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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# N! i4 N& {' [( h6 [
1. predict_fun.m为主程序;3 t r0 q* A' `" t
2. timeseries.m和 serie**pan.m为调用的子程序
( k5 \ I! g" x3 O$ |7 i) U* T' x& G' T
function ima_pre=predict_fun(b,step)
( Y( `! g2 Z& U3 D9 F; @; Z. T% main program invokes timeseries.m and serie**pan.m7 N/ ~2 _6 `4 f) m* c
% input parameters:7 R* k2 D* U, c! o
% b-------the training data (vector);+ \. Q0 S" P4 o
% step----number of prediction data;9 B3 U, g. p0 M3 c" n
% output parameters:( w6 A& }0 ~# g# M6 y& R$ v. t% ?
% ima_pre---the prediction data(vector);0 H; f7 O) i- h3 k+ A
old_b=b;
- M7 m6 p* Z* }; s, O i [6 _+ Mmean_b=sum(old_b)/length(old_b);# d( z2 c0 i3 Z) A
std_b=std(old_b);
' _6 _5 E+ y9 b. ^ W. Jold_b=(old_b-mean_b)/std_b;; K0 G9 j3 e |8 s$ o
[f,x]=timeseries(old_b);8 Y6 f1 e2 b+ |
old_f2=serie**pan(old_b,step);. B! n0 ~" Q( y- C7 d
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;- a( x- O$ y( b. R0 _
R=corrcoef(f);
, O; K) Q" D2 P" E7 o[eigvector eigroot]=eig(R);. a, K, o9 C: u$ r
eigroot=diag(eigroot);
9 Q# C9 I8 T+ b4 s) f( J1 X/ \! ga=eigroot(end:-1:1);# x3 h% x6 I. a$ _) l: D$ m d! _) P
vector=eigvector(:,end:-1:1);% [+ _4 [1 F" @
Devote=a./sum(a);
* g4 D ~- @5 x PDevotem=cumsum(Devote);
/ s1 G# k3 T; Tm=find(Devotem>=0.995);
3 \! @5 Q' }6 S6 f: c4 J+ fm=m(1);- D' m" `$ x3 ^4 f) e: N
V1=f*eigvector';" V& p0 O8 d5 e6 @% j9 ^+ y
V=V1(:,1:m);6 c( z' h( g! b% y) v0 H
% old_b=old_b;1 u8 s( H4 {+ @$ I \
old_fai=inv(V'*V)*V'*old_b;
9 {2 k; m9 M8 oeigvector=eigvector(1:m,1:m);
* V F' U4 D/ v( X. m# `3 `2 Efai=eigvector*old_fai;. P8 r: D& s1 ~6 \6 C
f2=old_f2(:,1:m);
' N6 q6 R/ \! v; `8 r9 k& H* d. }predictvalue=f2*fai;1 W3 K b1 `+ J6 N# |
ima_pre=std_b*predictvalue+mean_b;2 ]4 Z" @5 p9 O6 o2 l* |
3 |& m1 O, B% X& w$ W! f' ], z2 d1.子函数: timeseries.m 2 T1 U4 I9 @3 m8 b! { U
% timeseries program%) @" t7 U7 ?7 q6 F0 d) {
% this program is used to generate mean value matrix f;
: |9 ^4 i! r1 V/ Y; z1 ]function [f,x]=timeseries(data)
* d1 f; T8 F3 x1 W% data--------the input sequence (vector);
B: B( M% v$ `* _2 F0 K z% f------mean value matrix f;9 Z9 |- I W U
n=length(data);
3 p2 a9 n7 S; s; w. e# x# s( Qfor L=1:n/2# [/ b1 I# Z0 t4 k( q- z
nL=floor(n/L);' b% r" E% N, J7 \2 c/ z) |( E
for i=1:L
7 ?# L6 j4 T: b# v sum=0;' ] V( v" e4 _0 t
for j=1:nL- b2 ?& L( C! a, I9 f
sum=sum+data(i+(j-1)*L);9 } R/ Z/ }% X8 k
end
8 X, u- X( ~8 Q, @ x{L,i}=sum/nL;
& y2 [1 N6 i* D6 _) X- N6 {7 E* l end
7 |8 y2 k. x/ i8 X5 }! C/ \! iend( q; N2 x$ U, Y
L=n/2;
! o/ R# h. A8 M4 i( h) T. Af=zeros(n,L);
5 d/ E6 P% V" q: I0 Nfor i=1:L
1 t3 Q/ j0 j2 @+ H rep=floor(n/i);
% W" }0 H4 Z. M res=mod(n,i);
) X e% Y1 A! o$ `. r2 L# A b=[x{i,1:i}];b=b';
8 n% E* w) X/ [. f# U6 N2 v f(1:rep*i,i)=repmat(b,rep,1);
2 O; Y6 s" e9 z- z! I if res~=0
+ t$ ~, R4 \! b) ?0 `% t# ^5 a c=rep*i+1:n;
3 ~5 h, f4 [% i* I f(rep*i+1:end,i)=b(1:length(c));
4 d3 F* u7 {6 [ H2 [0 |* X end! K! J. X% M! o& o
end9 O) K: ^( Z6 [* `* V7 m
, O n: R6 s" I% V/ F% serie**pan.m9 f4 G% Q/ k/ t* m) t, t1 T
% the program is used to generate the prediction matrix f;
% B, h' }& j1 g3 s, @9 O$ a9 y4 rfunction f=serie**pan(data,step);
7 ]1 g/ j4 V' i; A P%data---- the input sequence (vector)
- {0 z$ N/ x8 Z2 {% setp---- the prediction number;
7 L5 f" b& d. [6 ]7 H# vn=length(data);
+ M. n+ Z7 @; c2 }4 c0 }# pfor L=1:n/2* T/ p; {* L- L V' f' g; ?2 @0 g& G
nL=floor(n/L);8 m% `8 ]+ P; ?3 S' F
for i=1:L
1 `! @* B' s! }+ b- e sum=0;/ i5 E6 z& s8 u v! V$ o4 ~# g* {
for j=1:nL6 r9 }! E6 t) j2 B( n. p7 W2 Q9 K
sum=sum+data(i+(j-1)*L);3 Q" s; u3 f) J: G0 |' ]
end
8 d: ?% ~: u. ~3 g; L3 ` x{L,i}=sum/nL;0 u' L# D9 k' U" q; c" s, Y
end
" c* x" C8 W' d9 W" Mend% x6 m3 \- X, c
L=n/2; l4 q' P |5 M
f=zeros(n+step,L);" ?% N; J# O3 V* t' ~4 o
for i=1:L
- \" W5 `/ ^' f2 z rep=floor((n+step)/i);2 _$ x: K) J2 f: {2 ^3 A. y. U& ^
res=mod(n+step,i);) O/ `3 m* ]) G7 ~) Q" \" Y
b=[x{i,1:i}];b=b';- l7 H* J; O, w5 |0 C
f(1:rep*i,i)=repmat(b,rep,1);
; A/ k! z0 e! S6 T4 Y if res~=01 M- I* E' y& `5 a
c=rep*i+1:n+step; s9 d$ z) W# e y4 _0 {6 E' M* F
f(rep*i+1:end,i)=b(1:length(c));8 L/ W: D1 c; z& O% }2 m
end9 a6 n0 t/ d! w/ j6 o1 h0 Y
end
/ {* ~! l4 Y4 T$ e! d M+ w5 |1 t; j5 N2 ^
二 最短路Dijkstra算法* |# {$ ^. i& G" l3 p- b! N
% dijkstra algorithm code program%
* S7 v2 |; Z: B- p2 L- |0 Y& M% the shortest path length algorithm
4 Z4 ~' ~6 o, {9 p/ N% M5 w! Gfunction [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)! o! E/ @1 _+ w4 [- Y9 w( O
% Input parameters:
$ a& ^0 x! u, `6 ~9 O% Input_weight-------the input node weight!
