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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$ ~/ \( |( g# {+ d7 N) _
1. predict_fun.m为主程序;
2 O7 \0 ^( S. L9 b2. timeseries.m和 serie**pan.m为调用的子程序
/ ?7 h) _& J" @. X
, o. [; r4 G. V9 g* w8 Afunction ima_pre=predict_fun(b,step)
6 ]0 z3 f3 ]7 {% main program invokes timeseries.m and serie**pan.m
6 _7 r: M, O4 W% input parameters:
2 F( h& B' q" y" ~/ v% b-------the training data (vector); l$ c2 `4 b8 ~: \' X7 Q' u
% step----number of prediction data;
/ T* ]. { F3 u$ _% output parameters:" z7 X) y5 s1 j- r) Q4 B
% ima_pre---the prediction data(vector); Z/ ^9 u5 N' `: M4 J; d
old_b=b;6 L5 O, a2 D ]0 ~
mean_b=sum(old_b)/length(old_b);' u5 o {4 Q$ n8 S1 [1 B n
std_b=std(old_b);7 L- E) u/ i8 C! ?3 R. _ ?% W
old_b=(old_b-mean_b)/std_b;
2 Q. `6 E# X( [ ?[f,x]=timeseries(old_b);2 s o2 P4 D" y2 M4 [
old_f2=serie**pan(old_b,step);! M2 k0 Q8 ^, ?8 c. X3 p5 S
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;/ ?8 J3 t J( u% R1 e( w5 K% n
R=corrcoef(f);
- y1 K3 D4 G% [" k* D5 }[eigvector eigroot]=eig(R);: @3 F; I- F2 p( z. G
eigroot=diag(eigroot);( q8 Q/ u/ {- ~* F
a=eigroot(end:-1:1);2 [; ]6 `3 _2 h- Z% a1 y; Z
vector=eigvector(:,end:-1:1);, B! Q3 c1 m3 X8 w
Devote=a./sum(a);
0 i& U' e: M/ ]4 Z2 _Devotem=cumsum(Devote); j5 K: x; x% k5 `; B w' o2 Q& G% K
m=find(Devotem>=0.995); W/ R; T. c0 F5 V y9 |+ T/ ^
m=m(1);% N6 ` f4 @$ x* D1 n2 [
V1=f*eigvector';
- X% A, n6 L: x: @& u3 XV=V1(:,1:m);( z1 Q$ o% i/ m' X
% old_b=old_b;! m! {; w U2 p7 L
old_fai=inv(V'*V)*V'*old_b;- M; }0 y; m4 C9 ^% P/ ?6 D
eigvector=eigvector(1:m,1:m);
" T, F c! y( V1 G( A$ wfai=eigvector*old_fai;
& @* R; D% M7 g3 C- |1 af2=old_f2(:,1:m);
/ [1 U: t2 }# A! k5 N3 jpredictvalue=f2*fai;
& }" H/ r# o4 [2 U; xima_pre=std_b*predictvalue+mean_b;
0 l1 }3 `1 u7 [/ E% d3 W. @, W* b! T. X' W/ n
1.子函数: timeseries.m
$ I+ ^' N9 X' U; n% timeseries program%& ~( U2 |7 `; I% P/ `7 k. W9 b
% this program is used to generate mean value matrix f;* i7 Q( l b. h X8 G0 u
function [f,x]=timeseries(data)
# x D% o3 K" |5 p8 c0 i% data--------the input sequence (vector);# P/ |) `" V$ e
% f------mean value matrix f;- m4 @, p% I, W }: l& Y" J
n=length(data);- T+ ^4 ?5 ]9 t' R: K
for L=1:n/2. L' o8 ]) m* m6 e) W" N! I
nL=floor(n/L);! l. V4 r2 l3 Z8 t4 o h
for i=1:L, `. Q5 |) ~4 I* N4 F+ N) c
sum=0;4 N4 p M% w+ o6 c/ E
for j=1:nL5 H; d# h0 ~6 m$ y& g3 [
sum=sum+data(i+(j-1)*L);$ \4 w) x8 @- z
end+ {% `5 e+ q K& f* |
x{L,i}=sum/nL;
4 d, g6 V, L3 p- i. J% I# h end1 p( [# k0 f) {" K; ~- a
end1 I3 q. j% u! i, ?
