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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: B+ c1 O& Q& @' {
1. predict_fun.m为主程序;4 o' ~8 W+ d1 O3 C3 R0 p) w: i& u
2. timeseries.m和 serie**pan.m为调用的子程序* D* \; t+ j4 U( r5 f5 o3 O
- L: {( b+ n' X I: v6 ` function ima_pre=predict_fun(b,step); M6 v- u8 _- f$ H
% main program invokes timeseries.m and serie**pan.m+ ^' j. s D3 i$ E5 F
% input parameters:, \, N r9 \! j) E7 M) S
% b-------the training data (vector);% h# f7 Y3 t- t! R3 p0 r) l+ S( }
% step----number of prediction data;* K/ \/ C5 ^$ C
% output parameters:) k2 _: B# W! A/ i% ^6 p
% ima_pre---the prediction data(vector);
% I) J. T% U7 v; } old_b=b;
) B, ]3 y5 W+ {9 m% V mean_b=sum(old_b)/length(old_b);$ p0 F* D& m7 |9 P/ }. s8 g6 c" J
std_b=std(old_b);
1 R; n4 _! H X old_b=(old_b-mean_b)/std_b;1 k# h) y* [+ V7 b
[f,x]=timeseries(old_b);
3 K! @5 v# s3 A0 W/ Q old_f2=serie**pan(old_b,step);
t6 ?0 o9 s* w5 z % f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;, z" d; O% l8 r% N
R=corrcoef(f);
6 B& J3 j7 W3 [ [eigvector eigroot]=eig(R);
# e, ~' P! n* `3 ` eigroot=diag(eigroot);
3 a, W, o; V# i4 A- V a=eigroot(end:-1:1);* h$ z Q9 { b. l5 o/ A
vector=eigvector(:,end:-1:1);! ]! d* ]6 e+ Y: L
Devote=a./sum(a);; n" s9 L2 x* s. [9 a4 S( f9 ~
Devotem=cumsum(Devote);3 W- S! z# _3 N( v; `3 K5 m
m=find(Devotem>=0.995);
( _. Q( t. j& I8 J$ ]+ [ m=m(1);
/ Y, H# f. S3 Y/ ~% Y/ @1 X V1=f*eigvector';" G- u: J4 j6 Y1 o
V=V1(:,1:m);
! @& L \! ^4 p0 m0 j M8 I % old_b=old_b;
0 ~, x* I" M" X! B+ Y, F, C old_fai=inv(V'*V)*V'*old_b;
' T3 m9 U/ f. U3 { eigvector=eigvector(1:m,1:m);
) l( H4 o( C' J) S$ W: s t7 C" T fai=eigvector*old_fai;* k% t N2 ? r+ M5 N* _4 ~
f2=old_f2(:,1:m);) c) Q" A% s h- O4 f2 N2 j% Y
predictvalue=f2*fai;' i8 l0 w/ ]2 a) K! O' F. w
ima_pre=std_b*predictvalue+mean_b;0 i- L; h, _ Q( g( j( b& N
0 U% \1 K+ \" T) w2 F 1.子函数: timeseries.m
1 l/ M/ w1 ^2 ?4 O# @0 ~ % timeseries program%
. f- I+ J) X) G3 k, w8 s1 H % this program is used to generate mean value matrix f;
/ j5 X4 Q a% G, b1 A function [f,x]=timeseries(data) , u) G; }6 t/ k$ N# |5 P
% data--------the input sequence (vector);
4 N$ ^2 ~( k" \! H1 U' z: {$ `1 T3 S( t % f------mean value matrix f;9 M: y* N3 B }/ d: d4 I( s
n=length(data);
! L) i$ F2 R6 w c for L=1:n/2
1 p# f1 g, D) @9 W( i8 T! T' C nL=floor(n/L);* q. j6 W, S% o) h; |. O/ v- Q
for i=1:L* I6 J' X. U# {$ Q, s* g8 Y
sum=0;) f) N/ p7 |- B) m/ ^% _1 V
for j=1:nL3 a0 P9 ?$ E0 x
sum=sum+data(i+(j-1)*L);, N z n5 R/ M3 s0 n, c
end
( T F0 o4 _) c" z% A x{L,i}=sum/nL; r$ }- I! s, ]
end
" x& |5 L( F C; B) w end
( d" L# }9 W! ~* F4 g L=n/2;
' B! C9 i5 s/ i3 n2 e f=zeros(n,L);' n) W' W( } m7 \4 p% f( O
for i=1:L
( t) O0 z I, n8 z rep=floor(n/i);
+ u! @/ z* P: y& w- V res=mod(n,i);
! | e' F; v" o b=[x{i,1:i}];b=b';3 O5 M2 L7 y8 F2 X2 N, j2 {
f(1:rep*i,i)=repmat(b,rep,1);
( X# Y& |* l9 P- V0 | if res~=0" \% r5 X2 f% ^( k7 c8 M- l$ n
c=rep*i+1:n;
# D( q+ i, k3 w+ _ f(rep*i+1:end,i)=b(1:length(c));, |: \2 I) \2 s& s
end' q5 r H' g- N8 [1 J
end e$ T! h8 N4 Z) E$ a, i" m
$ k/ l, j. I- M* d7 V
% serie**pan.m
( C; m& F0 I, S7 Q1 Z$ p" v3 G % the program is used to generate the prediction matrix f; 4 a* R) v7 l/ L- m1 |# r F1 u
function f=serie**pan(data,step);9 G" N1 _6 X) ?5 d+ E) G# U: o
%data---- the input sequence (vector)
' u* C( D9 g0 M+ M % setp---- the prediction number;
/ I/ j, O" _6 V n=length(data);
, A' x% b1 X% Z$ J for L=1:n/26 G. C- y0 j7 l
nL=floor(n/L);2 [& I9 E4 G; s
for i=1:L
8 ~5 _' h' Y* J+ E6 \! f% P \' T sum=0;- I; e' O* A* L* u8 m+ }" x) q
for j=1:nL0 H9 I2 M- u. u! ?: I% C
sum=sum+data(i+(j-1)*L);
; D9 I& y* E( r5 X, a: m end6 F; I0 v( w8 S3 Y1 Q; s3 Z
x{L,i}=sum/nL;5 y" m, l) x4 [9 P
end8 b0 V& y1 Y8 d6 J5 h
end
0 Q" f+ M: c4 _4 {; Q% r0 r; a L=n/2;) C7 a6 f0 a- r8 g* @
f=zeros(n+step,L);* x' ]% q9 n2 @
for i=1:L
9 t5 D+ D, Q; J% T2 m rep=floor((n+step)/i);5 j d! D3 Z) _7 v3 P* C; U, m0 U
res=mod(n+step,i);6 x8 C% R' P. Y( T+ t' T
b=[x{i,1:i}];b=b';8 L+ V3 l7 l# q5 p( C
f(1:rep*i,i)=repmat(b,rep,1);: K' O. H- `! O1 Q% b; k4 n
if res~=0
/ {0 ?6 x/ j1 h! X c=rep*i+1:n+step;
/ M9 t- L0 ~- m9 I- r4 [ f(rep*i+1:end,i)=b(1:length(c));
* Q1 x' W( S. r, H1 F! W end
) V9 Y: D. X) ~# v9 N2 ]; T; f end
2 E' m' \- A3 e$ \ 6 f! F( k; c# w. d
二 最短路Dijkstra算法) u) B) @! c5 J# A
% dijkstra algorithm code program%( M( o& q& l" W; e( c
% the shortest path length algorithm, K; C% |& q6 Q+ o5 _
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)
z; }. c4 L* }3 f: y5 g/ L % Input parameters:/ J5 i+ q; \. P; x2 B+ u$ L
% Input_weight-------the input node weight!