9 V2 \" C- T9 |! U2 s# C% start--------the start node number;- `* F1 J3 J$ C+ g% D
% endpoint------the end node number;2 Z9 x( I/ b/ v0 S! K3 f2 B
% Output parameters:
( ^: {: T" K7 `' I4 s0 P# |% path-----the shortest lenght path from the start node to end node;
a( [5 @+ k% o" ^8 Y% short_distance------the distance of the shortest lenght path from the
% F4 W7 E C1 S+ a% start node to end node.+ v& s) C/ J; M# k" [
[row,col]=size(Input_weight);
& U0 p5 t' ~! f! X7 i9 o) ~% X8 ~% M
%input detection: n( [9 O# E9 I
if row~=col/ h% l4 _. g/ c4 t5 @; K
error('input matrix is not a square matrix,input error ' );
8 w; _" P1 W; _* l% z! |" E0 ?8 @end
$ ?% M3 ^% W( ? \8 p V! G& Z5 E- ^0 Hif endpoint>row
/ Q9 a6 y* }8 |, _- y( Q error('input parameter endpoint exceed the maximal point number');
4 W( t# r& c* E6 Send: V& w' k# Q8 ~: k
2 ]8 b! O* C" g9 n
%initialization! e' X7 b* I Z
s_path=[start];
/ V* l( i& C4 Z- @( Kdistance=inf*ones(1,row);distance(start)=0;6 G# i' @ B3 y; K6 R/ N
flag(start)=start;temp=start;
7 L+ l$ K' k6 x7 g1 S8 V, }
]; ]& S2 Z! t2 Kwhile length(s_path)<row- i8 c& f6 w' j% o4 J
pos=find(Input_weight(temp, : )~=inf);
) ~2 U7 g* P& ^3 O8 f for i=1:length(pos)
1 Y- F. Q) c6 v& f$ x; @ if (length(find(s_path==pos(i)))==0)&
' C$ m# W, G) l+ @" L* L(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
9 G0 L$ Z+ [ W; w- }5 O* [( _ distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
( O3 {8 f4 s$ c' L flag(pos(i))=temp;# K l+ [9 I5 P& a8 C
end
& |8 b; S2 O X% A9 \* [6 { end+ w% j! Y/ c1 {& f- I O: i+ D
k=inf;" }( t; o' `* c4 T7 X
for i=1:row$ ]$ {0 }& A0 K+ u, l" w
if (length(find(s_path==i))==0)&(k>distance(i))
* E4 l* u3 J! e! }4 V* c. m9 f k=distance(i);; N9 f" u- e( P- T/ ^ c
temp_2=i;4 Q% P0 P2 `* z" o) O. K
end, v3 ^# o" i i$ f
end9 G' Z& ] F+ s% N$ V
s_path=[s_path,temp_2];9 C5 W" {: F) k, n2 k' \
temp=temp_2;
! q+ e$ O& ]9 @1 x& |end
6 g( P, ?7 j% S6 z5 I* V6 @9 l7 ]8 V1 C( W* I0 |5 K% C9 M
%output the result7 ]( Q1 R0 U* g: m e6 n( G
path(1)=endpoint;( {9 D: P1 ` |6 j R( S* w
i=1;
/ `! Y# L% U {, ]& twhile path(i)~=start
. `" }! K3 p4 p% G path(i+1)=flag(path(i));
7 q1 s- J$ D% k- g, y i=i+1;8 O$ _) q' ]% @, {2 m9 n& s* L, O
end% k" d' n( \: {4 b- F1 K
path(i)=start;
& f8 G8 q4 m" s h7 D! _path=path(end:-1:1);
2 @4 t- T Y }- A: s# R0 N$ C% hshort_distance=distance(endpoint);* F8 d2 s7 t* o% @
三 绘制差分方程的映射分叉图2 `+ Q$ s, r. V7 j3 a, v, l ]8 ?