L=n/2;
+ v& S1 y+ V0 l( D3 b( l; C8 Kf=zeros(n,L);9 f1 A2 U9 S0 q q
for i=1:L
+ p8 B9 R! J6 i7 ] rep=floor(n/i);$ D4 P& s8 f4 `9 c7 Y/ G& N
res=mod(n,i);
. @" X3 x$ [3 U; i, E b=[x{i,1:i}];b=b';
; ?7 Q! S& }+ j! g2 P* e f(1:rep*i,i)=repmat(b,rep,1);% ^$ d4 A& c2 v) Y, ]# S
if res~=07 F9 \' o d* z
c=rep*i+1:n;
1 V% X. v; Q( M0 B f(rep*i+1:end,i)=b(1:length(c));
2 T* ~- f' G8 N0 I s0 J& d( o! R end5 |0 s W W7 r' X- _: r, R
end
" _# `7 r2 p/ K; F7 W/ [( A4 n, Q3 E9 T
% serie**pan.m
( G2 V2 t4 o8 U6 g) O. N7 F! M# E% the program is used to generate the prediction matrix f; 2 C g% g" }. J
function f=serie**pan(data,step);; `) s( D1 {4 g, M- o
%data---- the input sequence (vector), n% t8 W. q+ m/ R4 a
% setp---- the prediction number;
& H# Z" g6 T/ Y% ~/ n6 B$ {n=length(data);
. H; e; h) U! Jfor L=1:n/2
: E9 ~7 f: G$ I9 D: u* c: T& N, i) | nL=floor(n/L);
- |6 \% J- d3 ^7 e* P for i=1:L! I5 e) d6 R* J' S; Y6 S. x
sum=0;6 } C" N6 P5 |: Z7 p2 M- q' I2 c
for j=1:nL
2 W2 x1 c; S- b% O s sum=sum+data(i+(j-1)*L);
8 u% B, s. v3 C- j end
4 ^( ?1 t8 q, n' m4 h x{L,i}=sum/nL; V! f' k* T7 B. D- o
end8 i# O5 a/ A% z* @
end$ g4 V+ T3 S) c5 n: {1 u
L=n/2;
% ]! L' d/ c4 q2 }* X& ?f=zeros(n+step,L);. x- F% V0 w) D( `; T- a9 z
for i=1:L
+ }0 f' F7 `. \ rep=floor((n+step)/i);
3 S/ K/ C' T! l; n res=mod(n+step,i);
; R1 W! D7 L, v& {# C# A b=[x{i,1:i}];b=b';9 |/ N3 e. ?) C2 Q2 @
f(1:rep*i,i)=repmat(b,rep,1);
% `, g& S6 V* ~$ r1 R6 Q, H2 Z2 V if res~=0$ L5 u9 k+ N' R y |: u
c=rep*i+1:n+step;
4 _1 Q V# k' L- Z; A8 V) | f f(rep*i+1:end,i)=b(1:length(c));
+ x3 R- f0 z% U- t& p9 z6 k end$ |% [! p( o5 @) D% ~
end/ f4 S1 X9 f. m1 m
3 y) ` {! }* ]2 O, A& E
二 最短路Dijkstra算法
! X6 [" G, g# s4 L, {% dijkstra algorithm code program%5 ~. A. }; |7 y- P2 H
% the shortest path length algorithm5 \# N/ A+ x6 u+ d, ]2 U. l
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)% A& V( ~6 G# C) [) ?- V- C2 I% X6 Q
% Input parameters:
! [4 h: n$ B/ z- v \% Input_weight-------the input node weight!
4 z5 T f6 i" J2 e4 Z% start--------the start node number;% u# m: [( ~) m; o5 a
% endpoint------the end node number;
6 W/ R3 f9 g" a& }" I: l% Output parameters:
2 E+ k% V" E+ j6 Y: L# y) B% path-----the shortest lenght path from the start node to end node;0 Q. ]2 k* P1 @$ m
% short_distance------the distance of the shortest lenght path from the
+ X! z, s# \2 f% start node to end node.2 O5 O4 o: l3 s( Q b% j7 v
[row,col]=size(Input_weight);
' |6 H/ W8 J& O( S: m6 {4 b" c3 r7 P. {$ y
%input detection- W+ Q1 A2 T7 k7 X
if row~=col
5 R8 Q8 }5 V) ^) ~/ ]8 T+ S error('input matrix is not a square matrix,input error ' );
* z9 }& a- b' o# ]$ r" Jend
4 H# o& k" t5 p5 t/ m1 Fif endpoint>row$ {* D J( R' ?; {
error('input parameter endpoint exceed the maximal point number');
! I% X7 `3 _, `( s/ v' R7 }/ @end
2 D, _' L7 W2 j. o* g% x$ R
+ f1 {$ I2 j B# E/ Z# B* p%initialization% A- M! v n* Z% j* ^2 _" w" F$ \( ~$ ~
s_path=[start];
* {1 |, N& @+ \ S1 J( Qdistance=inf*ones(1,row);distance(start)=0;9 {& S T4 k" z1 G* N- ]
flag(start)=start;temp=start;
: W" n2 ?( h* [; k4 o4 R$ R4 _; X8 F# L( }2 ?
