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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 l- \4 A: q( i9 C$ |* d
1. predict_fun.m为主程序;2 @' i: A* s& e" g, p) F, h
2. timeseries.m和 serie**pan.m为调用的子程序
6 I9 m; v# v6 }$ t! b
* D5 ]% P+ F8 F$ f1 J6 vfunction ima_pre=predict_fun(b,step)
: i+ i1 R1 X) N% main program invokes timeseries.m and serie**pan.m
" K4 u" }. c* u" W8 i7 u% input parameters:- Q k" a3 {& W
% b-------the training data (vector);
6 @5 Q x8 F( q) y% x4 g% step----number of prediction data;1 g- }; W. F$ j' f0 ]2 P
% output parameters:( Q$ [6 h, V8 c. g* ~
% ima_pre---the prediction data(vector);) s! N/ l# s- E
old_b=b;
~9 Y* \# |; b7 _; v$ |; Tmean_b=sum(old_b)/length(old_b);9 l7 R4 H# M+ ^+ I7 ?- k$ `" M
std_b=std(old_b);) y* `9 Q5 N8 z" P; K2 b
old_b=(old_b-mean_b)/std_b;6 U& G7 J) W9 b5 d: w
[f,x]=timeseries(old_b);3 O# W) h' x) ^/ I% {7 r
old_f2=serie**pan(old_b,step);
6 D5 R; i1 E$ d+ X7 Q7 ~% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;
5 ?* v3 Y# M, M3 ` d1 b0 fR=corrcoef(f);. l @* t/ j2 ^* o. h5 l" W9 J
[eigvector eigroot]=eig(R);* M. i0 W$ J% Z \/ w$ J
eigroot=diag(eigroot);9 q7 }: I) \1 p( f' F
a=eigroot(end:-1:1);9 E4 [" t( {( _# c3 q! ~$ P
vector=eigvector(:,end:-1:1);
1 F# ?8 u! J \" V- m; o, Z; LDevote=a./sum(a);
" \" p# [! p a# e8 C+ ADevotem=cumsum(Devote);1 x S" I5 X+ ^7 Q9 \1 @! n8 b; c* H
m=find(Devotem>=0.995);
+ F6 P+ D$ V* r: zm=m(1);
3 O: W$ q) ^. i* W1 d8 zV1=f*eigvector';
( n7 {, Y3 ^* ?% ]V=V1(:,1:m);
, ?& C# O$ m$ T2 C5 Y% o3 l% old_b=old_b;1 |, m( K4 N7 ?! M* ^0 h+ p) r
old_fai=inv(V'*V)*V'*old_b;5 K! s1 i* O3 A" Z2 k
eigvector=eigvector(1:m,1:m);7 ^: ? _, M0 @0 u
fai=eigvector*old_fai;
. A* [& t$ E# R! y# v. lf2=old_f2(:,1:m);
7 _1 J$ G& Z1 opredictvalue=f2*fai;
@5 V. y. S: }4 r# Iima_pre=std_b*predictvalue+mean_b;: _. u6 i" g* U# R# a
- T/ [% F8 \& }+ y6 b! \* D1.子函数: timeseries.m ( k0 l3 x$ y4 ?
% timeseries program%2 v9 x! j( T% e- V' l! U
% this program is used to generate mean value matrix f;
, j# [ O5 G/ X3 m" X. M4 d3 g- ifunction [f,x]=timeseries(data)
8 }% ~6 h. `/ x7 C% U7 A% data--------the input sequence (vector);
v! o" m& `& j% V1 l2 d% f------mean value matrix f;, P7 J, I, P" @, [7 k
n=length(data);
( {1 T* ^0 @% ^: Afor L=1:n/2- x2 v8 E9 R( H* ^! U% `/ @
nL=floor(n/L);6 z. p! ^# f/ Y8 n
for i=1:L1 V5 {; G8 |; W4 F u$ X6 M: S) e
sum=0;
, T) k' v1 u8 `& u* j. M( w for j=1:nL
3 P2 \2 a! B7 y a$ P sum=sum+data(i+(j-1)*L);. ]4 F. V4 o- s+ u6 N& O0 A
end; Y! t [8 v; o/ ?! J/ t6 t; z
x{L,i}=sum/nL;
5 `4 d2 Q5 g& ~+ ] end' b# G* ]3 [4 U6 v" g
end7 Y& x$ i, ` i+ @6 }1 _+ j
L=n/2;
+ x4 J$ Y# ]+ s8 o& Qf=zeros(n,L);
* @7 {- z# c% Yfor i=1:L
: u" U- a2 r0 p- R9 `% O. W$ s7 X rep=floor(n/i);. h/ ?+ H0 d' p. v! S2 N' A% q
res=mod(n,i);/ f( y# D3 M2 P6 Z, {+ n& ?, k8 ]
b=[x{i,1:i}];b=b';
1 d* E5 ^' L8 r- ]/ h2 [ f(1:rep*i,i)=repmat(b,rep,1);7 j, }- @, c1 {5 ^8 S- D( z+ ]
if res~=0, q% y4 y- _, ~
c=rep*i+1:n;% _0 a5 i( s9 ^
f(rep*i+1:end,i)=b(1:length(c));5 Z) r/ P! L1 U3 e8 n" K
end" o1 S* V" J; @, b9 b4 ~ o* I
end4 G8 i4 d+ v5 ]# W5 [3 {
6 s3 `& ^1 K# `1 r% serie**pan.m
7 J' e2 p- a" s+ l& @: Z% the program is used to generate the prediction matrix f; 3 F0 c& F/ s2 O" V
function f=serie**pan(data,step);
9 r0 p9 _' _1 U* }4 @%data---- the input sequence (vector)' L" h/ o$ e& T7 M8 X5 i$ `
% setp---- the prediction number;8 m0 N% l1 {' Z. o% s1 {# o
n=length(data);; [4 d8 _0 z, A7 l) t# r j- b
for L=1:n/2
C$ d# C+ E4 F5 f nL=floor(n/L);7 k& c# B) R+ V E
for i=1:L
9 a& `! \/ z8 p2 C* N: X1 s. k D sum=0;
% }7 i$ e% f4 {1 ^. P$ I for j=1:nL
( \9 j0 @' c; ]2 b# J, B6 v sum=sum+data(i+(j-1)*L);
* F/ @$ s4 x4 L3 G; p6 ? end) U* x, q7 ]. g( ^
x{L,i}=sum/nL;
# e/ A* q" p& \# o end
9 Q b' D) M3 I1 rend8 \4 `1 V9 P. _6 V# K$ y* M9 T
L=n/2;
4 d/ ^3 {3 t- ^/ k8 o9 Lf=zeros(n+step,L);& D& K- X0 A+ S2 c1 e# p* [) g
for i=1:L
P7 L3 I0 Y v; y& Y rep=floor((n+step)/i);$ Q* T7 ~; L- S: P- Y0 Y {7 ^( h
res=mod(n+step,i);9 p v1 s& u0 ^6 w& j4 ?3 G
b=[x{i,1:i}];b=b';
, u% L3 T5 @) U1 s f(1:rep*i,i)=repmat(b,rep,1);
: G' \; A$ d7 y2 \' s; J' D if res~=0
2 i& e$ U8 q2 z7 @6 M c=rep*i+1:n+step; i: J' I* [" P9 t" l
f(rep*i+1:end,i)=b(1:length(c));
! l* o$ Z2 v. d8 Z$ [ end
6 ^. d$ e& m4 @' l+ ?4 Dend
/ Q2 R/ ^ N: U$ M2 E& G
7 }) c0 [' \; v7 n二 最短路Dijkstra算法& j c# V" x' }* J b9 a/ L
% dijkstra algorithm code program%
* \0 v% Z+ O7 K) ? \% the shortest path length algorithm
5 q5 I, F( M" a+ ufunction [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)
: ?- I$ |* T+ K% Input parameters:
$ \- T. f+ r# h j! u% Input_weight-------the input node weight!
