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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& v% P u/ O( }* e* h9 a5 M+ g
1. predict_fun.m为主程序;
! c `; C$ v, ?! H; }' _ 2. timeseries.m和 serie**pan.m为调用的子程序( @' X% D+ X9 W
3 h! \# t( _5 @
function ima_pre=predict_fun(b,step)
$ V! x! H2 ]8 ~: N9 \) i % main program invokes timeseries.m and serie**pan.m
. X6 w1 G' C4 ?: B, N* r % input parameters:
1 m6 D+ o3 h6 X9 J9 g# _: @% U9 D % b-------the training data (vector);0 |( D. o% d; X/ |. F: \
% step----number of prediction data;; K; M7 u4 j, j4 X6 g0 e$ h
% output parameters:
: q# F# w/ \" E- J+ V& Y % ima_pre---the prediction data(vector);
$ b2 D7 G7 e7 U; a- a old_b=b;
5 D1 h- O" X8 J8 F4 d mean_b=sum(old_b)/length(old_b);
: x0 ]7 W: U1 u' ^$ F' h; H std_b=std(old_b);( z* [2 y) ?* a8 Q
old_b=(old_b-mean_b)/std_b;8 c' ]3 I; C& O5 l _6 `
[f,x]=timeseries(old_b);6 W7 {9 f r. V0 ?
old_f2=serie**pan(old_b,step);
1 e, C: @! h/ J) }! s6 b+ d % f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;/ F6 u8 V6 X, O/ t6 m5 q4 K
R=corrcoef(f);
1 Y: {1 y" Y, w9 R6 q [eigvector eigroot]=eig(R);- N: ]9 o& f1 Z; l0 P" R2 l
eigroot=diag(eigroot);
& g# F4 A$ B" E2 n- i" l' Q a=eigroot(end:-1:1);; Q8 _/ ^4 s1 M3 o
vector=eigvector(:,end:-1:1);3 w, b( j4 i. L" L2 X5 u
Devote=a./sum(a);
; L5 m4 r, e! L) V8 ^ Devotem=cumsum(Devote);* J' t v, [! V, g2 O
m=find(Devotem>=0.995);
8 J, d( i& I* u+ s m=m(1);& z+ u/ l0 G; |( W' i4 X m6 Y
V1=f*eigvector';" n5 e; @) E6 U2 Z
V=V1(:,1:m);
+ q9 [& H9 R0 B' `- x% I6 ?/ s) a5 j % old_b=old_b;7 A# K5 E, s) L* _* o, o2 g" \) h* P
old_fai=inv(V'*V)*V'*old_b;
9 y9 \9 a. j- ~* g' @; A eigvector=eigvector(1:m,1:m);9 F/ Y8 x/ A9 C! |/ S5 N- U0 V
fai=eigvector*old_fai;
]7 H. m. o' i! Q9 @0 Q$ s: m f2=old_f2(:,1:m);1 F8 C# [9 F- a3 q
predictvalue=f2*fai;) Y3 R2 C4 c6 k2 q
ima_pre=std_b*predictvalue+mean_b;
, y j. Q6 P5 C1 S. [: Z% X + Q0 ^( i6 s& O: y6 b; l
1.子函数: timeseries.m
! R3 [2 e) t8 U" E9 M2 Y8 g % timeseries program%6 E7 n4 C! Y6 b8 o' t
% this program is used to generate mean value matrix f;; Z& X- n5 a9 w/ e4 j
function [f,x]=timeseries(data)
; [ ~& L: c t9 m+ F % data--------the input sequence (vector);( V2 o; m6 C' w2 ^/ v! x
% f------mean value matrix f;
' e& n7 d6 Q( Q' t5 E; D9 } n=length(data);* u5 y6 V* Q2 z
for L=1:n/2% o0 I$ ~- {' B: Z0 s$ ?
nL=floor(n/L);1 X* M8 l8 v( b% I" D
for i=1:L# D, p4 u: {7 [! J( F
sum=0;
! j. R C, y v$ i for j=1:nL0 M; Y5 N7 e6 J2 L ?8 d
sum=sum+data(i+(j-1)*L);
5 _# V' j! A1 x" e) A- ~% j end
) r- ^6 |) T/ t. | x{L,i}=sum/nL;
; Z7 R4 {3 \4 N end( D, j2 e7 {3 q9 f
end
, x! @, U8 S* Q+ M L=n/2;
( N7 j2 w5 n4 Q. L7 G f=zeros(n,L);4 M, y$ k7 x I$ G" K* k
for i=1:L
W/ L( c) `& ?, N: A9 c) W: j9 W3 k rep=floor(n/i);, t/ Z7 w. U% A6 s' ?. B/ d/ F0 `
res=mod(n,i);
3 g" t4 I! s N$ U0 W b=[x{i,1:i}];b=b';: L7 x2 k5 \9 r" H- V3 D
f(1:rep*i,i)=repmat(b,rep,1);( S7 Y2 m" e& |" M6 R2 O- H1 }" ?
