R* T8 S, g0 T% g8 n" N % b-------the training data (vector);6 C" z" J& s& W. u5 Y2 T% X
% step----number of prediction data;
7 Y1 X. g# j, C. n, ~: U % output parameters:* m3 K5 L8 w3 Q* Z( M; T5 w! m
% ima_pre---the prediction data(vector);
! s& i$ l) N$ |" n old_b=b;0 j/ z$ {; Q3 {5 L3 w, h3 W
mean_b=sum(old_b)/length(old_b);
+ {; h& r0 D( [( p" j/ F std_b=std(old_b);
! E8 z( Q% I# s/ T. L/ e. ^ old_b=(old_b-mean_b)/std_b;6 Z! b% T) c+ q& ]6 t7 Y
[f,x]=timeseries(old_b);
# J; m. W0 P* S2 a+ }* Q7 l) T+ B5 e old_f2=serie**pan(old_b,step);
8 d/ j/ h+ U5 C % f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;; K' o5 _" i( ]" H# r) {+ u
R=corrcoef(f);
) c0 [+ q1 S5 p" |' | [eigvector eigroot]=eig(R);
0 N: D. B4 ~# U9 e& c, f, L7 d4 z$ E eigroot=diag(eigroot);0 n/ t! s3 ]6 [$ h) L! ?4 T
a=eigroot(end:-1:1);1 c2 q4 H# ?! l+ T5 Z ^# C" x
vector=eigvector(:,end:-1:1);0 p; }; Z; n% a
Devote=a./sum(a);
+ Z! i+ w( p( k* r& G8 ~6 M Devotem=cumsum(Devote);0 ?; m& C, k& u) b9 s
m=find(Devotem>=0.995);
, @$ J7 q" N( l4 W m=m(1);5 f. @- R T4 ^
V1=f*eigvector';9 R- {: a- _# d) H7 {4 Y0 e" N
V=V1(:,1:m);
) y5 R* s3 `9 x+ X % old_b=old_b;
/ L3 U3 n5 S0 U7 ` old_fai=inv(V'*V)*V'*old_b;/ K2 @# [ A8 a; V: s' W
eigvector=eigvector(1:m,1:m);+ \7 S) w# h- S6 E/ {# _3 R* }) `- ^
fai=eigvector*old_fai;0 j0 J; y9 d7 ~4 ?( J" ?% B
f2=old_f2(:,1:m);
/ }8 ?: z9 w, Z- C6 u' ~) C predictvalue=f2*fai;8 R, Z- Y! L$ P c9 p( [# P
ima_pre=std_b*predictvalue+mean_b;4 F- R- Q. l0 W2 E/ Z* T
5 Q! k& U, H z5 k8 `5 J6 ^* l
1.子函数: timeseries.m
4 h1 C& ^3 N( Q7 o- |1 a: h % timeseries program%- K( v, q; o8 ?+ j
% this program is used to generate mean value matrix f;& L4 X1 Q' T, V, j* a Q
function [f,x]=timeseries(data)
) o% h* d. g! H: k; c) t % data--------the input sequence (vector);1 P& v8 |, c0 ^$ b2 ?0 k
% f------mean value matrix f; z2 Z% o) Z. |) Z4 i7 }
n=length(data);- [ f( H5 z/ w7 ], K
for L=1:n/2' w+ Q! Y# u! E9 R+ p, a4 a+ j
nL=floor(n/L);
1 a$ w. |2 q0 l9 [) a7 ^9 A. @( G for i=1:L% |+ k# h& b( H3 N* b& S; n* v. W
sum=0;! {" L9 B/ C# T; H; Q2 N5 K
for j=1:nL
6 r, d3 ` k( e0 e+ R) J sum=sum+data(i+(j-1)*L);
) z6 j7 @4 N1 T7 l+ W, i1 V) R) I1 C8 f end! t. S1 ~/ i* v9 S- m' d8 U
x{L,i}=sum/nL;
( U4 z# G3 Z* b, } end0 T+ H5 d7 @* |0 N7 `0 \/ v! V
end# r( w% F- Z8 }- d L. x2 p+ T
L=n/2;9 Z( G! g5 q' [4 k) W
f=zeros(n,L);4 i. Y3 s% q. N( i D: H, z
for i=1:L
; @1 s* P+ q8 |1 t, h: r# [; g rep=floor(n/i);
" Y F- i, o5 a. S res=mod(n,i);
1 K# X# m* D9 }' k/ |$ r' p8 {8 R b=[x{i,1:i}];b=b';
1 Y- c2 o7 O7 L' o% J f(1:rep*i,i)=repmat(b,rep,1);+ y c" Z _! J% ~8 r
if res~=0
2 @9 i$ ]0 F3 D8 X5 Q c=rep*i+1:n;
w0 Q9 {, w; d0 R' s, R% [5 \ f(rep*i+1:end,i)=b(1:length(c));* t; ]' h& D" o
end
0 y- y5 [# k: E, U end" F- K2 i1 Q$ S2 i
% L8 a" D. `( h4 \; |2 J2 k# q
% serie**pan.m
0 O, C1 P7 s2 c6 F2 t) Y % the program is used to generate the prediction matrix f;
# @5 ^# z2 R. w( O+ { function f=serie**pan(data,step);" f+ s- Y: c( {# j( v6 h' ?7 `* m
%data---- the input sequence (vector)5 H% c5 _; c* V( e% e# p0 D$ a
% setp---- the prediction number;
3 L8 D: a E5 |$ V* P* m n=length(data);
' [6 s2 x4 H8 J% @& d, x for L=1:n/29 ^4 `! T8 Q2 e* D( s9 |
nL=floor(n/L); Q4 u$ N: a5 ?/ u4 @' M. E
for i=1:L
0 z$ H1 P: D3 I/ y7 S0 C0 x3 B sum=0;7 }, G I) P, p$ N$ ~8 g# t
for j=1:nL# [' ?/ w+ B: P8 R' Z! F& I. T
sum=sum+data(i+(j-1)*L);
% W l. M' G! }( K end4 U% \7 H3 ]; f1 Q! r' x
x{L,i}=sum/nL;
+ S8 Z: u; P3 q+ `# P end
* N1 U/ l/ Z- u, z2 k( M7 v+ z end5 c, ~& e8 H, u0 t" L8 e/ P3 i
L=n/2;
; n P/ Q, C2 q, \% ~' d f=zeros(n+step,L);
" `! K, e2 L$ F& ?8 [7 @. B for i=1:L1 k% o. ?" j% _" Z% y7 p3 Z
rep=floor((n+step)/i);
* c3 P$ R) m. _* u res=mod(n+step,i);" A, Q- Q) ?" ^
b=[x{i,1:i}];b=b';0 d5 t# [# Y7 ~5 T; X/ S
f(1:rep*i,i)=repmat(b,rep,1);
/ g5 i* {' J$ o! K if res~=01 n, Z* R* o; e' Z. M' d7 {
c=rep*i+1:n+step;
# V4 S R- r: Q: @. c f(rep*i+1:end,i)=b(1:length(c));4 e$ ?- T9 ~' B6 j" x2 X
end5 U$ e- e- W; y
end3 b- P, h$ z/ z. `& F/ R% t* N
V9 B, m; [9 s( v$ `1 M3 `9 R
二 最短路Dijkstra算法3 K& @0 o1 L8 V) D2 Q$ [( |
% dijkstra algorithm code program%
1 b0 w6 W y3 I6 s- J % the shortest path length algorithm
& ?# `# N* w, U( G) Q1 S: `) V h function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)
5 L5 H9 L% z) P" G/ r, Y7 | % Input parameters:
% E5 e& r' @( h9 \" V2 j; ]: A % Input_weight-------the input node weight!