' r- V- Y( g P% start--------the start node number;
$ G n3 ^/ h* p6 {7 m. D5 n& v% endpoint------the end node number;/ p' U+ _ L i
% Output parameters:. M: x* E- j8 F& I( h7 P
% path-----the shortest lenght path from the start node to end node;
' M9 @# _5 N, b, i8 M( R" n6 Y% short_distance------the distance of the shortest lenght path from the
; k: B& U4 o+ d G% start node to end node.
1 o) G' R' @ r% V B6 l[row,col]=size(Input_weight);5 E2 H$ r6 s' a5 e
0 \& @. V, p9 l, O ?5 G+ `/ w%input detection' [* ]" Y* N: P/ a) d, u. N' O1 X6 i
if row~=col+ |+ c1 a& G0 P. t3 y$ }: m; o' y
error('input matrix is not a square matrix,input error ' );
* C( I/ E! o% o5 q1 `* C9 rend9 `. _/ l3 t+ e
if endpoint>row
; S4 P4 H0 g# C6 H error('input parameter endpoint exceed the maximal point number');
1 x2 X3 N1 r/ b2 [- o& cend
5 H$ U" p0 s! j/ J7 Q% k3 W4 a3 _- U
%initialization4 m& [3 A/ K+ o- R. m; b+ u# b6 }
s_path=[start];
( J7 t1 P; [! T, o! r* c- C3 ddistance=inf*ones(1,row);distance(start)=0;1 g$ e! |! C$ y( L( W& z; \: h
flag(start)=start;temp=start;0 v" }5 L% L9 J
( t$ g" ~$ {/ M
while length(s_path)<row
& i4 m' o% _ l pos=find(Input_weight(temp, : )~=inf);
. E- h3 O) E8 L; a9 e" E, T# b5 I for i=1:length(pos), i- W) O0 F* b) c6 X3 p; E
if (length(find(s_path==pos(i)))==0)&
0 \# z: D- p, M! e% O(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
) L& A) @, p& x& w- { distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
7 f3 ^3 |9 \* h' k, Q% Y/ w1 J, p3 |' m flag(pos(i))=temp;- h, A4 [2 ]6 T% @3 j1 ^5 R# T
end; {% l, s2 g% Q6 N: a% Q
end/ N7 A) N4 w9 d3 [( ~) Y- a
k=inf;
: |% i9 g9 i! t [; z5 a for i=1:row/ t C) d. i* F
if (length(find(s_path==i))==0)&(k>distance(i))
- j1 y+ j" H; a( c; W8 |2 J k=distance(i);
/ B) J3 F4 W2 Q temp_2=i;% I' H5 p8 M6 U( v, ]
end
$ y5 U/ F- F# c- E8 g8 Y/ q end
1 b2 |. B5 |& U/ \' s& Z0 P s_path=[s_path,temp_2];9 J0 p! o- |* [
temp=temp_2;7 a. l' r [/ [* ~
end3 v: p3 t0 j7 G, L- d+ {! r4 Y0 ?