- r5 o: v- B/ Z! V9 C' m5 r3 Zfunction fork1(a); ( l- g' L: i& j
& H; T6 K1 E3 Q! B% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
- ^& t# W8 S: S6 L) O% Example:
7 c- g$ s) @; u6 F c% fork1([0,2]); R, m# B, d$ d% x
N=300; % 取样点数
3 k) T) p$ o Z1 T" h, M; e$ \A=linspace(a(1),a(2),N);
) ?7 ~* K: n# J8 k: p7 |starx=0.9; 7 Y4 q; r) k* Q( ^" I
Z=[];- U$ T7 c. @% }4 H, g! J* v0 |1 E
h=waitbar(0,'please wait');m=1;# z. U3 R3 }. Y# P2 ^6 q. ?
for ap=A; , v8 u0 @0 J* r3 ~7 f; C7 x ?
x=starx; 4 U" t/ u( z% W* }
for k=1:50; 5 C6 h2 Q ^8 U7 Y" Q# D
x=1-ap*x^2; , b' J1 x8 d7 U
end 8 q8 S/ U- o. x
for k=1:201;
. w$ Z; o: e4 P7 G) |. D x=1-ap*x^2; 9 n* T- t7 Y/ V O3 h
Z=[Z,ap-x*i]; . j4 n: H! t5 X( h! p. r1 k* `8 n
end
6 e6 a3 }" x* h l0 B waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);" j3 z Q4 X, P0 M( b3 M( C
m=m+1;
, V+ P1 l" H/ e) }0 A. cend ) J8 s) y& f2 Q, S5 v, L. F
delete(h);
' o0 y4 J$ {; h' i; t7 ^* P ~) dplot(Z,'.','markersize',2)
( y( \/ M' @3 r1 \% a( T `2 yxlim(a);" r4 L8 e+ a4 V( q. i
1 N% ]$ N) j# B1 ?8 X! E
四 最短路算法------floyd算法
5 k' w: O j3 yfunction ShortPath_floyd(w,start,terminal)
2 ]* N: d' A2 K/ Q# t%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
7 z% K5 y# h( B! T%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];5 ]7 V9 p" |2 Y/ g9 S& f. I4 P% `/ I
%start-----the start node;. q: o; Z8 v1 l- M
%terminal--------the end node;
N& g3 A) x" p; Q l# e4 Z, l: Zn=size(w,1);
3 d) V/ {* O1 M3 f K[D,path]=floyd1(w);%调用floyd算法程序" i$ O( r0 ?% e+ B2 O" e
5 J+ H1 [$ M4 m* q2 R%找出任意两点之间的最短路径,并输出+ M* a4 \" m2 b8 o& h
for i=1:n
( i: A- p* e' r1 _! b1 Z) ^. m for j=1:n
) P$ Y* @* }& U& m. b6 O# k" S- e Min_path(i,j).distance=D(i,j);# Y. n. `: n; R+ W
%将i到j的最短路程赋值 Min_path(i,j).distance" M1 f/ G, b/ c2 ]; b, y
%将i到j所经路径赋给Min_path(i,j).path
+ [9 L1 C3 E0 O2 [ s, C$ M' \ Min_path(i,j).path(1)=i;* W% ^9 O8 u* d3 x+ K
k=1;5 I0 g7 R- K' {5 e; ^/ p% _
while Min_path(i,j).path(k)~=j2 Y# [ f, J& T Q# H3 k. _
k=k+1;
, Z& x U" s9 u2 [ Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
% i% k g4 r1 M3 ~1 v end
! |( G$ H" Y1 e0 M end, O$ j- [/ _2 L6 h
end8 K$ p3 N7 s; D9 t0 n R
s=sprintf('任意两点之间的最短路径如下:');
$ N) O2 W3 c% V1 odisp(s);
/ m( ~" C' e: Z8 p2 u0 f! Nfor i=1:n- @2 p3 o( a3 j( {
for j=1:n
" l( p* J: ^9 X8 z& E% h% T; ` s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
0 d. b& ?/ j+ P7 H ,i,j,Min_path(i,j).distance);( y" b# R$ B2 c8 ?
disp(s);
! U2 i* ]! ^; q& ?- B- g# W9 |2 b disp(Min_path(i,j).path);
! Q. x0 [5 B f4 |% L% W end: C; y1 j. K% X8 ]/ T4 v* S3 H
end1 c8 |% r G9 G% B! V
5 G/ L" ~; k& }1 p, L* @0 Q%找出在指定从start点到terminal点的最短路径,并输出
! P/ Y- i3 C: v( a2 |) i, }' Zstr1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...1 n! ?0 A& B% o) u
start,terminal,Min_path(start,terminal).distance);
* R$ ~% H& ~2 A2 l! bdisp(str1);4 C! {) J5 ]! }9 y5 L8 Y' ]) z; `: g
disp(Min_path(start,terminal).path);
3 j2 k* b1 R# Q, S" e% x! U
6 h. y; Z+ K9 D6 I0 Y%Foldy's Algorithm 算法程序6 U$ h& p0 j" j; F" _% k6 S
function [D,path]=floyd1(a)5 v4 A; v2 m& d+ \) a
n=size(a,1);
9 N/ V7 T3 v0 }; u; @7 ]* s8 iD=a;path=zeros(n,n);%设置D和path的初值
4 ^+ M/ _1 A" k6 B8 d- Ufor i=1:n
8 v" e1 w" z- D/ E1 ~0 } for j=1:n
2 q0 q; g8 E+ y, e8 V7 Z; } if D(i,j)~=inf( k4 f( V" A4 t0 {9 V* J4 V* S% s
path(i,j)=j;%j是i的后点0 A* n- c2 t4 h' _$ Y# m
end
" {9 r1 w* z. {. w5 G2 z; P end
) L" H" `8 t" ~ O. x9 o1 C& r( Nend2 B8 x# @" \3 z9 j9 I8 b1 c
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
8 M- A3 b: \; J% sfor k=1:n9 o) c6 ^7 n) m' c- l3 X
for i=1:n" { i( e# l& T/ n$ `0 u
for j=1:n Z' q; c# j* X/ ^
if D(i,k)+D(k,j)<D(i,j)6 }6 E/ T( {, o" o
D(i,j)=D(i,k)+D(k,j);%修改长度
7 S' O$ P" O& O8 F path(i,j)=path(i,k);%修改路径; b5 Q4 N: [+ g1 `
end1 n6 L- Q$ C& I% F
end
/ B2 k) }, C) Y$ M H end. v6 _) \9 P ?7 w2 e* g# f' z4 x
end
$ t# E: Y _% `$ u, b! ?% T3 Z/ Y( a" T6 u( s
五 模拟退火算法源程序* ^8 ^) r6 q% N8 R) U* \
function [MinD,BestPath]=MainAneal(CityPosition,pn)8 @* X v% v% H: j3 ^+ A
function [MinD,BestPath]=MainAneal2(CityPosition,pn)
' x j' R: K4 e* N%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2 ^% w& |. L4 {3 U( g# L
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...* v; o3 R: J" d3 Y0 g, h6 }
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
5 r- C5 M- Q1 L% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;..." I/ u" z' z3 u! u2 Y& o2 c( T! a' f
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
c' X" T7 J0 L" v" q% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
# _1 H# J) G: o+ f, w. H6 S% J( Y+ T& l p
%T0=clock$ H6 u2 i3 o8 m- j$ f( B
global path p2 D;
) K) w$ F! }) f$ W4 |2 z) a0 T[m,n]=size(CityPosition);
' m0 n5 a' D n, s$ g%生成初始解空间,这样可以比逐步分配空间运行快一些+ C9 Z% D- t7 i3 a3 }) [
TracePath=zeros(1e3,m);
) \# J- \/ y' q+ L0 E; eDistance=inf*zeros(1,1e3);1 K' y$ o6 m' x; t9 i9 m
8 a1 X5 y- z2 i9 R0 X) \D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
, t. o3 n% Z3 D+ l5 Z (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
' w$ N2 X" c# L: {%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)1 \8 J( W8 a) h$ s: K/ a W7 ?