& J' `+ W2 v) \; T* d % start--------the start node number;
2 z9 H; ~* Q, W! a) j % endpoint------the end node number;$ _! O% \+ C4 i8 U
% Output parameters:
$ Q4 z5 S/ K0 W& b) I2 S % path-----the shortest lenght path from the start node to end node;
. I3 N5 G |; @% K( T# B9 P d. }: x % short_distance------the distance of the shortest lenght path from the
; Y. u! D2 K1 o p7 a7 f) c0 z % start node to end node.
8 \$ q# W! K0 } [row,col]=size(Input_weight);% a p3 A# v/ o. A8 b$ S+ k7 E' k
9 ?- x$ Z7 G3 R8 |6 F %input detection, R$ V: P# l6 I0 Q6 O5 `- f2 d7 C- _
if row~=col0 D% d" Q: q+ T
error('input matrix is not a square matrix,input error ' );. o; \. C' e! V4 Y
end* Q+ A9 ?) y3 \& U9 D! `3 h
if endpoint>row
( x! J4 }# Q- Q% A' c0 [( e, m error('input parameter endpoint exceed the maximal point number'); D3 t( v: j7 v4 m0 N
end2 x! N+ t2 ^& g% R/ |8 Y
/ t5 t5 f& l. v( v, U8 R" @
%initialization$ p0 A) g6 q6 ^1 y0 @. t
s_path=[start];& j5 \0 b* p; D8 z
distance=inf*ones(1,row);distance(start)=0;
" |0 a! m1 d1 V$ _, c. m flag(start)=start;temp=start;, K& a' d6 N0 R$ K2 N0 w0 K
! {0 B1 v4 Y. @* D/ o- m
while length(s_path)<row& ~0 b& A# w+ {
pos=find(Input_weight(temp, : )~=inf);
" C. B. V6 z& _) i0 X2 n for i=1:length(pos)3 Z. ~1 U: \6 |+ H( B' o
if (length(find(s_path==pos(i)))==0)&
% N& Y, m% ~. x (distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))# k$ o' U5 d) `
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));2 X t8 f# j7 {1 W
flag(pos(i))=temp;
' h, I1 K$ n: }6 a$ Q end# V f5 M F/ l' ^8 _) Z7 B5 Q
end, t$ p+ P/ j* F$ {- s
k=inf;3 T* P" Q- H. t
for i=1:row
2 b0 z3 u% I3 I# C2 W& P& i if (length(find(s_path==i))==0)&(k>distance(i))7 H# S8 f1 o8 \2 m
k=distance(i);$ S* H0 r7 c! u$ G% H
temp_2=i;
/ f- t" Z1 p% }3 N end
. t) W2 f6 [% ] end
; C3 d9 [' K3 K s_path=[s_path,temp_2];
% r2 F- o& g" W temp=temp_2;
' b& o0 t% y$ \5 x6 n end
) r/ S( r6 x6 l+ ~/ m. ~8 T6 W # i! c7 Z4 ^; f ^7 ]& _" q* \, {
%output the result
5 ]. l$ }4 K6 X7 R path(1)=endpoint;- d4 _' b0 P( b/ ~3 J8 a, _
i=1;
7 K: R7 S5 y; [+ m: Y( Z" p% v while path(i)~=start; {+ @9 Z; H. B4 F9 H
path(i+1)=flag(path(i)); z! C/ i7 B, S/ L
i=i+1;" T) X. d" c& O; O
end; L/ z6 X6 S8 q; `/ N& k
path(i)=start; M( t% [5 r7 M+ c" S
path=path(end:-1:1);; [- b! @* Q3 \9 d9 z
short_distance=distance(endpoint);
$ \# b' S; T: J1 a 三 绘制差分方程的映射分叉图: y S" k2 K6 r4 O! A
+ U7 B" d6 D k3 j0 _$ Z2 S3 L function fork1(a);
5 Q/ u% z! `; ?" k# a. p
) v- Y2 q) I# t4 r, t7 ` % 绘制x_(n+1)=1-a*x^2_n映射的分叉图
; m9 j5 G2 N: J; O. [- x" P. b % Example: " C* K1 Y$ \0 p$ _3 e' R. i7 ^
% fork1([0,2]); " j$ U; n( x; _# n4 k1 P* w5 V8 {
N=300; % 取样点数
' n4 s# X5 v. W! T+ d( \ A=linspace(a(1),a(2),N);
0 c* l9 F: c$ j3 g G- b starx=0.9;
5 d! R: Q% d; W- T. Q Z=[];
0 Z: `1 W7 q5 o+ r h=waitbar(0,'please wait');m=1;7 U# S8 D9 C$ V6 X4 N
for ap=A;
7 Q2 ^1 O2 X$ A x=starx;
. x8 L: L" O, ^. m9 N for k=1:50;
1 C* }+ v& b* D, T x=1-ap*x^2;
! l" J7 t, r8 C8 F; U" w5 t, v1 Z8 V end
+ k T# g! {+ d& a" p: t7 M; U for k=1:201; + `& @, l: r$ |
x=1-ap*x^2; 2 @- F9 B( N; |; b
Z=[Z,ap-x*i]; , D. T/ V$ }6 V5 h) e: Y
end 2 ?7 N6 Z4 d- e, r1 _, Q, {* i
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
2 A: \6 q/ s$ T$ v3 Y m=m+1;
$ C J5 p. y; L2 U! V end
+ ~$ {+ {/ a2 ?, o delete(h);
) _' D4 d: \# T/ V) m0 a( n0 Y1 k plot(Z,'.','markersize',2)
# Y2 w, C" S4 L2 Q9 P& a% ?% {3 R xlim(a);
0 S, ~5 o, G9 E4 _. \& l- S
- G8 \# G' {5 R% e$ X5 c 四 最短路算法------floyd算法4 u* P7 y+ x9 S4 V
function ShortPath_floyd(w,start,terminal) 7 P4 i/ h _- W( y( X
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
, ]9 V# Z2 Q; c2 @ x& t %inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
6 [/ C0 C9 U) p' h3 ]( W %start-----the start node;
8 h7 n8 H$ q- L% z l+ t+ y %terminal--------the end node;
+ T" }% W# \1 Z$ Z g n=size(w,1);$ s* E" z5 x2 f6 i8 K0 N" A
[D,path]=floyd1(w);%调用floyd算法程序' O8 C# d# N# U- B( x& |6 C" g