9 m0 f. L' A5 O+ a/ r$ o0 L%output the result
9 C5 ~: s; M( D3 \! {& v2 Z: ?path(1)=endpoint;5 I2 D# M3 J; J/ O
i=1;2 R8 `( E6 t6 c* a
while path(i)~=start
* U% k( s, R3 J, o! L* f0 j path(i+1)=flag(path(i));
9 |' e9 G* F( P0 n+ } i=i+1;" l o) p& }9 i, l; d. j3 M
end& B8 A N, w' \
path(i)=start;
9 O) `$ v9 ~9 Dpath=path(end:-1:1);. x' Q1 A3 r+ A: Z8 X8 ~
short_distance=distance(endpoint);, p T( ^- x& W2 C' s2 s
三 绘制差分方程的映射分叉图
0 k2 [5 n' d! ^5 K, h
& s; y; K3 t; P( h5 C5 [function fork1(a);
9 O* P9 [2 u0 P8 T/ z0 h; a0 z' w e+ i I, \
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
: \/ E9 V4 B1 {% Example:
# i/ K1 S: C6 ~$ B/ y# e% d% fork1([0,2]); & }, p) u8 U, H8 m3 E1 \9 G6 ~/ n
N=300; % 取样点数
. E2 q+ f0 P& f" eA=linspace(a(1),a(2),N);
1 M" a1 \( A1 m y! P Y% e0 Rstarx=0.9;
2 x: x1 f& J' I9 }Z=[];) n( f9 o) d6 t% G
h=waitbar(0,'please wait');m=1;1 L8 U1 I, ?) O: T
for ap=A; + k5 m+ l" p n* Y
x=starx;
0 r. ], W4 y) Y" \% ~4 T+ [ for k=1:50;
; f' ~! A# I, D1 }$ S4 T8 Y+ n* X/ K% A x=1-ap*x^2;
" L: `5 X9 q7 q$ j u: w: x7 @ end " k$ ~! D$ J' M, D# p6 ]7 x5 G- U9 N" ~0 O
for k=1:201; 8 a" n' s4 N, ]" ^
x=1-ap*x^2;
2 Y+ w: Q' J' R) G0 ?. ?6 I Z=[Z,ap-x*i];
, g7 d8 f, [7 a( P1 E! N; M end
# i1 v0 G1 ]! `$ H waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
9 g3 u$ u0 q1 G, U, S m=m+1;
" k; P: S X/ h6 |end & c& W, t, W% _3 d. ]) U4 |2 n
delete(h);
" Q5 A9 E- [, |; I$ uplot(Z,'.','markersize',2) i3 ^/ h* z! U% Q. I
xlim(a);
! O2 t% w& n2 i( f( T
0 L9 \2 t# { R7 i四 最短路算法------floyd算法
; T$ i4 ~) ?. v% A- |4 M" ofunction ShortPath_floyd(w,start,terminal) ' d/ V ]% y9 |1 P1 M( E( x
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
6 m$ F9 F1 n- J; D: I# S%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
' C3 H) n7 D4 l0 L9 D! y; M) u$ I%start-----the start node;2 i! V1 f0 ^9 d: y! g
%terminal--------the end node; ) x% x# f7 C; ^* K
n=size(w,1);& F: W% ?, v; L% S' j
[D,path]=floyd1(w);%调用floyd算法程序+ W/ b$ w' {- Z s% x$ e( X7 ~4 |9 f5 \
6 j# x9 ]" v6 h- h. n2 w. ~* t d%找出任意两点之间的最短路径,并输出% v( a ?5 l( A* b) ^* ?, S% k! R0 |5 C
for i=1:n# u# [+ ]3 k; `' s
for j=1:n8 l$ n8 ^" }7 R. n+ U& S
Min_path(i,j).distance=D(i,j);
% U" ~# s4 Q/ b# @. n/ _ %将i到j的最短路程赋值 Min_path(i,j).distance
5 ?$ Q, j* o9 A0 S( W %将i到j所经路径赋给Min_path(i,j).path
8 X7 c: o4 ~7 S* }- t2 z: s Min_path(i,j).path(1)=i;
4 ^* K( \: \- @" ~# n% D* y k=1;+ M1 f' D7 `4 K7 i% X: R0 [; V8 [. e9 U
while Min_path(i,j).path(k)~=j
5 {* y- P0 I* c0 \2 Y; M k=k+1;
2 A0 r R$ a+ A/ M" T Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);- \$ x( d( f- D) Z* ^6 _
end
+ A( X0 L5 _5 L; w7 s% Q) N5 d2 L' ^& O end
$ h% F8 z7 [& l/ q* c; \end& j& |7 T( ~0 u& j+ l+ `5 s" n" d
s=sprintf('任意两点之间的最短路径如下:');* e7 S9 I: y L2 D+ a! e, X
disp(s);% t1 y1 e$ m0 H3 p
for i=1:n$ |$ B! C* D5 E- e6 [' P
for j=1:n* U$ s3 j1 A6 a8 P: K1 N$ \( K
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...4 L9 J+ f$ g8 M; y4 }# M" E
,i,j,Min_path(i,j).distance);& V- W4 h# d. e M3 X
disp(s);
8 [1 x9 s" g+ K& C disp(Min_path(i,j).path); Z: J& E3 d' c' m I
end; N" d& J0 e. I# m+ T) k+ }9 N% J
end% b2 m* ?3 U0 \0 f
* a Q0 @0 y; G: b, _%找出在指定从start点到terminal点的最短路径,并输出/ w: ^* C/ C: V: x2 g/ s
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
4 K9 j0 _ y! T9 U& y1 F% o start,terminal,Min_path(start,terminal).distance);
! Z L D- V! |5 V' Cdisp(str1);7 ]5 A0 Z; \* r# ~; N* l
disp(Min_path(start,terminal).path);
9 G/ S1 V6 r* I1 F f
0 d% {8 N! I' W1 k8 a%Foldy's Algorithm 算法程序; I8 } h/ F, o6 T$ G
function [D,path]=floyd1(a)
- y# Y" a0 ?& o) [: i: F% Fn=size(a,1);. v) P+ S9 `( h* a0 P5 g$ `
D=a;path=zeros(n,n);%设置D和path的初值
3 e% K5 r8 Y2 P, R. efor i=1:n' H% x/ c% t- }5 p7 z" i. Q
for j=1:n
/ U$ _) i$ O! [& ^' U+ d if D(i,j)~=inf
" W; X6 |5 Y6 ~ path(i,j)=j;%j是i的后点' [4 s; E$ w9 c; l
end
+ _" e+ G! Q1 p end
) I9 s6 m( e9 N6 r0 `3 pend
2 B' c6 t" ?+ x%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
$ `( d/ L2 I- I. q3 cfor k=1:n
8 [5 h* Q8 U& d for i=1:n4 B) S5 y$ |" D0 ~4 X
for j=1:n! O3 I: t& O' x
if D(i,k)+D(k,j)<D(i,j)
1 Y1 N1 u* W, X, w$ j k D(i,j)=D(i,k)+D(k,j);%修改长度2 t9 F/ ^9 S1 g n' g
path(i,j)=path(i,k);%修改路径5 e/ S6 }" D& y7 g+ X8 r
end. v1 \, D3 k' N3 ?2 f9 `1 Y
end
" z# J- S1 A! O$ z end
, I+ i. w; M) h% e+ ^0 mend
7 L4 }: ?+ [, z2 W5 T) W/ q" n8 G9 R
五 模拟退火算法源程序
B1 a0 i3 g( |8 M5 w% n- Wfunction [MinD,BestPath]=MainAneal(CityPosition,pn)2 N }. B1 i& W. X