if res~=09 L; Q( {6 J1 B* a& p9 @, I
c=rep*i+1:n; O5 V5 z; w/ }$ ]$ x% O( B
f(rep*i+1:end,i)=b(1:length(c));
0 D& A! n7 ]) P8 u1 `1 d3 p end
* c, Z8 c+ |/ F6 g9 F end
% ^6 y1 ]4 V) _" E. ~4 {& \
6 S- S% ?- u: b5 j8 u, X' k % serie**pan.m3 _6 r* c8 t1 B
% the program is used to generate the prediction matrix f;
- ?2 A- p0 E' b; O7 R* p5 Z function f=serie**pan(data,step);
( { S) I# }8 o8 A% D8 T: A" } %data---- the input sequence (vector)
' o& q8 |* N0 @+ l6 Q % setp---- the prediction number;
+ S/ m6 M! v) `6 E7 x n=length(data);! a+ I6 }( S( }& U2 k- V9 y3 I
for L=1:n/22 R$ D+ |) e! i
nL=floor(n/L);
* g+ \/ u# k2 c$ Z0 Y6 e, V+ H- u) T for i=1:L5 x2 F0 @3 X/ c$ I/ i
sum=0;
4 R9 d0 X. e* t' G1 t$ d- E/ k for j=1:nL) o( U# V8 V7 V8 f
sum=sum+data(i+(j-1)*L);
6 S/ H; o' N* Y6 R; H( v6 s7 |" U end' p4 i! a' h2 |' A4 y+ F' Y N) J
x{L,i}=sum/nL;, h1 M) V8 `8 Q% e' w' ]8 g; l
end
9 K3 c. d, M5 ? end9 p4 |4 `8 L' e: R# `$ D: M' e$ K
L=n/2; u1 w" V/ J: |& B: f' P" m# N
f=zeros(n+step,L);
" o) H. ^. w) m for i=1:L
: g) m) y1 P/ ]5 L4 {' D rep=floor((n+step)/i);
4 D+ j' _8 l" e; O( T& D$ z" ~ res=mod(n+step,i);. e* Q0 U" ^8 U8 Z
b=[x{i,1:i}];b=b';+ U. Z+ {) J. G( f4 _. L; U
f(1:rep*i,i)=repmat(b,rep,1);# Z( j T6 S* b1 I% X/ k# M
if res~=0
) j& ^% R) S4 ^, S c=rep*i+1:n+step;
/ v0 T3 d8 b. ~6 Y$ _' G5 \5 A& S f(rep*i+1:end,i)=b(1:length(c));
$ ~! E& h! F) ]+ _; G$ e end: {* V3 E0 w/ Y8 _9 _: t
end* j s4 ^7 G% @9 M
% y' S( y* l4 r* V! |% w
二 最短路Dijkstra算法
+ G7 v/ g# d& R* l W& P, i % dijkstra algorithm code program%
2 ^# l+ o5 ?, ^5 d0 X1 n % the shortest path length algorithm
6 M" \& H# t1 e M function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)7 ? t9 y) V: F
% Input parameters:+ b2 v* N9 \' G) Z
% Input_weight-------the input node weight!
' J2 I6 D4 b: n% e % start--------the start node number;
; ~& C+ B+ |- v v# a % endpoint------the end node number;
" b4 K! n1 Y# q+ A1 p % Output parameters:5 q- [) a% e ^, q# b0 v
% path-----the shortest lenght path from the start node to end node;
, L2 n( o( a0 m % short_distance------the distance of the shortest lenght path from the, @' b7 _! W# Z& n6 y# x
% start node to end node.- T, ^3 i6 S \: R
[row,col]=size(Input_weight);
# }4 }9 e: j3 A( |/ T & d4 h$ M; ?6 u8 u& x8 i- Q1 e# f
%input detection
" q6 \+ J5 r% }% O5 Y q1 s if row~=col
O" q# V0 B5 G2 a& p) L: } error('input matrix is not a square matrix,input error ' );
% K& p7 n4 o4 X' ?; [ end
$ U L, }- m4 T+ ] if endpoint>row
: g$ v: G9 o7 k' a error('input parameter endpoint exceed the maximal point number');
* H8 Z& b: \% G end
7 M! A4 ]/ ?; \. I: O2 s
1 c6 C# r' @) \# N' y h %initialization$ n* {$ }3 Q& _1 A" l. @6 O
s_path=[start];
, Z0 o4 U/ \/ J2 J distance=inf*ones(1,row);distance(start)=0;
# `4 N& h" E( f. ~+ T* q flag(start)=start;temp=start;/ W4 W5 a2 p6 l) R8 n6 P
+ {9 ]& k1 h6 Q8 H) Y5 W3 r
while length(s_path)<row
+ F6 [3 G% I) r; m% X3 l s pos=find(Input_weight(temp, : )~=inf);% S* n3 _# F/ j* L
for i=1:length(pos)) n6 f! c, d Q; `6 |' G! R
if (length(find(s_path==pos(i)))==0)&5 }, e. u6 j( m/ w5 L$ j
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
, l( R" j# }8 d2 @. o* M2 i6 \5 r distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
4 j, X& }' l: H: v( j- z flag(pos(i))=temp;) q6 N8 v$ V- y2 \: p! ~% ]8 ?2 O
end3 ]$ P: f- ?% x/ ]6 [
end% e. a% `9 ]& b; R0 w. ~ E; s# ~
k=inf;
0 E& y- `+ \: p1 F for i=1:row: A+ R. p; g( ^9 G: j
if (length(find(s_path==i))==0)&(k>distance(i))4 a0 f/ n) h+ \9 R3 q. W. r
k=distance(i);( d i, d& ^- l0 s2 ]$ f3 i/ b# v
temp_2=i;
, k( K7 X- `+ o/ T end
& w- m) }- t6 A- u end, r# k( @5 {+ Z& @: j5 z
s_path=[s_path,temp_2];; P$ p# B4 y1 V0 ]9 M, z
temp=temp_2;
1 A( l( s' }/ y5 F1 z+ ? end
. F& v/ ^, p# c1 q/ W, L3 l: y
- v7 o: V2 L* F( V z" m. V& d %output the result
. @4 @5 B* n! H5 Q path(1)=endpoint;
/ x& f7 [6 D7 Q. T6 }& e i=1;