! B5 W4 H% k9 _" F %找出任意两点之间的最短路径,并输出( e& x. y# |" K! q
for i=1:n
3 G( h8 Y+ f, X7 t7 f for j=1:n
9 C' q5 v& E0 l* q2 O! L0 n( x Min_path(i,j).distance=D(i,j);
2 N& `, \- e& R) }$ T( n %将i到j的最短路程赋值 Min_path(i,j).distance
7 N1 u/ s _7 d( X %将i到j所经路径赋给Min_path(i,j).path5 O6 H5 Z U5 o
Min_path(i,j).path(1)=i;
" I- U- j4 { a k=1;. {; ~. U* G: E, l% K
while Min_path(i,j).path(k)~=j8 C- y# T8 C: |/ [7 R3 _
k=k+1;- M- U3 c+ a7 m+ M5 V+ y
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);8 `. c* J4 F9 C) I" r* h7 \
end
1 `9 y0 F2 l. D: F* a- \8 ` end
1 P6 ~0 E D3 q$ B* e$ h end
% L, Y+ Q4 u" y1 t s=sprintf('任意两点之间的最短路径如下:');! {+ t. z4 p& w/ a% I' A
disp(s);
6 M. x+ W+ k8 p for i=1:n. x1 X0 \$ r2 c& ?0 K
for j=1:n
* p8 B, A! t! s s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...1 Q1 g, W5 d4 Q8 L/ h
,i,j,Min_path(i,j).distance);
- p" V9 l3 `1 p/ B# b disp(s);
c* g2 J- F: x1 t4 q& K disp(Min_path(i,j).path);
N# t/ y6 H+ @& c# E) k1 {9 `, y end3 C( s5 T: j7 C% d h" Y% {# Y
end2 |- c/ j/ h' z' u* h* J# c
2 i1 ^& m Q. B# h" L
%找出在指定从start点到terminal点的最短路径,并输出) P5 G/ G. i) n; M
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...; N2 U+ C% O# ^6 C* U
start,terminal,Min_path(start,terminal).distance);
6 C$ \" P) z; _0 v) i* k disp(str1); g& Y$ {. I" C5 e; T
disp(Min_path(start,terminal).path);$ G% d' U7 ]6 x5 K5 W/ J
. M1 g" p1 T9 E1 o x %Foldy's Algorithm 算法程序" U! o3 E* G8 _$ V l* }
function [D,path]=floyd1(a)" ^# T" L4 c6 Q2 I! W
n=size(a,1);
5 u1 r& P7 z" ^" X ^6 D D=a;path=zeros(n,n);%设置D和path的初值' P, L* A5 b, E' I) ^: S
for i=1:n
5 c' W3 N: q) G/ {" ], Y! a! H5 o for j=1:n8 t9 ]' y# J# t- l
if D(i,j)~=inf
7 w# _" Q, C* B9 k path(i,j)=j;%j是i的后点
" V* c3 N5 |9 m, H9 v6 p end
+ m8 P: ?. T6 m end
1 c( S T1 Y3 |8 N end
. T9 J$ k( C' I. P6 d0 U( v %做n次迭代,每次迭代都更新D(i,j)和path(i,j)
* n8 p2 ~1 h$ D- U; o$ W! T for k=1:n
$ n7 R5 M3 }- d: ?% U% q- A for i=1:n- l. G3 k; l$ U- v! L& H) ], m1 y% L! H
for j=1:n. l# u$ H7 P6 m3 Q+ e
if D(i,k)+D(k,j)<D(i,j)6 ~2 t& Y6 T% H- e" A% E8 q
D(i,j)=D(i,k)+D(k,j);%修改长度
& x) Q. e2 g6 _4 O/ w2 m path(i,j)=path(i,k);%修改路径
G3 }+ w! C2 L9 z end( _' G# P* ?+ S8 A) Q3 J
end) i% X5 D7 z; }2 O: T4 Y
end
$ a9 F. B5 E: {3 j! P" a end8 A; i: P7 o$ |) D7 u
; \4 j0 ^% m+ E+ K# s* ~6 `
五 模拟退火算法源程序4 T7 x |4 r! _5 h% Q
function [MinD,BestPath]=MainAneal(CityPosition,pn)8 X# N6 x! k* ~; g$ X: A- S* k
function [MinD,BestPath]=MainAneal2(CityPosition,pn)
( N3 ]* m8 m6 S+ x! A) o' J* c6 r4 f %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* t) i D5 N+ B4 d" ^
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...3 y& t9 L5 l5 ^+ }# }% _
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
9 U x8 u5 A6 D% ?8 E % 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
# e" d( W* y0 i) B3 F6 J % 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;.... p8 H2 B, ^, h1 o* n% z
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];7 r! \8 X8 p3 O9 c; I
- B$ ^9 l' y* s' Z! C %T0=clock3 j6 i N- m E0 {
global path p2 D;* X" m6 j, G0 A8 N8 w/ c
[m,n]=size(CityPosition);. ?& T1 @: Q$ f2 S- R {
%生成初始解空间,这样可以比逐步分配空间运行快一些
2 U# ]# ?2 _9 E TracePath=zeros(1e3,m);5 `( g3 D& c# s/ G. B/ T
Distance=inf*zeros(1,1e3);
H, p7 E+ Q( n5 @' [5 M i$ `+ L 5 i0 O: O/ D% z7 W2 A u
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
7 r' o3 \0 F& }" W7 a% D (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );$ m* a# {$ L3 }) i# d( z2 x
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵); m: J" r5 \& h% `9 h
for i=1:pn$ i- V& {1 [: T1 G
path(i,:)=randperm(m);%构造一个初始可行解
2 c9 ?% v. s& L) d* A. c }5 s& i6 O end
2 W f, z ^9 J. A0 z3 [ t=zeros(1,pn);2 M- C% j4 t) w3 x# Y- G9 d( j
p2=zeros(1,m);
( b$ Y, l0 F, L% l, ~+ |& c6 z: C ' V* e- j; p7 M4 |
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );7 c8 h' b9 m" n9 q: d
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=' ) ;