while length(s_path)<row
$ T- O3 R! r8 n4 K; ? V; O pos=find(Input_weight(temp, : )~=inf);
9 u3 Y; D; Y$ s% ~ for i=1:length(pos)3 U" E* {( t8 w- P& |
if (length(find(s_path==pos(i)))==0)&& I8 G2 J9 d; W6 C; K G% v0 o. n
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
$ R! Z* h% U4 i/ O. N: ] distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));$ C! L8 ?% s# \. p1 K2 D& Z
flag(pos(i))=temp;
' B# S* p4 s1 Y( y5 P- L X* X8 v end
2 V: h0 j- y0 z- b0 c end
' x4 H2 G8 O( t; F8 j- v k=inf;
2 p+ V3 V( s0 p( s" z* k* V for i=1:row+ g- u8 p* Y6 S; U: T/ N; W* y
if (length(find(s_path==i))==0)&(k>distance(i)); x3 V+ H, n6 f2 I/ d
k=distance(i);
+ m' _, R" X% \. a9 K# ] X temp_2=i;
5 L* W9 h* ? w: j. S' o- W end
0 z& j6 L5 p+ k, b9 C$ d$ f" y: M/ B- d end- W8 V: q" G; {$ O' V/ m$ X. h
s_path=[s_path,temp_2];& q/ R4 x0 i3 P* T; ?
temp=temp_2;
3 i5 V8 \/ u' p- |8 k3 h4 ^4 o1 xend P- F- r" T r& N: @$ G8 y
. Q% m+ |1 t8 o3 l X \& \% w%output the result. Y+ I; w+ \ H8 X( F0 k4 R4 i
path(1)=endpoint;1 B- f+ q7 U7 z9 h
i=1;0 |% N% ^7 R- Z9 U/ l
while path(i)~=start& a6 D$ j# n1 b; l: h1 |' Y
path(i+1)=flag(path(i));
6 g1 N4 d& C9 G2 @ i=i+1;4 F- [- l0 }7 |* j9 e3 T# Z) Y
end+ e L5 R0 s: z5 L8 @
path(i)=start;! _2 M" r$ O" o8 P$ Z' H! i
path=path(end:-1:1);
; q' }1 }$ u3 {" U5 c- N! W+ S( Fshort_distance=distance(endpoint);
$ l( T& t/ \: ^7 u$ b三 绘制差分方程的映射分叉图$ e3 T+ u( t; x0 L
9 i8 D B3 x5 Y. Z" w; c
function fork1(a);
/ Q, { [+ J: |/ ~0 H! K- B$ r; _* V* z2 |" ~, c+ m
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图( G1 t: d. f4 |6 R" m% n
% Example: . i8 l6 [. e% ?- W$ j$ Q8 a/ ?8 o
% fork1([0,2]);
3 ~: v8 I" [% B- Y" a, ]N=300; % 取样点数 6 k* N2 k+ R$ ~8 o0 J" f( [: n
A=linspace(a(1),a(2),N); ) Q; ]; @& t: D; O6 `3 B+ w. S r% R
starx=0.9;
, G! h) n$ @1 z0 g% n# CZ=[];- l, c, H3 l* z' J
h=waitbar(0,'please wait');m=1;5 O- W' w8 ~& Y! r
for ap=A; 7 s3 r/ v% N. E' l! l
x=starx; 5 L/ K% v6 m6 ^' j1 ~1 r5 u; d3 M! @
for k=1:50; 6 W3 R9 E2 b3 F9 d" A; ~
x=1-ap*x^2; 1 C) |. p# P* @6 R7 l( ]
end
3 \4 c* p5 t7 K( s' K' D for k=1:201; : o, V! x' E. {$ Y2 {3 w v8 O
x=1-ap*x^2; 8 e, l6 ?, i5 K7 t1 b+ ^! P6 b" M, S
Z=[Z,ap-x*i]; 0 y) |" A, K3 s% U; X
end
# X. X& _- z- y$ m8 H0 E) E% I" l waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);9 x& K' O4 z6 b6 y3 p8 [
m=m+1;
/ h% ]+ t9 [# }; ^0 O9 s+ }( rend
