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升级   48.42% TA的每日心情 | 开心 2016-11-7 00:15 |
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签到天数: 7 天 [LV.3]偶尔看看II
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一 基于均值生成函数时间序列预测算法程序
% h# Y5 y \6 E( G# O1 X' S) m- W1. predict_fun.m为主程序;
" i6 r& c/ i5 m0 w2. timeseries.m和 serie**pan.m为调用的子程序
% d' X) U2 r$ ^2 \% T, P$ | ^ t( y+ E( X4 d) ^7 }2 x% P
function ima_pre=predict_fun(b,step)
( V% R3 }- P* k% main program invokes timeseries.m and serie**pan.m3 a E G' {, u% H0 b
% input parameters:2 j( J2 D- ^: k% [' O- E
% b-------the training data (vector);
3 L' `: Q# K' v4 R5 M* k% step----number of prediction data;
V+ L9 f4 d# U" O4 P$ P% output parameters:
: A1 `# q8 |) c' |* s3 A3 U% ima_pre---the prediction data(vector);
/ _ Z" ]# A/ Q5 _" q3 p) {/ J: Kold_b=b;
5 A2 W) e4 I# y! a% J, tmean_b=sum(old_b)/length(old_b);
6 E) F5 I! |: w) Y( g9 u9 ]8 a+ bstd_b=std(old_b);
c1 K- ~3 P4 a2 Dold_b=(old_b-mean_b)/std_b;
! L, u8 O& N3 u$ g; ?! F2 \" c1 B[f,x]=timeseries(old_b);9 N% A4 ~2 I. h% X! | W
old_f2=serie**pan(old_b,step);7 V6 W9 C: Z [. x8 ^$ o
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;8 k. _2 s. z* x8 R. R8 S( `# {2 m
R=corrcoef(f);
" q3 i! i1 _0 M# _9 ?. q[eigvector eigroot]=eig(R);5 U1 @) r" B% i- M0 v# _; r
eigroot=diag(eigroot);1 q# x: O, S. F) s- K X9 [
a=eigroot(end:-1:1);
& G- N# h/ q+ i0 ~2 i8 V9 t. i) T' evector=eigvector(:,end:-1:1);/ e0 W" M' L2 D2 R; v/ ?( e
Devote=a./sum(a);9 Z; g4 F' h. H1 u I* D4 o
Devotem=cumsum(Devote);+ S4 c; M( G6 y5 [5 ~$ p
m=find(Devotem>=0.995);* d0 R9 L5 L! g; Q% L& W' ~
m=m(1);
6 G/ F! E; D2 d, B- X- {V1=f*eigvector';! F! J: R J- n$ _8 e1 Q
V=V1(:,1:m);
1 d2 i. V9 `; D8 @0 o3 W% old_b=old_b;) l6 ]2 t- S0 C! q" D. u: g
old_fai=inv(V'*V)*V'*old_b;# |1 T: a; T+ n* }" v, t
eigvector=eigvector(1:m,1:m);
! e3 Q2 G( l% yfai=eigvector*old_fai;- W9 L$ D8 c4 ]& u; Z9 e
f2=old_f2(:,1:m);: h; B- ]; L0 I) h
predictvalue=f2*fai;6 `. A7 E# D9 \" G# E0 v' x$ m
ima_pre=std_b*predictvalue+mean_b;
& N/ ?7 Y5 {: \/ L! \( K! \4 E- ?+ R7 L* B
1.子函数: timeseries.m 8 u% ~3 H3 Z2 j. Q& u) D5 G
% timeseries program%
' `2 `1 t6 ~, y7 ^5 k) E$ I% this program is used to generate mean value matrix f;: ~2 Y6 {) m; V/ @
function [f,x]=timeseries(data)
+ j1 D( p5 J* f$ @+ h& {" t% data--------the input sequence (vector);
' Z- t7 I: Y. S) c3 N% f------mean value matrix f;
- d$ d4 ^ E+ ?5 ~n=length(data);
6 y" L. D2 H( O% ffor L=1:n/2& T( e9 I D. P; W7 G- _5 R
nL=floor(n/L);
& }# Y2 H# J, H! H for i=1:L
, w5 B2 m$ \5 }+ P* | sum=0;
& a9 [6 E- X+ n: L for j=1:nL
7 I7 t u9 Y: |9 u' { sum=sum+data(i+(j-1)*L);
: r# Z* ] e" H: G7 s: r/ } end6 e( m9 [2 m% a& n w
x{L,i}=sum/nL;
6 [7 K+ q1 `" _- h end0 J |! F0 y0 e4 m
end
8 ^) T+ g+ t, L/ a* w* z% T" {$ W4 ^ FL=n/2;
6 D+ h, g) Z4 m0 Rf=zeros(n,L);
% s9 t9 G9 L5 I, n6 I6 _for i=1:L
9 s- \; v8 K! b( B6 a/ o rep=floor(n/i);
P. f8 k! K4 D5 } res=mod(n,i);4 u5 ] ]- w+ _ ~; |
b=[x{i,1:i}];b=b';
3 G, M% s. u2 A# x( S! ~ f(1:rep*i,i)=repmat(b,rep,1);4 X/ F0 `0 V3 _5 W5 |, R! x
if res~=0
# j1 I1 {8 q% i2 u4 m c=rep*i+1:n;
3 x* c" K1 [* j$ F: j9 ]! G f(rep*i+1:end,i)=b(1:length(c));5 I. t# F7 N! ]4 R% a
end
L! c/ w+ C# p, c6 vend
, S+ S" O; X) @/ [7 G
* b) U% j+ Q3 U4 N6 S' |1 W% serie**pan.m5 O4 a3 q# f! J. t; u
% the program is used to generate the prediction matrix f;
7 P! m x' {, J% o6 b6 Zfunction f=serie**pan(data,step);
3 D e0 {, O/ G+ V%data---- the input sequence (vector)5 K7 S6 E! D/ {6 M4 f
% setp---- the prediction number;6 ^$ j* Q2 B" j7 X+ a
n=length(data);
2 j. w# a. G+ ?) h2 T8 G7 j# G5 f0 Nfor L=1:n/2* H% F. \9 ^. o! r/ p- C
nL=floor(n/L);" l! H- M, v, b* m# r
for i=1:L! ^/ x* t. b Y( B; m' t) e
sum=0;
( Y8 R# K) A6 o) w! ~ U for j=1:nL7 W- y6 K9 T$ v2 e) n- c0 E" }6 z
sum=sum+data(i+(j-1)*L);
$ F" H( [5 l# ^ end9 u* f; O. i J, {) G: [: `" A
x{L,i}=sum/nL;
9 C1 c2 W5 c; h7 p) e) o/ |$ Z9 n end
& _! P% R3 w7 }. _* Aend
X/ I& U% T% E3 mL=n/2;6 A$ M( F3 u3 k$ Z& _/ D
f=zeros(n+step,L);
( ]0 O7 L0 {, h5 H. ^! N0 @for i=1:L
