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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
- m- o, q# i4 X- s9 @# A8 b 1. predict_fun.m为主程序;3 H9 t/ {/ i: s9 x5 B( \
2. timeseries.m和 serie**pan.m为调用的子程序' l- @9 B6 W- I6 `
1 E# O' u; C8 e+ B4 E' C
function ima_pre=predict_fun(b,step)/ w3 H4 X0 f- |! Z: W
% main program invokes timeseries.m and serie**pan.m
7 U% w6 ?$ {5 A7 L7 u# W O9 h % input parameters:1 F+ ^/ j& u; \0 y
% b-------the training data (vector);
! W( F$ {& u" S8 I % step----number of prediction data;
" n) J% s- J6 k$ H1 }, k4 s % output parameters:
* U# e0 u# ]9 N, i1 C0 z % ima_pre---the prediction data(vector);
5 d' A$ m( h# V" v+ J# g2 v0 g old_b=b;) {* B( C9 s0 `, I
mean_b=sum(old_b)/length(old_b);% _: S8 t8 N' F I( e& m* ?+ h
std_b=std(old_b);
5 l8 [" [7 g( F# `+ z old_b=(old_b-mean_b)/std_b;
. R) { l, E D; p! A9 k: E [f,x]=timeseries(old_b);
0 z( S1 z8 v0 ?: b; I4 B& t$ } old_f2=serie**pan(old_b,step);
3 ~, M" M& z! I9 q, F0 o % f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;1 F8 v8 L5 Q1 x8 t% z |" t8 d
R=corrcoef(f);* D2 X) ~2 Z8 R/ n- ^, B
[eigvector eigroot]=eig(R);
5 B, K) ]& u" K5 J) B- s3 n0 G1 i eigroot=diag(eigroot);
8 z1 X, d" _0 E4 K6 @- r5 M# Z0 e O a=eigroot(end:-1:1);
% |: g/ p& X2 h' M" S$ ~% J" g vector=eigvector(:,end:-1:1);
; E& A" G2 c, k+ y7 c1 v4 R Devote=a./sum(a);- C1 T1 V" V" ~0 r6 `8 A' x
Devotem=cumsum(Devote);
% W4 F) t l9 v$ ^ m=find(Devotem>=0.995);
4 h: |! c, _* ?1 s m=m(1);: z' B+ w1 |) i& j
V1=f*eigvector';5 G7 j- O5 A. Q; D5 m, p5 ~
V=V1(:,1:m);% l/ h0 B7 p- O4 @0 k
% old_b=old_b; L! O- V0 r* F0 W* m
old_fai=inv(V'*V)*V'*old_b;8 x: o: ~; A5 r# H
eigvector=eigvector(1:m,1:m);
6 J4 G% k6 A; L fai=eigvector*old_fai;
, H" E2 }6 z5 | f2=old_f2(:,1:m);$ ]+ z' s$ q/ z2 F8 _) W3 x
predictvalue=f2*fai;
$ d' T, g; J1 ?: L$ @ ima_pre=std_b*predictvalue+mean_b;
% Q h$ v7 ]& K9 s: v' u$ h0 z , \" p" p. n- r4 Z
1.子函数: timeseries.m : `7 Y# i+ ?6 S+ v, _( Z
% timeseries program%
; C! H) r7 y, ~4 H- k1 ] % this program is used to generate mean value matrix f;
( w0 P5 h9 y: c: H; @ function [f,x]=timeseries(data)
6 E4 ]' q p8 d+ \9 d6 k % data--------the input sequence (vector);, t K6 x' X6 d/ U0 J
% f------mean value matrix f;. \" j, l; t; z2 ^0 D! f. e
n=length(data);$ B7 Z6 k9 F! x- ]8 f- d
for L=1:n/2+ k% m; I8 V6 d3 V P5 i/ t
nL=floor(n/L);
/ ~) i; W- z3 @6 W& O1 W: ] for i=1:L8 ^$ B7 P5 a" _4 J( S5 q7 y0 l
sum=0;0 z5 _. e; A V" x* e; u
for j=1:nL% L5 C! y/ x8 O) f# O/ e3 n; z) ^
sum=sum+data(i+(j-1)*L);. M; B& m! Z5 ?; n1 x
end; V* X2 m: p$ R1 W" Z7 u! a9 c
x{L,i}=sum/nL;+ p( @3 B: y2 ?7 N
end
! x; n ^: M3 ^) G0 Z8 B8 P end( R+ S7 a9 t" A; g6 b; v
L=n/2;
( _3 ? Z5 t; w3 ]0 n' Y f=zeros(n,L);
# R( S1 o4 g% z+ o6 | C" v7 n for i=1:L4 H% j' k& p+ {7 T; y9 x& N
rep=floor(n/i);
7 q( Z! ~* z% v& B; r( _$ E4 Z res=mod(n,i);
1 D; O& t! C# k& i2 m V b=[x{i,1:i}];b=b';
- L4 Y) w& a9 Z f(1:rep*i,i)=repmat(b,rep,1);
3 `" ?0 k6 \& _; g$ Z7 B& |$ H! V if res~=0
5 R0 x3 Y/ Y' D y3 f; R c=rep*i+1:n;7 L: l/ x, c* x* @: U3 x
f(rep*i+1:end,i)=b(1:length(c));
2 v% u+ u' Q* A, y- a" B1 w1 H end) s1 ^: s/ T3 Z/ P2 O3 z( f
end
/ A4 |4 {( N; f2 p- r; s
4 f8 M% ^ y2 a; w % serie**pan.m
( l4 `$ B: w4 I) G, i3 d+ Z % the program is used to generate the prediction matrix f;
: h3 B4 d8 C/ u function f=serie**pan(data,step);
! w: J0 J4 {. f %data---- the input sequence (vector)
# q8 m8 u) R5 c- }$ d. ^ % setp---- the prediction number;
4 k5 a; i7 K% d/ P n=length(data);
, M9 q P' }3 U# P% c* N7 v0 j for L=1:n/25 X1 N+ j. d! ?2 z: m" L
nL=floor(n/L);' h2 Z9 H# t; f* b) j, C
for i=1:L) m, q) p: L- G) U/ r
sum=0;
1 h$ L1 T9 p1 l- [/ z for j=1:nL
/ P0 e' C( k1 w9 {# S0 H: z sum=sum+data(i+(j-1)*L);3 A# u/ ]) F3 e# y! P9 ~
end7 ]8 C/ c* X4 u
x{L,i}=sum/nL;6 N& T/ T R/ w- i. b1 [3 e
end
' r* I% B& Q; L" J1 z; v end
6 B2 |/ P' L. Y! P" _# Y# b L=n/2;, A! X% n. k5 S8 m
f=zeros(n+step,L);
3 m {( |6 m& `$ C, ?$ ^: K* ~" z+ g* Y for i=1:L
' n6 |: J+ k1 D: t7 }. h rep=floor((n+step)/i);0 S/ J$ q, b2 i6 h, V8 Z; B
res=mod(n+step,i);
8 b+ _4 o3 Z1 a3 L5 P$ J b=[x{i,1:i}];b=b';
5 a$ I) \* Y, m+ v, C f(1:rep*i,i)=repmat(b,rep,1);
/ H! F y4 i& J4 ] if res~=0
. `) `- _3 d* z% I$ Q# \6 V c=rep*i+1:n+step; A& g9 n3 i# i6 Z* \
f(rep*i+1:end,i)=b(1:length(c));
' F( j% ?* @7 _6 `% b end) N7 f5 y- s: ?% \6 ?$ W6 w
end
# g7 H6 \5 ^& S- ] c/ a
6 U3 K4 I4 }, |0 B! m5 v 二 最短路Dijkstra算法
& ^2 G" a; A A4 Y2 M % dijkstra algorithm code program% C0 d6 _ c6 r' V! z6 G$ D
% the shortest path length algorithm$ F1 g) w b8 {7 y
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)) a' U. }6 Q# P, e K9 _/ z2 ?