: H$ V b7 v6 T3 R( k8 P* z$ @ % start--------the start node number;
0 l) {$ g2 n* @+ M% i % endpoint------the end node number;: {: j7 C2 ^8 t p
% Output parameters:0 E8 |( U% d. h7 I' p) j, U0 k) C! s
% path-----the shortest lenght path from the start node to end node;/ h( @, I1 G- M1 p' D Y- G+ U; P+ w
% short_distance------the distance of the shortest lenght path from the
4 @1 [9 [ O1 s& C5 P$ g& a % start node to end node.
5 I$ ?3 z6 f9 @! m7 D [row,col]=size(Input_weight);. i, z j7 i4 Z& i- T/ m" P# N/ o6 X3 K- e
( ~7 M& J5 y% T
%input detection( w1 @! X8 O. y7 k. Z% N
if row~=col V9 z5 g8 E6 n
error('input matrix is not a square matrix,input error ' );0 g1 `& ~3 A/ l6 T+ S# _; C; m
end
% {- O* O5 I* Y/ t5 [( i. X0 B) l if endpoint>row8 p" n Y @) \4 i {/ {
error('input parameter endpoint exceed the maximal point number');! h; ?# ]/ E- w
end4 f& l, x8 i: W7 @0 `2 i( Z
6 y0 A* r& r3 O d
%initialization6 \6 E/ {6 K7 h) U3 K, i! b w
s_path=[start];5 f0 @ ^5 p' o0 N
distance=inf*ones(1,row);distance(start)=0;, j7 w6 Q) t% W7 D& Q8 `5 |
flag(start)=start;temp=start;
4 D1 U% d- T0 r8 X% v - `! k" l2 J1 E! Y
while length(s_path)<row7 p& s% O! u3 O4 \6 @- H( k
pos=find(Input_weight(temp, : )~=inf);, W i, n6 H. ]6 P+ E
for i=1:length(pos)! a8 B, W& W5 H5 J. ^ g
if (length(find(s_path==pos(i)))==0)&
) J: x% |8 B+ A& P4 j) g (distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
3 p* ` U( V. `0 q" _* K distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
; f% q: a9 `* B: A8 I flag(pos(i))=temp;6 k) }. Q: o: j4 s0 T
end
4 t0 y$ f# ]$ i; ^. a) V9 s! b end
( S0 R% D3 h* ~+ Q k=inf;' r% s5 j+ R/ Z7 p9 }
for i=1:row
- z0 f* _3 U$ L+ l P+ h if (length(find(s_path==i))==0)&(k>distance(i))
/ v$ g* B0 ^8 D% u! _' L3 X k=distance(i);1 z' K+ e6 C3 T! Q: l+ X, w
temp_2=i;
# X: J i6 `9 M2 \$ ~/ N, ~9 h+ F1 M end- E& [+ q1 l: u: c3 I
end: L7 ~# v4 c) p" k
s_path=[s_path,temp_2];+ {: R: e# a4 S7 Y) w( t# D
temp=temp_2;
& U& ~2 A/ w. w; j4 ~ end
9 N- m9 c1 J4 m/ O6 V% S; u' l
$ ]* R V1 G' q6 B% @7 v %output the result
. i/ F: v+ P z path(1)=endpoint;7 S: s% S1 B3 H1 K- F) ]" X% E, N
i=1;) G; w$ t8 X# p' G$ B, j4 l6 u
while path(i)~=start
3 d7 L( q; c1 ?7 \4 m path(i+1)=flag(path(i));0 Q( g; n& |+ T# c2 U
i=i+1;& v; }& E; @. y, P
end
* f r4 d4 y6 D" r* t7 Y: o/ N path(i)=start;8 I; ?; @' }% X! i1 d2 j1 z
path=path(end:-1:1);
8 o, ` ~. H- L; V short_distance=distance(endpoint);0 T5 |. s1 e2 X
三 绘制差分方程的映射分叉图
' q" ~9 K' ?( F. Z6 e* Y
( a& K6 x7 u2 u+ ^1 a1 \$ R function fork1(a); " h3 y3 n% b: q E1 w
/ J9 N( p2 q' T* i* m % 绘制x_(n+1)=1-a*x^2_n映射的分叉图
* Q3 H& ]2 o& o. p % Example:
) D$ V# t/ z0 @# m6 n % fork1([0,2]); . @! k, R% w5 J0 n- E. O" @
N=300; % 取样点数
! M" q: ~; w9 [3 T5 ~ A=linspace(a(1),a(2),N);
1 x# R k% [' u$ Q- ?6 K starx=0.9;
) b W) q6 B' P: _$ H: S2 n Z=[];
! |8 D4 y: @) E1 h* W h=waitbar(0,'please wait');m=1;. J2 J: G$ P/ T' P5 D
for ap=A; 2 b# D& i3 R" m! E
x=starx;
. w; \5 s- i" p" A) X for k=1:50;
, Q$ p, ^/ F6 C7 A# Z4 T. s% z. E x=1-ap*x^2;
8 q' e' @) E8 _" V( N. z2 r end
( }* S4 M& N. D for k=1:201; . t- Z2 u+ X$ M. U3 x! X
x=1-ap*x^2; : f. h- F' i _6 b5 x. Y
Z=[Z,ap-x*i];
) A/ D. k( ~3 h9 T2 x9 f end - c' y; v u! o0 ]1 m
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
& D. Z6 t5 L5 S0 q0 c2 D m=m+1;9 }; Z; U1 L, n+ H' d1 ]
end
- ]0 s( N7 R7 @8 ~3 N+ B delete(h);: h# l! p2 {. w
plot(Z,'.','markersize',2)
7 Y& H3 n; z+ D- H' R5 G xlim(a);8 z2 E) m! o6 g* G; r
& _3 ]" {- P8 U
四 最短路算法------floyd算法$ l4 S) @* \1 A- q1 L# ?6 f
function ShortPath_floyd(w,start,terminal) ) v$ p* G8 E5 I N! P& w% p/ E
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
$ R0 T8 P' b3 ], G %inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];( u8 g* G- v6 e, D. f% W P
%start-----the start node;6 X. z/ ~ }) h& }( ]6 k
%terminal--------the end node; + U9 Y. m# A- t6 f" @3 ]4 `
n=size(w,1);