1 y9 y; V$ P, e) K2 I# j rep=floor((n+step)/i);- l% c! h3 U5 x- k
res=mod(n+step,i);& E9 D" `$ q7 }3 }) k7 T* W% P# r
b=[x{i,1:i}];b=b';
- J3 W: u$ L' w i f(1:rep*i,i)=repmat(b,rep,1);
4 o/ y7 x' D8 r- ]' m if res~=0) N" c+ b7 u+ \) O
c=rep*i+1:n+step;5 ~ d- O$ F1 z2 ?" d" M# P7 I t
f(rep*i+1:end,i)=b(1:length(c));% L4 v5 i" s. w% @
end m4 F5 ]/ K7 ~, u
end) H- W' I- g( Q# `2 q
5 [( O3 s2 `1 I. C3 z! i
二 最短路Dijkstra算法! o0 ]6 [" [2 y& }
% dijkstra algorithm code program%
3 E! g' m( a9 Q- p% the shortest path length algorithm4 p" s; h( k/ L' E. c
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)
, X4 c j. k5 J# F% z7 n) |) D$ C$ R% Input parameters:4 | [/ } K4 k0 G- _' L- l
% Input_weight-------the input node weight!
. {7 w7 w2 x3 j4 c% start--------the start node number;
7 h& |5 g: t1 r/ ~3 T4 K% endpoint------the end node number;* ^' t- Y# k. d( A
% Output parameters:
" C1 n% L) `( D4 z F) F% path-----the shortest lenght path from the start node to end node;4 n2 e ]+ C* G( d4 t
% short_distance------the distance of the shortest lenght path from the
1 O$ O( N+ j; D) w" o6 A% g5 |% start node to end node.
+ X6 q1 t1 s' W1 d[row,col]=size(Input_weight);4 Z( O# x4 P* ?9 Y) {! ^
4 J o) b) H& }& W) M, V, J( \) Y
%input detection/ z2 Z% v, K' H8 X
if row~=col1 L, j" T1 ?3 T! }) d
error('input matrix is not a square matrix,input error ' );
% c) V5 D0 i% q$ H; Q2 `end/ B" ^1 c2 S1 N9 G% E8 H
if endpoint>row# I% l. O! P9 U
error('input parameter endpoint exceed the maximal point number');) f Z) c' h7 u/ F) [
end; Z# x3 W, R1 M0 \% u
9 r1 m7 m7 E6 k2 M9 k- O% v5 l%initialization1 G* S3 Y3 u8 d; s6 T4 | Z
s_path=[start];) ~5 K7 w8 Q/ {' J8 w
distance=inf*ones(1,row);distance(start)=0;6 D/ L" s& h' Q0 w% z( h3 F" g! @7 ]6 y
flag(start)=start;temp=start;& v! U) C5 h& x$ }( i, @2 `
' Z6 |* A( {& q3 `" q2 R+ v
while length(s_path)<row" B0 t, f, x0 R0 @! r5 L
pos=find(Input_weight(temp, : )~=inf);
/ I, O8 J7 {4 b1 ]9 b7 u5 v R for i=1:length(pos)
) {8 n) A& c% F% V* G if (length(find(s_path==pos(i)))==0)&
0 l( O q1 A! R(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))8 }: |0 g) {" p- U3 t
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));" [2 A9 [0 x/ Z( j% k
flag(pos(i))=temp;
2 G7 }, {# N. z2 Z9 M; v9 A end
) s" D2 ], q, t1 d: ?2 d end) _- h* h5 v0 V! J
k=inf;
( F$ }4 Q/ p" K% R for i=1:row I$ [$ i# ~+ Z$ ]
if (length(find(s_path==i))==0)&(k>distance(i))4 Z) x' r+ ]9 _% _
k=distance(i);, c! X; V; P( k* v |; T
temp_2=i;
9 f3 A. Z0 m- c& T end
/ }/ Y5 n5 h6 E5 K% I7 T end7 y+ ~8 y- ^ t% n1 I3 n7 W
s_path=[s_path,temp_2];/ t5 A' L& H' N$ j" N
temp=temp_2;
+ V9 o0 x9 ]* w! [end
1 u; t3 ]8 R# ` ]$ c- ?9 Z/ @$ b2 V) ^
%output the result1 r. s- w& u8 @1 E7 K* o
path(1)=endpoint;
. ~" a0 Q$ z7 @3 R# ~% Si=1;" s. p3 d3 h, t) d8 G9 T
while path(i)~=start1 A3 A$ a+ O; l- l- c I
path(i+1)=flag(path(i));9 h# Z, @: o. w/ O* q/ i$ k
i=i+1;
& d( y) B/ L, x# bend
, x8 f. G4 |8 K) xpath(i)=start;
7 i2 h3 a; _3 h. c. B9 D# x; tpath=path(end:-1:1);: S& v c) X5 z/ f9 I" _: T1 w9 S
short_distance=distance(endpoint);6 t4 k2 `% l1 ?$ E: m
三 绘制差分方程的映射分叉图' n- n, e$ D; M3 X; s
: x+ {% T( A/ n# U3 y' Tfunction fork1(a); _8 {0 }6 T0 u& D3 v7 d1 C( I) q) i
7 c( F$ j7 J+ c+ F! U8 ^
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图3 s+ K( O, {% C9 B
% Example:
2 ~* y/ `# L' X# u, @% fork1([0,2]); / \* N; h/ _4 k4 Q% O5 p6 j
N=300; % 取样点数 8 J0 w5 e- E2 O+ j o# N2 |6 q
A=linspace(a(1),a(2),N); 2 k" d; A6 s3 x1 j- Y- A- @
starx=0.9; 4 z) a" U* i- k4 [
Z=[];$ r% Y4 u5 L$ O& B( P; H. k
h=waitbar(0,'please wait');m=1;. V0 n( ~. m7 e: w, \0 o9 G
for ap=A;
* l4 ]; |" y& W9 m% V k2 A x=starx; 6 }' g5 g6 R8 |" J5 o: d
for k=1:50;
: s2 i. ]# G: v6 ^7 x3 Q/ o( Z- c x=1-ap*x^2; 3 {; E2 f# O) S# a2 ^# B
end 8 Z; p, q! Z; S5 T8 n8 c
for k=1:201;
; O b8 V: @1 U# K1 O, H* B1 ` x=1-ap*x^2; 2 M$ `$ a/ ^. v4 W
Z=[Z,ap-x*i]; 0 m; @4 i# g9 [2 g) r* U
end
: e4 V+ D$ S! L$ f7 c, j waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
" Q, Q" Z4 u6 k m=m+1;