% Input parameters:
( P% }& ~5 p6 b3 r! D % Input_weight-------the input node weight!
2 o" ^ V4 F, v7 G % start--------the start node number;
% D% e: c H2 {$ C % endpoint------the end node number;
! X& G* a, W5 x8 A' ] % Output parameters:
4 J1 k4 I# Y: a" [ % path-----the shortest lenght path from the start node to end node;
0 {% t$ W# b' m % short_distance------the distance of the shortest lenght path from the. g: s, r A2 h3 R
% start node to end node.0 P) G4 T8 P J1 H" ?
[row,col]=size(Input_weight);
' a7 `, p& @" v
# l) o0 [. S/ q' b1 U' @; w, D) r3 c7 M %input detection _7 N+ A' o5 C
if row~=col
3 v( ]$ A$ F+ o4 Z6 |# Y error('input matrix is not a square matrix,input error ' );
/ E5 n- S0 P D6 r2 J end: @( l9 w2 S ?+ J* t
if endpoint>row
$ X0 k* H& }* m* P f- d1 B2 {, | error('input parameter endpoint exceed the maximal point number');
8 b( V& f; F0 i end: x( N# Q; C7 u( [4 T% G
2 |5 A2 \* K( e0 d d; P- }5 ~
%initialization0 T5 F* }$ i! K/ l" }
s_path=[start];( @* }: \2 Y4 @" k" `: W0 k
distance=inf*ones(1,row);distance(start)=0;
7 t; ^9 L0 I& \$ x, J flag(start)=start;temp=start;
/ M F1 [& u2 k) g) ~+ i
" W% p) A& b, E; m* S) C( P while length(s_path)<row& m& ~: q! R! U3 |4 M+ c+ `
pos=find(Input_weight(temp, : )~=inf);
2 u" c- i0 ]$ ]+ n4 k/ _: J3 o for i=1:length(pos)& ?$ F, x% r0 }+ U! i' [
if (length(find(s_path==pos(i)))==0)&8 k# i. |& L0 W! ]
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
4 |4 _3 A9 G& I+ ]" {1 y distance(pos(i))=distance(temp)+Input_weight(temp,pos(i)); t' C) R$ C- L, E+ s4 x
flag(pos(i))=temp;, [6 \) c1 `" @ g
end
& K9 g8 f5 y+ Y& Y4 _0 R end
6 i! ^* u# u, a2 `4 Y k=inf;
+ Y4 Q2 Q1 J- S2 Z/ a! i" \% b for i=1:row6 f7 o- p6 Q, s+ |
if (length(find(s_path==i))==0)&(k>distance(i))
! w! {9 B" t7 O% x# g* e; P k=distance(i);
3 ]8 K0 z! Q1 x' Q( G' B' Y% O7 Q temp_2=i;
3 g( N# S2 f% O1 n, S' `" u- ` end
0 I6 h& I2 d% s5 g- G# S2 t0 G, q' x end; j6 Z$ M! S& T% @6 M( I
s_path=[s_path,temp_2];, O* I2 Y9 c$ p! \
temp=temp_2;
6 U$ @1 t+ P* ], S% x% c/ m6 e end
5 E3 ?# B2 h6 f# Z% ~
! l5 F) b1 e; ^* D" k, X* d; P %output the result
2 a$ D3 y, {, `& b. a& t path(1)=endpoint;8 N2 M9 z8 ^) M- ]; C' e4 R9 L
i=1;( o: I+ P& J) ~% }; F
while path(i)~=start! E! \1 a M* _& F! R
path(i+1)=flag(path(i));4 r, t; [; z7 L* u; f
i=i+1;
7 K$ S! y, X7 Y( E' Q. e end
; u1 J% X/ W3 g path(i)=start;
2 ^: h# o1 B* \2 f( K5 @ path=path(end:-1:1);
* {8 R9 o$ y; W9 m- S% F3 X: V short_distance=distance(endpoint);! @" H( D# ^1 y$ z7 q
三 绘制差分方程的映射分叉图
3 s. j- l6 M7 ^ {: O R : O; v% O9 e# g- ]( X
function fork1(a); ; L$ z0 v: y/ @; e A; N
G! L3 x+ J+ ~% Y6 L
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
6 Q4 z% P3 m; B! l* `- i5 x" L. P g % Example: 8 ^( R4 R) r$ x( E% E; z
% fork1([0,2]); ) X& B' {( r0 i0 H2 \4 B
N=300; % 取样点数 V4 J2 p1 n3 w+ U) B* C: F
A=linspace(a(1),a(2),N);
& [+ d0 w7 ]% G. X1 y! G+ z starx=0.9;
0 R. T) g/ b! @2 v( k! b r1 b Z=[];
$ Y: N( m. @+ s/ P; v0 |( ^ h=waitbar(0,'please wait');m=1;* n1 y+ N: G! y2 u
for ap=A; - Q8 r& u$ R7 f6 }, i4 `. W$ I
x=starx; % o! z& ?# ~' b. C+ q
for k=1:50;
5 Y9 X8 V" s Q/ r( w, a x=1-ap*x^2;
5 s5 |2 a5 j7 W! J# S1 f% ~5 e end X0 }2 t3 X) h9 ]2 x6 L
for k=1:201; ; r7 B; |% e" P
x=1-ap*x^2; ! \# X$ R/ s0 K9 [5 R3 ~# \
Z=[Z,ap-x*i];
6 F. O9 ~1 l4 c5 v( B- c end
# R, Z9 {2 _' n waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);2 O8 D @0 H2 o" N: ^+ s* \ T
m=m+1;- \5 X4 [* ]" y4 E; W
end 1 c9 V9 L& @5 n' h
delete(h);7 s8 H! V9 j( n4 d6 r' g# d
plot(Z,'.','markersize',2) 9 _$ C m# v6 J1 o4 n S$ h$ _
xlim(a);9 d6 b, D7 w% e2 c
9 ^1 O+ \7 {+ _2 h 四 最短路算法------floyd算法
! g, {$ N% S7 w, X8 W" Y, H8 u function ShortPath_floyd(w,start,terminal) - Y3 i0 X8 ]( G6 f; |$ D! |5 M. P( H
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
7 V# @: ~2 b# v( \; ]7 ?) I %inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];- a- F g; ]+ x# ]7 s, t# T8 Z( z