4 v6 p$ Q% N$ k' T [D,path]=floyd1(w);%调用floyd算法程序- S9 J" [8 Z7 v2 b) Z+ K
6 _- m) h/ x3 p" B+ _1 L
%找出任意两点之间的最短路径,并输出
5 l9 c. b% D( P4 B for i=1:n( Y5 x5 X/ S6 z' Z$ Y, R
for j=1:n; W6 C7 D1 h- Y( R+ T; I5 Y# ~
Min_path(i,j).distance=D(i,j);" R+ w% ^' r7 E
%将i到j的最短路程赋值 Min_path(i,j).distance
; Q0 `, e8 f. e9 @+ c7 q3 [$ G %将i到j所经路径赋给Min_path(i,j).path
) ` R' u! w9 J Min_path(i,j).path(1)=i;
4 ~" F& i$ N1 s; A- ^ k=1;$ |" ]7 Y* a+ e0 p" D
while Min_path(i,j).path(k)~=j
( z. J1 C) F! _! t k=k+1;
\5 m5 P% L! S, T( y, o( h Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
# T, A( L9 q0 L. C9 J! o end
4 r$ l2 r |) d end1 h( u' e5 L! p. M' ]7 p1 R
end% I* E- ^- |: B/ A4 `1 A7 K, z
s=sprintf('任意两点之间的最短路径如下:');8 I) J0 w, P3 [! B. |9 h7 M( s' r
disp(s);
6 t. p G- L- e1 A$ q5 V1 U for i=1:n2 n! h' f' I `% F% r/ C
for j=1:n; R6 A! T+ y, n& Y9 c
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'..., O( d/ f3 E, ?. h) o
,i,j,Min_path(i,j).distance);
# l' q* G$ Z" f1 ~3 B disp(s);8 l4 r: j! u7 D- G- |( E6 l
disp(Min_path(i,j).path);
. Q/ @. g' ~$ a: ], y$ O# E end9 `% u2 ]0 c- ]1 U& B* ]& [
end( q3 b* E J d& z7 ?2 ` E; K% o
2 i! u: C( a, s
%找出在指定从start点到terminal点的最短路径,并输出
! h, g& {: i3 A7 v2 O @ str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
, W7 w4 I. D: u# ^0 }# }7 v" A start,terminal,Min_path(start,terminal).distance);9 R! R# A( @* o- B$ ~
disp(str1);2 G( |! w5 z- e$ Z9 X) f
disp(Min_path(start,terminal).path);
: `" G( V( }. v4 j7 ~% K
# S% v8 r: t" U8 T% q, u5 [2 U %Foldy's Algorithm 算法程序
; x4 x: l$ f h8 i function [D,path]=floyd1(a)4 o n' c, q' v5 |$ L7 E
n=size(a,1);
/ @2 i) v, X3 D" v+ w8 q D=a;path=zeros(n,n);%设置D和path的初值* _1 j& Z, S x& W
for i=1:n
* D5 @' D% {, f9 g6 m" Q$ \$ r for j=1:n
' b6 X3 W. I/ M% n* a" r7 h if D(i,j)~=inf
2 }2 ]5 l( f9 p6 g4 s! h path(i,j)=j;%j是i的后点
8 b/ N9 o/ j2 H! u end, P+ I! U- N* n# g* R, W: T% N
end' b `. C& P( E: f5 j7 K7 e
end0 f2 ?6 b3 v# r8 |' C/ S2 t
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
% @ ]: j" R) h0 e" V3 J' @ for k=1:n$ B- t8 e; O; q
for i=1:n
7 M4 T3 c! M, y for j=1:n
% a' v0 Y: e N0 j! j if D(i,k)+D(k,j)<D(i,j)$ _7 x1 |2 u4 Z1 s% S; z
D(i,j)=D(i,k)+D(k,j);%修改长度
# h5 D! T" @; c' h2 W/ ]. p3 C path(i,j)=path(i,k);%修改路径
- y8 Y/ x. L. x end$ ^ _ E: E9 k! l, _& Z2 k
end
z- ^' Y; s, O5 }/ U5 E) { end) D! ^4 U3 n; L. U* Y' L. `) f# j
end
' g& Z( Q+ [9 `$ Z; E: R4 Z ; F! s( ~0 \' O! o, s) \; w6 ?! z
五 模拟退火算法源程序: ?( j3 c! K m
function [MinD,BestPath]=MainAneal(CityPosition,pn)% e& V6 _' p9 ]: \/ C, {
function [MinD,BestPath]=MainAneal2(CityPosition,pn), b& V W: L6 k) x( V# o5 O
%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" G3 I8 J6 F) d0 r) w
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
# |0 [0 p% a* b, w3 k % 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;..., ]& k5 j: `7 A; j: M
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...6 a _- Z' X* v% R3 x2 t
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
# \; r- i, B1 Y, f % 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
4 _% {* c. l* L, Z2 v# t& I
1 U/ P4 V T3 ~5 x. | %T0=clock
$ f( d3 ?4 @* Q8 E global path p2 D;7 m2 W! B+ p8 [7 m
[m,n]=size(CityPosition);
- a5 P$ Y) y/ u1 y3 c( [7 F" w: G$ e %生成初始解空间,这样可以比逐步分配空间运行快一些
/ C: |$ L3 L+ t" Z% X3 k- z8 i TracePath=zeros(1e3,m);
3 d0 {1 N; L( [3 ?/ ^/ D Distance=inf*zeros(1,1e3);
3 M; d4 O) {7 N( s+ J, \& ~
* _& n9 r5 h, h- Y a$ s$ @# \ D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
/ [% y& e' \5 B! E( }3 j' t+ Z: J2 ^ (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );& v5 O5 w& ~ h7 y5 q/ d$ x
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)* T. D/ t. o/ P' l( G# w
for i=1:pn9 j1 l( i4 ~0 w' f6 ~
path(i,:)=randperm(m);%构造一个初始可行解' n! t( E* v, @ N- F! Q; B
end q4 g! h. g# w0 c
t=zeros(1,pn);" u: G0 {2 c" h! |+ U
p2=zeros(1,m);
) o$ O- w7 j- Y