) c& b( h, x: v' e9 g% z while path(i)~=start
8 h4 P6 s, y6 E }9 I7 w path(i+1)=flag(path(i));1 T4 a& [: k" T6 V5 o
i=i+1;
5 ?3 F2 A X& S% w end+ K9 }: w }6 ~# v0 e: d* Z
path(i)=start;# s0 m/ S6 B8 s" N8 }& V$ s+ w4 Y
path=path(end:-1:1);
1 Z/ N% X/ k% d b# n! @: z short_distance=distance(endpoint);
8 `; t& t K, O 三 绘制差分方程的映射分叉图
( \; j2 w7 ?$ K/ b2 F! Q 3 p/ V4 J7 l$ ~
function fork1(a); / J( k( r* Z. G. G3 G% q, \( a
. O" V o% E e
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图( t) B) ?- a: w6 ^4 Z/ H, P5 l
% Example:
4 ?& p" w; ]0 G/ H3 P % fork1([0,2]);
0 G+ {, ~* w7 r- Z N=300; % 取样点数
3 ]- \! s' s* `9 M3 d A=linspace(a(1),a(2),N);
: Q& Q* F3 Y; a; }3 F( y; L% ]$ [ starx=0.9; ' s7 R5 V1 v& _) ]/ Y
Z=[];
, q0 O' d* r% m3 x, e0 z; U" L& ? h=waitbar(0,'please wait');m=1;, c/ Q3 B. Z; c% x& t' |! X" v
for ap=A;
( K: N. \7 a5 F/ i x=starx; # O3 M' {0 h @
for k=1:50;
% B0 ]9 K, g5 H0 a x=1-ap*x^2; ; A$ E3 r( Q+ G E; [
end $ U/ P; _1 y1 l% y
for k=1:201;
) Q; O& q$ f. c5 l4 [* {: |5 m5 s x=1-ap*x^2;
1 Y% y3 G+ B+ P/ r L Z=[Z,ap-x*i];
4 [- i! F9 t) u3 t9 _ end 2 D. o* m0 x2 h1 e+ f5 X; K# F9 }
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);: m2 ^' _! q& ?! D! H) ?7 W
m=m+1;& B' Z+ t% N# _) E* C
end * U( A5 x" W: t0 z- K; E$ u2 v
delete(h);; t7 W. o, h, g) w- K
plot(Z,'.','markersize',2) ) z' C2 |% D: ~# O+ [+ {
xlim(a);0 f& @" K! [, Y) u8 C9 t
2 y# [" ~& Q5 Y7 {4 S" K. d t 四 最短路算法------floyd算法, ~% J; x( R Z$ x
function ShortPath_floyd(w,start,terminal)
. R0 U) Y3 h$ o' v* z. F9 c, ^ R %w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;, t* k% u: r! i0 k) W
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];7 O$ k3 b6 k+ U* b9 h8 n: q
%start-----the start node;1 ?" n; X* [3 [" H% ]( m" x
%terminal--------the end node;
1 }2 b5 P- N$ @- s n=size(w,1);
( P) y# H$ T# X4 N [D,path]=floyd1(w);%调用floyd算法程序0 R: `8 u& Y# D8 G7 r
: \8 L- w h- p! }7 X9 O %找出任意两点之间的最短路径,并输出5 H& C# [5 b& `" e( C3 C
for i=1:n
! M E. _. ]$ g) h. J& _ for j=1:n% A+ k$ u# x" @
Min_path(i,j).distance=D(i,j);
$ j5 ~# S& H) h% D6 @2 Q %将i到j的最短路程赋值 Min_path(i,j).distance- V$ O9 X. {* z% [2 Y$ n: H0 `
%将i到j所经路径赋给Min_path(i,j).path' Q, J( Y: a& j1 a
Min_path(i,j).path(1)=i;8 {3 Y9 A9 B" W- c1 h/ @
k=1;
" h3 y- b/ F& U while Min_path(i,j).path(k)~=j7 E* k/ x9 w3 a9 u4 e9 o
k=k+1;" \3 T" Y5 D( \; _4 o- O' c1 ^
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);( @3 g, A$ @5 J+ _7 `" L* [
end
* ~+ J O/ \, X7 _; R0 q end
r- R: F. Z# R, c7 _ end5 @$ G8 K5 m! }
s=sprintf('任意两点之间的最短路径如下:');3 _ T' S: F) N; X
disp(s);) u8 n8 w; U% q2 Q
for i=1:n
8 [! u1 W7 u' q- z f5 i3 g) Q0 g for j=1:n3 d- g) Z- ]( J$ ]2 K
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
& k/ O/ f2 t1 ^3 S( n9 k0 c ,i,j,Min_path(i,j).distance);
. s4 P0 G+ ^; E+ v- D( y, H disp(s);
+ F7 k5 S+ w( Y/ c disp(Min_path(i,j).path);9 |$ l" z6 H$ T' v; {
end) }+ S# R$ q0 e
end
- B+ V& h( ~9 ]5 ~8 x% p: E9 C , i/ b, X A9 m3 s/ w' U
%找出在指定从start点到terminal点的最短路径,并输出$ G9 b6 G* F& t4 j s( M
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...# h$ `5 `+ D: h
start,terminal,Min_path(start,terminal).distance);8 ^. @+ s# H. d# a
disp(str1);
* Q9 G/ w6 b7 O disp(Min_path(start,terminal).path);
}' B1 A# ~. d/ |+ C+ a
2 A- |+ @( t3 ^" Q# t. K %Foldy's Algorithm 算法程序* L7 o3 I6 [+ I# H8 t5 r, Q
function [D,path]=floyd1(a)4 h4 j/ w8 q3 [: A. D/ B
n=size(a,1);
) ^: X- @1 T& w1 Q D=a;path=zeros(n,n);%设置D和path的初值
5 X& H" k1 O1 q9 E2 ~ for i=1:n+ `8 _# k0 b% _ T4 `# m0 T
for j=1:n
9 p1 r) N# h5 H/ [% L+ K if D(i,j)~=inf
6 z3 p8 W: {+ X2 |2 B path(i,j)=j;%j是i的后点. ]7 w4 ~- @! r, i- F- B' K
end
& ` t* h8 q6 B, { end7 \; o+ n* \, N9 S
end
1 V7 A# i- s$ P %做n次迭代,每次迭代都更新D(i,j)和path(i,j)
/ E. j9 o' W A2 F, h* [7 E2 `" K for k=1:n& b; z' A0 q; Q2 z X
for i=1:n" r$ s' O, {% O& p( ^# ] E$ n
for j=1:n/ a/ n8 ] O+ \5 r- Q) f7 n
if D(i,k)+D(k,j)<D(i,j)