for i=1:pn
, ], z( @5 N/ i& p8 s6 Z path(i,:)=randperm(m);%构造一个初始可行解
) X) n0 a9 l6 r5 J* A( bend7 S! Q( |8 o, t( q
t=zeros(1,pn);; l' B9 [8 m P% A+ I; \9 e
p2=zeros(1,m);6 g8 i( T1 v X2 J0 h) f7 Y
5 g d, v8 g$ N) @! J) kiter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );, t0 n4 }8 g M& u: ~1 i9 N
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=' ) ;
D- R, }, l4 R: a0 k& 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
! D5 U0 }/ n) A%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1 e) `1 Z* H s3 O9 E+ [2 ^/ z
%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! z) ~& C: N" d7 d0 I2 a* N
%会收到到比较好的效果
1 `/ `( W# n' b5 v/ g. k# G3 G' C; O9 ~8 Y% S1 Z
T=1e5;
. v* H# j& p' V5 z S) ?) lN=1;$ U$ @& ^; Q5 g3 v5 R
tau=1e-5;%input('请输入最低温度tau=' );( N& M. R' p) ~* |8 r& ^
%nn=ceil(log10(tau/T)/log10(0.9));* E8 w! `1 d; W( ~, r$ L5 X& I
while T>=tau%&m_num<m_max o0 l' d7 t6 }# V
iter_num=1;%某固定温度下迭代计数器' W3 u- T1 k; ^: H+ I: Y2 O( g
m_num=1;%某固定温度下目标函数值连续未改进次数计算器9 e8 \% W& \6 a' u% [9 D, o0 u
%iter_max=100;
; k( `, Q8 l/ s+ v %m_max=10;%ceil(10+0.5*nn-0.3*N);7 a8 o$ Z K) H' f1 z
while m_num<m_max&iter_num<iter_max. L% n& [: K3 z r3 [
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:& W9 M1 z7 t0 _! }
%用任意启发式算法在path的领域N(path)中找出新的更优解5 _# O9 G' a. ~; S
for i=1:pn& c' d% f/ D k& ^% E% b8 Q% q; ^
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);: d2 L0 G6 \7 F" r/ U. r1 ~' e: [
%计算一次行遍所有城市的总路程
; p& s/ X/ I. ]+ ? [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
" v9 f2 ~1 N& ^. y3 v2 G' [! t Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);# P! R& v5 ]# D0 [
end
8 i7 T8 U% r+ f" y %Len1
; N$ R3 E4 x& u& G6 a! i %Len2
$ P8 I3 a2 R+ C2 | %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand5 N9 r+ F( J) D N3 }: y3 C5 [
R=rand(1,pn);
, Y1 i1 Q- c+ P/ n5 |& B" `1 l) ^ %Len2-Len1<t|exp((Len1-Len2)/(T))>R, [8 F! E# x1 e, Q4 G/ i- O4 p5 Z
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
7 R. a8 L1 d8 x6 c4 s7 e7 H: C& i path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );+ X& _& M8 O2 m, I2 ]# i4 X+ ]
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
) B% h3 W* F8 l6 _# W' G w [TempMinD,TempIndex]=min(Len1);
$ V3 c2 P: ^! P1 } %TempMinD) Z8 M S% {4 p. U2 [/ N# l$ G: l
TracePath(N,: )=path(TempIndex,: );' [% ?+ p' b+ b- |
Distance(N,: )=TempMinD;
: e0 H! {: i j8 `+ i0 h0 r% M* H N=N+1;; [3 C' s$ K$ l5 @) B5 l1 D
%T=T*0.9
! x; p! x( Y. }0 y& w& f, e m_num=0;
2 U. f% f) _! `8 W& R else. p# \6 m) O+ S# k: y
m_num=m_num+1;2 L' W, {5 z' W+ A5 \
end7 e# P1 v4 L9 ]$ O1 Q4 H
iter_num=iter_num+1;
6 [" c" X; \7 @5 A- w end
7 T$ l& A( x$ f% T0 ^' g T=T*0.9+ C0 w* p8 _7 }3 Q% z$ _: w
%m_num,iter_num,N' K! p& h8 I- g
end
6 p6 q5 [) L# I[MinD,Index]=min(Distance);6 R* O7 z2 m0 w2 N$ F. m. f6 ~/ x: f
BestPath=TracePath(Index,: );
! _5 g ^! S' B7 E- g3 t2 V! L7 }disp(MinD)2 [* E" I9 \2 t" {4 d
%T1=clock8 z! `' m! y: i5 Y4 U( E- N
: q) g5 _& n) b/ m- P4 F. |% X
& [# ^0 I/ {: X" X! S4 {. r%更新路线子程序
1 Q7 A& ~' L+ W$ P% }2 m* i/ @function [p2]=ChangePath2(p1,CityNum)
I; r d8 `2 N& `2 Sglobal p2;
1 s/ J) y( N3 ^; O& s% C- kwhile(1)
5 l; Y" R: j3 \& o7 G5 W R=unidrnd(CityNum,1,2);! o5 O$ ~8 C9 b: ?