function [MinD,BestPath]=MainAneal2(CityPosition,pn) W* H3 z2 @ T- A" x5 V+ E& o
%此题以中国31省会城市的最短旅行路径为例,给出TSP问题的模拟退火程序
, s, E+ k7 t/ j' @& |%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;..." X0 ^' o" A: ?( N* _- e E
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...' L% Y/ b" l1 X# x
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
6 i8 [" I1 @8 O. k n d% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
0 f7 u2 a; l3 M' ] v d& n% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
) `+ _. Z. B6 A: c2 [
0 p* P j& }6 f: e* z%T0=clock+ {2 q3 o% t; Z6 r
global path p2 D;; m& ~' Q* i) G' I- r
[m,n]=size(CityPosition);. ]5 `* _1 L' S/ X( @+ d1 ^
%生成初始解空间,这样可以比逐步分配空间运行快一些& D" _ B" _: Y' u) n
TracePath=zeros(1e3,m);3 M' S9 x1 I+ A2 ]- W8 Y
Distance=inf*zeros(1,1e3);
' N, D8 n1 @5 q' u. c4 [9 {3 S t0 z6 A0 m; f9 F; i6 ~
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...# q" G0 ]6 b3 F5 ~% \( s, C' c
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );9 m+ D1 R' U7 L
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
2 c. i: x4 g4 O( R. x( s) ^; m" G3 ifor i=1:pn: c4 D- A- p: J
path(i,:)=randperm(m);%构造一个初始可行解2 M( R7 |$ D, k; @) A9 s( c5 a4 ~$ D
end
" |5 T( N) W1 Jt=zeros(1,pn);
+ P. Q6 c. z0 N3 U3 Sp2=zeros(1,m);
2 S5 d; K+ c1 O& U$ T
8 u- w7 E8 A/ A6 U1 p3 S( Iiter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );6 A1 Q; m1 {* Z1 U4 n( K3 y- |
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=' ) ;+ j; ?- v9 H4 [7 g
%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! S W8 z( P& D, N( u/ t! i( L& Q6 O
%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 C) d$ I6 ^5 ]/ |5 X%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
9 ]( Y+ ~8 n9 H3 h+ h# |7 U%会收到到比较好的效果
- V( d1 p ^! X- S% \
+ v b, {9 z) m5 ZT=1e5;6 L! f% F2 S+ B3 l! {) w
N=1;
; C" p7 C) g8 Etau=1e-5;%input('请输入最低温度tau=' );; K7 G8 q1 i$ ^% R0 m
%nn=ceil(log10(tau/T)/log10(0.9));
, q4 s. a% v5 t' [while T>=tau%&m_num<m_max $ o4 r$ a7 `3 y, B8 E
iter_num=1;%某固定温度下迭代计数器
; ]/ N( n: ?" D* | 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 t" {7 X- G* ?: P6 }8 a! C %iter_max=100;
5 ^% E2 b0 p. T& y' C %m_max=10;%ceil(10+0.5*nn-0.3*N);" |% I. b$ u% M, t
while m_num<m_max&iter_num<iter_max9 ]4 @) b+ ], Z
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
% u" h4 _) d$ ~# J0 N %用任意启发式算法在path的领域N(path)中找出新的更优解/ Q; E s2 ?) }
for i=1:pn2 t" a: v6 I" U4 |) u
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);1 X3 i# A: n0 b, Q1 X. w
%计算一次行遍所有城市的总路程 9 o7 `3 L, X( ?5 M
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
* B) ^& ~, j, `- Q1 d Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]); Z; |$ o/ H$ @5 a0 a* q9 E+ D
end( m }! M2 A. T, {) O, h
%Len1" E( A; q$ W3 n, o8 E. I
%Len2( Y, ?+ h/ z% {5 x% Q
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand* D Z% _9 m+ S: k: a
R=rand(1,pn);
( G3 @0 S8 l$ U! Z) c %Len2-Len1<t|exp((Len1-Len2)/(T))>R
/ y# W, ~( Q8 C( o! f- X if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
5 ?2 Z, U( s2 e4 q3 W path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );# g5 y4 f8 c; N+ N; s/ Q' f
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));, p" r1 f: A- ] v
[TempMinD,TempIndex]=min(Len1);
$ q! ^1 P+ a1 T* r$ g0 C# C %TempMinD; S' p1 t* o5 p) n
TracePath(N,: )=path(TempIndex,: );
. [. Z7 v* [( M5 M; X8 l& j Distance(N,: )=TempMinD;
$ h" F j8 j; g/ W1 C N=N+1;8 E$ ~; H! ?0 W$ }
%T=T*0.98 G# W' V% D x3 P/ ~+ j
m_num=0;
' Y& O( _5 u) e" ~' ~+ v& Y else
5 v! G2 s2 h& W9 s m_num=m_num+1;
6 U- [% p, H! c& ` end+ v8 [# n6 p* H" q) a
iter_num=iter_num+1;) q" N& [) u- r/ z/ V
end+ S) [; V3 R) R" a, V* D
T=T*0.9# A( N1 L/ d/ G; g- q
%m_num,iter_num,N
! t0 Q$ C# [- I; Wend 1 q/ C/ L% {9 ]* p. S
[MinD,Index]=min(Distance);/ S* s% L4 F/ V* C+ F
BestPath=TracePath(Index,: );1 X) Z( \7 P% Y8 P' K
disp(MinD)1 t2 }3 Z& w- t! Q6 j& V
%T1=clock
, }' U# K0 w* ~6 S8 ~7 W) f1 {+ E( R. O
& Z5 H0 c9 y& q; V 8 n% r, e1 ?5 J$ K% X, R& p- P
%更新路线子程序
+ Q: ]' z0 h4 x- U' w- N/ H' Cfunction [p2]=ChangePath2(p1,CityNum)
) g! `7 {4 C, d: m% m7 e/ Vglobal p2;& }- k1 [, q5 Y7 D! i9 K+ }
while(1)/ O/ Z. h$ G N, V6 P: ]) V# Z
R=unidrnd(CityNum,1,2);
! ` o# x4 l; o% L( w8 p) A if abs(R(1)-R(2))>1
5 E; ^/ O8 H* \- S break;. c; b |) c1 ?! R, S2 z7 S$ T
end* l: U5 d0 j5 g# M
end
) a" ~, V5 }8 a! vR=unidrnd(CityNum,1,2);; l4 A7 O- d4 Z
I=R(1);J=R(2);