%start-----the start node;9 V; f+ z4 U7 q/ w' _0 L7 O3 N
%terminal--------the end node;
! w" R4 u+ N/ E4 X- p n=size(w,1);
9 L& R% P" h1 N' k" d- R7 q [D,path]=floyd1(w);%调用floyd算法程序
1 N$ T0 L' Z( [2 h% { 1 ]( ?5 Z! a9 F: o4 L, e
%找出任意两点之间的最短路径,并输出
4 h, w/ Z% @4 h6 H1 Z, b* @ for i=1:n
+ A" X! I/ T R4 X for j=1:n
% c9 }% `: o2 {1 x& f+ b Min_path(i,j).distance=D(i,j);, O" t W0 H' Y! ]! K
%将i到j的最短路程赋值 Min_path(i,j).distance$ ?$ j' |) _2 K c
%将i到j所经路径赋给Min_path(i,j).path
1 `1 m; r+ O4 f' r9 b Min_path(i,j).path(1)=i;) I n" U f. S; U9 ]! [7 ~
k=1;
2 q% C6 Z8 o, K$ {# Q! T while Min_path(i,j).path(k)~=j6 y* D: C* Y* J3 n
k=k+1; @$ u& t4 \( U% o
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);! S* ~/ [3 l4 B# W
end" A6 v# S- |3 t. ^% Z
end# ^1 \! D* a( P6 e# {$ @5 i
end
/ a- n. i1 U1 T$ A* ^3 C; F s=sprintf('任意两点之间的最短路径如下:');! x' U1 \9 G) @* k* G
disp(s);, u! N* F7 n, `
for i=1:n
4 w& A1 N. `- g8 ^- U for j=1:n
K: ^" }; p% d+ f s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
/ |$ d6 ^+ j2 K ,i,j,Min_path(i,j).distance);, I" e* `" S M( _
disp(s);
' i# q$ f- O# t/ i disp(Min_path(i,j).path);
" R' h. ?( U* w) D9 q. @ end" {/ a* _7 K9 s0 Q0 g/ A
end7 _. ^2 F3 V7 ^
- I1 e. t' G9 G! Y; U3 O
%找出在指定从start点到terminal点的最短路径,并输出 b$ N; e% i# H3 D# s7 d3 K3 @# K
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...7 z. \. o4 S: o5 G# w# t
start,terminal,Min_path(start,terminal).distance);6 v% u1 l) U. I
disp(str1);
5 p. \8 Z5 x; C disp(Min_path(start,terminal).path);
; |" |9 w9 @; Q6 d 9 ?; b7 S5 |9 J0 K8 F9 V0 }# O
%Foldy's Algorithm 算法程序
& C2 W1 Z' J* r1 o' k# F7 P! H; | function [D,path]=floyd1(a)
( b" K' Y2 @1 E4 G( |9 R" L! U/ c n=size(a,1); o; m' ]$ _- w, ^- s- t+ s
D=a;path=zeros(n,n);%设置D和path的初值! P% b" j' x, n; u( ?! n% P
for i=1:n$ Y' P8 Z) u1 g H$ k* t
for j=1:n
# R6 Z$ m4 O! o if D(i,j)~=inf m3 b- ]1 I H2 R* h9 j. L5 ~# m
path(i,j)=j;%j是i的后点
/ Q- \! G w# p- q end* F4 _7 X v6 ^& h* Y
end
/ M4 ~' N( p+ `: E- V end7 k; [# l- v/ Q
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
1 n. l7 E, Q, R+ h2 b for k=1:n
, B. g9 L/ `2 k2 k, { for i=1:n
9 e: X0 ?7 g" ?. F# S! R. V7 v for j=1:n2 m* A" l' G% D
if D(i,k)+D(k,j)<D(i,j)
, h% @( ?5 L( T; L( x E3 g' g D(i,j)=D(i,k)+D(k,j);%修改长度
: P5 E6 j# F" {4 z& d6 E V path(i,j)=path(i,k);%修改路径
8 r: @; O2 d. u' D% Z; X% c. h end
& _% l( x k) v. {* J4 q: Q/ v' C end% Y9 e5 W! O; ~3 Q0 X. f
end8 W8 G( y) A8 a$ b1 t/ @
end
& R/ t# f0 _4 @2 h : l# }* L, f7 @0 Q# N
五 模拟退火算法源程序. x# k. n" J, Y* A, E5 m5 e
function [MinD,BestPath]=MainAneal(CityPosition,pn)
1 @3 X+ J4 O, Q/ A$ ~( q function [MinD,BestPath]=MainAneal2(CityPosition,pn)
9 Y! u7 ^7 C. z; E7 Q %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( p7 y; i$ a6 R2 {: e
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...8 G" p1 E y: L( E* W0 |
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
+ T: X) B, S0 ^& \ s$ E9 ~9 g( o % 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
1 o3 `( L( {/ S2 [ % 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
" c$ `6 P! v* { % 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
8 p8 P* ~! j* | E' b; ]9 ~) H ; d. B9 S; g- _% K! t
%T0=clock
% V- O$ A+ D1 K global path p2 D;
! B+ v/ a2 e3 c1 D1 p5 [ [m,n]=size(CityPosition);
& W5 d' h( f, P3 T8 q %生成初始解空间,这样可以比逐步分配空间运行快一些8 E3 A( L' V. k$ H3 u
TracePath=zeros(1e3,m);) [( s' h! D8 S( C
Distance=inf*zeros(1,1e3);3 }) U) O0 k, x: e5 F, w* P/ Z3 h
: `2 y4 k6 D$ G! X D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...0 ~* S7 C$ d& ^
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
e' J& b# V* H6 d9 P %将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)0 e/ E5 d( Q2 t( B$ m# {8 z8 m% N* b( z
for i=1:pn
" j9 H& x3 L9 v1 L9 p8 O path(i,:)=randperm(m);%构造一个初始可行解
4 U" n1 M% j1 e* G1 r/ }8 I- Q end
q$ G4 b. \7 Z0 [ t=zeros(1,pn);