9 ]2 ]. ?' I7 e0 ] iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
$ C- _8 k# e! C; c9 R( f2 p: i 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- }) z$ H$ P8 [ %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
" r+ i# A* d P' y: I %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. N& K* q1 m; z: Y; }$ D6 k
%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
) P6 h- p7 ?& V$ x, w } %会收到到比较好的效果6 m0 V& h6 F9 I8 b
0 N4 m6 b7 w t* j% m+ Z' p5 y T=1e5;" P" q2 o# M9 H1 Y) j. s% l7 x6 B/ _8 q
N=1;
( [) g7 R5 J$ {, R tau=1e-5;%input('请输入最低温度tau=' );9 `& [. o5 p( e+ V1 x
%nn=ceil(log10(tau/T)/log10(0.9));
0 h2 S2 o6 ~+ p+ N7 Q: k9 u while T>=tau%&m_num<m_max
( r$ t) j/ H# V' Y: p2 k iter_num=1;%某固定温度下迭代计数器
! C2 D+ y- A" e m_num=1;%某固定温度下目标函数值连续未改进次数计算器
/ Z4 i% h- F | %iter_max=100;4 K% y$ s: o# E4 z: z. R5 a
%m_max=10;%ceil(10+0.5*nn-0.3*N);
, t# O1 X2 ]6 z, f4 [; O/ } while m_num<m_max&iter_num<iter_max
$ `3 D1 e$ j/ W1 s; J1 _ a& k; _ %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
4 m8 J9 H3 e7 b6 q' G% ~ %用任意启发式算法在path的领域N(path)中找出新的更优解; \0 _ I1 ^; s1 v: v8 G6 q9 k- k
for i=1:pn, }4 K. X3 z, ^4 f' P4 L3 z: {, V
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
& X8 z s4 L' u9 F+ X- I+ q% ~$ x8 o %计算一次行遍所有城市的总路程 - b) M. Z5 v' y8 }0 u: w# c2 S8 {
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
! R9 X" 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))]);, y8 a0 f( C. y9 Y" L# P
end
( M. W& d6 n. i/ q- k# _ %Len12 e9 l% W7 Z1 A7 e
%Len2, Y! q/ @0 z( {8 e
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand9 P9 s; Z+ x4 u# `. u C0 Q! F
R=rand(1,pn);
: h4 R: r# | \; t2 D# N m %Len2-Len1<t|exp((Len1-Len2)/(T))>R
1 t! I6 s2 R$ O% J, H9 g& _ if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)/ D* o' F6 J4 r4 E
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
/ d& n2 Y0 c- e+ v7 j+ V Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));/ t; p! E4 x2 Q, W0 H) y
[TempMinD,TempIndex]=min(Len1);# ^, }, z* _2 d1 e
%TempMinD+ v; I2 G% e. U& d
TracePath(N,: )=path(TempIndex,: );
1 ?) I8 c- y k' Q4 n& { Distance(N,: )=TempMinD;
5 ^! M. B, B0 [8 Y# X# u4 R N=N+1;
0 k6 L z/ x! B, s %T=T*0.9, y! n7 c8 ~- s% X: k7 a- O
m_num=0;& Z2 J. J+ X% Q8 s! T% y
else
' D. e( n$ A. |. L$ ] m_num=m_num+1;; [2 k( N- I3 ]
end! N& f9 Y" M8 a2 \( \
iter_num=iter_num+1;
- ~" X% I) u& M end( [2 `! T! _" |
T=T*0.9
/ O; @9 c$ U d* L %m_num,iter_num,N7 P" }5 B8 n2 u* A# x( e: _
end
' C5 F; g9 ~1 o [MinD,Index]=min(Distance);9 d% a0 a, P/ d
BestPath=TracePath(Index,: );& d' W1 N: C5 A- y% q& V; {. q
disp(MinD)
& }3 a! U' Z/ G$ s %T1=clock
+ k7 @2 x' t9 z% o) c
/ s) t! ?6 q0 N% z4 @- C7 e$ ]
& d1 }, y7 N& `4 \& `2 E %更新路线子程序 2 j* [) t0 G5 F
function [p2]=ChangePath2(p1,CityNum)4 H; D- d( M' t l9 c: c2 E/ w
global p2;( O3 o1 d# ^0 a& }
while(1)- [) m+ O& F& K) C1 H7 ^
R=unidrnd(CityNum,1,2);/ ~: u: J6 r6 A7 v2 Y5 v8 A
if abs(R(1)-R(2))>1
% t' v/ l( H' R/ b( r( S break;0 g1 U1 a7 c; f. q6 t
end% q7 G3 I6 l) H# R1 z# M! p8 L& L
end% r6 R* G2 O! m8 Q# M
R=unidrnd(CityNum,1,2);, [& X2 z# i0 f% {+ E8 E) a
I=R(1);J=R(2);
2 z9 P3 e; V3 o; d. }7 B) \ %len1=D(p(I),p(J))+D(p(I+1),p(J+1)); ~: a. o% x, B- x" {$ o" A
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
' y9 L( o7 X% M% i! G9 e% r- G if I<J" E+ D. O6 ]0 R( a# R, F
p2(1:I)=p1(1:I);
' \+ ~% G; j* F& `: p9 y p2(I+1:J)=p1(J:-1:I+1);
+ d5 Q7 w+ ]+ f _; z: y p2(J+1:CityNum)=p1(J+1:CityNum);
/ `8 |( q }5 i else0 R6 N" a: T: H# H- q+ Y B
p2(1:J)=p1(1:J);5 O2 ^* I& }' |/ H( D) l* {( V
p2(J+1:I)=p1(I:-1:J+1);# w, ^ g. U7 M$ ~/ g
p2(I+1:CityNum)=p1(I+1:CityNum);9 f- t+ q3 T' _' D1 E) M! l! o
end
7 l# G2 }0 P: ]1 e/ V; Q7 h9 H 9 X2 O' Y+ h% `6 t
六 遗传 算 法程序:
1 D1 J& l: b& i0 K+ S( Y1 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!4 P) w# t6 ^# g. p$ I
' R9 x o( C, _2 x/ p/ F
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