+ z2 W! P! t L& x' J$ Tend
( ^' U# i% O; H, n; T) Vdelete(h);. }& N' s% E# V% I4 l; a
plot(Z,'.','markersize',2) , X, C8 c3 v1 [. c' R
xlim(a); O! H e& u8 o' A1 o- ?3 X
C- |' v3 ]. W3 o
四 最短路算法------floyd算法4 G5 c5 W! J) ^0 [$ \
function ShortPath_floyd(w,start,terminal)
3 S" a9 m0 C( `, v+ K%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;, Z) y8 S6 ~ l! y
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];& g3 }4 n n) o6 U, R
%start-----the start node;
, E" x! U$ N7 C+ j$ A) y2 V7 Z%terminal--------the end node;
0 A: V1 F f! |2 ^7 l8 f3 tn=size(w,1);
9 P w& S: \: E9 c9 o# Z[D,path]=floyd1(w);%调用floyd算法程序
/ Q, p" M2 w) v8 `+ r1 c [ ]* M& L Y* Z7 z. o W0 o2 j D! {& [
%找出任意两点之间的最短路径,并输出% C' c/ i/ N/ Y- n; p4 ^
for i=1:n M3 l( j8 v* U( t; W: o
for j=1:n* P; a+ P7 V( P- `1 v) f* R: Y
Min_path(i,j).distance=D(i,j);. a5 o9 h e0 p% E0 e
%将i到j的最短路程赋值 Min_path(i,j).distance* \ l: j8 p+ u" E( e
%将i到j所经路径赋给Min_path(i,j).path2 c7 R) B- j, M1 d8 L6 S
Min_path(i,j).path(1)=i;$ h9 }1 ^8 O4 p
k=1;* y7 n5 r* C* E K* b' H/ h7 `! r
while Min_path(i,j).path(k)~=j
3 D/ S( g, I6 [5 O3 ~ k=k+1;( L$ n& I, ], r( A
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);4 h! n- D, u. P; _
end
?7 F! W0 Y! X5 l! `/ k end
5 X8 G0 e- r' hend
1 ] g" o8 L9 L, m6 k. Z' V" Zs=sprintf('任意两点之间的最短路径如下:');# ?) q0 M/ t. {! J9 D3 @$ `$ G
disp(s);9 x5 R7 a- S# A1 M
for i=1:n7 n h' q0 h- L2 n' n
for j=1:n& S$ E; W, o! S2 ~2 q
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...$ d0 U& `+ A# D* O; }
,i,j,Min_path(i,j).distance);
4 b( i9 \5 { x6 U. ~8 P disp(s);) B `& |" U" `$ a9 K
disp(Min_path(i,j).path);0 N; i. B. f; D9 P3 \3 X
end, s' G3 |, d7 @4 X
end
1 C/ `( u3 ]* n7 W4 C1 G. M, t) h8 D) p# n$ i* u7 l
%找出在指定从start点到terminal点的最短路径,并输出
" X+ m6 e* e6 m, P$ S8 Lstr1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...* v6 S/ f* E& b+ U4 m. f1 x
start,terminal,Min_path(start,terminal).distance);
# P. B! C, Y# Ydisp(str1);
2 d8 L7 b- F9 R+ C6 S( Tdisp(Min_path(start,terminal).path);
3 F: k: V7 y. z% {+ @
3 R6 }0 Q8 R8 v( o; ~%Foldy's Algorithm 算法程序" v8 ]8 d/ E4 c" V* n
function [D,path]=floyd1(a)
/ o. W0 ^8 A8 g. z3 c& ?: An=size(a,1);: H; A+ w* r \( J+ V
D=a;path=zeros(n,n);%设置D和path的初值
2 B5 L9 Q- R" }for i=1:n
/ Q( p* t' {* ]& P for j=1:n
2 M; Q8 d0 ?5 E( c! S if D(i,j)~=inf3 }: W7 |$ S0 S! F+ ]& h0 z
path(i,j)=j;%j是i的后点
L1 @# d# a9 \ end- R( h7 o1 ], h6 ?, L
end
/ B7 B! P% f7 V' n1 V) xend
; [: o# K* S/ M# L8 _7 p%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
/ a- t6 [+ C% V f7 r5 W, nfor k=1:n& Z! w9 a( X1 ^: H: y
for i=1:n
- O- I4 Q( i, z7 C5 u for j=1:n- e1 z. W. A5 b" [
if D(i,k)+D(k,j)<D(i,j)8 ^) }8 \; G: O
D(i,j)=D(i,k)+D(k,j);%修改长度
$ ]. B: z! O' d; d" o path(i,j)=path(i,k);%修改路径
7 q/ m6 y* l6 B, E1 v end
% h$ `: z3 k' V& w( ? end6 l$ j* J% P4 ~1 N
end7 B# I0 {# D; A' K
end& v- K0 ]: m( ]$ ^
1 n) \# g. _$ a2 e9 \五 模拟退火算法源程序
" O5 v+ n) x1 u/ [: p" zfunction [MinD,BestPath]=MainAneal(CityPosition,pn)
& i' i+ j, C' rfunction [MinD,BestPath]=MainAneal2(CityPosition,pn)
, u+ f' Q9 U+ u%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: u! k1 ]- s# S/ n' v
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...9 F! X2 A8 R U4 @
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
2 k7 f; ]' M% c% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
6 Y0 _0 U5 _2 [" @: r. q9 k7 q% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
( V# J0 O6 f& M( k5 t' F* {. Q% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];$ x4 N) j+ c9 S
T) r4 M& @ w/ A
%T0=clock
& Z4 Q) I! y- E. h# v" m5 \; bglobal path p2 D;
: ~: N- E; ]! a( a, w. T1 j[m,n]=size(CityPosition);- z, m J6 T o( j; }
%生成初始解空间,这样可以比逐步分配空间运行快一些
5 f) ]( S( [! B: }5 fTracePath=zeros(1e3,m);
5 y, V0 _ c* N2 sDistance=inf*zeros(1,1e3);
; s7 Q, |+ C. i, S( H- D5 r/ R' A% h4 n; J
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
! Y6 A+ N) \! G; N, H8 _" V' K6 R; G0 |( k (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );0 ~& i* G! H0 S" \