5 W" p3 c' n% G w% Q %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) L3 B7 c5 j7 L1 q. L1 V; u
%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8 V+ ?" b, n3 n* d) V
%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& j' j0 V$ l( g8 x$ |
%会收到到比较好的效果# @" ^, q, D/ l; p u
. i9 d4 Q v$ P9 B0 Y
T=1e5;
' Y+ V. X" H) p8 ]# J$ ?4 {4 L N=1;
8 k, J/ ?3 j6 D: h! h: i9 I) H8 c tau=1e-5;%input('请输入最低温度tau=' );7 i, `) D( W3 o& E3 e& Z
%nn=ceil(log10(tau/T)/log10(0.9));
2 @# H% L# g9 x" v4 f+ \4 h while T>=tau%&m_num<m_max # N% @$ I8 S& k- }) _' H9 m1 O4 w
iter_num=1;%某固定温度下迭代计数器
, F. F( Z* @1 |7 T m_num=1;%某固定温度下目标函数值连续未改进次数计算器) t8 b( s i3 D+ @. u9 @* }
%iter_max=100;: _* k* `. a/ Z) N% n2 K
%m_max=10;%ceil(10+0.5*nn-0.3*N);6 w& x0 L4 L* f7 k' N6 P+ f, W
while m_num<m_max&iter_num<iter_max
: ~7 l& K! d/ h; ^/ q7 a) | %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:5 _7 @, N: ~0 s0 j
%用任意启发式算法在path的领域N(path)中找出新的更优解% Z6 @( O* O8 |$ Q
for i=1:pn
& D: g" W3 |4 C3 D7 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))]);
" U- W. F/ M, c7 w1 ~ %计算一次行遍所有城市的总路程
: `: _7 y5 C: z% t. L3 Z0 g4 r, @ [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
3 W% W9 E+ ?& \, E, L Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);" K! T) i Q3 j6 K' w) E
end- I. x. v5 A/ Y; J) i. ?: I
%Len1* ]! n# [) Q# w) L
%Len28 d, ]$ |; R$ _5 j( W
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand* m0 ?, w* M4 A g6 t4 p; A. o
R=rand(1,pn);' y) P. [, p W- t, e' ? f6 j4 x
%Len2-Len1<t|exp((Len1-Len2)/(T))>R
. m/ Q6 j. B' z: l2 s- |5 O% R if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
. m( N' i+ z, r5 y9 w4 v5 W8 A path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );1 r" J- Q/ s2 M% [' U2 ?
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
3 A: k1 {( e+ q" Y+ y! j [TempMinD,TempIndex]=min(Len1);
/ X% n+ o* O. Q. X9 M6 { %TempMinD
2 B9 z Z/ R$ _$ r( F TracePath(N,: )=path(TempIndex,: );1 J& d4 B0 u1 g1 Z
Distance(N,: )=TempMinD;
6 ~! E- W* z- R N=N+1;. S9 M9 C* P. s4 A% Z% U
%T=T*0.9
/ C) \) T& Q; V1 X m_num=0;! P, D% h# M& R8 ?9 A
else
4 ?1 S0 d% h; p g2 M4 e m_num=m_num+1;
9 K& w, a# o/ o. @7 [7 C6 b* D end
0 f' k. N9 P4 u( P iter_num=iter_num+1;
^8 o5 S5 b* t/ U! a end
' H- g5 O5 e; p+ y, Q9 G( I T=T*0.9
3 G9 ?5 {. }: |7 {0 R! `$ y %m_num,iter_num,N7 |( e$ H: z/ c$ u1 F+ z
end ) ~# `7 m c' D" B
[MinD,Index]=min(Distance);
- h# F0 h* F" f5 W BestPath=TracePath(Index,: );
( q6 D9 M; ^ h8 t: r; N/ V disp(MinD)1 H7 g, k% K1 r, E
%T1=clock
7 w( o+ ~( S8 z& z. d; R
0 I7 @$ U8 s$ ]& W$ i0 ` L- P 1 ?7 i8 I& M/ f; X& |; q" ^5 Q
%更新路线子程序 6 W5 v8 m& e# a
function [p2]=ChangePath2(p1,CityNum)( r& g' m% f# ]- R* T
global p2;
; B a" E$ t' ^! O% }9 x0 a/ t" t8 P while(1)
( O: c% O! b0 N' `- U: E' o8 c R=unidrnd(CityNum,1,2);
8 L4 o4 k9 L( ]4 m: H if abs(R(1)-R(2))>13 A4 G& c# f4 A& r
break;
% ]9 L! l) x' m1 m, h' G end
4 x- D& o# E# [4 z+ M end6 Q7 D! ?4 C: g* E$ ]4 u
R=unidrnd(CityNum,1,2);) S; B% i: m' f; R8 @, T
I=R(1);J=R(2);
# z& b' i( f' \) |: U: J, B %len1=D(p(I),p(J))+D(p(I+1),p(J+1));1 O! [1 T( `/ {0 ?4 h0 Y5 D
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));# Y v' e2 ]) {9 m
if I<J
% E, u$ y$ d3 T/ [2 x p2(1:I)=p1(1:I);2 K9 N4 v$ b1 W N
p2(I+1:J)=p1(J:-1:I+1);% F2 {: d% }' m6 X/ v
p2(J+1:CityNum)=p1(J+1:CityNum);
1 F; t1 ?( |3 r7 ^+ H% I/ U else9 G) f. r6 c7 L9 O& }7 T( E i
p2(1:J)=p1(1:J);9 ~! R: b9 @/ }) A$ q5 p: v2 C
p2(J+1:I)=p1(I:-1:J+1);1 q, z- A$ [( S3 m/ o+ p
p2(I+1:CityNum)=p1(I+1:CityNum);
, t8 |- d0 C. a+ s j end
8 E4 g. l+ z7 {! `
& W& H% s! l/ s& i) q. P 六 遗传 算 法程序:8 p1 H5 _, J! t$ {7 u8 Q3 z' i7 _
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!: Z6 d8 [5 q. Y
3 w9 `. i2 N5 Z+ o
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
! O2 {6 v8 i, p; p" B7 _ % [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) |7 E$ v+ N4 a8 V4 r. \1 e$ h
% Finds a maximum of a function of several variables.