2 r% ] J; S; L; k! A9 Y i2 e z' R8 I % [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
3 d7 m: d2 L- Q9 Y- ~7 I8 A" G % Finds a maximum of a function of several variables.; W" C. i5 h% H$ ~3 O. c
% fmaxga solves problems of the form: 4 U) c0 P4 b; Y0 C( s7 N& B0 Y8 b9 F
% max F(X) subject to: LB <= X <= UB
* f" f" ?" E/ ] % BestPop - 最优的群体即为最优的染色体群
3 [( T( c! W) d % Trace - 最佳染色体所对应的目标函数值
+ f6 X0 L3 g8 m/ w5 {# _ % FUN - 目标函数4 j1 R2 g3 i6 _* a$ c m9 w. W: X
% LB - 自变量下限
, k0 z* Y; E& s5 n2 s % UB - 自变量上限8 m4 c" S, m4 S" @2 ?6 l
% eranum - 种群的代数,取100--1000(默认200)' | X5 u% `# e# R
% popsize - 每一代种群的规模;此可取50--200(默认100). u( N p) g# _
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
7 o) n/ Y. ] X$ R I % pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1): @1 h; s9 H6 R$ c
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
4 S( N2 v; ]7 u) P1 g% j j % options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
) t6 V( I- Y$ V7 C/ o %码,option(2)设定求解精度(默认1e-4)
* X) X# e$ a" l %
~0 Y3 y! }# k* k+ A % ------------------------------------------------------------------------ x) B' \* n$ a! ?2 O5 [8 _. c
, }5 g% u# l, B/ Z% X: g- M3 {
T1=clock;# }& r4 O$ y8 _2 d, v# j' E r% k
if nargin<3, error('FMAXGA requires at least three input arguments'); end
9 U; g. U1 v3 `2 w6 O+ z# v0 i if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
. l/ w4 }( H, n5 d- ? if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
& s7 A3 d4 a: F% S$ y2 m if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end7 y* x5 v. ]+ w9 j" N
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end2 {. E6 S* |6 m4 g( @- r9 E' k v
if nargin==7, pInversion=0.15;options=[0 1e-4];end% D9 L( S1 Q* G0 z! e
if find((LB-UB)>0)
, O6 [8 Z2 n, X; G0 n- u error('数据输入错误,请重新输入(LB<UB):');% F) @& _5 L. u$ E1 r1 l9 N! x
end
7 h; S! ]" x$ S7 E |3 Z2 u s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
$ O& t9 l6 I6 b9 b/ ~5 l disp(s);
4 X% P% \. |4 ]4 L( I" V+ g
$ u) B1 u( l8 b( ~& r9 L global m n NewPop children1 children2 VarNum
0 Y% z1 g( o! r2 ^( P0 N& w # _$ U6 o! {$ \9 e) b
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);: W7 F4 P, t% w: O: s; C8 m
precision=options(2);%由求解精度确定二进制编码长度
+ B ]) d8 M4 c4 y2 ?8 w bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
, X+ d! g. n4 p2 f; E [Pop]=InitPopGray(popsize,bits);%初始化种群& t% n* F# d" O& R' {# O
[m,n]=size(Pop);
" C1 r. v S& h N" Y6 s NewPop=zeros(m,n);/ C: N' C( F, R' y
children1=zeros(1,n);5 A( x9 R, [; r
children2=zeros(1,n);9 {) ] r0 x! W! A. k
pm0=pMutation;/ C7 |6 f1 Y, q! T0 M
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
/ g4 f' E v6 Z( c$ Z/ M. i0 g1 \+ ` Trace=zeros(eranum,length(bits)+1);
8 G' c* ` G! \, ?7 S3 z+ V: _ i=1;; C9 h0 F, c' x% E
while i<=eranum- `+ X$ b% J! y* u s
for j=1:m' B, d1 f. s8 b. ]
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
/ d Z5 ^ R/ q end
9 i* q- I R( _ h) S/ k0 W8 b' F- u [MaxValue,Index]=max(value);
7 v2 n, d. M$ Z+ K- _( z BestPop(i,:)=Pop(Index,:);* X4 j) h% w, u& a3 t3 a Z) |8 l
Trace(i,1)=MaxValue;
' a- B5 Q3 i& d5 v Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);, O3 K9 Q, r( w# [% d4 \
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择% L# Y9 S9 `) X; C# N; G( {
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));' J4 d+ ?! O4 {& h
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率# Y( j4 s2 e' f2 U7 e
%round(unidrnd(eranum-i)/eranum)& y, H4 G( E/ H% Q( Z
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异7 N8 t3 ~) x1 ~2 R
[InversionPop]=Inversion(MutationPop,pInversion);%倒位$ J# Z# m4 U L6 R) R( J* u8 v
Pop=InversionPop;%更新
/ Y, n: J- S. @0 E. |8 |; E pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
$ u& p) u! g# [% L %随着种群向前进化,逐步增大变异率至1/2交叉率
7 v; q+ C) G. ~$ u' P: d p(i)=pMutation;# b: ]) q; h) u( m8 b
i=i+1;
! b, Z) W1 {5 D" R" [ end