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)8 b2 _, c" i' B! Y. K; y, \4 t
for i=1:pn
8 }. l( C, J5 t q& D path(i,:)=randperm(m);%构造一个初始可行解$ M! P8 p6 o4 {/ S2 i2 n ^
end! W7 I9 z* L* Y( D% a
t=zeros(1,pn);# f+ t8 J" @( {% p' U8 h6 v
p2=zeros(1,m);; G/ j( ?) ]4 n9 T
. W( p: [0 A$ q
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
$ F3 t* U5 [3 g$ f/ pm_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=' ) ;# Y& g# D7 ?: w/ |* h# p
%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8 R: c! S$ X4 t
%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! Q- h" i- R; ?8 v u* k6 I8 ~
%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
7 U! x) C" s7 Z5 r%会收到到比较好的效果7 o0 S, H ^$ n; C
6 C3 G+ T6 V( N% F6 pT=1e5;3 V; \: n, F8 f9 h, k
N=1;$ |. N4 R' N u" C" L
tau=1e-5;%input('请输入最低温度tau=' );
5 ^, Z" a: N- g. ?! R" Q%nn=ceil(log10(tau/T)/log10(0.9));/ k" O# }& U% |7 a. t3 }
while T>=tau%&m_num<m_max
# p5 C" `/ ]8 K2 _% ] iter_num=1;%某固定温度下迭代计数器
3 [1 f g* N( [' y" E5 z% w% ? m_num=1;%某固定温度下目标函数值连续未改进次数计算器* l6 c: A# i" L
%iter_max=100;3 E. C! u1 W+ \6 Y# W
%m_max=10;%ceil(10+0.5*nn-0.3*N);
6 K, j7 i6 ~# S' N' a0 l! U# | while m_num<m_max&iter_num<iter_max
, M, D) Y6 K t0 i' z+ m( q3 D %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
$ Y" P: {, Y+ J" r3 B1 K$ q %用任意启发式算法在path的领域N(path)中找出新的更优解% C: z4 T! R p! |7 h
for i=1:pn: g1 s: d7 W8 H) y6 Q; g
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 {/ O% N, y* b# m" O%计算一次行遍所有城市的总路程 5 K& B9 F4 M5 w5 w, Z/ ^$ o
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线7 v* r2 o4 w- S; n9 n% q
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);" D# F. Q9 U; u/ a# ^
end
+ t8 G6 F( g% n5 d( L9 n. ^: | %Len1- S, g. {0 P, J" w2 E, [" g
%Len2- A I; ]* j! v
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
3 t& \! q+ `) O R=rand(1,pn);# h2 H. ~' \2 g2 A, e- D: X2 d
%Len2-Len1<t|exp((Len1-Len2)/(T))>R5 G. |7 ~8 Q+ o0 b! {( }
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)' y7 H, z2 }3 U3 H. }8 e5 b
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );( O( L$ O5 |8 ?$ P
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));% F3 L/ ]8 k5 z' H' O" Q
[TempMinD,TempIndex]=min(Len1);
5 o( A f: ]/ w' m& n* E- v %TempMinD9 @6 {# a" e' G D& B5 w9 g) b
TracePath(N,: )=path(TempIndex,: );
; f' ]9 Q) k' N Distance(N,: )=TempMinD;
/ C7 A r5 }! j N=N+1;
( q1 H( y M. [# s& g* G% g %T=T*0.9
- \2 p" S/ F+ k3 j" k" A# | m_num=0;
5 ^+ x/ M$ W# E; }# f0 X else6 U. r5 G' y e- k/ \+ i/ b9 ?
m_num=m_num+1;, [/ k5 X$ b2 r7 u
end
3 e7 T/ R/ i+ z3 ~* ~2 N iter_num=iter_num+1;* r5 F; {. z( W9 r% U9 Y
end
7 X; V% G9 }1 R5 H, D3 t) | T=T*0.97 {0 N& J! B4 x T3 h5 ]
%m_num,iter_num,N
" x) |" W4 m5 n2 h4 c/ Wend
- Z0 g7 H( i O% v9 b; X$ m) D H[MinD,Index]=min(Distance);
! o) E. R6 v1 M3 yBestPath=TracePath(Index,: );
+ s8 x% E4 u+ F, Z( i0 w, r$ xdisp(MinD)
4 T+ V, r- C Y3 b: y `1 u/ D# y%T1=clock& [) A6 t Y3 U$ [& a; c% p
$ [8 w, g- E) T) y9 j
X1 \( c( q% p5 j0 k
%更新路线子程序
$ b8 W1 ^! T+ O3 pfunction [p2]=ChangePath2(p1,CityNum)5 C' C/ x! W1 e9 B) e' Y5 w* U7 N# a
global p2;
3 x* z ?; `7 E* G' e& C$ l, Jwhile(1)4 U, v: {' u9 i/ z( Z5 l
R=unidrnd(CityNum,1,2);
1 j) c; U+ P1 N3 h/ ]+ h# `' p if abs(R(1)-R(2))>1
' |( Y& @7 R, j: w break;
8 L/ x9 P& `4 Y6 h) G+ i& {" H end5 G% Y5 P P1 B! a" j( ^
end; @) g# @3 i! ^
R=unidrnd(CityNum,1,2);3 j/ a$ |& R$ Y( S: H6 i/ ]* ~
I=R(1);J=R(2);# U% i0 {( M# R$ ^
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));& G1 f& f8 x- I" j: z& b
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));8 o$ e+ d% e7 ~% o& T
if I<J
2 h; }+ ~+ b/ P# l5 c p2(1:I)=p1(1:I);
7 m6 P" |% ]; [- Y$ K: N+ A! c! e p2(I+1:J)=p1(J:-1:I+1);
/ [5 P; c" \$ p$ n' m p2(J+1:CityNum)=p1(J+1:CityNum);
, u! N4 d/ L- e, nelse
& W& U$ C5 F, y" w% Y8 L' B p2(1:J)=p1(1:J);1 {3 B7 q2 q. l. ?+ v2 B
p2(J+1:I)=p1(I:-1:J+1);
: Q. f3 i) `7 @ p2(I+1:CityNum)=p1(I+1:CityNum);
0 X# g& {& ~5 c; o% {% Cend
0 L K7 K# o7 m8 m$ t) R) t- Y n& `
六 遗传 算 法程序:: d& \1 W# U* H4 a" }
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!