; n. t" y V& p D(i,j)=D(i,k)+D(k,j);%修改长度9 m, f7 J! N" U
path(i,j)=path(i,k);%修改路径
) t8 N$ m0 X* d end8 X Y1 L& o( e! q4 ~& F5 v
end( f7 R; m) h! `, G6 ~+ X
end6 O% N6 i$ }) j
end% a2 w G9 d$ D& K
9 L! Q7 U+ X3 U. Q; D 五 模拟退火算法源程序% _, g# M: k& g. \8 q1 H2 j: \8 G. N
function [MinD,BestPath]=MainAneal(CityPosition,pn)8 @$ _9 g! O9 q" |0 r4 i/ x
function [MinD,BestPath]=MainAneal2(CityPosition,pn)
9 h' W5 ^$ Q, F, j5 p7 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 Q! i% ^% M& }" i. _ c
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
8 `" |' i" K$ G& [ \: p" u' M % 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;..., w/ V7 O% b& o; ~
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...) \4 c# q+ E( H, b% F
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
* V8 [1 w( o7 S9 f. q % 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
0 ]0 Z: ]- a8 ^( O
: G, H v5 z! i, l; }. T %T0=clock( o& y7 ^( o2 }; P
global path p2 D;4 ~% W1 r) E; O* V* b+ h
[m,n]=size(CityPosition);6 N* N2 h, S2 k
%生成初始解空间,这样可以比逐步分配空间运行快一些
T* c; ^- A- A! d2 a. r TracePath=zeros(1e3,m);
; ^ I. D" L* t& g: v Distance=inf*zeros(1,1e3);. a2 e5 B& y1 m- F+ h6 i
) p8 }3 L6 r V/ \
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +.... P, D) \8 w! v2 {6 v1 T5 E
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );: H) N: D# L* h7 q5 x# z
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)+ ^$ Q$ i7 R" ], k" z7 W
for i=1:pn( d9 `4 a2 |7 t9 q) J. h
path(i,:)=randperm(m);%构造一个初始可行解
. c7 d0 L+ D1 d7 } end
1 a, A3 N7 j. k/ l* f2 J t=zeros(1,pn);8 g) K9 e+ u0 B3 R2 b
p2=zeros(1,m);3 }8 m, E& C# Y4 w* k$ v
: l) r1 D5 L6 ^1 t! l
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
. r! X2 [4 ? f 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=' ) ;( a: P2 a8 u: ~% t- @
%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/ _. |* B3 T0 w. _1 k: _
%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
+ P* h# M Y4 \7 G8 H %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
* p e$ h, `( b' L" P8 {/ }, m %会收到到比较好的效果. u% i( f; E- u8 l# O
/ h* m1 {% w8 L: z T=1e5;
- q1 R) L1 P# _9 R" h N=1;
$ L) E0 c {' w. |. n tau=1e-5;%input('请输入最低温度tau=' );3 s2 q. b/ [8 ^3 h" x
%nn=ceil(log10(tau/T)/log10(0.9));" ?3 O7 ~, S4 z; w( U
while T>=tau%&m_num<m_max 2 R2 ?1 Q' Q! j1 \! ]5 F3 E
iter_num=1;%某固定温度下迭代计数器 _! b: f( L- ^: k
m_num=1;%某固定温度下目标函数值连续未改进次数计算器3 I. J8 {' U* v/ ?5 L( D
%iter_max=100;
8 X; D% x6 r& O %m_max=10;%ceil(10+0.5*nn-0.3*N);
! N' a2 J: f( N1 X while m_num<m_max&iter_num<iter_max
5 D, r8 H% C% X9 j %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:7 D: m* i* ^9 D! r. A. Y
%用任意启发式算法在path的领域N(path)中找出新的更优解
/ @) y, q B2 o- M4 u for i=1:pn J. u/ ^. o j5 C4 R. |7 W
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
4 P5 W" V9 n5 |, ?$ j" J( d %计算一次行遍所有城市的总路程
- h8 X7 `8 _5 s' U3 z$ d7 O [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
$ X8 k, w7 d/ `7 d$ O4 f. a Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);0 K7 `# D) S( g1 F- P8 x
end
" D& Q. {/ A' M" E0 n/ v %Len1
$ h4 q& c% m: `9 v' w %Len2! f! y5 m, J3 j% J# ~
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand' D* a8 r0 G% T/ @
R=rand(1,pn);
, a7 S, s- G- f( [1 i %Len2-Len1<t|exp((Len1-Len2)/(T))>R, t# f* ]! }* E5 n5 s) n+ U
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
! X2 M A. b v9 F( P% Z path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );& k% v; y$ h% \0 ^. h, G
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));2 u$ i, b9 U0 {5 J7 l) C: Y
[TempMinD,TempIndex]=min(Len1);0 T! k7 a% j0 H, `8 x# o1 J
%TempMinD/ t6 g& d+ @4 _+ g# @) W
TracePath(N,: )=path(TempIndex,: );! p+ m3 H, ~% i( j' ^) s
Distance(N,: )=TempMinD;5 P- J# P. L- Y+ T% n
N=N+1;4 I' b3 i: p0 D% v! p6 h
%T=T*0.9
0 }8 a2 I1 r! E" Z0 n m_num=0;
2 @5 ^5 p& R7 ?% S" l2 F else* p, d6 M- p1 }( T2 b. S R6 f
m_num=m_num+1;* T8 Z8 m4 ?0 A0 i; z& b( ?