3 O$ P/ q' F; }# n* w5 w5 K%len1=D(p(I),p(J))+D(p(I+1),p(J+1));* P2 _% \+ |" G8 k) ?
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
, X, F3 }! \# E; {if I<J
4 V; G' p( l" g: y) W, C p2(1:I)=p1(1:I);
3 t: {8 ^. X5 a. S$ b p2(I+1:J)=p1(J:-1:I+1);
6 n K2 G* r4 B# P p2(J+1:CityNum)=p1(J+1:CityNum);
+ U7 g% A. y% e( F8 I2 pelse2 I& D: T0 i3 f# S1 L' h1 s
p2(1:J)=p1(1:J);
( ]5 T# P3 z/ R" [2 e3 W p2(J+1:I)=p1(I:-1:J+1);6 U- V$ g2 h* _1 l6 I$ K! I: N6 ^' d
p2(I+1:CityNum)=p1(I+1:CityNum);% x% L1 p& G1 f/ o0 n: R
end+ I; ^2 T! `; p, H" f C. R
( J/ B W' K, ^ F; `2 y
六 遗传 算 法程序:
# a) X& y6 I$ G/ {! w 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 H1 x; i+ y( F, z
1 A1 ]- [$ X& J0 \function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
2 E* x* n" U2 I- @9 U% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) 6 K- M! M5 n8 o" M2 P( B
% Finds a maximum of a function of several variables.
, i( y2 G2 Z% z% fmaxga solves problems of the form:
9 }2 z# w5 S& x1 V% max F(X) subject to: LB <= X <= UB . `& { ]3 {/ u, L- ~9 H4 m# g
% BestPop - 最优的群体即为最优的染色体群
: R) Y. E- `( s) n; q- V( u8 ]% Trace - 最佳染色体所对应的目标函数值
3 L7 w( E2 l3 M" M" d% FUN - 目标函数
0 t3 s" p6 z9 x$ H {/ e% w% LB - 自变量下限) ^5 v2 S: D T) Z9 [/ k
% UB - 自变量上限
% l( w: }& ~# t3 B# H/ G& P% eranum - 种群的代数,取100--1000(默认200)
3 D; Y+ z P2 x7 J8 I% I2 Y% popsize - 每一代种群的规模;此可取50--200(默认100)
# i/ U/ H% x. C% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)( A( l- {7 [9 Q7 l7 s2 B
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
0 }$ S7 K8 T4 o. E( m9 k- S2 L% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2): v' O$ K V5 a/ a
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编+ G$ \& z* O! P7 v% C% H
%码,option(2)设定求解精度(默认1e-4)
+ ]+ O+ z( b2 t% j& q%; C, [ T v+ K: E7 ~& Y
% ------------------------------------------------------------------------
' v. R9 ?. g, B }9 @, Y' ^( s& q; d7 A$ g8 \
T1=clock;3 o Z y" e2 S& c" @" M
if nargin<3, error('FMAXGA requires at least three input arguments'); end3 E0 @; _3 C% j9 S1 m7 h7 A. V0 t
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
0 ?- A' E3 r3 @& a$ E4 S3 _if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end5 |% c8 ?% D) s0 `
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end: S. ]* K0 |5 Y2 G9 J O, r6 b
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end) B8 R; o% c5 s- C& L& L# I6 d
if nargin==7, pInversion=0.15;options=[0 1e-4];end- f* z% ^4 n: x- J; U3 M5 T
if find((LB-UB)>0)
' \% A J# U/ S* u" H# S0 N error('数据输入错误,请重新输入(LB<UB):');/ v# A* ^% l, u6 ~% \
end7 i/ ^$ d! B% t/ O
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
4 J6 b$ ]6 c# z5 [& o* e/ Pdisp(s);3 f/ N4 a% ^! I. ]; r* Q
" V5 Q, F/ T( d5 |global m n NewPop children1 children2 VarNum! p. _ x# Z- S, y: |+ E" T( T! L) y
8 g" E7 X p. C
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);9 D$ f0 P/ t( L8 h' u
precision=options(2);%由求解精度确定二进制编码长度
7 O9 g( f1 A4 j3 e/ J8 O1 }1 vbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
, x$ ?- g% b4 ~' G2 M- ^9 K; M( F[Pop]=InitPopGray(popsize,bits);%初始化种群7 l- z/ a; m/ v! d3 B* D1 M8 W
[m,n]=size(Pop);
7 z& O) ]8 ]# y+ w9 K3 N( dNewPop=zeros(m,n);
Q+ M4 a, S6 F+ q6 \5 cchildren1=zeros(1,n);
h( _; v. n& C- v- J- k; o* [8 kchildren2=zeros(1,n);& c/ l$ X \* Y+ c3 k3 M2 g
pm0=pMutation;
/ s7 {# _/ W6 d4 ]BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
3 O! c8 T0 `, S, W* ZTrace=zeros(eranum,length(bits)+1);
% I& y1 @7 `/ J- ei=1;- b0 U$ @" |" v5 g$ w
while i<=eranum
i$ e8 J+ |( V7 h1 w# H- C; j for j=1:m; e. |8 f6 n. B6 V8 X2 ^* w
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度" _/ ]! K* o5 B+ {5 ]
end2 m& ~* w* q$ |% a) I! l" L+ q( \. y4 W
[MaxValue,Index]=max(value);& T* K4 \9 u6 G4 ?# b3 F& z3 ?