2 T7 A% G! b U# x* ^2 o/ B
7 d; y" N( G% V8 |/ z. F0 e; Nfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
( z/ u) v( h! F% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) " ~* G$ h. h4 H5 {4 _4 S. w8 e
% Finds a maximum of a function of several variables.
6 D8 c. d. R- j( Q% fmaxga solves problems of the form:
* k6 i' A+ s( t. V: w* ]& Y- T% max F(X) subject to: LB <= X <= UB
$ v- p" v7 j/ H q% M! F% BestPop - 最优的群体即为最优的染色体群
1 s0 g3 |5 d: t d. L% Trace - 最佳染色体所对应的目标函数值5 r5 a, i6 u5 I* l
% FUN - 目标函数
/ h& ~6 d) S7 a* D! F; K% LB - 自变量下限
- \8 K7 T2 f3 W( D* h" K: u$ N+ `6 u% UB - 自变量上限/ J6 Z0 R6 }4 W5 N: P6 ?: A# ?
% eranum - 种群的代数,取100--1000(默认200)- L! R0 r6 c6 N- t5 `
% popsize - 每一代种群的规模;此可取50--200(默认100)
3 m u: p$ ~8 x% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)" ]& a5 P" w! X* E* ~1 S8 s* l+ l
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)7 O& m+ C# q% N2 P* P- n! Q9 @- m
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
7 l) K# v) n$ ]2 q- }/ a% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
5 [ F+ T: v% p# N/ r9 e%码,option(2)设定求解精度(默认1e-4)7 j, y4 ~6 D2 G
%. k. u; L1 z" o- ?( s# \
% ------------------------------------------------------------------------
: p$ h9 v* q3 c, \' A- M5 ^/ _; H% Y' z% j5 I' v1 W9 u
T1=clock;
. l ^% z7 t" g9 S2 A1 e1 b7 uif nargin<3, error('FMAXGA requires at least three input arguments'); end
. c, k' t$ F) Y9 b' V" Oif nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end& b! w1 s- Q3 H
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
% x- z) j0 l2 }1 o2 \if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
* f6 m2 X2 F' M; h% ~if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end1 Y2 X/ H% |( `1 B% Q8 A
if nargin==7, pInversion=0.15;options=[0 1e-4];end6 V0 T3 W% P9 r2 u# X. D) s
if find((LB-UB)>0) G- h8 I3 a5 e; t
error('数据输入错误,请重新输入(LB<UB):');- K9 \, S9 h: w6 R
end
/ Q X. W% o4 i# V/ ts=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
8 p9 ?4 r% h& Ldisp(s);
! ^. q( k" c1 Q. u: a: m' K) C( K) L E- b% Z' p' @7 x
global m n NewPop children1 children2 VarNum
! k {+ b+ o: P. v5 ^4 N8 z. p; [- `1 h4 s6 o7 a1 N
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);9 l, ^$ j& z9 Y3 ]7 _
precision=options(2);%由求解精度确定二进制编码长度7 u: N! M, z* T4 j* w8 r0 i5 Y
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
9 |1 I4 A! W1 S7 T/ d* m[Pop]=InitPopGray(popsize,bits);%初始化种群: g0 z3 K' r* P/ T) F
[m,n]=size(Pop);
' }+ F& `& S* m! Z1 G1 b! cNewPop=zeros(m,n);& x6 n% E7 |: k. g
children1=zeros(1,n);3 E: R4 J4 R: w4 S: ~2 E4 X
children2=zeros(1,n);9 @+ O5 N! Y2 }* g% e' D0 c* p' C
pm0=pMutation;
$ H0 w8 }+ A; R+ jBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
+ e, W( A5 k0 P1 sTrace=zeros(eranum,length(bits)+1);5 J1 ?' U3 w0 W' H6 ^( E1 Y/ z
i=1;) V$ Z+ _$ P8 k+ H. G
while i<=eranum
+ ]. Z+ S) k! o for j=1:m
) D; {* b' [% B. ` value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度, G q( e. I+ e
end5 `! }! @! s- h. z. I8 E8 [+ h9 Z
[MaxValue,Index]=max(value);2 e: a) d A! \: U
BestPop(i,:)=Pop(Index,:);
# {$ ~3 e0 W; r) n# i Trace(i,1)=MaxValue;
; Y5 _& K7 U. z/ {6 f) a Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);5 ]* ^3 r" h' C/ L! d( m& M7 `
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
& T6 R1 i/ [0 q. x$ S+ M% L[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));8 g( k4 `+ L5 i/ T, G
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
6 a% B: {4 m3 q$ c5 u %round(unidrnd(eranum-i)/eranum)
3 d+ `1 ^" x1 V2 p9 D! c. ] [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
l. i9 R, q. [* o3 x2 d3 ~ [InversionPop]=Inversion(MutationPop,pInversion);%倒位9 E* H" z- P) h7 F( G
Pop=InversionPop;%更新2 a7 o _$ d0 m$ P) M, z
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); ! b+ S' p3 ^# |3 O3 C" s8 a$ K7 A' W
%随着种群向前进化,逐步增大变异率至1/2交叉率