/ |. g9 N) w2 i( @/ {" ~delete(h);
. q3 D8 ]) X0 e; I- ]$ wplot(Z,'.','markersize',2)
9 e# v- I" e4 ?: Nxlim(a);
( D. c! Q: f& E! v- [
: p f5 U9 W1 p' k! m0 Y四 最短路算法------floyd算法/ Y9 D. {) y9 b0 X
function ShortPath_floyd(w,start,terminal)
. X Y4 j7 u7 ?; F9 B7 M%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
: _" Z4 Q, c9 R%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];7 M: e$ } J& P+ c) E" k# J. d# q2 `
%start-----the start node;
, a- s& ?! e$ h2 r8 j7 m4 A, U%terminal--------the end node;
6 P. u6 A4 ?/ h2 Hn=size(w,1);& }# R7 W* D$ }* O8 n
[D,path]=floyd1(w);%调用floyd算法程序
7 a l* l2 Q9 T0 o) H5 }
% ]) }1 R1 {! _+ Q) n) t%找出任意两点之间的最短路径,并输出7 ]) n! j1 y, y/ `& o1 h
for i=1:n
% `4 @- H( W2 t7 o$ r. |! s for j=1:n
" b* M8 @2 ~5 M/ [7 \" [ Min_path(i,j).distance=D(i,j);: O1 }4 P( K* H* Z8 w; G1 q; s
%将i到j的最短路程赋值 Min_path(i,j).distance
* a$ s+ d) L9 k: t$ t' W+ j0 N l %将i到j所经路径赋给Min_path(i,j).path
( p3 w) M8 g2 V8 z Min_path(i,j).path(1)=i;. f6 H2 n5 f: W5 {+ ^$ {
k=1;
$ E4 C* {4 r' n% L while Min_path(i,j).path(k)~=j) j+ N" a: `9 M6 e
k=k+1;
$ v" A$ ~& {7 ~6 b" a! B Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
+ ^5 o7 E* Z9 a2 p end
, Y# G9 z5 o9 g- m end
# G$ d* e" l; h$ o9 qend
' L( o+ R2 Y5 d$ @ Q2 l% A* @s=sprintf('任意两点之间的最短路径如下:');
% @/ V8 \# M! o; Z) \disp(s);
- | E% {: B, U; s( z& I+ `1 b& i* Gfor i=1:n
- A& g# a/ ~, U4 U) q4 p for j=1:n
" Z. Q* `' V, ] ~9 g& B8 t s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...- @* y: ^7 f+ n! Q* U `
,i,j,Min_path(i,j).distance);
! E4 J: }/ i4 V2 B0 _6 U disp(s);# T% u+ T+ N8 C8 @" e/ F2 i3 r- Y9 v
disp(Min_path(i,j).path);
7 s" _0 K: I) c; p) j end
4 e9 s9 U$ n7 u2 w. h6 [& ~end) }. Q1 M3 W9 M4 [) c0 P* m. Q! `
& h7 l- M- c( o7 ] N%找出在指定从start点到terminal点的最短路径,并输出# i7 n0 k9 z8 m& e* I5 v
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...# E/ m( W m" S+ _" ?
start,terminal,Min_path(start,terminal).distance);
, [0 {/ R' T" ~6 e3 \+ G, Z) j; cdisp(str1);
, Y" q8 i! q J2 f2 Qdisp(Min_path(start,terminal).path);5 h& M; u% ~2 E; }
0 ?$ I7 m* o/ j8 G/ |1 T) i
%Foldy's Algorithm 算法程序0 U6 q8 ~, C) j- x, Q: D
function [D,path]=floyd1(a)' \. ^5 o2 ]( k7 f3 @3 g
n=size(a,1);
% K- h2 c f" zD=a;path=zeros(n,n);%设置D和path的初值0 q' u( z- g3 c6 J: Q) F
for i=1:n" D; h" Z7 L) L- w. Q4 x# o/ P+ C
for j=1:n
, }8 P# ]; {& U4 K/ n( ]; } if D(i,j)~=inf% U; K# w" r N. k: E0 s- q* ?