, {, }4 p9 t* g* c& P2 p V % fmaxga solves problems of the form:
: l/ f3 j9 T ], ] % max F(X) subject to: LB <= X <= UB 1 e9 x& C. \1 U0 @3 P- @6 k% B' @
% BestPop - 最优的群体即为最优的染色体群
: s; e. ]$ U1 x& ~ % Trace - 最佳染色体所对应的目标函数值0 J$ b" f" P0 V5 K* T. k
% FUN - 目标函数' N7 ~" m! _* c3 E r& A5 I
% LB - 自变量下限
7 i9 j$ q- l3 X8 Z0 u( q) P % UB - 自变量上限
p7 [1 J* h) t: _- z J% o % eranum - 种群的代数,取100--1000(默认200)
5 `8 w* s2 Q! B. A% v# ?. Q% b % popsize - 每一代种群的规模;此可取50--200(默认100)
& h ]7 k4 L) y7 ^ % pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8); d$ e$ Y b2 I" E0 F
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
7 q4 y9 y7 s0 t % pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
, r& `9 l2 F& ~ Y$ x. j % options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编+ `* U S) [6 h3 I
%码,option(2)设定求解精度(默认1e-4): x% d- f6 r. i( q. V* S
%
+ H6 K" n- v& X: Z# C% _& E- c, x( Z! A % ------------------------------------------------------------------------4 ^; Q! u5 ^0 s1 q9 D# n
6 a% t+ @$ R( J* i
T1=clock;
, ?& L1 C, q& c! O7 @" v if nargin<3, error('FMAXGA requires at least three input arguments'); end4 m# }& F5 U7 W Z$ V% Z( j' t2 k
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
0 H; h: W$ v# y& {5 t; k if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end2 @, b* z/ |( e0 D
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
8 t5 G z# u3 s; H if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end$ u3 ?/ m5 j; v. |3 U
if nargin==7, pInversion=0.15;options=[0 1e-4];end- R0 y5 f) j) \' |
if find((LB-UB)>0); P) X9 c& V) P+ F0 H" ~
error('数据输入错误,请重新输入(LB<UB):');
% E2 I1 n) W" |* p8 R/ f( q end) [, X/ y G! i; Z2 @$ \! [, A# P/ a
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
: J6 u( C7 W7 P" s: @8 ~ disp(s);& {1 p4 N* c+ u( X, U
5 d1 F: u/ `2 U" U
global m n NewPop children1 children2 VarNum
6 z9 }5 o- [+ Q6 x- Y ^8 [* j$ G. d
- p2 h. l: W) L/ y3 B! _ bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
( i7 [% E4 H" h" z5 Y( `& X' t precision=options(2);%由求解精度确定二进制编码长度& H5 w0 |. o0 `# ^: ~/ y# a8 U6 J+ T
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
4 K+ t& G/ n5 P- D5 i% \% B. e [Pop]=InitPopGray(popsize,bits);%初始化种群5 ` K# r! S6 i3 ]
[m,n]=size(Pop);, C/ d. q6 l$ y5 o/ o y* n
NewPop=zeros(m,n);8 p4 s/ ~- A# P& W
children1=zeros(1,n);
/ V/ x$ i7 v% a& L! U children2=zeros(1,n); {& G1 c, `1 \8 M: y
pm0=pMutation;" p z: A1 H+ ]' W6 F4 r- _
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
( r+ {! k5 U2 | e) K Trace=zeros(eranum,length(bits)+1);8 X& b/ y( L- w1 I* p$ O
i=1;
! S: ~. f8 c3 ^3 V) y: r while i<=eranum- V& d* K* z0 E9 R* Y
for j=1:m
! ~8 e2 [, r) G, B( Z value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
# t4 [4 g1 A! v# s# h$ }1 s end' X. {/ L/ H' k* y
[MaxValue,Index]=max(value);
( x6 {$ _5 O! a* E9 A BestPop(i,:)=Pop(Index,:);
9 Y2 w+ W1 L6 Z8 h4 [" F& c Trace(i,1)=MaxValue;9 c3 b* I0 T, k: U, P
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);! w3 b- V' h! \# j. A
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
6 |2 S8 j0 H6 k1 B7 A% N% \) b [CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));( D5 s, j+ w# T
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
7 ^% v+ r2 e+ f2 N %round(unidrnd(eranum-i)/eranum)/ K- P8 T, J& }" E! a
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
4 }7 k% N; N* p [InversionPop]=Inversion(MutationPop,pInversion);%倒位# B: p9 N5 w! M- C6 |
Pop=InversionPop;%更新
& H9 }! i, u& E! d' k6 A! U pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
: r& R. g+ J& W9 ?& t$ o7 W %随着种群向前进化,逐步增大变异率至1/2交叉率3 H! o5 D9 M" f a9 ]
p(i)=pMutation;5 F1 B7 I' x: m1 N% d* s( @. E
i=i+1;
) f3 a$ K0 [5 A* ~+ D2 n8 L end* s; Z e/ P" Q6 Y% |
t=1:eranum;
5 U% b. Y+ R' W( Z9 l; q plot(t,Trace(:,1)');
/ z$ V. d+ H' I) v- D 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)');
/ o0 l0 b8 n7 \% z- { [MaxFval,I]=max(Trace(:,1));
$ e0 T& O. W# w+ ]7 _ X=Trace(I,(2:length(bits)+1));
. a! F& R/ x0 E. N: e% I hold on; plot(I,MaxFval,'*');6 l3 K" j6 K% R7 j+ U
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
: z" i5 t' M4 Z& o7 E 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,:)));
8 f( ^2 j, P) q- X$ x disp(str1);, u* u# a: w5 G
%figure(2);plot(t,p);%绘制变异值增大过程
3 ?( v, y' _% j- ^7 }% e/ x T2=clock;/ |( z4 G) a1 N0 T