( V* E! g% E# M; a/ j8 s p(i)=pMutation;4 ]) C: Z& @/ b2 I
i=i+1;
) z7 T. f: ]0 _0 m; l- g+ eend3 N+ A3 Z( `5 j
t=1:eranum;6 O( c t3 ]: |% P) {' k2 U
plot(t,Trace(:,1)');
# h8 `5 L# \; ytitle('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)');; ]. ]" b& E9 H- E6 Y
[MaxFval,I]=max(Trace(:,1));: z: `9 ]6 K" n$ G9 }
X=Trace(I,(2:length(bits)+1));
o: i0 T T2 Dhold on; plot(I,MaxFval,'*');
& I/ i3 W8 q1 b: `# U. _text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
/ L& Y5 `4 S# Z: Qstr1=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,:)));' n/ Q, `. D7 v7 k
disp(str1);
2 e$ p3 b' O4 _. b% k! L%figure(2);plot(t,p);%绘制变异值增大过程' }) A# H3 L8 G4 y9 I6 S3 M8 B
T2=clock;( M: S o1 R! y, e0 {: y
elapsed_time=T2-T1;
U& G3 P% x. d! C$ ]if elapsed_time(6)<0
2 B3 r X) j+ e4 c8 V% N) g: Z+ J elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
3 L' i! F( t" @2 Y4 K. }end8 n* l/ h0 ~! S' ]/ }* d- Y
if elapsed_time(5)<0
6 L" N: N _8 R elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;1 C& ^9 i- Q( y) e/ {
end %像这种程序当然不考虑运行上小时啦
+ n; h4 ]" \; p8 E/ Pstr2=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 P" G% a. I& O; x
disp(str2);. q+ z, R1 y$ }0 o: ]- F3 r
' v& \* P/ M; }) S0 p* \ u
% k$ h, C* ~- H0 o%初始化种群
+ j% Z1 Q7 p/ h. t%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
* X, i! ^) ?) ?. f8 u9 o% T& wfunction [initpop]=InitPopGray(popsize,bits)
- Z! f* \, Z1 f5 [3 Hlen=sum(bits);6 V9 Q1 _/ ~7 H4 s
initpop=zeros(popsize,len);%The whole zero encoding individual
7 i: \1 T: T2 q) f7 V9 l* e9 \for i=2:popsize-1
: H. b0 P9 ] }+ s& P- Y) z# t! @. l pop=round(rand(1,len));
* E$ @) O% U" P8 `2 r pop=mod(([0 pop]+[pop 0]),2);
, O0 V4 }$ M, L {6 H %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2), ~8 k1 J5 `* h% B
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
6 ~( Z& G8 L# j' v initpop(i,:)=pop(1:end-1);1 _5 b( ]4 X& B3 X. e& D' Y! B: ]
end6 `# ^" t5 g- o; L; v
initpop(popsize,:)=ones(1,len);%The whole one encoding individual) |# O% D, F$ K( [ m
%解码+ ^+ _4 P: p) H1 \! e4 t0 `
! D, s3 i' M4 u% U0 {
function [fval] = b2f(bval,bounds,bits)
% M( a5 M9 v$ Q( A) ^8 M0 P" L% fval - 表征各变量的十进制数* G- \8 I) V8 d8 ^
% bval - 表征各变量的二进制编码串; [+ e5 S W5 a! E! h9 I5 O$ ]
% bounds - 各变量的取值范围
+ W/ g' R. ?6 Z( D) O% bits - 各变量的二进制编码长度# k% q/ D f, J) J4 A4 I, q
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
. X, f% f; M! l/ Q( l. EnumV=size(bounds,1);
9 [6 `9 H" @3 r; N! b5 }cs=[0 cumsum(bits)];
/ S7 ^8 b6 o( U$ N4 f# z9 hfor i=1:numV4 H6 C8 F) k# {& h& x9 M i- ` K
a=bval((cs(i)+1):cs(i+1));0 n- S. s; H% ]7 ]6 {1 g! r
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
. A+ n4 s D8 gend
8 N( _; I: O) y% v6 w+ E6 `. |%选择操作% {9 V7 M- k0 b: G4 T# E
%采用基于轮盘赌法的非线性排名选择9 i+ L Z4 ~3 f( j; H
%各个体成员按适应值从大到小分配选择概率:
9 ]1 c3 H$ z( n/ `' S/ M%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1( d/ G$ S, G& L
* Z" i7 O5 v& M, H5 p6 N9 G' l
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
/ j# R4 P4 A# o$ Y' lglobal m n8 O' Q2 D( l+ F+ }
selectpop=zeros(m,n);$ l4 N& l9 E1 E: r1 _) Z& \
fit=zeros(m,1);& u* m5 c9 S- ]6 W+ p- E& Q
for i=1:m2 z% r2 [ c4 D$ [- K
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
7 y: p0 `. O0 Tend
6 F! P/ D+ \; L4 H5 gselectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
2 ]4 m- q( ?8 r( I6 M' \9 W/ Nq=max(selectprob);%选择最优的概率
; H* B2 ? E3 Yx=zeros(m,2);, r8 ^1 [; k5 L. s6 V
x(:,1)=[m:-1:1]';
" Y2 V7 a$ w! M" J[y x(:,2)]=sort(selectprob);
g2 R9 l! f) s/ b/ {$ @. s- E! Y, gr=q/(1-(1-q)^m);%标准分布基值
: B4 A) _" X8 T+ ?; ]% nnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
" J U) V4 n, e% V0 S# \6 Y6 a' Enewfit=cumsum(newfit);%计算各选择概率之和
1 v" W/ i8 `4 g" F- BrNums=sort(rand(m,1));& g5 f+ s0 ^' W6 i
fitIn=1;newIn=1;
/ i4 j0 q* _0 R" }6 bwhile newIn<=m# B8 I# h4 Q7 Y- |3 g/ x6 w+ l
if rNums(newIn)<newfit(fitIn)