if abs(R(1)-R(2))>16 s+ C6 [ d! i: d5 _0 X N
break;
! i4 g; s5 C; \9 Y, |5 y7 |9 q end- C7 L5 w5 H2 ]
end
% Y: \% V; h( V+ {: OR=unidrnd(CityNum,1,2);# W- ~# O) V2 J" N0 X4 D, B
I=R(1);J=R(2);6 \1 @: E1 D3 Q
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
/ f _% R: }: k9 ?* [%len2=D(p(I),p(I+1))+D(p(J),p(J+1));
2 ^: }) q" J- B/ rif I<J
; y7 g, w& Y& y" L- u4 _ p2(1:I)=p1(1:I);# U' f: u/ @" {& c3 R$ J. N( J
p2(I+1:J)=p1(J:-1:I+1);
: m' Q' i6 w! y( t* p! e$ } p2(J+1:CityNum)=p1(J+1:CityNum);
1 ?! L: f7 B, pelse' }( Q: N) j: Z/ P8 l$ \
p2(1:J)=p1(1:J);7 s8 u' |* K! E( ]7 t& m( q, A% _9 ~
p2(J+1:I)=p1(I:-1:J+1);. t" t% k, O# L' D- l" i
p2(I+1:CityNum)=p1(I+1:CityNum);
0 ?; y. V ^$ D/ G& v- A* zend0 ]* _) a& R7 K6 W+ |
; t+ _! ]1 h: j* @! D六 遗传 算 法程序:
! z5 L2 k( G' ~/ P) y 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!
5 X- u0 q. R6 `* C
. I/ ^% a, H8 x* E% d/ Kfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)9 T8 X- h4 g: A3 f3 v; f
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) J0 p3 L& w8 F7 l# z
% Finds a maximum of a function of several variables.4 j; M9 f9 A/ V: Z8 \
% fmaxga solves problems of the form:
" W# a$ E( `% q4 ]! F8 X! M* ]% max F(X) subject to: LB <= X <= UB
4 k3 I5 Y- v9 ~9 a% F( Q/ F N% BestPop - 最优的群体即为最优的染色体群
3 Q0 @: u# ^' F r$ v% Trace - 最佳染色体所对应的目标函数值# _# |) _+ y4 R# e$ s; z, b
% FUN - 目标函数
9 i n, @ b( R; v" r* m% LB - 自变量下限
1 }/ N7 P) I& {$ y) d% UB - 自变量上限
" V/ y9 O: U; j% eranum - 种群的代数,取100--1000(默认200)
( t3 k5 a5 W- U9 K2 K6 b8 N% popsize - 每一代种群的规模;此可取50--200(默认100)
6 C1 \( I& _& c# G% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
2 c" g2 E. E) e8 X8 s6 c, I% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)8 |; Y) S1 X. B) ?; t- E1 X
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
! G0 F' t+ }4 |6 R/ r# x# }, f) L2 p% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编1 [! e5 ?7 d/ f6 a/ Z+ N8 w P1 |
%码,option(2)设定求解精度(默认1e-4)
3 B7 {/ W8 J" ^" v- _* D0 o%
, G7 \7 n! O9 q/ z, \% ------------------------------------------------------------------------
* O$ M o' t+ r( Y2 C" M1 O& V0 O& }2 H% N8 q! e
T1=clock;: p! \/ H: _! E; p
if nargin<3, error('FMAXGA requires at least three input arguments'); end: V3 b: Q* B* t1 C
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
; E6 s1 g7 G2 ~8 e3 rif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
3 ^( Y! s6 y0 b$ Z" \if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end5 d& k: C/ D3 e5 M$ u
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
, x1 @' s" x9 z4 W+ V8 B, ~3 u5 _if nargin==7, pInversion=0.15;options=[0 1e-4];end% ^2 t$ M/ P6 E' D/ k c5 f
if find((LB-UB)>0); g) f9 g1 } k/ _+ W& x
error('数据输入错误,请重新输入(LB<UB):');4 v4 Y1 E) X9 M; M! s7 ^7 X4 [9 D
end
- r) E. o( H$ q4 Fs=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
2 z; v3 Q' E# ]- F0 Vdisp(s);& `+ h( t# V0 Q( W% h4 `
0 {! k0 t( A4 J7 G
global m n NewPop children1 children2 VarNum- j. ?8 C& W: a" o* U7 c" U* m8 _
+ n! }2 |6 b( w1 L p# Q* ~
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);) r& z& H* Z) M2 s
precision=options(2);%由求解精度确定二进制编码长度
5 l4 A% R: D: S: D7 a/ r, Sbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间. v, r6 w, g' K) I; d) G( H
[Pop]=InitPopGray(popsize,bits);%初始化种群
) a2 {; @6 X; n0 ^- s[m,n]=size(Pop);
2 U, \6 ]+ n' o6 Z; { i( U4 e6 BNewPop=zeros(m,n);0 G _& G6 F2 h h6 K
children1=zeros(1,n);
* Z0 R/ K/ _2 Gchildren2=zeros(1,n);
% l) Q1 n, Z7 k( Tpm0=pMutation;0 w* ^5 P- A( F4 E1 X$ @- ?, w
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
! u* W( j& q/ oTrace=zeros(eranum,length(bits)+1);, i- v/ Y" Z" L
i=1;! y! D: j6 v* E8 D. I4 m) ^0 U
while i<=eranum
7 k0 P, O2 G$ \: r+ k for j=1:m
' i0 A1 I2 S" ~) @ value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度$ x* z9 I1 }% m+ I
end
' `2 {4 x2 F: A3 G [MaxValue,Index]=max(value);
8 O" D) D( p+ ~' v" ^ BestPop(i,:)=Pop(Index,:);0 g5 i3 l X @2 U! S8 ^% g& Q
Trace(i,1)=MaxValue;) N9 Y1 h7 q* A z! ^
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