* G" H9 l7 h" [3 h% e0 P; Y p2=zeros(1,m);+ S' a; v) R# R( C, m) R
6 i6 Z+ M, p' ^; i, I
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );& |- U; e: g* U2 u+ x) C
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=' ) ;/ f1 S! u; `) p* s: u+ B
%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 T9 h$ J/ e% \3 z& S/ h %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5 l& ^( p/ Z% R: n
%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; W3 X2 W _5 k
%会收到到比较好的效果
5 ?& W" I& e& z( u3 C - ?5 |4 d. Q* _5 w
T=1e5;
$ e$ y. j6 n. i+ d N=1;# l( _% |9 J; ~" |0 @/ Q
tau=1e-5;%input('请输入最低温度tau=' );! \, L4 S1 {7 s! Z9 l: G2 n! X
%nn=ceil(log10(tau/T)/log10(0.9));
: H2 L* R ^2 I0 ^ while T>=tau%&m_num<m_max
6 l% C+ V( \# L: o iter_num=1;%某固定温度下迭代计数器* U! K4 c( r" ^9 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
, ]% ^- l# y' w7 w( s" e3 a %iter_max=100;) a! W: l# h3 l+ U6 B0 {$ J
%m_max=10;%ceil(10+0.5*nn-0.3*N);
( ?9 }% D% ~: `: j g% A while m_num<m_max&iter_num<iter_max
0 A- ~4 o% S, S) d0 a) t' X %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:1 H* Z$ Y7 M9 O3 c
%用任意启发式算法在path的领域N(path)中找出新的更优解/ ~# L- a0 N, ^9 o* f
for i=1:pn
/ z. `2 @' K$ P* z: u! U! N Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
6 o8 u0 |3 m$ ~ %计算一次行遍所有城市的总路程 9 x( _: j$ x. l8 }
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线; v/ X: ]) N, i" R
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
$ U7 v3 f _8 P$ p9 }! n$ z8 B end6 n3 T% j4 o: U2 E
%Len1
4 |7 W+ ]- V. w L, y/ u. F/ i& X5 N, ` %Len2
6 i- R1 W2 { t& O- l, ? %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
$ A* _; A: ^. j3 j R=rand(1,pn);$ e3 Z: C4 p& Y) ]) l, {) V) H
%Len2-Len1<t|exp((Len1-Len2)/(T))>R* M) w) X9 Q& ~7 Q
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
6 O0 R& ]5 l& J; R path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );, p8 H5 ? q% j! ]
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
+ L. C( f% p; x) E [TempMinD,TempIndex]=min(Len1);
, x1 e* B' y4 S5 I: ^& q0 M3 C %TempMinD* }; O% g- C1 H* m8 b4 ]
TracePath(N,: )=path(TempIndex,: );5 T% u% F! C9 W9 j! B q- l
Distance(N,: )=TempMinD;
1 n/ d: f. H. `! i. Q8 ? N=N+1;
. _& x, } n+ w- K; O3 P( ? %T=T*0.9
1 J9 {, j9 c! C4 K8 r2 @. D m_num=0;3 _0 D6 ^, w0 I" n
else
9 ?, c+ Q: Y2 t, i/ f$ R% [ m_num=m_num+1;
' X; P! h$ v9 X4 p% `8 ?! n0 u end/ o% x0 a) y% ]$ y, U
iter_num=iter_num+1;
: ~3 {9 x+ k& e8 M8 v+ | end
. X' I$ r# p% g. O7 A9 f T=T*0.9
: g. ~6 c2 G, J" @1 {6 |- t+ G %m_num,iter_num,N7 u* A' J6 P6 J+ I7 F
end
+ N- U* @/ Y, B& V! q [MinD,Index]=min(Distance);# k5 V: B/ ]1 t+ e
BestPath=TracePath(Index,: );
- h( t. q1 V8 ^" g0 U* I disp(MinD); s1 a7 d/ u; X3 i
%T1=clock
! |6 j, }3 B4 S; v& n2 h2 b( q 9 I( l4 `1 ]2 P; B" d
: O7 v8 L8 u3 Q
%更新路线子程序
/ u& j+ D5 [& h) x5 n) S7 {; e: J function [p2]=ChangePath2(p1,CityNum)$ N* F) [1 v$ d8 l
global p2;) j- G i9 s; B& j2 r, U
while(1)
5 L+ @3 l/ j7 n9 @* ~0 H R=unidrnd(CityNum,1,2);3 }$ ~ {& A) n5 H
if abs(R(1)-R(2))>15 Y) s; j9 n* J2 \- e" U
break;
b* \$ D2 E! c' z+ b( _ end
4 n5 J4 y6 s, C2 v end5 X- H! P; I5 p& [! n' t8 m
R=unidrnd(CityNum,1,2);
( P5 a) ^* H, H1 s9 Q% \* m I=R(1);J=R(2);% _: b6 q6 `9 j: D* s8 v% U) y
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
7 \, p4 }7 G6 i %len2=D(p(I),p(I+1))+D(p(J),p(J+1));
/ p5 I6 d9 n7 i if I<J
: I; ?5 ^" [) L# c ^, J p2(1:I)=p1(1:I);
9 _. n1 ] ^: ^ p2(I+1:J)=p1(J:-1:I+1);
1 f: _# w0 d* l- z p2(J+1:CityNum)=p1(J+1:CityNum);
2 B, d7 f# G' V+ F& J( e else
4 Q; F$ W: ^ O) X) A8 W& s1 R p2(1:J)=p1(1:J);2 @5 ]" n9 T3 q( ]1 w3 P! X5 T. o
p2(J+1:I)=p1(I:-1:J+1);
$ z+ `& c/ J0 a6 L6 R3 l# e( O p2(I+1:CityNum)=p1(I+1:CityNum);9 q5 G! p W$ N8 d. U4 r, `, `
end
6 g4 x/ J _) X# S: M - r* V/ n5 I9 A% |* m# K+ R
六 遗传 算 法程序:: G/ n' {5 |1 `% F: q. j! M3 ~
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!# c y# \3 P3 u4 ?