end& E8 p! a! V( `# Z3 g
iter_num=iter_num+1;
+ t+ P5 i8 t. g end! d0 t# ]4 d' m
T=T*0.9
9 h/ I5 G7 j, F# q/ }7 f %m_num,iter_num,N
. M1 Y8 C3 U" r- G9 T8 {1 A end 3 W a o2 Q1 \; i: G4 Y, P
[MinD,Index]=min(Distance);$ l7 g% y' ?- b
BestPath=TracePath(Index,: );
$ K- i* [0 _* N% V2 x( K disp(MinD)* F6 K6 U1 {8 m
%T1=clock" R( c J M$ X" d, U
O, X- v& x2 F6 E+ n/ K; ~% H
( `" I( Q2 H& j: l! Q %更新路线子程序
- G) U) w/ C/ ^9 L9 U function [p2]=ChangePath2(p1,CityNum)1 t2 P; `" p/ I; E2 d$ e8 I
global p2;
* c/ F! Y$ e9 S8 S& h2 z$ J while(1)
7 U4 j! |9 I: H7 P& v0 H b Y R=unidrnd(CityNum,1,2); q! K/ Q$ T/ x: ~! U
if abs(R(1)-R(2))>19 p: p9 N i" H. n3 i5 r/ M
break;7 b8 L: ?( [$ L% j5 B1 _5 d, D5 Y5 S
end( b1 g# _7 |" b% g7 P) W
end* g0 `' O6 g1 m$ h/ v
R=unidrnd(CityNum,1,2);
# ~$ |8 ^* h6 g5 O5 W9 S I=R(1);J=R(2);6 P+ L3 k, z# y; y2 p6 c
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));/ g& {. l& @. O/ R1 I
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
& K4 X% S2 t6 `- w. b4 @4 R. { if I<J5 D) `5 l( r! Z0 ^
p2(1:I)=p1(1:I);
; z$ j$ Q% p" t0 B4 k! e p2(I+1:J)=p1(J:-1:I+1);3 H5 I3 u9 s/ S8 J
p2(J+1:CityNum)=p1(J+1:CityNum);
& `$ x3 G0 b! {7 a' \7 H/ u3 E else' S1 _4 f! `5 ]+ k) z3 A$ H$ k
p2(1:J)=p1(1:J);5 i5 v/ h* C7 _- X
p2(J+1:I)=p1(I:-1:J+1);8 q# P0 E' N- _3 R0 i/ [3 Z+ [+ E* k0 E
p2(I+1:CityNum)=p1(I+1:CityNum);
' g5 S9 x' o6 H A+ x end
, }: F7 J) e; ?& P( M+ `
$ s/ ^2 v& ` s 六 遗传 算 法程序:7 U# ]3 {6 [$ f8 F: ^6 Z
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!
0 O8 \( v- S! x2 u7 Y, _
" i* `& v# D1 S7 g6 X& G4 ^ function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)6 {6 R6 X9 J( P# \3 ]9 j
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) 0 f& k1 b& D; c
% Finds a maximum of a function of several variables.
5 R4 r2 g# G, {7 H % fmaxga solves problems of the form:
2 O& J2 c. }! J# ?1 ]$ G) Y % max F(X) subject to: LB <= X <= UB 7 H' r! j( a0 b( N" h9 V3 V9 M% X
% BestPop - 最优的群体即为最优的染色体群, ?, N7 R/ y. F1 n3 t& c$ S- @
% Trace - 最佳染色体所对应的目标函数值* w& r0 O# x; |5 ]. Z( H: b
% FUN - 目标函数
, z7 h$ ?+ Q- m( f n+ Q4 e % LB - 自变量下限 `9 O9 a* l( k4 e$ Z1 u
% UB - 自变量上限
4 A' V- a7 o2 d % eranum - 种群的代数,取100--1000(默认200)
. m6 _9 K9 ^( m* w! U % popsize - 每一代种群的规模;此可取50--200(默认100)- X1 D$ o& a' d
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)' C- I0 C7 ^4 D9 D7 g7 i( w- I
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
" a5 ~; a, S7 n* K4 p! U % pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
; a1 H" ?( V, Y8 X# |3 r % options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
+ H- i! V* j1 Z0 [0 s* X* W- z %码,option(2)设定求解精度(默认1e-4)
% z% Q) J, a" ~' b8 T" ^7 W %
4 K- t( q) f; T4 L+ |* l, w; p9 u % ------------------------------------------------------------------------. u: Y$ P5 l1 `- U, N
+ J, y0 f; f6 u4 b3 j# Q T1=clock;9 H! k7 o- C1 b
if nargin<3, error('FMAXGA requires at least three input arguments'); end
3 ?, \7 N8 y$ ^4 p if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end- ?- F8 r3 z: \9 ?$ Y8 q
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
: G4 C* y) B$ y+ r if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end/ o: @ j1 y' D. J7 O
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end4 s, A1 g8 O4 I7 m" |# v
if nargin==7, pInversion=0.15;options=[0 1e-4];end
5 _0 Q+ J# @* }3 H5 T; Y if find((LB-UB)>0)
( a3 Z& E/ t# R: U1 k$ a error('数据输入错误,请重新输入(LB<UB):');
2 `0 D* K5 Z9 z( }$ D% y+ V; w end
* u) P* `: @9 Q, p: s! b s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
2 ?$ i9 s! Q9 }5 R disp(s);" o7 h Z# ]3 h. l
6 m8 U) N, [) D7 w( N/ W
global m n NewPop children1 children2 VarNum. y4 a# k. F1 v1 B
1 ^5 ~* K9 ^" L' v! i' h
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);0 w- F8 S' D& y; f, o; s
precision=options(2);%由求解精度确定二进制编码长度0 M. k+ `/ N' l* Y+ C
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
* u: {5 k& Z" f6 p( g4 e* m [Pop]=InitPopGray(popsize,bits);%初始化种群
- r; M5 @: t" _ [m,n]=size(Pop);$ V7 c/ e1 p" \, D7 `: Y
NewPop=zeros(m,n);
3 u+ L" a( W- U3 J( r$ ? children1=zeros(1,n);! R8 H- t, A! J ?