; Q' d, F& d/ _1 ^ [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
F t \8 S6 z6 m. y6 a! I[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));5 ^! J: j/ t' d
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率- w7 @' c+ z9 o( P2 M
%round(unidrnd(eranum-i)/eranum)1 Y% ~3 t" b* ]/ u5 p
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
; t: C$ M# I! |( Z( A, ]. y7 m [InversionPop]=Inversion(MutationPop,pInversion);%倒位
& {+ i& d1 W C% m; a) k* B2 a* n Pop=InversionPop;%更新
; R" b# S" u4 ^3 B7 s8 l$ ~8 MpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); % r% {8 {0 J f9 ^2 L# z6 n* b
%随着种群向前进化,逐步增大变异率至1/2交叉率
- P; N. r k4 _' i6 ?2 V' C/ w p(i)=pMutation;
% A# p: K" s0 u4 m7 {" e& ~ i=i+1;
$ {% u0 o, C+ s* n+ a& oend5 y0 E* ?% u7 c$ ?$ b6 {
t=1:eranum;
2 R; \: A$ H3 b. _$ x2 zplot(t,Trace(:,1)');9 D. q; m3 t. l; v* u7 _; z5 H
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)');
& N+ n2 {, e& A+ x" v" M- h[MaxFval,I]=max(Trace(:,1));. B! R3 U! M5 R- L4 {
X=Trace(I,(2:length(bits)+1));
- s% a! t# j5 u! vhold on; plot(I,MaxFval,'*'); E1 m) l$ w8 f- h8 [% m
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);* L, \8 W7 ~1 D! Y. t$ ~9 C$ |+ H
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,:)));( x2 V7 M, L" b$ P. y" A9 c
disp(str1);
% ~+ u& d2 J9 P% |/ q5 d%figure(2);plot(t,p);%绘制变异值增大过程
- H; ~- A* F9 z+ a+ M1 K! ?" u; O) cT2=clock;& B* v) w( _8 ~2 i' `
elapsed_time=T2-T1;
) u) v1 B# a$ G1 h: Mif elapsed_time(6)<0
4 L1 ?( P0 @ R# f elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;/ @0 J4 @# F, F, J0 B
end
4 r4 ~( |# v n( m& Z! Tif elapsed_time(5)<05 t" T1 _: s, e- n- M r# y/ S* y
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
' R4 f: M2 r+ h1 Eend %像这种程序当然不考虑运行上小时啦+ A: K% s$ ^- v) 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));8 z$ n. k0 ^. u9 F6 k. E0 I% l
disp(str2);
4 `' ^/ k4 \, ~/ w Z) ~' X1 y K& C" n3 P6 ?8 A- b# N
7 O5 s, q- t2 e4 v) w- y; B
%初始化种群" n: J1 d6 M+ C6 X* I0 U
%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
1 M3 s. E1 [' C. Ofunction [initpop]=InitPopGray(popsize,bits)
, H* D' O% {+ e- llen=sum(bits);
B, M T- H' x7 Binitpop=zeros(popsize,len);%The whole zero encoding individual
6 D0 w* q j8 p t6 lfor i=2:popsize-1
* |& u8 M Z+ B! H0 @5 V5 M& t pop=round(rand(1,len));% G8 ]) h2 d, S+ w9 O. C- C8 d& B
pop=mod(([0 pop]+[pop 0]),2);( [7 t7 F; n* B. i
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2): U5 [3 [6 k8 p" M+ Z7 t5 T9 O; ^
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)6 b8 D6 v4 Y' V0 r; y* V6 ~* C7 c/ h
initpop(i,:)=pop(1:end-1);8 S; E6 b' y8 o* ^ k
end7 `+ U9 A; {6 \$ ?. _: E0 o" U
initpop(popsize,:)=ones(1,len);%The whole one encoding individual
0 K% c0 Y1 l. G0 y: Q; U# Y%解码
. }9 F2 @& l* u" ]4 U2 I
+ r4 O' v) ]8 ?8 e. O8 D5 zfunction [fval] = b2f(bval,bounds,bits)
C( `/ X$ L& [% fval - 表征各变量的十进制数. B3 ^; h5 i5 c/ x8 g0 c
% bval - 表征各变量的二进制编码串& f# R( ?! `$ {( p
% bounds - 各变量的取值范围
6 z i( L9 T: y* V6 f7 F% bits - 各变量的二进制编码长度 l8 F9 |3 M- {9 @+ d
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
) r# P0 F$ b0 _5 {numV=size(bounds,1);+ k5 c4 ] o7 k3 s/ i% s
cs=[0 cumsum(bits)]; 3 s! i! P+ w7 c1 G, x
for i=1:numV
$ O3 c! I# ?- O3 i* P a=bval((cs(i)+1):cs(i+1));
: S9 L7 [; O1 C8 C4 |/ X fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);. c W6 M. x; I
end- |/ T4 F+ w& L; c9 l( m- O# _# J
%选择操作" J# b' s/ R, H* w" e
%采用基于轮盘赌法的非线性排名选择
6 I/ j& b! J7 W3 l%各个体成员按适应值从大到小分配选择概率:5 T' |7 n0 g3 h
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1( D( t) \" I4 L4 I
5 q( J8 G+ y4 E7 D# Z7 h; [
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
' R; `( e" t2 e% w: }% J4 D8 aglobal m n
$ d3 s: k5 e- ]. X: O- lselectpop=zeros(m,n);
4 [2 @7 j1 [' v) C. cfit=zeros(m,1);* s2 j8 X3 t4 Y7 J* Y: a6 F4 S4 D# l
for i=1:m
0 m" N/ ^5 M: a; w6 ^ fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据0 a1 x6 H; j0 Y7 a
end
' d: I$ R/ T Eselectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
5 e3 z) m% }5 D& vq=max(selectprob);%选择最优的概率3 R6 k3 P2 s7 n" A# E
x=zeros(m,2);- L/ o" h% K/ D1 f/ ^+ Y
x(:,1)=[m:-1:1]';