$ Y& z1 B# F4 E3 q c% w* q, l t=1:eranum;
2 a: H' S" r: W. b, b, b" T% h plot(t,Trace(:,1)');. v, B& h: @; B1 l3 l8 b: n
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)');
1 u' Y4 u) U: s [MaxFval,I]=max(Trace(:,1));
% P( j/ i1 S. P: n9 I! e$ M0 ? X=Trace(I,(2:length(bits)+1));
l& }- O6 h( R$ o hold on; plot(I,MaxFval,'*');6 y& O7 v$ f2 ^9 G: J8 k
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);; p9 V/ b+ Q. u) W! I0 }
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,:)));9 W, y5 [' \! R5 F9 \! s/ O1 @
disp(str1);/ E" L$ r; Q: I% X$ _
%figure(2);plot(t,p);%绘制变异值增大过程 C7 P3 N7 W) `! d
T2=clock;* s6 w' ~- l3 G3 Y
elapsed_time=T2-T1;
: W8 K1 @ A9 N4 @ if elapsed_time(6)<0
7 r8 T; Q% f% H. o1 C elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;6 \" o. y& b! H7 ~1 P8 P' x9 H
end
2 E" S- B6 ]; ^) b7 [ if elapsed_time(5)<0' b9 A6 B9 R' p9 o9 w# X
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
T2 v2 ]* o6 k* [. X& @ end %像这种程序当然不考虑运行上小时啦; @8 X' _# n8 E- H
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));& I0 y% x2 x [9 c% w' ~
disp(str2);
+ y# H+ J( _5 V
/ t8 ]9 n+ O) p- ~/ Y3 J 2 D# h' W# q7 k; [0 u
%初始化种群
5 N. _6 @; y; _, ?* 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/ R v I6 n, J( I1 S
function [initpop]=InitPopGray(popsize,bits)
+ [3 s) @8 ` p4 k+ k len=sum(bits);# L% F, k3 B4 m: V3 }
initpop=zeros(popsize,len);%The whole zero encoding individual
' F: _3 v l$ T/ l for i=2:popsize-1
+ i! p( G8 Z6 {( _4 \ pop=round(rand(1,len));
$ D/ \# a" o3 S2 ?+ w) H pop=mod(([0 pop]+[pop 0]),2);2 q; [6 |9 e# a+ ^
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2): W1 H& P' E& S' h# z
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
) G! T9 D+ R6 V' I initpop(i,:)=pop(1:end-1);0 B8 Y: S$ w" g( a+ v! L
end, P) x6 t& c) H5 n g) G
initpop(popsize,:)=ones(1,len);%The whole one encoding individual
0 E* {* d" a6 C, B" B %解码" j! v1 A2 j: d2 W' f
* c7 r) Y$ K( c6 S* f function [fval] = b2f(bval,bounds,bits)% n" H7 s; i4 a* F: P2 I$ A
% fval - 表征各变量的十进制数# K) c( {' T9 Y' l# a% n _* N
% bval - 表征各变量的二进制编码串. n* d( s2 D! e; U
% bounds - 各变量的取值范围. p& F1 {& Z. i9 k+ m. \
% bits - 各变量的二进制编码长度) }: O K }% W+ h" h
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
: y! o3 L7 |' G. I) C# ^ numV=size(bounds,1);
& P+ _/ {/ _ g6 C+ K, l cs=[0 cumsum(bits)];
( A5 M. A# z" a5 g! N for i=1:numV
3 o% O- F( n. u# i q- n# L a=bval((cs(i)+1):cs(i+1));
+ T" ?6 P4 b0 ?1 N! a+ Q2 K1 F fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);, V) j* L4 m7 p! P% |$ c8 n
end
, Z% t4 Y* X4 `, } %选择操作
/ d* r5 V& k! I& u T( I Z %采用基于轮盘赌法的非线性排名选择
$ ?( z% D. L- w %各个体成员按适应值从大到小分配选择概率:
6 _- ]7 i% r+ r% V( e2 H %P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1% @* k% |+ c; B% q; ~
" P+ K" S' E% \3 C3 J
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)0 o; d# ~' d- X* d
global m n% j) R8 R1 V1 N
selectpop=zeros(m,n);
+ Q# Z7 ^" j1 i% V9 K, d3 V' c fit=zeros(m,1);& Q" P+ B4 Z, }8 z$ A7 Q
for i=1:m
3 O0 N7 }1 S% o/ c fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
9 q: P" G" R6 n end4 P* n6 ~8 d7 F. t6 m1 l5 }6 \8 a
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
1 n' D4 `' n/ p3 w q=max(selectprob);%选择最优的概率
8 I7 `, E- Y; I+ u2 L% o5 ^; ` x=zeros(m,2);
8 }1 m0 K& J' F/ ]# g# ^) E x(:,1)=[m:-1:1]';
# w0 q2 n/ W" y. }+ a [y x(:,2)]=sort(selectprob);
. {1 _0 m- @4 Y L6 q6 s& e" x r=q/(1-(1-q)^m);%标准分布基值 E: [: A6 F6 Z7 r- y) |4 k
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率# P& E. q8 v3 {7 f
newfit=cumsum(newfit);%计算各选择概率之和
F4 B" f6 ~7 y/ N$ X* N& }9 x! D$ M rNums=sort(rand(m,1));$ g+ J! d0 H+ S; ?5 H8 L
fitIn=1;newIn=1;
% X( m" J3 [, R while newIn<=m5 T) ~2 V4 A- O" W
if rNums(newIn)<newfit(fitIn)
) U. i" Y& O- z4 p; A selectpop(newIn,:)=pop(fitIn,:);
" t6 v# R( t" R# d/ ~1 S newIn=newIn+1;% O+ y i' t' o0 {/ s% T
else
5 v7 a- Y/ \! j& Y fitIn=fitIn+1;