children2=zeros(1,n);4 f7 c' W w+ ]4 f
pm0=pMutation;
& t! f/ n2 A8 k; T) t# U4 q" \+ ? BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace1 b, Q. g# s; i( e
Trace=zeros(eranum,length(bits)+1);
, H; n: m# {1 K- A5 `- H4 ?$ p i=1;7 |9 P2 z( M. i9 I; F0 Y( N1 R5 V: k5 V
while i<=eranum
7 G% U: D' q; E) q; X7 q for j=1:m: U+ }# X; S# o& m- A/ b! E0 H
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
: ^& n8 e. Z: u- p) Y end
% B# b: t) y; \" s. H8 U! t I& J [MaxValue,Index]=max(value);* L' o& Y' [1 r+ n% ~4 b% u5 F2 }
BestPop(i,:)=Pop(Index,:);
6 L7 t: Y0 u8 i2 E% y' \ Trace(i,1)=MaxValue;6 k" F) C' o6 o
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);3 L2 U5 }* h4 ~% A: i/ q: {' G0 T
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
3 c" M( t/ Y8 ^" l0 j3 L1 |7 ]5 U; D [CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));- n4 m$ P9 W2 K) y: p6 ^
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率5 d. U+ Z& W4 v) h" I6 \
%round(unidrnd(eranum-i)/eranum)
, c! L2 z2 p+ e4 v* ~ [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
/ t! h5 l. a+ f/ [8 v [InversionPop]=Inversion(MutationPop,pInversion);%倒位
x, S/ V5 M: F2 ]$ Q' x9 S- @! ] Pop=InversionPop;%更新) ^! ?6 Q$ E" W- {3 [0 o
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
5 m( U+ g$ w, Z/ M %随着种群向前进化,逐步增大变异率至1/2交叉率
4 m f7 p) B$ N0 U8 |5 N: l& c p(i)=pMutation;
5 e2 L- o/ E* _ z i=i+1;- H2 [& e K7 g% V. |, D
end
4 h3 v6 P# p7 ~5 C3 a1 {$ W t=1:eranum;
! L0 i. D% c; K) ^0 D plot(t,Trace(:,1)');
7 R& H* ~# J- V 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)');" s2 E. e7 I! N
[MaxFval,I]=max(Trace(:,1));# i: G1 H+ x1 U `
X=Trace(I,(2:length(bits)+1));# v% K# j) V: p6 O
hold on; plot(I,MaxFval,'*');
, @. Y, M2 V5 m, V' n$ ?! ~ text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
% A0 D' ~1 T- s6 P 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,:)));& V/ u% t1 G; a) P8 s
disp(str1);
- i- i# X0 z- B %figure(2);plot(t,p);%绘制变异值增大过程
/ Q( X+ k% s' S1 }" O% o' C% l7 c T2=clock;
" ^/ {6 X1 j2 _ N6 ? elapsed_time=T2-T1;8 O& R7 l& _8 K& ~+ r: l) \2 V
if elapsed_time(6)<0
. L/ Y! t! q% u8 r2 j3 z K elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
E6 T/ ~2 L' H+ l% `5 t; v end/ z, W: B; H- d! |- k3 }
if elapsed_time(5)<0
0 O+ {% O; Y( a3 V elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
6 l T7 D- X) t end %像这种程序当然不考虑运行上小时啦
+ I# }% e. @6 a) d str2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));& {3 O( X( l6 a6 S
disp(str2);
9 ~$ N4 a |/ J# |- ` $ R$ ]4 ]' y# J- d
6 F5 R" y8 g/ i. W5 c %初始化种群
2 F# Y$ q# h3 P3 p! @ %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
: k9 D t" W/ R* d# F function [initpop]=InitPopGray(popsize,bits): R( m1 w) I) L6 Z
len=sum(bits);
0 M# c, o8 v# X7 p initpop=zeros(popsize,len);%The whole zero encoding individual) S6 d k: U6 w
for i=2:popsize-1
. F, d4 H o+ l4 }% ~0 P pop=round(rand(1,len));, W1 t/ r+ q" f3 v
pop=mod(([0 pop]+[pop 0]),2);
3 ]1 O; Z$ p7 U %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2), C, ~* Q( a$ i" x' }4 P# C% R: K# G
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)( ~. P! J% S& y$ |/ A, k; J/ Y
initpop(i,:)=pop(1:end-1);
7 j; L/ Z: o+ z. x end
- f$ ~2 X+ F1 Y! Z; W7 G1 L5 E initpop(popsize,:)=ones(1,len);%The whole one encoding individual
6 x, n; P. u, y %解码
. Z7 _8 O# C5 Y6 m5 V! H
6 o" S' o; u& Y% q/ p1 b9 i function [fval] = b2f(bval,bounds,bits)- G; j% w* I: e$ M) _% l! h
% fval - 表征各变量的十进制数( X* U# E8 C: J& p6 z8 I
% bval - 表征各变量的二进制编码串$ T s2 c: Q# s0 x$ }' n
% bounds - 各变量的取值范围
& P# v6 U, A* U% t* [. I % bits - 各变量的二进制编码长度
' O/ z6 k) B3 R7 d$ A: f scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
& D/ i" G) g, ?# Z7 A numV=size(bounds,1);5 f: I, |. s2 G( m+ L4 H
cs=[0 cumsum(bits)];
3 F; u8 f/ w P- b! g for i=1:numV
% @4 K2 H- a! W3 | w1 I/ F a=bval((cs(i)+1):cs(i+1));; m( S M! D* B8 E$ X3 E
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
) ?2 n7 v- h! l) Y5 N end4 y; W5 c: C6 x
%选择操作
, ?6 G) @8 ^1 G$ [ %采用基于轮盘赌法的非线性排名选择
2 m2 E- s0 A$ l %各个体成员按适应值从大到小分配选择概率:
6 [4 c' o: z' Q; o C %P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=10 M7 B6 L" T& b! h
) {1 `, J7 @' z' ] J function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)8 `) B/ X4 M- x8 }- \2 ?