2 R9 g1 Z0 B( b; u @[y x(:,2)]=sort(selectprob);
$ |1 ?; J; m$ V! V1 e1 @r=q/(1-(1-q)^m);%标准分布基值
/ s* P2 g. i3 C. z1 c6 Dnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
" Y7 D: R1 ^. x$ N! qnewfit=cumsum(newfit);%计算各选择概率之和# L) a$ Y% `3 k. e, k3 t3 o- }* B1 |
rNums=sort(rand(m,1));3 g7 H9 m- q2 H0 n& J
fitIn=1;newIn=1;1 t! S' W* C# R
while newIn<=m: |8 z1 m" s* F; n# U
if rNums(newIn)<newfit(fitIn)8 R6 z- q6 G1 s& K
selectpop(newIn,:)=pop(fitIn,:);; [% |. g& [. D( ~ k' D' R
newIn=newIn+1;
, O6 O% [6 r2 F! |! q* H+ g else
3 Q3 Q2 R, k% s! B1 w# { S fitIn=fitIn+1;
' v9 I" b3 s* H, [& f end* O+ X- N- B2 p6 r: G% a6 @
end' W( a1 G; ?5 I+ m$ x+ @6 ]
%交叉操作5 a' D) X9 P/ h
function [NewPop]=CrossOver(OldPop,pCross,opts)
& f4 k1 b) M* ]. b. l7 ]5 ?1 `%OldPop为父代种群,pcross为交叉概率
4 Y" {. r0 Y. x6 B( Vglobal m n NewPop
( n( C1 j' k5 H: |r=rand(1,m);
( W1 P$ l6 Y, O" i% o' dy1=find(r<pCross);
& T1 K. ?2 V- N4 a0 q5 L/ ]3 }, }y2=find(r>=pCross);9 `% k: r" X9 w) T( q
len=length(y1);
) A* o( C3 p* U% ?6 gif 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
+ _& F0 [( q8 H y2(length(y2)+1)=y1(len);" E/ v8 ]7 j6 V4 J! i. x
y1(len)=[];
4 Y0 S; j. O* g! c8 hend' D: G: S0 L) o r9 S
if length(y1)>=2
% `$ Y g1 \. E) ?- R8 n8 H1 m for i=0:2:length(y1)-21 ]$ K; i+ a- M
if opts==0
* O; x o( V6 l/ I/ }2 s$ X [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
: f" C; N! x. M$ _5 R else
8 U6 B# A" X6 o [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));7 D0 c z9 l$ U4 t# J
end
9 j% F- u- `+ a$ l, |* L+ a$ n end
7 G; K4 u( g* z" u! lend
. L9 i# A. {) y5 D3 Y0 e- INewPop(y2,:)=OldPop(y2,:);
! z0 {, B! j3 ]% Z3 P2 |- D; B7 z" L7 e( V( a" e
%采用均匀交叉 ! A6 x! J" u: \* B
function [children1,children2]=EqualCrossOver(parent1,parent2) \3 y$ F9 q8 E, s, G) l( ^9 x
+ s9 c4 ~* c. m: sglobal n children1 children2 6 q3 t8 a# f% t& ?% S [3 W
hidecode=round(rand(1,n));%随机生成掩码 v8 E6 H$ V$ ^+ b
crossposition=find(hidecode==1);# R$ ?' e( [' q7 \, e
holdposition=find(hidecode==0);( U4 N, J; e; b
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
0 ^3 u# v- d$ [* L4 [children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因7 W$ _" z7 P9 V
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因& d+ L! K! l3 [1 i- w3 W
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因$ l9 x+ t- B# i) r1 L5 w+ W" X
z5 W" M. ^$ ~0 n& i%采用多点交叉,交叉点数由变量数决定+ F( {. S" e$ @- W
3 u% C7 z$ m4 L( L3 Ifunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)
+ E" X5 O7 q/ i; S5 [$ L5 R
9 g2 m4 d/ j e+ b- J! B5 Fglobal n Children1 Children2 VarNum
+ s- X* v" z6 w! i$ W0 NChildren1=Parent1;2 o. n, w4 [7 h
Children2=Parent2;
; J5 D3 h/ q2 s, k( q' F7 `- EPoints=sort(unidrnd(n,1,2*VarNum));1 M B' @% j/ H0 b. r
for i=1:VarNum
8 o9 X. e- m- z: c8 s Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
9 A9 R1 d5 O2 g2 I5 L Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
. t! U2 \2 _. wend
$ K. H* U2 O* I" ]0 ^
0 _" Y* V: E* t. G% h. n. O) t6 s- a%变异操作1 k" E& G8 K% z% k& q# f' z
function [NewPop]=Mutation(OldPop,pMutation,VarNum). o; z( G1 _% b0 S
8 r6 j: C0 X6 i7 U: N2 }
global m n NewPop: L: E: R! y! r6 b# e5 N& w
r=rand(1,m);# u% Y4 d+ }7 F' m1 \5 Z/ z1 ~
position=find(r<=pMutation);
7 c% K. w6 w0 ^+ q( E9 k+ m& R( Blen=length(position);
0 M7 v2 p s [# a2 d% Sif len>=10 s* O2 G4 k o9 S
for i=1:len
7 X. Z" O% z, b" { k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
4 i+ R0 ?, I! ^& u- R1 k for j=1:length(k)6 V2 e8 j7 Y3 _6 x+ B# y
if OldPop(position(i),k(j))==1
7 z( h4 r4 N' J9 p* e OldPop(position(i),k(j))=0;/ P2 {# C. G4 i- c, G
else* p4 P" b2 B' C; [' \
OldPop(position(i),k(j))=1;
9 i: R- @# ^% N; q. u: N end
' j! Z# s/ }5 S# z `9 p8 o end
. P% o! ~/ n/ L3 C end$ S4 r! m3 q" q! q; @, t
end
. Q2 Z0 l7 a% RNewPop=OldPop;: D6 I' V7 y1 Z5 J3 Y2 l% S$ B
' L5 m7 e4 e4 d0 _
%倒位操作 n. f+ q& [! F6 m
& R8 k0 i& n/ f2 K$ d6 Tfunction [NewPop]=Inversion(OldPop,pInversion)/ e7 s1 Y( u5 G* S" s# \
& n3 R" z8 p' M4 K1 T ?: n
global m n NewPop$ @1 Y* v: R$ ]; h5 h' W, G* c) x
NewPop=OldPop;