) H% H1 a1 \8 V4 o! } end% I, H# ^, f8 ~7 G
end
8 ?( G+ X# K* w2 }# N) C/ U, V" M, X %交叉操作$ [0 Q4 {0 ?1 i" m: o' q2 D% f
function [NewPop]=CrossOver(OldPop,pCross,opts)
: u$ w7 d& o, m0 ~ C %OldPop为父代种群,pcross为交叉概率
, R$ }% l. `( k- R0 B% R+ u global m n NewPop
$ L2 @9 H6 |" |. ~' V$ K2 F r=rand(1,m);
7 ?6 k( G: I2 x( ]) N8 } y1=find(r<pCross);
- u& F2 A0 e, {, ]6 G y2=find(r>=pCross);" ?3 _- y% D. c4 G
len=length(y1);& k% \/ j7 d& e" X
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
- H9 ?! J1 d5 w0 j* r y2(length(y2)+1)=y1(len);8 q i# T9 Y" R1 {6 n1 d
y1(len)=[];
# l( {( k' w2 }9 ? z8 M end
9 q( T1 D1 s- Q" t5 [7 }4 O if length(y1)>=2
: n& L& A! A9 ~2 ` X5 o for i=0:2:length(y1)-2
% \( K7 Y" Q6 N% P, k if opts==0
. O9 T/ A) b) s# Q$ @% ^5 Q# r [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));8 {" k/ A3 P* n& Z6 `) P
else
: h1 Y! ~0 ?+ p [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
( ~4 c; B2 h" M5 f end
$ o/ U. T' l" {8 U+ |" d, t end
* D5 I6 W" y" F* O3 J end% _2 ?* D3 h8 I8 Q$ v/ K' Z7 r( Q2 w
NewPop(y2,:)=OldPop(y2,:);# {+ s: o4 t D: X7 `. ^* c
9 e- g4 y' Z$ P %采用均匀交叉 : [8 `% n( R7 Y+ p9 |% F
function [children1,children2]=EqualCrossOver(parent1,parent2). l8 f/ {0 g' S0 k" \4 o6 \
# @( ~9 ^% _7 G) U4 p- V global n children1 children2
# S( d2 }- o. l4 E( F' h hidecode=round(rand(1,n));%随机生成掩码1 t( t9 ?0 \% P" J
crossposition=find(hidecode==1);
3 u/ b/ [) z8 _2 Z holdposition=find(hidecode==0);
/ U8 F# {4 P/ d6 |' h children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因& v6 H$ E* _9 D/ p: ?# \
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因: h) N! k( @! v5 B4 o" N* u
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
5 w# u2 T3 n6 V children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
, a8 B; \7 N( O# B9 v& g . F- h! d9 R. m0 T$ s6 I
%采用多点交叉,交叉点数由变量数决定
$ p9 V9 x4 |% O, _) e, v( C7 R( J # _- u/ J* g( m: x; E% T% y
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)* i: }8 L: j G, `+ K/ G
2 V9 K2 I/ x0 }5 q+ f0 q global n Children1 Children2 VarNum. P0 W5 E* k+ T9 Q( [0 I7 P/ u5 T- h# v
Children1=Parent1;
8 A/ u6 i# f" F1 x3 E Children2=Parent2;
# S* T* |7 p' B+ j# ` Points=sort(unidrnd(n,1,2*VarNum));8 Q! y$ h; |+ v6 M L, ?: _- z
for i=1:VarNum
, W- Y5 R1 f; `' a% j1 C3 i Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));( }; K7 X. j. s
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
1 Q2 ^3 ]2 B" U, W/ r, p0 W4 G end
- F- D! P: \4 j1 ^ # e8 s; }6 D, i( ?6 Z& U
%变异操作
0 ^; V$ P$ H" p+ B* N2 R function [NewPop]=Mutation(OldPop,pMutation,VarNum): z; j9 I. n3 g3 [: y
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global m n NewPop
: k8 I5 X( v/ ?- y* Y r=rand(1,m);; T. M3 f ^; ?7 s6 v: ~
position=find(r<=pMutation);! u# W! r! }0 N4 T& ~ w
len=length(position);' F# T3 \% f4 P# n+ l4 t9 ^- Z
if len>=1
6 R7 _+ ~. x) R: L for i=1:len1 s. k' W% Z5 o* f
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点9 r4 E& a- N, ` z' J c2 F
for j=1:length(k)
[% R% D9 Z. z# s if OldPop(position(i),k(j))==1, Y9 X# Q5 C& |7 F* r- n
OldPop(position(i),k(j))=0;
, u/ S) r/ E; p5 {# p; Q else
0 x) [0 X# X/ D) p2 x" t OldPop(position(i),k(j))=1;
Y' I5 ^/ }6 e2 b" B9 V7 q end
6 s% ] F: m1 `& k; W& e end
5 h3 a. u0 D) R5 v$ f/ x end
) j/ P- g0 c2 d0 t. A3 p9 R% P, [ end% j. s$ t8 A3 q; g& G
NewPop=OldPop;( H) B* {& t$ u" Q* H# k1 T- Q
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%倒位操作
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3 Y- C" p( }; c. S function [NewPop]=Inversion(OldPop,pInversion)4 g, G, H! b' S6 R3 W! I" ~+ l
0 u; n3 ~6 N T5 [, a4 j/ C global m n NewPop
4 X& W# o1 b B6 z NewPop=OldPop;/ Y: N. d; e: s7 ~! P% m
r=rand(1,m); _$ A) C2 }3 G' B
PopIn=find(r<=pInversion);
/ w! H7 F! G0 {; f9 } len=length(PopIn);
! h" t- p/ |' S" |+ p& V- }' u if len>=10 s* V- U& T3 S6 Z8 D! n
for i=1:len
8 [5 \8 P: ^$ ^. ]6 y9 `( q8 j d=sort(unidrnd(n,1,2));