4 v6 v# n, V8 P4 e J
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
( v* D7 r: E% d, J$ w3 {) c# y % [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
5 L, j [" D, g! `; U % Finds a maximum of a function of several variables.
0 X. t! U1 X3 g3 U- ]7 S" S % fmaxga solves problems of the form: - C0 C! W' k1 q: u- @- P) `; U
% max F(X) subject to: LB <= X <= UB
9 g7 a" F5 @- J/ u% U! C % BestPop - 最优的群体即为最优的染色体群
6 A R* g3 }5 w % Trace - 最佳染色体所对应的目标函数值5 K# U# M# o% J6 H3 Y& \* I" v
% FUN - 目标函数
) R# v; a7 k, i# b % LB - 自变量下限 Q8 n8 Q! e6 g8 p( x
% UB - 自变量上限/ L/ t7 A' D* G4 W1 |% v. [3 Q
% eranum - 种群的代数,取100--1000(默认200)
1 `( J! r- ?) _- s2 l4 u5 f4 t % popsize - 每一代种群的规模;此可取50--200(默认100)
6 T& Q/ n0 P4 L+ { % pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)! @3 B" J Z, r! s* W" c5 J( s/ R0 U
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)! M5 u) {. @( l, F5 E0 q6 @
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
2 b6 v; G0 A7 s+ [) O2 f % options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编5 S% u* Z2 T% F' l) |/ u
%码,option(2)设定求解精度(默认1e-4)
7 N+ j) V+ s1 l3 f" w %9 o' x. }% P9 X' Q. E% X& ]' T
% ------------------------------------------------------------------------
Z4 V! D! q% z" q' \' ?
* m+ f! b: h; s3 L- ? T1=clock;
$ J4 V: G4 q6 e, M if nargin<3, error('FMAXGA requires at least three input arguments'); end
( X0 \1 o' [" J: m if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end) \5 K o& t% b' K0 _+ `5 o
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end. L+ g$ R8 o( u4 a) f
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end0 a. \. c. x3 v H1 ~: u! [! ?* E
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end6 O9 ]7 G" E8 C
if nargin==7, pInversion=0.15;options=[0 1e-4];end
U4 W1 }1 M" Y+ f3 s$ g! L if find((LB-UB)>0)
5 V4 R+ X2 x1 d+ X8 N4 ~ error('数据输入错误,请重新输入(LB<UB):');
U9 G) o, b' H' l+ L! i3 o. o- a3 W end
9 ?! }: o6 H# Y+ w s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));- A# K+ r; A7 h3 [5 A- V
disp(s);3 t0 K! ~* U' I" R# _! G8 E5 r
_$ s5 v+ }+ v/ ^* W& Q. R4 U
global m n NewPop children1 children2 VarNum
: t- i7 g" e, S. n 6 A0 |0 v' b# H4 B! S
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);& H+ }) J) k& F) b5 R
precision=options(2);%由求解精度确定二进制编码长度
, s; a6 e& m$ J bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
. A+ | w+ Q7 l- B$ H [Pop]=InitPopGray(popsize,bits);%初始化种群7 N0 K$ H& y7 _! P+ ?- t8 J* x
[m,n]=size(Pop);) {" R) U- A0 y0 Z1 I
NewPop=zeros(m,n);
7 W" `/ ~. C& E, S' }, n children1=zeros(1,n);
( y X! R* t8 g- Y/ F9 N7 u children2=zeros(1,n);' v# Q0 m, }. `5 [! d
pm0=pMutation;$ q9 R( y, g* J+ Q& n
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
6 s. S, B. W# y: K$ @5 i Trace=zeros(eranum,length(bits)+1);, |7 \" o& z) o W6 n
i=1;
: Z6 L1 m, w! k while i<=eranum# Z6 c/ J- `! c% C! e( B2 R
for j=1:m2 Z: r/ M H9 M
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
% ~' E- F( c$ i end
. r) ~+ y8 l5 D3 l0 I [MaxValue,Index]=max(value);' ?) ~- O3 i7 `$ D1 x
BestPop(i,:)=Pop(Index,:);2 H# n2 j7 T5 L1 N. V
Trace(i,1)=MaxValue;
. j* ^: P3 P; l) r: A Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
$ u1 Y, r: y; |) r [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择& C: v, v1 s' R( O
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));+ x4 x# a& l' Y$ @" K% r
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率' W; ?) Q, w0 H; l0 j8 h! N
%round(unidrnd(eranum-i)/eranum)$ y; W; l9 R- W; V* t
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
& c+ K5 Q5 G* S6 Y2 y: A: b1 w& _ [InversionPop]=Inversion(MutationPop,pInversion);%倒位* d. k2 S: h* p5 e% a; g( G ^3 R9 I
Pop=InversionPop;%更新' q/ u% m/ [$ j# ?2 m
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
( F4 I6 |0 B/ j- C8 y9 z+ ]9 F4 | %随着种群向前进化,逐步增大变异率至1/2交叉率
' w6 N9 V: {: f. | p(i)=pMutation;/ y* G7 z( l; [" {$ y) H8 W) K7 M$ [
i=i+1;- o; @2 Y, F9 }) r