3 M7 Q" T# ^& s2 A$ o' G& [0 E; zr=rand(1,m);" ?- @5 f( g! O) v3 V- f
PopIn=find(r<=pInversion);
7 o8 r( ^3 w( g- v6 ?- ]4 Ulen=length(PopIn);
9 o# S$ I1 m0 S9 U6 oif len>=1' S1 B8 ~) W( z% V" [
for i=1:len
& w& q0 w1 B! Q- R$ L: f' V d=sort(unidrnd(n,1,2));
9 j" k3 T8 z- B- l! s" O4 P if d(1)~=1&d(2)~=n
: {2 p g. z$ _' }0 Z" r NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
! u# N* n2 y! [, h NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
" w5 A" ]) \' A; Y7 { NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
8 j O$ k5 v1 k* r4 X end$ g; U7 C x6 V+ ]9 E% I" L
end
: [/ v0 @$ q5 m7 uend! n$ p6 t# \: Q/ r6 u9 H( U
0 X8 r1 A4 D! ]9 ?( ]+ P. {* B七 径向基神经网络训练程序
$ \! ?+ O) ~* N7 e N1 ^( v1 [5 {' s0 _( S* Z- F8 ^7 ~" A2 p, g
clear all;
8 n2 X( V: a o# f# Yclc;
8 a- U( `% [; z/ a! K%newrb 建立一个径向基函数神经网络+ ]' `3 n8 W# x4 ?# y
p=0:0.1:1; %输入矢量+ P* y C! }+ C
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量9 V" ~, ]* [" u; I
goal=0.01; %误差 a% J% v8 O- F; P# @/ H; s1 ^9 u/ Q
sp=1; %扩展常数# T9 f% T7 S& G; A9 X2 A% U
mn=100;%神经元的最多个数' o7 T5 L2 i! W. ]% A T
df=1; %训练过程的显示频率- W. ~% i4 x' G9 K! z& B& A
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
6 t0 u8 G: [+ W/ u, c9 \- Y% [net,tr]=train(net,p); %调用traingdm算法训练网络9 ^1 F3 Q: P/ t; d
%对网络进行仿真,并绘制样本数据和网络输出图形
o( M. F; H- [' ~A=sim(net,p);1 P& J1 v! s- l, \4 x" p
E=t-A;
% @! h6 f+ j- Z5 G4 k+ Z; L$ U# Fsse=sse(E);9 K8 _- r+ ~0 w, y) l
figure; # V9 R) g. N; O: I& _( F m
plot(p,t,'r-+',p,A,'b-*'); D+ S. Q( H% N4 E7 R+ ?$ m
legend('输入数据曲线','训练输出曲线');8 ]- p) B, q" C' {, u
echo off
) a8 F# @% M& u; R2 d2 H( o! w. s5 k( D$ q
说明:newrb函数本来 在创建新的网络的时候就进行了训练!
! T4 `! \. \' T' Q2 d' O" W) j5 Y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,
# u6 r% g: n4 u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!, o) q- {2 w5 O9 I. a
/ c+ Q* i( l) N& B' r
+ e. W, [. D4 U+ n& r2 h1 S( a* A
训练结果显示:. l1 M0 k& J2 b/ p$ N7 a
NEWRB, neurons = 0, SSE = 5.09738 r" C% U0 ?8 \
NEWRB, neurons = 2, SSE = 4.87139* E: s, z! S: F! m
NEWRB, neurons = 3, SSE = 3.61176* w6 ~) k1 [4 n6 k2 `+ Y A
NEWRB, neurons = 4, SSE = 3.4875% N, U: E% x; c! ?$ V* A
NEWRB, neurons = 5, SSE = 0.534217
- K$ _* R( f5 U5 A H0 O4 Q$ T4 i' A; hNEWRB, neurons = 6, SSE = 0.51785
! Q& ]4 `. O6 h5 l, s8 SNEWRB, neurons = 7, SSE = 0.4342597 V* }7 {7 P, ]
NEWRB, neurons = 8, SSE = 0.341518
6 ]. C" L% g5 ^; }; n$ n3 {NEWRB, neurons = 9, SSE = 0.3415196 \2 w* ]) w) j/ W7 t5 a
NEWRB, neurons = 10, SSE = 0.00257832# e7 J7 J; n4 u8 K: Y6 [) g W
3 j7 Q i3 n4 D z' N" ~! @
八 删除当前路径下所有的带后缀.asv的文件
& o- F5 P0 b: K说明:该程序具有很好的移植性,用户可以根据自己地0 i+ a$ y: f" s" t, k
要求修改程序,删除不同后缀类型的文件! 9 E2 q# ` n, h' L3 i9 k
function delete_asv(bpath)
R2 x& f: O1 ?3 a6 B%If bpath is not specified,it lists all the asv files in the current% J4 }- \) w q E- m7 z
%directory and will delete all the file with asv $ H6 A4 t' S+ c) R! M
% Example:6 z) I7 B# a: y n
% delete_asv('*.asv') will delete the file with name *.asv; Q$ G; K- H! p$ `$ p4 ]5 g/ g
% delete_asv will delete all the file with .asv.! v1 S" J j$ O Q5 G
! P7 P2 r* [$ x! c- r& Zif nargin < 17 R) N+ ~- g; X3 O/ [8 e
%list all the asv file in the current directory6 c+ K; _9 V( q/ @6 j
files=dir('*.asv');
2 B1 j/ E. G1 B; {; relse
9 h+ U+ ]' @& T( L' s$ w% find the exact file in the path of bpath
6 R3 ]4 Z# B y5 V+ f, A5 X+ I [pathstr,name] = fileparts(bpath);
! g0 K4 A0 i/ Z3 } if exist(bpath,'dir'): T; }: n6 v# t: X8 p, ^
name = [name '\*'];3 n6 q8 U. n3 i$ z0 G
end9 n* h4 r6 D X' i: P- ]8 e5 J- p3 |
ext = '.asv';+ W4 C8 e- @4 A3 {- d0 {% Y. r! j
files=dir(fullfile(pathstr,[name ext]));
/ z1 R. Q* [- B3 C0 W7 Q1 cend) s* B& O0 t8 \
& b! H5 y8 I5 S p1 E; N R
if ~isempty(files)6 j2 D7 v- L: u1 Z* Y( W
for i=1:size(files,1)
- r4 _0 Z* d3 o/ e3 r. Z5 y: [ title=files(i).name;. b7 Y$ G6 U7 _) r: K2 m
delete(title);
3 g1 o8 R* } ~' M2 @ end
0 T5 O7 k! F K: Y) `end- P1 O. ]! Y% C/ J3 L/ p
1 s& k5 w/ h7 _( h$ N% |9 u" @" c/ \2 w/ @# T' T3 S8 E/ j, u/ Y
同样也可以在Matlab的窗口设置中取消保存.asv文件!
, T+ p( |; l5 z* q' X |
zan
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