elapsed_time=T2-T1;8 m2 P; K" K0 I7 A% v
if elapsed_time(6)<02 _' j- l& W( y" f5 l& ^
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
, B$ m C0 e8 r$ c& @% \0 E end
$ Y0 ], S i/ U; z2 t4 b' Y- k if elapsed_time(5)<0
9 P% D# M V1 E: { elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;8 {7 k9 N5 C( ]3 G6 }
end %像这种程序当然不考虑运行上小时啦6 i6 a% U2 l Q, L
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));
( L% x* u7 S4 V# z6 v( C" | disp(str2);. F: S/ E. G9 ?; U5 O5 s
) u8 S4 E- \( {* y8 k) o
3 _4 m; ?2 i3 ^# ^$ h q* d! \. F6 x4 i
%初始化种群! Y6 K0 I( H. M
%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# e* U/ e) G3 T0 @, `
function [initpop]=InitPopGray(popsize,bits) [3 h9 A4 h, u$ r* X
len=sum(bits);
6 M: A# f9 t# O0 g/ o+ x initpop=zeros(popsize,len);%The whole zero encoding individual- e5 M/ c/ ]' q
for i=2:popsize-15 P3 e6 J; o% a u* {( i6 t7 ?
pop=round(rand(1,len));
+ D5 J! Q m" }" \' _ P- ` pop=mod(([0 pop]+[pop 0]),2);
3 F$ b; }) l0 `3 m. G8 G8 G# X8 i %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
( B' F) E7 E. E7 F- c& i2 O %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)( {# N* p$ R# ^& C, W
initpop(i,:)=pop(1:end-1);! S) Z' f9 [ g. H6 ^ w$ ]
end
* x4 i& \$ M* P! D1 e initpop(popsize,:)=ones(1,len);%The whole one encoding individual
9 ?, {. s) _' F6 C' e2 j. b %解码
$ H2 m% Q, e8 C, w% I3 Q" A7 x
. | r' G4 O- F( U function [fval] = b2f(bval,bounds,bits)
% b& W p# [' c( X( X2 V. w % fval - 表征各变量的十进制数
6 G; d1 g4 r0 z: N % bval - 表征各变量的二进制编码串
/ m5 Y1 z0 e, l" B6 U % bounds - 各变量的取值范围: a- }0 ` O9 @9 M7 {7 e8 b
% bits - 各变量的二进制编码长度
+ u7 \/ ~- U* w3 Q" }7 T& u% g# C) H scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables$ J0 I. B; I3 C5 f$ U/ h
numV=size(bounds,1);
l- ^& ?* S0 T/ u3 x cs=[0 cumsum(bits)]; ' V8 q! B n% g4 U; d1 a2 Z
for i=1:numV9 c: h4 Z3 ^; \
a=bval((cs(i)+1):cs(i+1));' A$ ~. ^% C! s! ]9 f
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
. H5 G' M6 o0 l: t end
; q2 \: o$ {4 \4 x$ g8 E %选择操作3 }9 j* h5 V* q1 i2 H4 `
%采用基于轮盘赌法的非线性排名选择
$ E1 l2 }# _" v5 @# I$ e' u6 d %各个体成员按适应值从大到小分配选择概率:
$ F) I$ _8 O8 s; S" ^7 i# j. F- a %P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1" ]/ i8 `/ h# g9 J& A3 |1 V- f
" r$ ~$ \3 V: M/ Q u function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)2 Q$ L: v* }8 @! q% H v4 O: K
global m n6 h# b, f4 r9 B$ ~3 T
selectpop=zeros(m,n);
6 c7 M0 d0 B2 F fit=zeros(m,1);% |8 J% Y2 Q. G) I
for i=1:m' u% k ]$ F) ]; d7 n! T6 w' l
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
! d& W9 Z0 t' k" C) s end: c( r3 q D. [ o/ {% ]
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)( W/ b0 g: f" @+ V
q=max(selectprob);%选择最优的概率; x3 B: s. h7 ]
x=zeros(m,2);& X. V- S' C% H7 w2 }9 |
x(:,1)=[m:-1:1]';
) K \+ R }# m# N& B, {+ ^3 O [y x(:,2)]=sort(selectprob);
8 |5 _1 m1 Q$ e7 _; H/ A r=q/(1-(1-q)^m);%标准分布基值' t- O. b; p4 V1 U/ |7 q, g) Y& ^4 g
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
4 q. m% E/ H) r+ U newfit=cumsum(newfit);%计算各选择概率之和
9 l$ f' \' q3 c0 G5 j rNums=sort(rand(m,1));
: D! ]+ W$ b. F/ h fitIn=1;newIn=1;
6 j w* L+ N# j0 R while newIn<=m' E8 r) F2 a) b$ [
if rNums(newIn)<newfit(fitIn)
/ N, j3 l, `& y# }& L Y selectpop(newIn,:)=pop(fitIn,:);
( \/ |' I$ l* n) @ s! ~" e newIn=newIn+1;8 U3 U% i9 A& g: }; Y: ^8 l
else- x- d" Z6 W+ b# g# G/ l
fitIn=fitIn+1;
; q |: Q* h; f+ u0 f0 ~ end
2 e: s3 C/ H% T1 ^; d9 f$ j9 N! t# B- Z end# Q5 M* ?8 }) X2 A! J
%交叉操作
" Y8 P1 f! v# Q6 G) F) C function [NewPop]=CrossOver(OldPop,pCross,opts)
1 x% Q) ^$ i) r %OldPop为父代种群,pcross为交叉概率2 k, [# F# G3 V& Z: q! N
global m n NewPop : B, x2 b3 e! n! @* S
r=rand(1,m);
9 Q7 b- M: b S, E y1=find(r<pCross);8 B8 `2 U7 d7 V' o& f
y2=find(r>=pCross);; [3 Y8 u* T- s& Y* v
len=length(y1);9 Y- C s7 q# ]" x6 U M
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
. L: f9 g+ L, A& R9 V y2(length(y2)+1)=y1(len);
" W$ J0 K5 |( ^$ i4 B9 y! y9 X' X y1(len)=[];2 y( v8 H. d6 S
end* i: V% d7 i7 {! S8 N/ g3 s! \
if length(y1)>=2
* B1 K' C. n0 E$ L/ q& Z9 ` for i=0:2:length(y1)-2
/ E. v. S- j8 B5 M0 ]3 q if opts==0
* T2 U* D" V, k/ u; H9 j [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
) g2 h; _' X' W& P* Z) ~: c else
! X4 G; W1 O4 l2 E9 r [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));3 ^& ~$ I9 ?2 p$ g
end8 M* ]4 x) W& }$ Z% P# [$ y
end ; z0 _) q7 ?" T2 ?