global m n
; \# S. c/ a( F) w n8 d selectpop=zeros(m,n);
' a5 k' E( x3 h8 j fit=zeros(m,1);( r5 U) x5 A$ E: S' ~- F
for i=1:m
3 G7 D$ g+ H4 I, ^$ B3 x fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据9 G' d' I5 { c; {: ~# w2 E
end ]7 w6 V; W9 ~8 r
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
/ B" K+ u3 S2 o2 ?; c& V; e q=max(selectprob);%选择最优的概率+ Z$ C- ?4 ]# _* s& I6 Q
x=zeros(m,2);2 t9 d) i- s: ~/ s: f# ^
x(:,1)=[m:-1:1]';
& _* r% @. P# }# r6 L! ~$ x [y x(:,2)]=sort(selectprob);
1 V# K* b/ d9 B7 @* d3 F r=q/(1-(1-q)^m);%标准分布基值
4 C( V/ O3 C5 M7 l, ~: ] V newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
" J' v( n2 ~/ w5 R' n' J2 r newfit=cumsum(newfit);%计算各选择概率之和
8 f& V f7 `, ~$ q! Q$ `: j rNums=sort(rand(m,1));) X9 s+ d: x% Y) _/ |/ i5 `$ {
fitIn=1;newIn=1;5 ]- E& ^: `3 V7 P; m& {8 o) W5 i
while newIn<=m) ~! }1 ]" H4 d2 n
if rNums(newIn)<newfit(fitIn)% y1 x) Y" E! Q7 B! C: L
selectpop(newIn,:)=pop(fitIn,:);
! v: w6 L! [+ _5 M newIn=newIn+1;# a) y4 v! d+ M4 w) N
else+ [" Q) F; o2 M& O0 N1 f- H
fitIn=fitIn+1;
9 E2 l$ g$ Y5 Z- ^! g end7 b8 Y1 F& T. z" u8 y1 t2 d
end
/ c+ g/ {/ B: N' P& F& p %交叉操作
( {+ Z" \" @6 J6 @ function [NewPop]=CrossOver(OldPop,pCross,opts)
" Y" `5 K: d0 l+ X5 } %OldPop为父代种群,pcross为交叉概率. i8 M+ o# C# i0 M+ W* D
global m n NewPop
& f0 B: Y$ C8 O8 m) P/ e r=rand(1,m);; [% m4 o1 F: i2 N
y1=find(r<pCross);
5 W5 V6 ~/ v2 f/ n y2=find(r>=pCross);
/ I7 S9 o" f" O" v len=length(y1);; b6 Q9 I$ Z6 w8 h0 R
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4 z9 m1 Q) d/ X: D$ F" }; U
y2(length(y2)+1)=y1(len);
5 H e2 Q b9 ?. ^ y1(len)=[];
/ a$ l8 c# h4 X! u9 [5 a end
0 o: {9 c* e( a3 d6 M if length(y1)>=2
! c6 b: P) ^# J& q7 { c for i=0:2:length(y1)-2
l" c8 E! s( T7 Z if opts==03 F- b5 c. G9 n0 t3 X
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));, J& T( c8 N) Y# h$ A
else
: d) ^: K# Z0 |+ l; S: h6 @ [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));# h9 x7 T: D% U+ s" E5 o: \" S1 \
end) {7 d( `2 K, w3 h
end ! A. D8 Z4 `8 o: }' p
end
8 X( _+ }6 V! T) T7 z NewPop(y2,:)=OldPop(y2,:);
! D5 [' _/ J1 L8 c+ @
2 Q4 W Y: ^+ | %采用均匀交叉
2 x8 R$ v T5 R7 \ function [children1,children2]=EqualCrossOver(parent1,parent2)) j7 q! C) j! \5 @# j
) d) }5 w. T+ z! o2 H( x global n children1 children2 9 _! {, w. z9 l+ c+ _: Q. x
hidecode=round(rand(1,n));%随机生成掩码( @, i$ {* p! ~) p0 A! Y
crossposition=find(hidecode==1);- f; o8 u) X% I3 X1 v9 A
holdposition=find(hidecode==0);4 u" W* v3 D0 N& w
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因6 Q |# S& h2 q Z z
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因+ c L; O9 ?3 k" a7 j
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因' Q; V+ \: C& z2 V' H" L% S
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
0 Q, K8 z) b6 M! D6 f& C/ U9 F
, V9 ]# k% Z1 `. e# \ %采用多点交叉,交叉点数由变量数决定9 [' i3 [# N& o0 r6 E! r9 {! p9 p
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function [Children1,Children2]=MultiPointCross(Parent1,Parent2)6 d1 x1 c$ v) q
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global n Children1 Children2 VarNum
0 \$ ~9 l# G+ _ Children1=Parent1;: B! _7 n) r$ j
Children2=Parent2;
& P, R" P: {! O/ N2 t Points=sort(unidrnd(n,1,2*VarNum));
% A$ A g" j+ k7 @! n7 b: F( Z" }# v for i=1:VarNum
`/ z7 g8 x+ ?- X; S$ T Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
6 b1 s. r' ~! H m1 v) s Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
6 ~, C3 S3 H/ h% |' a4 K& ~ end
5 C: \0 a5 _% z# Z. a7 s4 }
8 I5 K9 Y. B0 S4 {$ C9 R* {6 J% \4 _ %变异操作
: w; q$ Q2 K, P4 P$ g: n! k4 A function [NewPop]=Mutation(OldPop,pMutation,VarNum)
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global m n NewPop+ g8 O) w+ v! m @* V4 T
r=rand(1,m);
" D& e7 h: y" B; k" z position=find(r<=pMutation);
2 H ^5 s( {& Y! V3 T1 @. x& a9 j len=length(position);
1 N( L8 M! F" ~, \: b' A' e2 X% H if len>=1
( B2 ]: E6 T0 T6 o# @9 M for i=1:len5 ?: ~/ g" R7 ` {
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
1 Z1 ~& Y9 X% H0 q* Z for j=1:length(k)0 \( t4 ^2 _% _" H2 {- j
if OldPop(position(i),k(j))==1
( i4 k& R% h0 K) o- U P3 R( y OldPop(position(i),k(j))=0;& b( a* v0 j6 [, @. ^0 A e
else
, A0 t& M6 \2 T( o) ]6 U( J OldPop(position(i),k(j))=1;
5 D% K" {! z# w4 w end
) Z4 I8 z5 E; A end
) _5 ^* x! j/ m6 s5 W& D( l5 e end
( _. ?# n) v0 J% D5 @ end
' k: h+ Y a" C6 y1 B, N5 Q- g- c NewPop=OldPop;7 }, I, N6 G: q
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%倒位操作
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function [NewPop]=Inversion(OldPop,pInversion), g2 z6 d, K6 G/ ?# ~
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global m n NewPop" @) M$ l( a9 M7 \- D' Z; a
NewPop=OldPop;' n' \5 B# j! E& V+ T1 m* O
r=rand(1,m);
. ?; i$ W, N( l3 g% B7 L5 Q# j$ ]- _2 v PopIn=find(r<=pInversion);
4 N j( ~5 H- R/ A1 a+ l len=length(PopIn);
' L2 L7 p# O/ h/ b4 i if len>=1. e9 F0 n% g# G* {& Y, j4 y' ?