end4 o }: T) Y/ G3 U& A8 M
t=1:eranum;
h5 S6 r) T/ ?$ Y9 ~2 b. a" w plot(t,Trace(:,1)');9 x3 W& b5 I& E; P7 |
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)');
) R$ a' c% L/ ?( C' B! w2 T: t/ f [MaxFval,I]=max(Trace(:,1));4 a% K& W5 p+ z) Y" t. k# r$ h
X=Trace(I,(2:length(bits)+1));" q( T/ V' D, }
hold on; plot(I,MaxFval,'*');8 C+ x3 Y# n( e$ f
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);7 q' j4 Q4 c: W f/ Q: ]; }
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,:)));! f! W; g A' c8 B* L6 p. N. N, u6 H
disp(str1);
% `& q+ A" S- W7 h K' c: H/ H %figure(2);plot(t,p);%绘制变异值增大过程. X, _; G: S8 j) A# }
T2=clock;; S9 b/ K2 J) [) P3 U: R
elapsed_time=T2-T1;
: l! e) ^( N4 D- s' ]. w2 V if elapsed_time(6)<0
5 j$ P, i4 Z" f0 | elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;* ]. C" _ ?- e) h! w
end) x% v# W2 l" @: ]
if elapsed_time(5)<0
& m, x9 d ^# i, |5 p0 Y" T- v elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
6 A, ]+ L9 S7 B6 h$ N$ ]5 ^: x end %像这种程序当然不考虑运行上小时啦
7 `! x& }3 ]3 F- P: 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));2 P, @" D2 b/ `. S) Z+ s1 s4 e
disp(str2);5 K+ `+ l$ h" y
7 J/ @% d6 f4 ~; A, B
4 i+ Z& G6 }; w, n7 B
%初始化种群
. A, P- Q4 m: V, _ %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
/ B9 j6 O" K+ O function [initpop]=InitPopGray(popsize,bits) v2 ^5 `' h1 K9 `" [
len=sum(bits);; Y$ R5 j! v; N0 [. E: S z0 P
initpop=zeros(popsize,len);%The whole zero encoding individual
0 f2 l( O6 g. F4 A" d for i=2:popsize-1$ i4 f) \$ T1 X) y9 a
pop=round(rand(1,len));
/ i! M: D6 h2 e# ?) f k% ` pop=mod(([0 pop]+[pop 0]),2);% m" ~. `4 o( P% H) G5 r
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
. {8 W$ Z: Q' O0 F %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)2 v8 n0 I$ j" C' O3 u
initpop(i,:)=pop(1:end-1);6 f& B' }5 s- O) L
end' S0 G- J; R; m' _* R
initpop(popsize,:)=ones(1,len);%The whole one encoding individual1 ~6 \1 n% A" F$ h5 l. x! J
%解码
" B% m) r* W8 c8 S) w$ e5 K 9 s' }! X8 L3 l) g$ E7 s& G& v
function [fval] = b2f(bval,bounds,bits)
! `4 G/ ~+ O# O% a/ \* [, H) T % fval - 表征各变量的十进制数! y( o9 `3 w' Q' ], A# }
% bval - 表征各变量的二进制编码串
3 ~9 ]. `) z/ N# P* b' U % bounds - 各变量的取值范围% V9 W6 s8 i2 `
% bits - 各变量的二进制编码长度' l5 g! t% g C5 F# X1 l
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
8 B; I; e8 }) I$ z% c' ?: N3 O& x) c numV=size(bounds,1);
" S# d# q) n q4 n- v cs=[0 cumsum(bits)]; ' |3 i! w- R. P; } H' Q
for i=1:numV
, P f3 ` t& \" s$ } a=bval((cs(i)+1):cs(i+1));
( \! ] F1 O$ D( S( F6 D fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);7 f2 _* C5 P0 e" L. _
end) S/ Z0 \: g" J/ `8 G+ a
%选择操作
! o8 S; B; i, q& z% Q& [: F7 r %采用基于轮盘赌法的非线性排名选择* | {. A2 l0 l/ W
%各个体成员按适应值从大到小分配选择概率:) v9 w2 r3 |( F" Q6 k0 ]! |
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1
# Q' q1 g0 F! h6 P y; u
% ~* L5 y# T2 e function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
2 e5 L6 |5 M5 \/ f0 [ global m n) E& d7 V! \4 {# E3 ^7 t& _
selectpop=zeros(m,n);
0 z4 ~( d% ?! T3 H0 h5 Q fit=zeros(m,1);$ `/ v# B0 P {/ N) q4 g
for i=1:m6 f" ~1 G9 G% N3 E
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据0 L( ~1 }' Z; T
end6 s# v8 A% l/ b) _4 }4 ^: ]$ x2 q( G$ ~9 V
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)) o0 p; N5 E( v, h4 u
q=max(selectprob);%选择最优的概率
: d# S" ], O% K. n. Z x=zeros(m,2);; B: d% ^8 L* o0 A# j6 i6 q. k0 ~* z
x(:,1)=[m:-1:1]';9 O: ^" A% y1 W* S- Y
[y x(:,2)]=sort(selectprob);
/ u9 U/ `: `; x r=q/(1-(1-q)^m);%标准分布基值; K6 E3 j- {' p9 p
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
' l' _9 D* G9 q4 |' M" N" b newfit=cumsum(newfit);%计算各选择概率之和
& M+ r# a% D/ s rNums=sort(rand(m,1));+ \9 n! [1 N) g+ P Q! A5 l
fitIn=1;newIn=1;
& ^% }/ J! W- d* G) x while newIn<=m
0 w8 V9 N5 X" b+ x$ } if rNums(newIn)<newfit(fitIn)
Z% o* N. L0 T1 P selectpop(newIn,:)=pop(fitIn,:);
3 y/ G5 \# _0 y/ Q newIn=newIn+1;
; E" {6 t! {" d3 x" ?* f! H2 ^& N1 G else