& n- |5 H) r8 o# ?; h9 O4 V selectpop(newIn,:)=pop(fitIn,:);& h/ d* B7 Q1 E# \& f9 T- M- `4 F4 V z) c
newIn=newIn+1;
' m' `% U R) p5 S' v, p" U else& x9 _0 i6 Z5 c+ m. ^: z
fitIn=fitIn+1;/ a; L$ b, N4 V5 W
end
# Z5 [' x v$ y' L0 r& a) h. [5 Vend! a1 L( ]9 t; [
%交叉操作
- q4 N q. k( x# I# ]function [NewPop]=CrossOver(OldPop,pCross,opts)7 k; I2 M$ j$ `0 r0 ]6 _
%OldPop为父代种群,pcross为交叉概率
. F& X! ?" i& a! ` J7 rglobal m n NewPop - @' G: Q% H! W( o% r4 q
r=rand(1,m);0 s2 b- g P6 b9 m( t) U. D. i
y1=find(r<pCross);% ?; `$ `7 k6 X( \2 f5 T# I
y2=find(r>=pCross);
3 J% x5 [& \6 l; f* c3 elen=length(y1);4 m, m' V+ z$ N. I; i& d% Y
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0 K$ D) j- z( |
y2(length(y2)+1)=y1(len);+ b& N5 A( w/ Q i5 r! h
y1(len)=[];8 t c9 j4 x c0 G+ x B: k) S1 r! @* n
end( N7 [$ H# z8 Q: }, b
if length(y1)>=2
7 d/ m4 `- T' E! n) h# s/ q for i=0:2:length(y1)-2' ]5 A; _5 H( `: _3 w- r( Q$ y
if opts==0
3 u. |* y2 h6 \% F2 m ^ [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
5 I: ^* G7 f5 c else
/ J5 X" W9 w0 H3 l9 A [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));# i0 j' ]- c% {5 q6 o5 ]) D
end; e- A- }5 M9 a' Z/ `. v1 w
end
1 c8 Q7 y! h7 k/ cend- m, A. K% t$ |9 v% d. r6 I: h- D Z
NewPop(y2,:)=OldPop(y2,:);
+ Q- r3 W& Y( V5 A- T( t" C/ D& p- u8 J- H
%采用均匀交叉 8 j. l, t7 p/ q
function [children1,children2]=EqualCrossOver(parent1,parent2)
4 p3 `4 g* C; ?3 o0 S3 d( q% ?, |) D. V4 b
global n children1 children2 " u f. b; f* a6 G8 t# V# }7 M0 c
hidecode=round(rand(1,n));%随机生成掩码! \2 f- d. }9 P! r4 [& H
crossposition=find(hidecode==1);2 D+ O$ A" S" ~. [& {: G1 |) R
holdposition=find(hidecode==0);8 K* c+ n2 L( ~, `; K
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
^' {+ v5 D4 F3 n/ n* i7 p) N% Rchildren1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
! r$ l2 c3 t4 s% m! J# Z) }$ ~children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因+ u% }: @+ `$ C% Y
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
3 Q ]+ |9 h1 p% }5 g
! ?9 N0 X+ o) x# _- }4 ?# O%采用多点交叉,交叉点数由变量数决定7 G$ k; H$ L7 ]2 a8 b
' c- S% O$ T, J+ l" I- e: Tfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)" K6 Q$ @) s& j, l; g
; r5 D& ~+ R0 z F, O6 Qglobal n Children1 Children2 VarNum+ T) }0 y8 M( \3 i! b- T, W) i/ h/ c
Children1=Parent1;5 W& z1 |3 x# U4 Z
Children2=Parent2;
, I5 d# @3 L' x e: m- _: ^# nPoints=sort(unidrnd(n,1,2*VarNum));
8 {5 u; Y y8 ~2 o _. xfor i=1:VarNum0 H' C* {4 i# K$ T' ?: Q9 U8 Y' |
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));' e$ e5 z( i% v7 U3 F# [8 x3 Z
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
8 ?; O% z; Y: Dend3 l5 I7 l+ w# w4 o4 c
7 Q3 E; {: I# h0 u%变异操作$ U t o. D |9 L9 U9 U
function [NewPop]=Mutation(OldPop,pMutation,VarNum)' T. S) r$ H# T( `/ x
( q& w' B9 {8 S9 x
global m n NewPop
$ _( _1 D1 O) ?$ {9 e, ur=rand(1,m);
: X; s2 l5 `% T6 ^position=find(r<=pMutation);
. d+ k/ W L: k$ y3 flen=length(position);
* Z* p' }1 u/ }+ O) a# {& aif len>=1
1 s6 W) X0 e, ?( x3 [6 q for i=1:len0 M/ b- u- }# a7 B
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点8 M* [1 K* {) u8 p5 l; t, \
for j=1:length(k)4 N& t0 U% ?' z- ]1 y. Z
if OldPop(position(i),k(j))==1! _. n. u4 O$ L/ i
OldPop(position(i),k(j))=0;
8 k* P* ]9 H. k+ L0 e else& h; Y" t$ U+ f2 k1 K
OldPop(position(i),k(j))=1;: Q1 V2 _0 T& p$ n) \: x6 y9 `
end
8 V! o* k" p0 ^4 j end9 _* |5 Y) @% [- ^' Q3 S1 a, @
end
, l s3 A2 C0 E3 o6 ~; u0 fend
0 H/ b5 B1 | h9 W3 y$ M F8 wNewPop=OldPop;
" a8 }7 F( X: p' \9 a9 z- {7 H0 n0 m w3 j- Y
%倒位操作5 Y- |8 p8 e. }) @3 ^# V
" a# n6 z' |$ J. Jfunction [NewPop]=Inversion(OldPop,pInversion); `* n1 g7 b) G, l4 m, A2 F
0 D6 t C" v/ v& L- X5 }- Z: I. C4 D9 Lglobal m n NewPop; j0 a ~" L0 R
NewPop=OldPop;5 v& ] j3 I9 w( O0 G
r=rand(1,m);! A' G/ A" [0 Q3 m3 a @4 C& Q/ @" f
PopIn=find(r<=pInversion);3 {1 A/ V- T5 k! H* c( w' Q
len=length(PopIn);