- P6 L5 f. z0 n _ if d(1)~=1&d(2)~=n; r6 x, W6 x8 r' u% n
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
/ D2 S' v! L7 A7 U$ g# z NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));) O/ p. N. q Y. n& T( l. I
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);5 j, j0 m! C4 `+ E; A
end. l+ D) f9 r' C4 n$ Z0 f0 z& t9 d
end
9 H0 J( u4 ]8 C: N$ L4 T end
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七 径向基神经网络训练程序 F- b7 m2 W1 q
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clear all;7 t' x7 f8 E* c, B4 w4 m9 a
clc;8 d* ?2 @ H' x# N* u
%newrb 建立一个径向基函数神经网络4 G0 H: P9 ` ~ l5 f0 Z6 D
p=0:0.1:1; %输入矢量
5 u8 Z, {( ?5 w& x/ x. Y t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量7 U0 Y$ h T, b1 N# o
goal=0.01; %误差3 r0 t( d6 Y* X9 o3 x$ o9 I+ o3 C
sp=1; %扩展常数
3 f- d/ g1 s2 f2 M, r0 P, P mn=100;%神经元的最多个数
) Z$ s- y: m+ u4 Z/ R, [) a df=1; %训练过程的显示频率
/ B* m( ^! m, [% _, y" W3 D [net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络" ^& i, _ K) R6 \
% [net,tr]=train(net,p); %调用traingdm算法训练网络
7 w7 \ ~/ V, ]9 G- ^ %对网络进行仿真,并绘制样本数据和网络输出图形) i4 F8 J/ P; s) J0 `
A=sim(net,p);6 E0 w; O4 p5 p
E=t-A;
6 _ d: b1 l: ?' L# M5 O' Z sse=sse(E);
4 q( ]% [4 J+ v$ }$ m figure; ; H! z- @% L3 Y3 H, A5 s
plot(p,t,'r-+',p,A,'b-*');
5 d9 ~! J9 W$ J$ R# Z3 @0 _; J legend('输入数据曲线','训练输出曲线');7 C, d: Q+ e/ t4 p9 x3 A& n
echo off 4 s2 C( s" l2 |( [
; c0 c+ i) l1 j4 P7 i0 p 说明:newrb函数本来 在创建新的网络的时候就进行了训练!1 I' ~2 C6 t8 }, _( a( V( x
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,9 t( b# F& E4 x( t: L, 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!6 z8 I5 g" m- A+ {, P4 V
4 P! _9 v9 t' t- g
, a; {- p1 T9 `/ J# e0 m/ S( k# } 训练结果显示:/ @" E4 a. b& Z& l7 L0 ~
NEWRB, neurons = 0, SSE = 5.09734 n' p. v B' d5 c# \
NEWRB, neurons = 2, SSE = 4.87139( {8 T* _) U3 u$ M3 e' D) _2 ?( X
NEWRB, neurons = 3, SSE = 3.611764 b5 V5 {% v2 I% W- L2 r
NEWRB, neurons = 4, SSE = 3.4875
+ f! y# _7 h) r/ N0 u1 `5 H NEWRB, neurons = 5, SSE = 0.5342178 N- h, L' B* I# k9 P
NEWRB, neurons = 6, SSE = 0.51785+ ?9 z f6 Q9 L- Q4 Q
NEWRB, neurons = 7, SSE = 0.434259
. A% c7 W5 C" l) S4 V NEWRB, neurons = 8, SSE = 0.341518
, Q6 o# T0 K ^* } NEWRB, neurons = 9, SSE = 0.3415197 m: H5 p! p5 ~$ K; e( Y
NEWRB, neurons = 10, SSE = 0.00257832( D. ?0 r1 G1 q6 Y, [
2 ^- G5 D0 `$ ?9 |+ d 八 删除当前路径下所有的带后缀.asv的文件
% }% r% p/ X4 Z 说明:该程序具有很好的移植性,用户可以根据自己地! k _1 p! F, `6 x" N
要求修改程序,删除不同后缀类型的文件! ) @9 l$ a, J. t, u) ^ t( D
function delete_asv(bpath) 3 }4 [3 y- U( [( x0 ^% J
%If bpath is not specified,it lists all the asv files in the current3 c( [3 M) R: q$ \4 c% T1 \1 H1 ?% ^
%directory and will delete all the file with asv ! T# p8 c/ b z+ I ?* Q4 W7 O
% Example:
/ K3 C7 @; x) `- c8 }" E8 j* K$ j % delete_asv('*.asv') will delete the file with name *.asv;: ~0 |) u& U( A% m
% delete_asv will delete all the file with .asv.
( N" B$ O8 C2 M4 |2 g9 m! M
9 H' C* k0 b8 \' u; W/ L X if nargin < 1
) X( h, a% G \* l %list all the asv file in the current directory9 X# m u7 a% w& i& L" Y2 b1 `+ D4 T
files=dir('*.asv');
9 I, j8 T- w8 E: i @! l) a6 \ else7 R4 I8 S W: z" q8 m8 _
% find the exact file in the path of bpath
. m0 a# q. Z0 `( A+ b) O, Z0 e [pathstr,name] = fileparts(bpath);
4 p% [' x6 D) c, e if exist(bpath,'dir')
% t$ k9 m+ S. h7 T2 N5 e name = [name '\*'];
! q5 D/ G" Y( [ l end5 f. Z& U. g' e9 M
ext = '.asv';
4 Z) _# m; \" i$ Z3 c( i* _, X/ _ files=dir(fullfile(pathstr,[name ext]));1 R6 K3 b5 F5 i
end6 _2 a7 t2 R6 ]0 }
$ W( P3 d+ x5 I9 {
if ~isempty(files)
X; K* P: D8 Q& Y( e for i=1:size(files,1)
8 r1 M# x0 e- G b, A B9 ] title=files(i).name;0 N' ?0 y' y1 d/ Z3 _0 f
delete(title);8 o& X0 V* ?" ]6 `+ I' c: d
end! H3 \1 x9 A8 c! ^# |1 z5 ]5 ~
end" h2 q4 }) b W$ N' y+ \4 Z
; R- ^9 n1 z+ h" y" d
8 W; _/ H" H9 n. S 同样也可以在Matlab的窗口设置中取消保存.asv文件!
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zan