. w) H& W# ~3 W- h8 z/ d: V fitIn=fitIn+1;
) d( r) z! O( R9 ^ end8 L6 H. ~5 ]+ B- Q5 r
end6 `% F# b1 v' U. K4 Y& z& I) d
%交叉操作$ c$ X+ G! C0 [6 l% z: e' P( ^
function [NewPop]=CrossOver(OldPop,pCross,opts)
/ m @" W4 v! l( `9 [ %OldPop为父代种群,pcross为交叉概率
2 m% R, o2 y' V2 y0 b global m n NewPop
! e f* S) ~) _% w3 W' G6 N8 c r=rand(1,m);+ P. s7 H2 t" X" w. b; A
y1=find(r<pCross);. ?" o9 {# H1 f: Q$ f% `1 g4 Z
y2=find(r>=pCross);2 r m: G/ J, g* L! j$ b! t! u" c
len=length(y1);) b% Y/ j) `) Y: n. {9 j9 D* l D
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
. K. g' h8 H q8 d$ ^# S y2(length(y2)+1)=y1(len);# N8 h6 L7 V4 s1 z5 b/ x
y1(len)=[]; f F6 Y7 s8 L& H0 D; }- d4 W+ d
end
! P% M9 c' D* U4 l7 x1 `* E if length(y1)>=2
2 O5 i+ ]- E( z$ \. b for i=0:2:length(y1)-2' [3 h& x' w+ E0 g
if opts==0
! ?! P3 M; F6 ?; ]' ?0 l# [* e [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));! a* s$ c/ J% G) n/ w
else
9 f! w+ q) O) Z& J" c* S [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
- \# u2 x9 ~; A" [" v' x m end
* j6 l6 C3 ~: j8 i! l0 S end
6 ^9 ^$ M; A4 w5 T8 W end
2 T- k- b1 X& j# L4 _6 @2 j( M NewPop(y2,:)=OldPop(y2,:);& K" L3 v' F2 T! |4 }2 y y4 A
! h' Y8 \; A) c" c %采用均匀交叉
6 u! ~& X7 \8 {3 s* L function [children1,children2]=EqualCrossOver(parent1,parent2)! O* ?; O3 \5 n, @7 H0 z* S8 n
0 X* e7 z2 J6 G) H
global n children1 children2
3 L$ {# ?' C* c0 s% Z- S( B) Q" j hidecode=round(rand(1,n));%随机生成掩码' m# m3 H+ J, E! U/ }; i5 _
crossposition=find(hidecode==1);1 W& L. T/ z8 ^; D
holdposition=find(hidecode==0);
2 G, d- S/ G& n; G! E# P! t- ]6 N children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
a! ?) x2 a/ O' u. C# i. r/ u children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
9 d8 Z, C: T; ^$ k/ `/ D& Y7 @ t children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
2 `/ U% O/ ~" J0 o( Q children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因/ r' E% z2 E& {5 S7 j# t
/ o6 e0 _: n8 i2 k. {' c2 w- u2 i! M %采用多点交叉,交叉点数由变量数决定
z$ X# {; |% B) L$ q% {! Q, D% f V$ G2 _# F* i' R: m9 |5 A
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)6 n! g7 _8 f ^( v( `" W
! ^$ w( g& U; H! [" R
global n Children1 Children2 VarNum
8 k* C7 G6 j% o/ a+ ` Children1=Parent1;# w9 W2 b) I4 w! Y- f; g+ ^
Children2=Parent2;# K4 d) e! Q3 H4 V. L: S$ ]
Points=sort(unidrnd(n,1,2*VarNum));
0 F* v& ^6 c5 m& A for i=1:VarNum
8 N/ P8 n- v" F- k0 A- m Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
1 w2 K1 c: o. B/ n0 ` Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));. C% T3 S, | x+ t7 _$ ?
end
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%变异操作/ U8 A s7 V7 |/ l& d8 b
function [NewPop]=Mutation(OldPop,pMutation,VarNum)
: x3 I; S; S" T
4 ?& i8 _4 ^, J3 [& B global m n NewPop
9 {: ^6 K h2 p. c r=rand(1,m);
0 w5 v" O2 }1 Q+ w# i position=find(r<=pMutation);. X9 z; I, I/ b' C' f
len=length(position);& r' E% c: [0 z) M/ h% c
if len>=1
& q/ o8 s N: G# t7 E, H- P0 X* X for i=1:len
8 @: u9 ^( d# \) {9 s" R! W0 B k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
6 V/ v' r6 u% }0 y% I for j=1:length(k)
# j" }3 M! e* G if OldPop(position(i),k(j))==1
9 E. e0 U2 j: f: U# Z U OldPop(position(i),k(j))=0;
* t K" T7 P/ r8 M- {3 F1 h else
& n7 ^+ p3 Y" C! A5 ] OldPop(position(i),k(j))=1;
8 Z4 _" ]7 F8 N, t' G6 w; ] end
! K# T2 n2 t' i0 p; ?9 l' B+ q7 A end
}+ `. T4 z9 t) @ end
( b% S" O1 [" W% M; ^2 N& Q6 V' w8 A1 B/ o end! M/ G3 }7 f9 P$ n
NewPop=OldPop;$ |+ |8 @, g' q/ w7 K) s$ E/ t
6 A8 S& R' r& T* n %倒位操作
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; x3 J2 h! Z* \" m$ q9 R E* Y. x function [NewPop]=Inversion(OldPop,pInversion)
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global m n NewPop
4 B7 ?- s! e& S: M7 A NewPop=OldPop;# A% Z& Q9 v. C3 ^/ k
r=rand(1,m);
5 ]+ w" `# J# T PopIn=find(r<=pInversion);
" R k' S8 h, v! k) w8 Q% U9 \ len=length(PopIn);0 b# S6 \" b/ p1 [) q7 l
if len>=1- q, R; H+ G. D6 _# J( H0 ~