BestPop(i,:)=Pop(Index,:);
2 w% p2 W6 H: v2 r) A Trace(i,1)=MaxValue;% q2 y5 ~: z/ V* {6 N
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);: e9 p; y8 U7 r! R6 C, K
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择# y8 j& \+ `2 U' {# q7 J7 P
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
% u. T& l$ r3 e1 P%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
4 b. l' a6 m( b9 q# Q+ p %round(unidrnd(eranum-i)/eranum)
8 F: k2 P1 z! p c/ O; T5 N( X+ U [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异1 {) I- H' f! m" k5 T5 K1 R6 g
[InversionPop]=Inversion(MutationPop,pInversion);%倒位
' ^0 Y) C# A9 `; b* ~+ D$ C) X# \% E Pop=InversionPop;%更新" u) v/ ~, i3 w: f1 j6 v- B# ]
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); # F6 L6 R# _% @1 I
%随着种群向前进化,逐步增大变异率至1/2交叉率" S- |6 w0 Z9 _& Z, r) j) l
p(i)=pMutation;
- g) H7 [, S6 }3 p0 j# W# F i=i+1;
; ]- r9 H! o( C$ }0 L6 _6 S: aend6 Z7 [$ W& n8 c$ ]! x
t=1:eranum;
' X# ?" z, Y, D5 Y. r2 j0 I) qplot(t,Trace(:,1)');
, d) h0 N6 ~7 ~8 ptitle('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)');
# } E' J% ^8 O! Q1 t* z ~6 h# G[MaxFval,I]=max(Trace(:,1));
5 R# k2 R* Q8 H2 EX=Trace(I,(2:length(bits)+1));
* ~5 D: E Y+ o0 O+ X1 K6 J' Thold on; plot(I,MaxFval,'*');3 U2 r' e: r6 ]' M
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
& Y% J% ?+ x6 N7 Kstr1=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,:)));
! k. ^0 H# _/ r0 Z6 E# `; ]disp(str1);
4 n) I H! B# |# w4 Y%figure(2);plot(t,p);%绘制变异值增大过程
7 R x# r( j6 m& h6 _T2=clock;
; l4 s/ K G$ Q x# a. Xelapsed_time=T2-T1;
' Z. G/ A( V6 Q( u; C, D: `$ jif elapsed_time(6)<0
, a$ C# g' J* R; p* @, g6 `0 l5 C, b elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;6 t; p. u! @ X$ C& H
end
9 c' Y+ f5 I" e5 O8 O7 s, Gif elapsed_time(5)<0% n0 @3 m: c5 N8 ?7 {1 c
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;, a+ _7 R* ]) V2 _
end %像这种程序当然不考虑运行上小时啦# Q/ ~6 v) ]7 [1 ^* |$ k# H% V0 L
str2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));4 w r7 o, f( c) l
disp(str2);' E+ T9 H4 ~* C! R% I
, N k" G3 t: ~( I* S, r. J, O1 Y( ~& \* H5 ] y S- I6 V
%初始化种群# \4 \* z0 W5 t' E( [! r- a& S
%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( ?0 I, b3 _4 |) j$ ]6 B% z
function [initpop]=InitPopGray(popsize,bits)
, N1 ~" V+ b* a% |+ p# xlen=sum(bits);, J9 F8 j, Z; y- @
initpop=zeros(popsize,len);%The whole zero encoding individual
( W" v) \, n8 |$ J1 j* h2 R3 \for i=2:popsize-19 b; A* A% H7 Y6 Y1 V1 d" n
pop=round(rand(1,len));
4 k9 o/ H) O+ B$ T pop=mod(([0 pop]+[pop 0]),2);2 K5 o3 `1 d* M4 @5 p; y) L1 S
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
$ w9 d6 }' [3 u" U: { %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
0 K7 m3 v3 Y3 O- m& J1 G, Q+ t initpop(i,:)=pop(1:end-1);& f1 h) k8 t1 l- s
end
: K1 S5 M e( e P- Tinitpop(popsize,:)=ones(1,len);%The whole one encoding individual9 b; U4 Z- Q7 N! u* x: s* F2 i5 |
%解码9 Q4 o0 _' g" U
. @" S- w8 P3 |4 l4 e( P
function [fval] = b2f(bval,bounds,bits)
m, j5 Z: T) C8 X: \% fval - 表征各变量的十进制数9 t( M+ K o. s+ O* |
% bval - 表征各变量的二进制编码串
* W" }! ? s7 @3 v% bounds - 各变量的取值范围% c6 v: B$ J7 U+ v2 @
% bits - 各变量的二进制编码长度3 }3 Y# x: _* _6 v$ O& a: @
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables( m3 h1 r+ [# Y' E$ z
numV=size(bounds,1);
, L. }) b. Q+ k0 Gcs=[0 cumsum(bits)]; 4 C0 |, L7 u. z. I) C3 v
for i=1:numV! H" e7 {, S k: W
a=bval((cs(i)+1):cs(i+1));
7 e! i- Q* \7 ~! R9 q' G+ { fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);8 Y7 [! k9 n; o3 N' m7 _6 d. m
end
; ^, s/ ?* o- {%选择操作5 k- {; @% H9 @! P0 D2 T! x
%采用基于轮盘赌法的非线性排名选择! U- R: H/ e7 Y
%各个体成员按适应值从大到小分配选择概率:
, b, D% I' n1 c4 z%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=13 H+ q! I1 c: n5 Q5 I* _* w- G( G
7 }+ e5 e& z8 B& g. ~
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
. D3 m& D% v! y7 }; jglobal m n m. G% D) @* G
selectpop=zeros(m,n);) [0 t0 \( ?4 v
fit=zeros(m,1);
% q, K$ _8 L" Z$ Pfor i=1:m
2 B" M. z8 q* G* m fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据2 Z2 [% {8 D' H9 M8 M9 E
end, q3 T1 w" i s6 f+ Z) L+ R8 m; r
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
) C7 s& G7 K' O8 dq=max(selectprob);%选择最优的概率2 h$ Y3 z* f, s7 ?