end+ ]* a/ g/ U* B X: U1 y
NewPop(y2,:)=OldPop(y2,:);. _2 z" ?( _1 x) o
5 M& g" y% F0 C6 e: z% m %采用均匀交叉 . N% |/ o' b3 M3 f
function [children1,children2]=EqualCrossOver(parent1,parent2)
9 q' @( F; \0 D/ Z4 @( I* ]5 h1 v; v+ _' x ( ]/ n$ x6 R5 d1 n4 V% ]
global n children1 children2 5 A; {" c3 @& K. V6 h e2 E
hidecode=round(rand(1,n));%随机生成掩码
7 E0 }- ^' e N, q" d: X crossposition=find(hidecode==1);7 n1 x3 J3 M3 Z0 R) ]
holdposition=find(hidecode==0);. v# _ v3 ]+ y1 |' V$ I4 o& b+ A
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
& C3 D M( M! l, g7 | children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
) D* t! P; k* E% A children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
* ^$ N7 l- p* j/ o2 h5 p8 q+ q children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因( D5 l; {& |$ Q, }* f
7 s% @. s' f0 R %采用多点交叉,交叉点数由变量数决定
. h6 w& k6 Y0 t9 m3 s+ |: [
6 n: O/ ~* ]( G5 K function [Children1,Children2]=MultiPointCross(Parent1,Parent2)
+ Q8 _$ _7 O& I0 {- c* l0 {
* E0 @! ?, t6 I$ T% `+ v. v global n Children1 Children2 VarNum
4 d- d' D- S% X' }% D9 S* q0 I Children1=Parent1;/ J+ k u' V i/ e0 `' }7 G1 J0 e
Children2=Parent2;+ ?/ f/ w: t- o6 M+ T
Points=sort(unidrnd(n,1,2*VarNum));
& R W! a, `" A, e0 R* v for i=1:VarNum$ a5 F. J# Y4 @ j: c& o0 ]2 ]6 F
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
7 M* Z: k, P+ R9 O+ ^ Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
5 ~3 u( | s+ c end3 X# d+ t8 [: j! R+ r
5 K# R- ^1 o0 O% s' w$ W %变异操作
/ L d2 a9 t' j function [NewPop]=Mutation(OldPop,pMutation,VarNum)
, R; L# A9 y5 ~' s( U 9 I8 q5 N6 D8 C/ F
global m n NewPop
' K7 s* A6 N$ O2 h: Q8 K* P r=rand(1,m);% x+ ^# u( r3 f& ~
position=find(r<=pMutation);1 C" A: p# X0 X6 U8 {
len=length(position);
' l7 c* l+ ?" T/ n; @! Y% o! X& c% t if len>=17 s% g; b* ~1 U% I/ t
for i=1:len
9 q4 X9 M" \. G J: e9 l* n k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
& N) }% J( U4 W for j=1:length(k)
3 f2 w4 X; m7 Y) Y2 L if OldPop(position(i),k(j))==1
4 d6 D# V% X' x" U! k6 B2 a' } OldPop(position(i),k(j))=0;0 z" n& p1 X9 c/ u6 S1 X" W* ^; h
else
0 f0 `8 {/ m; W7 l" h' m7 o OldPop(position(i),k(j))=1;
' L# r8 ]0 p- U end) m" Q( n' h( Y ^& \# V
end
8 q6 A: O' N- G( c4 w end
! u1 H4 z: E; T. N0 L& ^ end+ d3 X) D q C
NewPop=OldPop;& X8 d5 |) I. o* L
# A$ ?+ n u& p8 |
%倒位操作
1 w& l0 F7 G. F! o& {. a/ { & Y; Y$ D- }2 r6 I& S j! t
function [NewPop]=Inversion(OldPop,pInversion)
2 U6 q+ t8 O! t/ r # q4 c3 G2 L! V
global m n NewPop W8 M* V& i& Y: z) ^) v7 j8 [
NewPop=OldPop;2 ?3 ^; b( s2 t2 ^5 D
r=rand(1,m);0 j- ^7 m/ o8 @2 ]2 z
PopIn=find(r<=pInversion);
0 L1 D, ~. S- G1 S3 s0 d* F len=length(PopIn);
6 P' B6 S5 W% p$ S if len>=1, P! I/ B/ k1 ^; P. l
for i=1:len
( S7 @# r" e) j9 p/ k: d: W- |7 e d=sort(unidrnd(n,1,2));
# \; d7 _2 p- z0 R% D) d2 x if d(1)~=1&d(2)~=n; L7 S% [" d' Q5 W
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
5 V. E: P4 I# l5 u& e( B NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));$ d# T2 }5 t! ]0 W3 j) C' v, F# X
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
2 s2 X" R3 [. g" ^; { end
/ y! b: _0 U* U8 z5 f6 z3 P end2 Q/ t8 T) b. I4 V+ p5 l1 q
end7 i* U( _& O; T
+ _* R1 m/ u: T' F, l 七 径向基神经网络训练程序
1 t1 S' ~+ r7 T5 f# u
; b: j: H8 G; U' A t% i( O clear all;
5 [* ]( V! H; N" T* ]: D) U clc;! v r) X) y& G+ I$ p1 Q% @! Z
%newrb 建立一个径向基函数神经网络/ q% {, S" X2 {) T5 v' P, w
p=0:0.1:1; %输入矢量
; n" ~! L* V! R( h# q8 f( W' ? t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量. g% ]' h v4 i& f3 }+ m T; ^
goal=0.01; %误差/ P$ U. a9 N9 L/ h- w- }
sp=1; %扩展常数1 Q3 j8 X5 K. G# F1 J* a, ?