6 t0 [: l" X1 Y$ q3 P% Pif len>=1
* p. Y/ E# j8 p for i=1:len
$ P4 q- b* l I6 t d=sort(unidrnd(n,1,2));
2 h' N; q) g! s5 {( e if d(1)~=1&d(2)~=n
# E# w! O8 `2 Q0 p0 V. V NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);( R" R- y$ i# ?( K. |& U" d1 A
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
- K8 O" _8 O- j NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
7 V9 r1 c4 g/ f! _ end
% ~0 E: R" N0 l end8 j4 r& }5 A: }6 n( A% x8 _% }
end
) p" l( H* d' A& r
0 I# G3 {3 d% | C/ t$ ~七 径向基神经网络训练程序& q. G, s2 F g% O) G" D
s' K. C9 R# qclear all;" [( F8 h% r$ {* m4 Z9 ~
clc;6 Z* `+ c' z e5 s- z9 |
%newrb 建立一个径向基函数神经网络: [2 c: l$ e( @, B- m1 T
p=0:0.1:1; %输入矢量
% ^' w3 U6 s; J/ r. tt=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
3 L! q5 t7 N0 ?" N/ k0 A( D Sgoal=0.01; %误差
' e' [$ b, x2 ]: k4 [5 l7 k; tsp=1; %扩展常数
$ K4 R$ q/ J) l7 [& Z6 @; Bmn=100;%神经元的最多个数! [% ?8 _) M5 U$ z0 g5 h
df=1; %训练过程的显示频率
- M8 g* O4 s/ v: Z S& E% i2 m! D+ C% f[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络1 t' Z& p; P$ I
% [net,tr]=train(net,p); %调用traingdm算法训练网络 O) I3 n9 J7 [8 Z& r! ?, w( T) i( S# Z5 y
%对网络进行仿真,并绘制样本数据和网络输出图形
7 p% t3 r% V& AA=sim(net,p);2 N$ q& ~9 m9 Q) D' G5 P
E=t-A;
+ D! O2 A1 w! S! _! Psse=sse(E);
" e7 ^: x! w" L+ H. x( ~- I4 Sfigure;
+ _9 i0 ~2 T/ y; U( yplot(p,t,'r-+',p,A,'b-*');
8 f- p1 X% A2 T5 ^6 @$ ^: M0 E% mlegend('输入数据曲线','训练输出曲线');. p% T* p, G0 }9 d/ Y: u
echo off
$ G+ O+ u. v& n+ ?& a4 _2 |5 E( _. \3 w
说明:newrb函数本来 在创建新的网络的时候就进行了训练!+ v- g$ g8 z# s
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,* N) t; T& G! w+ c% n5 u* d* q
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!) n7 T' P" p R+ E0 g5 ^# `( B
! V0 T9 ]: ?+ E9 ~
8 H" V) j, R9 Y+ |3 R _& b! v训练结果显示:2 w0 B- z6 q% l7 G6 x5 W8 @
NEWRB, neurons = 0, SSE = 5.09737 U! A$ `2 B; K
NEWRB, neurons = 2, SSE = 4.87139$ w# I6 n% V' {% ^! v
NEWRB, neurons = 3, SSE = 3.61176. P4 A8 d$ [7 M6 r5 M2 `3 z
NEWRB, neurons = 4, SSE = 3.4875
5 o* Z' k b3 u1 ] h5 pNEWRB, neurons = 5, SSE = 0.534217
8 k! i$ g4 p% LNEWRB, neurons = 6, SSE = 0.51785
( v3 ]# S3 l! Y- \' X; _6 ONEWRB, neurons = 7, SSE = 0.434259
4 a/ K# X8 S) k" NNEWRB, neurons = 8, SSE = 0.341518
+ n8 a( l8 G# @; DNEWRB, neurons = 9, SSE = 0.341519
6 B3 T4 y9 t# hNEWRB, neurons = 10, SSE = 0.00257832
; ?; h8 f" M* _# h& } L8 h' q. p% y1 w$ q. D, t' l
八 删除当前路径下所有的带后缀.asv的文件
% N$ U4 t7 {0 Z说明:该程序具有很好的移植性,用户可以根据自己地1 E0 \7 o) ^5 `' H
要求修改程序,删除不同后缀类型的文件! ' x2 s% f# p6 P* r* L
function delete_asv(bpath)
: g) ^% p' b5 f( `' ^%If bpath is not specified,it lists all the asv files in the current
3 p$ F2 k. k! H%directory and will delete all the file with asv
8 s+ A5 [# e/ o. j" \ [) o/ |# F% B% Example:9 i6 Z) b- t" W9 O6 n2 z# K
% delete_asv('*.asv') will delete the file with name *.asv;
4 T4 L( e) B [- i; @% delete_asv will delete all the file with .asv.
: N/ b& m3 Y n* j+ r4 }8 y( k7 p* z1 A7 V& z
if nargin < 1
! z! Q5 B! N5 H6 p. A9 v; k%list all the asv file in the current directory& L/ i9 ]; M9 e
files=dir('*.asv');
6 q2 r, u; Q q7 E) ^else
h) ^2 _; k$ A$ ^ D% find the exact file in the path of bpath
: ]& p# D: h5 K6 U. Z [pathstr,name] = fileparts(bpath);: }7 q5 ] K, W
if exist(bpath,'dir')& M: x( j/ m) |9 f) k; J6 f1 z( h. i' p
name = [name '\*'];
$ `6 a3 }) F# R3 g' h0 w end
J( N! U1 M8 t* \: n ext = '.asv';2 h! J: i; I3 F( b+ @4 I
files=dir(fullfile(pathstr,[name ext]));) R# g! {. g* D# u: h7 ]
end
3 X3 i0 z4 i* w/ {2 e/ h& h" v5 P2 F& h; C5 a1 Y
if ~isempty(files): \0 r+ J u6 ?, c; i
for i=1:size(files,1)
) N- v+ |& }0 d6 J6 r5 A title=files(i).name;7 a7 |* Y( p& Q6 c
delete(title);- S" }) M: E: w/ [8 P
end
% d9 ^4 @ F u( mend) j ^# e' K2 r' O, Z; A/ W
' j, N$ C. x# a, z& p* l
' L% E4 p# S( g1 R2 Z+ t% N0 z' e同样也可以在Matlab的窗口设置中取消保存.asv文件!5 a+ j& a- H" } E4 F K4 v& B
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