for i=1:len5 E) b9 O |7 t6 r
d=sort(unidrnd(n,1,2));
7 Y4 T9 [) e3 v8 ~ if d(1)~=1&d(2)~=n- [( `: L. O% n+ Y4 {
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
( @: v& \' N! x) w9 e0 V3 o; H9 T) i NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
4 c; G" w) o2 Q9 I5 u NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
/ S* y7 S! R q/ |0 `5 m: \ end
1 Q n3 G9 L$ G, m0 m: l end9 Z) q8 q, d; n+ T( P2 z* d* U- p
end! l) y$ d0 M9 `0 a1 a
- V6 Y1 B0 L, R- e. V+ W& M! h0 H 七 径向基神经网络训练程序
0 ~5 @- ~; s6 d! g) @$ h R. a 9 ^- ]- J' P# q ^+ ]4 J
clear all;+ B y& m) i# T# M" V
clc;
: R# ], ]4 m9 p1 [4 P. @ %newrb 建立一个径向基函数神经网络# r3 ~& O) P2 }5 B) R* m
p=0:0.1:1; %输入矢量
& H8 h3 B) g& W0 A9 _ t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量* t* B- ]3 e" g$ s6 W1 r
goal=0.01; %误差7 l2 U: |/ Q5 K3 E4 s
sp=1; %扩展常数
5 G* m) x2 I- L' l1 c9 F8 z \ mn=100;%神经元的最多个数
5 A' x) d4 ` l, g+ o ] df=1; %训练过程的显示频率
1 L, o B. j2 Z0 b7 I9 ` [net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
6 I. L, R$ z3 o9 k% x4 ?" k. L, q % [net,tr]=train(net,p); %调用traingdm算法训练网络, V; I( K; {6 w) I
%对网络进行仿真,并绘制样本数据和网络输出图形
- K3 T7 a8 e, c/ X ^7 _0 g A=sim(net,p);
2 ]& C7 C `' { E=t-A;
& p# w; e, v2 C, T sse=sse(E);" \* L. Q% x7 n$ f O
figure;
% _0 Z2 x0 p- \/ j3 A plot(p,t,'r-+',p,A,'b-*');
: z6 v6 F( u9 N% t+ M4 b8 X+ X legend('输入数据曲线','训练输出曲线');
7 c4 C" X" z/ @; z5 `! U& ^ echo off 9 N0 ^9 J) ?' G: y% g
% M, N+ H; H* U! K2 C; R4 b 说明:newrb函数本来 在创建新的网络的时候就进行了训练!0 k6 {4 O0 y" H5 R; I
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,6 x4 \* J' u! L
那么继续增加神经元,程序终止条件是满足精度要求或者达到最大神经元的数目.关键的一个常数是spread(即散布常数的设置,扩展常数的设置).不能对创建的net调用train函数进行训练!
) m* D, f( N& ?' N$ s, V( [% k
; q }: I! J z$ S8 K. L
: z0 K& I& U; H' `8 a1 Q 训练结果显示:
9 D% i1 g! w X! G) Z8 M3 f NEWRB, neurons = 0, SSE = 5.09736 k) o* W6 I1 v
NEWRB, neurons = 2, SSE = 4.87139
3 ? v3 a. t7 ]5 Z NEWRB, neurons = 3, SSE = 3.61176
: L, r: k! L% s4 _7 F3 | NEWRB, neurons = 4, SSE = 3.4875' ^; c. i5 `4 B
NEWRB, neurons = 5, SSE = 0.534217
# Z' B7 J5 ~6 x- {2 x NEWRB, neurons = 6, SSE = 0.51785
6 [: |* j7 N. d9 l) @( t: U NEWRB, neurons = 7, SSE = 0.434259
) N2 j: N' q$ h& Z) ^ NEWRB, neurons = 8, SSE = 0.341518 e: c6 b& z8 U- I
NEWRB, neurons = 9, SSE = 0.341519: ^' {$ n1 G- I& N$ K8 v3 K
NEWRB, neurons = 10, SSE = 0.00257832! R. L) S+ t+ T t) }" ~
3 a$ E9 j7 h4 |5 j* j2 L) Q 八 删除当前路径下所有的带后缀.asv的文件, h0 n2 l6 M: _" `( x
说明:该程序具有很好的移植性,用户可以根据自己地
' z" Z+ d7 K" W* C" s1 t" [! K 要求修改程序,删除不同后缀类型的文件! 1 Y( }5 A- X( Z" y
function delete_asv(bpath) ( }& C' P* D' L& t" A' u K
%If bpath is not specified,it lists all the asv files in the current8 v% ~+ i$ }" S" q& ^
%directory and will delete all the file with asv ; ]% Y7 @) v$ h3 i( O: s
% Example:
3 E1 c$ ~+ F- ]$ w% C& e % delete_asv('*.asv') will delete the file with name *.asv;
) |4 l7 P; s9 q0 r % delete_asv will delete all the file with .asv.: m3 r& d7 [: Y
g* l, U- Q7 B8 K8 f7 r
if nargin < 1
3 i. P W3 {2 q4 P T; p' | %list all the asv file in the current directory" B0 \3 p$ N( K6 W: n
files=dir('*.asv');
( |2 F2 u$ A5 h6 Z( \: B else- {! a* _3 Q _3 }2 ]2 ^
% find the exact file in the path of bpath
7 c& ?* ~3 \4 f, g- [( A [pathstr,name] = fileparts(bpath);3 O& A) G, I# T) g
if exist(bpath,'dir')* M) z' }# y% S. E
name = [name '\*'];
7 R9 {7 |5 { H$ j! L0 f4 s end
) o* ~, K, A* d9 h+ _ ext = '.asv';
5 ~; u2 `6 }( Y" i files=dir(fullfile(pathstr,[name ext]));5 r0 P: W6 r0 V, F; R- P7 y( P
end
- J7 s2 S) D5 {* H+ J( q+ A+ C) ^: Z
2 I7 Q) D% A- I2 V8 Q if ~isempty(files)
9 M$ I3 Z- X6 o% @' @3 h9 o for i=1:size(files,1)$ ~" b7 X# V I U1 r
title=files(i).name;
; _. H, y6 k W delete(title);
+ Z8 t4 ^4 w3 X" c# H end
3 Q- E" n6 `3 ?8 y" {; Q$ n& A- O8 I end
' C& @" H6 p# e1 h+ \% I
7 o. U' b$ ^; X% i% }0 [# |4 t
; Z2 i3 t- J, G- n- ~ 同样也可以在Matlab的窗口设置中取消保存.asv文件!
2 b' b" p# y* z/ T
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