mn=100;%神经元的最多个数
# z$ J4 {& k; O4 G& t df=1; %训练过程的显示频率
1 Y& E$ ^0 E8 s% N [net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络& L6 Z& \8 _1 B$ ?- k9 u8 S
% [net,tr]=train(net,p); %调用traingdm算法训练网络
2 l7 B9 a, A5 g+ I6 N %对网络进行仿真,并绘制样本数据和网络输出图形
; t' u2 x, e4 i- ^ A=sim(net,p);: u$ C- y4 \3 Z! u- A% `
E=t-A;
+ `! a3 y( N y+ `, w sse=sse(E);
# ?% @* X: ^( D; d; X figure; # [7 r" e7 q" z
plot(p,t,'r-+',p,A,'b-*');
: \ o* M5 j# E' I+ o$ @ legend('输入数据曲线','训练输出曲线');
J5 R6 S0 E z; t$ c" l echo off
( N, b% s* Y( g& ?8 `9 _8 {( b 7 {& ^& |% ?7 Y
说明:newrb函数本来 在创建新的网络的时候就进行了训练!. e0 D L3 r0 a8 f5 z
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 p/ Y ?* w+ F% l 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!) M' Q% G& o) S( L; U9 c7 \& Q
4 F8 O# S& ?) T* J# A; c
1 V0 k" y# s7 N6 j8 r( L 训练结果显示:
+ k9 K5 T& S" n B NEWRB, neurons = 0, SSE = 5.0973
- t- B* F( S* l$ t6 i9 @! B NEWRB, neurons = 2, SSE = 4.87139
5 m* r1 q8 v- x- [ NEWRB, neurons = 3, SSE = 3.61176* u3 `: c6 e8 A0 I
NEWRB, neurons = 4, SSE = 3.48753 h. G- a$ P' S o" o& C) Y
NEWRB, neurons = 5, SSE = 0.5342172 \6 n1 \7 X7 S; j
NEWRB, neurons = 6, SSE = 0.51785
! {% v; {' V7 _7 x' w7 T) y* S" F NEWRB, neurons = 7, SSE = 0.434259
% o9 |' B! r) r$ b) m! d! B NEWRB, neurons = 8, SSE = 0.341518, s; O, a2 W c) o R' a) Z
NEWRB, neurons = 9, SSE = 0.341519
' L; m' {( T2 {) J) o! T NEWRB, neurons = 10, SSE = 0.002578324 u5 {+ R# n* u1 a
# e0 p; K3 s- Z, i+ Y6 M5 F5 l5 v 八 删除当前路径下所有的带后缀.asv的文件4 k5 ]$ S5 g( k/ {6 g2 m _: c" g, c
说明:该程序具有很好的移植性,用户可以根据自己地; }. ~# h' q+ q5 U
要求修改程序,删除不同后缀类型的文件!
; o, f# D* I5 V( S function delete_asv(bpath)
9 S& ^2 Z t! W |8 u0 ^ %If bpath is not specified,it lists all the asv files in the current/ T3 x/ f1 M- K, s& ]
%directory and will delete all the file with asv
( }+ c: f2 g6 o % Example:$ b) L3 n2 ~6 O
% delete_asv('*.asv') will delete the file with name *.asv;9 Q4 K! P! M2 B& O0 d' l; J" U; r
% delete_asv will delete all the file with .asv.
: t/ S, L& O# f% F # ~0 A6 C0 R' B) w4 a8 @9 B
if nargin < 1/ p, B8 k0 u: v% E/ v% B0 s
%list all the asv file in the current directory
; {3 i+ _; |4 {: P9 A5 d/ i3 M8 a5 d files=dir('*.asv'); O [- @9 m" q" C0 x) Y
else* _: W1 O: w& h7 I$ `
% find the exact file in the path of bpath, Y! h# u G7 |! L
[pathstr,name] = fileparts(bpath);
" s5 D" s, N! F V/ W5 Y if exist(bpath,'dir')
) { Q3 K0 U3 V0 d3 ~ name = [name '\*'];! y4 D( h& F2 L/ c- \
end
5 W. J8 x0 k5 E7 e+ B ext = '.asv';9 s; c. \8 Y$ R( n& `, p+ c9 A( h
files=dir(fullfile(pathstr,[name ext]));( y6 o' U) B3 K4 q/ X8 N. o+ K: U
end
( q4 K% D/ s/ u 8 A/ e3 E7 ?* B; `% v% H# {4 \) A
if ~isempty(files)
$ U3 m8 a6 m5 l* j) v [6 s for i=1:size(files,1)
# R8 j3 L4 _5 D. | title=files(i).name;
. I8 A7 z; g2 V7 ?+ ^% i8 o* m delete(title);% Y3 M4 P2 l( Y, G) V$ ~2 q' }( h
end
8 `$ H4 D: [; f8 F# u [1 p$ S* e end
8 [- e, ?" Z" N3 v! M8 o 2 D( E( n2 p$ N7 I
5 y6 c( j8 @4 | Y | 同样也可以在Matlab的窗口设置中取消保存.asv文件!' L' Z8 S/ |* Z4 ~# g6 n! H
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