x=zeros(m,2);: Z; Q P. P9 U$ t/ r
x(:,1)=[m:-1:1]';5 t5 m, \) P9 p/ t/ F0 V* T- k
[y x(:,2)]=sort(selectprob);
$ V7 l6 h1 A& j7 i$ Y1 N. Kr=q/(1-(1-q)^m);%标准分布基值
6 Z% U* p0 Q0 Bnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
6 j# t3 k! K2 R# Y7 Y, W) l$ Jnewfit=cumsum(newfit);%计算各选择概率之和; d; P/ X; h2 b
rNums=sort(rand(m,1));
2 ]" F7 R/ u6 M4 h3 @' E0 rfitIn=1;newIn=1;
1 L0 c: k+ M, p+ r) hwhile newIn<=m
9 C) t% S% x( J! ^7 K5 d% q if rNums(newIn)<newfit(fitIn)" R6 v! W8 o4 l7 @% R- J
selectpop(newIn,:)=pop(fitIn,:);
. y6 a# D: L" y5 ~5 m2 ]& [ newIn=newIn+1;% h' A0 |8 f" g& v7 Y; y: W5 C
else
X& ?2 ~, B7 U; w, g0 D+ L4 [ fitIn=fitIn+1;0 T) w. G5 f0 f- G7 b
end% X X+ V4 p0 M2 V, t
end) a6 g1 p# K% i4 M+ a! [: ^& z1 P
%交叉操作. \1 w+ u' j! ~" i+ \
function [NewPop]=CrossOver(OldPop,pCross,opts): @5 h, `3 h5 {# a
%OldPop为父代种群,pcross为交叉概率
0 j9 r4 T. @7 G% e/ q: Nglobal m n NewPop & M: W. G4 j0 Z1 c2 m3 [
r=rand(1,m);2 p& D0 ]9 f- j
y1=find(r<pCross);5 m! x+ {. J. t- `8 M
y2=find(r>=pCross);
, V6 {2 R8 E8 p1 o2 Dlen=length(y1);* X0 A J9 o( `. P# {
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+ U- W; T- _; _1 @ j
y2(length(y2)+1)=y1(len);' o K, m" K- h7 `
y1(len)=[];
; N7 @, g2 ]6 ^, A; ?! z ]0 Xend! ]3 L+ h! n/ G0 O$ y0 D
if length(y1)>=2
9 e, g8 L: l/ V" g for i=0:2:length(y1)-2
5 [. Q0 D$ k' e& G6 ? if opts==02 o$ @! x! S S- W- _5 k
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
# D- P9 `% r2 @' i7 [$ C% ^/ ?; n else3 [' { a- h0 X$ D' i$ `5 m' r
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
1 n ~- J/ W& P* [# r" K1 Q' C end
2 u" B- m$ Q' n" P& l/ S7 c+ e+ M end . \7 i c4 E$ n
end6 R; G" ]5 R5 f+ \9 B! E
NewPop(y2,:)=OldPop(y2,:);
+ n* o0 M7 n5 O& ]$ F4 \5 j% c1 Z% ~# E6 u
%采用均匀交叉
# e, v! w O8 a/ bfunction [children1,children2]=EqualCrossOver(parent1,parent2)4 B1 ~2 x, d' N; g% v$ [/ {/ ]
- w+ m& J5 k _, Q4 Vglobal n children1 children2 ) u; n% N2 r7 @) n1 \
hidecode=round(rand(1,n));%随机生成掩码
r" \6 p8 O, t4 j& |- Q0 C, P, scrossposition=find(hidecode==1);* S( P* }2 d! }- Q6 I" ?, }
holdposition=find(hidecode==0);
8 H9 O* e3 @& B; z: i- Pchildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因7 m7 O; G+ J+ y W) l3 W, K( m
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因- N5 `1 [ p0 ?' _" S
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
2 o9 E* f: ]5 \6 Y6 Q J schildren2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
! G% A- ]5 X- x8 s" m3 ]
9 a% Y: R! `- I! e; [" Z%采用多点交叉,交叉点数由变量数决定
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function [Children1,Children2]=MultiPointCross(Parent1,Parent2)
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global n Children1 Children2 VarNum3 B# E. s/ r; M0 _* P# |/ l: R4 }( W
Children1=Parent1;# `2 U8 X" ~( D7 F# D0 x3 ?& q
Children2=Parent2;& s5 o0 _: r7 o5 F* i
Points=sort(unidrnd(n,1,2*VarNum));
! H* u1 q- `; g J; pfor i=1:VarNum* |5 v; J& v. F2 B9 M
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
! V8 ?; H4 _, I( f Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));* l! {3 `1 w) ^- W6 [7 D
end
" j% R; m/ W S0 Q: O+ |5 Q4 X( P: E9 |* b+ J% u
%变异操作
, W4 R9 ~7 s, G) [' Wfunction [NewPop]=Mutation(OldPop,pMutation,VarNum)
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! I# O, c+ C0 U5 Mglobal m n NewPop
1 q/ e4 N# L$ F/ g) E" Ar=rand(1,m);- x$ f7 [ y3 D2 \+ N
position=find(r<=pMutation);
' Q9 ^7 B+ s2 n3 }. M' u" J: H% a/ elen=length(position);: ^- h$ N$ R& J2 j- r
if len>=1
' a$ C$ L5 N- r: ^5 E: _5 [ for i=1:len+ j# i) Z* z/ q. t* e
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点1 N; l H, _# |$ U, X
for j=1:length(k)
+ c2 g& s# m2 O" x, E2 _ if OldPop(position(i),k(j))==1
2 M, c3 j, j M- n A, S5 ?" R OldPop(position(i),k(j))=0;
/ x( w' R/ y2 Q+ D$ R) } else0 f6 ?/ c3 {! F. [
OldPop(position(i),k(j))=1;* M9 F1 W$ e1 P' J
end
9 U: u5 P' Y. {5 R- Y; J! l% R end
* L4 n4 ~) f& O) v end
) _- R0 N& e" \1 ^# Mend
8 `; {$ e2 Q: D+ zNewPop=OldPop;% ^- O" D" w* q. [. f, D
1 @$ T8 Z: R: ?7 x7 j: n%倒位操作; o, T2 ]; Y: A* J
5 \0 W( D- k1 t6 m7 nfunction [NewPop]=Inversion(OldPop,pInversion)