for i=1:len
$ _: G7 A) f; m# Q/ ~2 ` d=sort(unidrnd(n,1,2));
+ F9 J" U% S- _0 y3 ^ if d(1)~=1&d(2)~=n
; u0 i: e8 }, U' r/ L5 F$ f NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);; e, `5 w, ^2 S. H6 q
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));/ `# P0 E' p- j7 o/ }
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);( }$ M8 T2 V) F. R& n2 p( g
end
3 g ~& i. X- U" s; ~ end9 D9 {' t& K' X8 p5 l
end
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七 径向基神经网络训练程序
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7 ]3 E4 y5 m4 v- @ clear all;
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%newrb 建立一个径向基函数神经网络
P a6 `' X* R4 i p=0:0.1:1; %输入矢量
( |/ t/ S3 j0 L, G% s' I1 ?7 T2 M t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量" f- m$ u! g5 B8 Q; |
goal=0.01; %误差
) t4 v& a9 u# q) J8 t" E0 M0 d: i sp=1; %扩展常数
9 u$ z; o0 y S6 M. j mn=100;%神经元的最多个数& T/ ~! E* Q" C
df=1; %训练过程的显示频率
& S8 C. n, f9 _/ p( ?- I0 H+ c) K; N4 n$ h [net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
- B* J! a8 }% v1 G % [net,tr]=train(net,p); %调用traingdm算法训练网络
1 I, d) b! U( y! N! a$ r %对网络进行仿真,并绘制样本数据和网络输出图形
" Y( x- i- n7 U; \ A=sim(net,p);
) z3 C" d* G3 S; d E=t-A;
/ F* B* n" j* F0 {2 o: }. J sse=sse(E);1 W- X4 n7 Q# H. i: T9 _
figure; 8 Z, r( V$ K" k' K" u
plot(p,t,'r-+',p,A,'b-*');/ g ~. n: u2 g* ?" w0 K0 Z
legend('输入数据曲线','训练输出曲线');5 G% z! U( y- W8 P2 E! Z8 K3 U
echo off
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说明:newrb函数本来 在创建新的网络的时候就进行了训练! k5 {8 K# ]! K/ j& k
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,/ _) _: P2 Y% m0 x9 v
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!0 M# H+ E8 E. @$ o* i6 C0 h$ u
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9 I) a' [* f/ j* Y/ T; F 训练结果显示:/ O' [ [! _, ?; F9 Q1 a2 H3 I E5 a# h! s
NEWRB, neurons = 0, SSE = 5.0973
2 Z) a0 x4 _6 o NEWRB, neurons = 2, SSE = 4.87139/ q8 S4 h% _8 g- l
NEWRB, neurons = 3, SSE = 3.61176
5 D. d" G! e5 p8 D/ R" J NEWRB, neurons = 4, SSE = 3.4875; Y+ z$ f+ L1 X6 B3 A9 X
NEWRB, neurons = 5, SSE = 0.534217' h5 _& |* X( C5 C5 \- j
NEWRB, neurons = 6, SSE = 0.51785
: ]6 Z0 T7 q' @ NEWRB, neurons = 7, SSE = 0.4342597 r: B) m* }2 Y5 l, b# i
NEWRB, neurons = 8, SSE = 0.3415188 [4 g6 n2 e! C
NEWRB, neurons = 9, SSE = 0.341519
7 ]0 G* Q. R" u6 b NEWRB, neurons = 10, SSE = 0.00257832+ Y0 m* K' X. N! F$ ~
. A. O3 z3 e- j 八 删除当前路径下所有的带后缀.asv的文件7 [; ~' U% X( r/ p7 _( w4 G: w
说明:该程序具有很好的移植性,用户可以根据自己地+ Q# M$ @3 L/ P( v0 ], q, a
要求修改程序,删除不同后缀类型的文件!
6 j( j2 g5 ?$ M" q: _1 ~( l function delete_asv(bpath)
0 [- M* I" ?" |" f8 ?8 t! E %If bpath is not specified,it lists all the asv files in the current% A1 q- n1 b: H e* Z, B& H
%directory and will delete all the file with asv
; j) h) d) o" T2 B' [" s % Example:
6 G* n! q- p/ G# ] % delete_asv('*.asv') will delete the file with name *.asv;9 o4 X" E2 o. ^- v
% delete_asv will delete all the file with .asv.
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if nargin < 1
( D+ h* u8 Z8 x0 v$ w% v8 } %list all the asv file in the current directory
2 o" o* m! H7 C9 g3 g: _# q& a% A8 X; p files=dir('*.asv');7 G% g: O9 ~" ~3 S4 X2 I4 i9 T3 _
else
9 }7 y/ {" ^9 ^% P* }: R. a % find the exact file in the path of bpath
& `" t4 h, i2 N& i3 n; i [pathstr,name] = fileparts(bpath);
0 r; `3 ?, y Y! |) x& e2 O if exist(bpath,'dir'). h1 i$ [6 C, j" \4 e
name = [name '\*'];
$ p, C. q6 S9 l/ t: \: T end
/ o7 i4 w9 H/ b. T: M ext = '.asv';
9 L: G# h5 Y1 e0 x1 i files=dir(fullfile(pathstr,[name ext]));, u( ?: x5 S6 h; S: b
end3 {4 R4 Y& A2 ~4 _; v
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if ~isempty(files)* f* L( Y3 s: q$ R6 F' @1 j# @# r
for i=1:size(files,1)
- _& X$ `5 z$ t- ~+ J title=files(i).name;
8 }( E- b' D+ X$ G5 t& r delete(title);$ q7 R* R5 Q O! h0 O
end
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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