" J7 ^, Y5 t, ^$ ~- x/ v
5 b$ k! E- e1 b. C- G1 Xglobal m n NewPop
* e0 a% o" y2 j* ?NewPop=OldPop;$ T. }5 ^# P% j. i: l3 m
r=rand(1,m);& {5 \) `+ u2 u; S! r
PopIn=find(r<=pInversion);( d+ ?: u' M& d, K
len=length(PopIn);
) _) |+ G( f* v& {5 o: d7 kif len>=1" i6 U& u5 p! F+ P2 R- W* E k
for i=1:len
* t+ l+ } H' d. j4 f d=sort(unidrnd(n,1,2));
/ `1 q4 M# y8 x0 @+ A3 ~ if d(1)~=1&d(2)~=n
$ C. ^: l( t& N" n0 z NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
6 ^$ v& {) ~4 P M$ F; j/ w, u9 ] NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));+ P6 c. g) h. a3 ~/ G( ?# u
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);% b$ O! r% t2 }" E: E
end
: Z9 U( R ^( b7 F3 L% n end
% X! p( [8 r/ E; Send8 h- k3 E$ R( ]$ U
1 E4 C8 k \0 w5 l( n& J" Z$ n6 e3 w, i
七 径向基神经网络训练程序
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clear all;1 y$ [6 H! S2 F* Q
clc;
( x+ H% y; I/ U3 R3 W- l' e%newrb 建立一个径向基函数神经网络
$ l& K8 f; U \, Q6 r. Sp=0:0.1:1; %输入矢量
2 ?; Q4 D( [- c/ At=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
% \7 N0 H2 r5 _! c. B- N& Wgoal=0.01; %误差
4 Z c5 L6 Y9 J& {3 l8 ?4 msp=1; %扩展常数
, L1 ~7 @8 X6 o2 e: ]mn=100;%神经元的最多个数9 M+ c: h5 ? L/ Q- v
df=1; %训练过程的显示频率6 `& a4 T" }9 S( C! n! p
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
" o0 N/ F$ d* F8 e- ]: r5 N% [net,tr]=train(net,p); %调用traingdm算法训练网络
* T9 X- F4 \5 f! K%对网络进行仿真,并绘制样本数据和网络输出图形
3 i2 I! g& @+ D1 j# c- \/ AA=sim(net,p);
- K* q$ M; y7 P- s, kE=t-A;- y, U3 \# Y2 t% o
sse=sse(E);
; A a$ X8 v$ e, kfigure;
+ \$ X% ^# f7 |- aplot(p,t,'r-+',p,A,'b-*');
/ p8 |8 g: G1 O' E& Llegend('输入数据曲线','训练输出曲线');8 P9 {% d- g- H& W/ ^
echo off $ a0 I$ b% [! k& y9 D
1 {# p* D7 u: |1 J说明:newrb函数本来 在创建新的网络的时候就进行了训练!
7 z/ Z$ |: w `& S4 u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,
o: M6 A* f5 l! K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, z7 {% X: K7 U# Q
9 k2 {) Z5 F+ }
7 u0 D( _& E( f: q1 u y1 Q' p
训练结果显示:
$ N, n! ]% G# y! x& h" h9 WNEWRB, neurons = 0, SSE = 5.0973" Q' B. x7 N+ {* h
NEWRB, neurons = 2, SSE = 4.87139
9 W% c/ d D4 }9 x4 ^" {NEWRB, neurons = 3, SSE = 3.61176( J1 G0 J5 i/ M6 z- D
NEWRB, neurons = 4, SSE = 3.4875$ q7 f% \5 l# x6 X1 |( [
NEWRB, neurons = 5, SSE = 0.534217: V; J. s M5 i( [
NEWRB, neurons = 6, SSE = 0.51785
# ]5 n) Z8 `# M7 D( tNEWRB, neurons = 7, SSE = 0.434259
3 {2 I, `( J7 v% BNEWRB, neurons = 8, SSE = 0.3415180 n1 [8 ]0 C: S$ K1 t( m' _
NEWRB, neurons = 9, SSE = 0.341519
% A& n! G; r6 V6 b( BNEWRB, neurons = 10, SSE = 0.002578325 e p* u& l/ c$ C( W
& A$ B1 y5 g; e
八 删除当前路径下所有的带后缀.asv的文件$ {( b+ L4 ~& e
说明:该程序具有很好的移植性,用户可以根据自己地9 P/ U& h; _$ K, y6 E
要求修改程序,删除不同后缀类型的文件!
) W+ a+ C5 ^$ y; [6 P* p' vfunction delete_asv(bpath)
9 \4 G7 P$ J) u% W%If bpath is not specified,it lists all the asv files in the current
1 f5 a* U) {8 J4 e" o0 C6 V%directory and will delete all the file with asv
% E/ r8 P9 p/ V1 x% Example:
) j5 F( P. M+ }8 l6 Z% delete_asv('*.asv') will delete the file with name *.asv;! {; G' ]2 I* u( u- G) B: b0 h0 i
% delete_asv will delete all the file with .asv.3 M8 ^6 r5 I) h- K& y# B4 K
, N% @5 b8 `9 T' Z
if nargin < 10 J/ p! r( E3 n0 | y0 S% ~7 ? c& ^
%list all the asv file in the current directory2 |; v/ d9 @* R2 U6 w, a2 E+ K
files=dir('*.asv');
* M* C- A1 h( felse& R, x1 L1 }1 Y6 p R
% find the exact file in the path of bpath+ Y# Z f" T" v) i
[pathstr,name] = fileparts(bpath);
" _7 i" Y- N* O8 S1 a6 t) s if exist(bpath,'dir')) \# x/ |" h) ?+ C
name = [name '\*'];6 h2 `' ?5 h, T& A
end
" n* n" R0 i3 S$ J4 g! b" H ext = '.asv';/ s; m0 O1 O. ?7 `
files=dir(fullfile(pathstr,[name ext]));" `8 D) C' z7 M
end' D* I2 S0 e" e, K. o; o K0 T
6 h: _4 a" W& S
if ~isempty(files)
8 n2 ^* d/ H* {( h* x for i=1:size(files,1)/ J& w2 ]2 c9 ^2 \3 `
title=files(i).name;
! w) _9 C# e0 ?+ d' m! F* a delete(title);# a* V1 o, }9 X2 {, o
end
1 [, k7 d3 x5 |end" S% s( N. k4 m0 k; \1 O
5 M1 _! B( ?; \& C8 X, C5 T ?* x7 t/ e" J4 j* E
同样也可以在Matlab的窗口设置中取消保存.asv文件!% u3 f0 l% H1 V0 \" b" E, j
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