path(i,j)=j;%j是i的后点; b5 B5 A% o6 _/ i
end( G/ X0 q7 Y# Q4 x
end! Z4 g; c) E t/ S& T
end" ?5 w% s9 B3 m
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
% K) w: {8 ~! O k/ Cfor k=1:n
1 H% Q R( x" x9 m- U& P for i=1:n' X" M5 a$ M& k6 }7 x9 Q
for j=1:n8 o( [+ H' ]/ m" q5 o
if D(i,k)+D(k,j)<D(i,j)+ I3 u0 U% }& a
D(i,j)=D(i,k)+D(k,j);%修改长度
! A r% t9 H: c- H. @ path(i,j)=path(i,k);%修改路径+ o0 ^1 l& m. y
end
7 J- C% G/ F: E" t% U* e M2 J end8 @ N! [3 z7 _. g
end
% L2 C3 }" ^2 t3 w) E" n" F9 aend! _& _8 B' x; `8 q- G
! r; a# _7 P& O; I1 {2 M
五 模拟退火算法源程序
6 `# E, K- ]) J5 j( Ufunction [MinD,BestPath]=MainAneal(CityPosition,pn)7 Y9 @& P6 R- H$ [7 Q
function [MinD,BestPath]=MainAneal2(CityPosition,pn). Q$ y! B0 @* P
%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
8 z4 n* \' g" @ ?$ O% q- Q+ {%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...# Q, w0 h& R) h- R6 A, X
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
8 Q& `) }' B- v9 E% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...; n2 M8 A2 h5 a' T; w% s5 n. x1 r
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
6 h1 m0 U! I% u. j% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
$ N# o, ]9 F! d1 s3 y. Y; Z- a
) d b) N* c5 ]1 M+ |%T0=clock- ~* Z0 I7 [8 w
global path p2 D;
7 m. f' a% R# ~[m,n]=size(CityPosition);, K. L: D/ X6 n
%生成初始解空间,这样可以比逐步分配空间运行快一些: _# W9 ~$ z. N
TracePath=zeros(1e3,m);& W) W8 v3 Q- l- Z4 V# Y; [
Distance=inf*zeros(1,1e3);0 j3 s; \$ B/ d/ }" ?" z( O
; D$ B6 I4 [6 L( Z& y* E1 J, `7 Q
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...& t7 Y: R/ B/ E1 P* X0 u- r9 Z
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );9 w& f8 h, {8 \7 I+ E& j2 u
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
( _! N" w$ a+ ?5 Z: `3 Gfor i=1:pn
2 A) W7 X! {* V7 J path(i,:)=randperm(m);%构造一个初始可行解 v( k* I- ^. w6 p1 d
end" u8 G$ c6 E+ y. }" D, b/ J& H% m
t=zeros(1,pn);8 E& o1 u. u7 a- \- o7 g
p2=zeros(1,m);0 l! {" w% q6 s7 k
$ m/ Y3 D) E9 s' g1 g( xiter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
# Z6 [' G1 y9 y: om_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=' ) ;/ ~ L7 Z+ U* P" V* w, {4 [
%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2 ] N5 E! r" A: V+ @# t: N% `( 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+ Y- t/ b9 I2 a8 [ ]! `4 i
%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6 D" d6 Y3 X. j9 K
%会收到到比较好的效果$ w$ T8 o6 ~! P8 F! k# Z/ \+ |4 y
' w" \. h- S4 E# [. f/ b* }T=1e5;# l( o5 }) Z9 N) v" m4 Q. J+ G
N=1;0 I; g% i( ]; }* Q2 v( t/ {1 m
tau=1e-5;%input('请输入最低温度tau=' );
# f* Z: f/ q6 w& \ w5 c%nn=ceil(log10(tau/T)/log10(0.9));
* i: `- |0 ~; P# ?while T>=tau%&m_num<m_max 5 _( Q: K) G; i7 o
iter_num=1;%某固定温度下迭代计数器5 \, ?$ p }) x4 J# m
m_num=1;%某固定温度下目标函数值连续未改进次数计算器* P+ ]8 U* T Q9 z
%iter_max=100;
9 _9 B( O+ Y" B9 I% Y4 q %m_max=10;%ceil(10+0.5*nn-0.3*N);
: c ~- P/ P$ ]$ F; Q% O while m_num<m_max&iter_num<iter_max& b% Y- x$ i; ?9 n0 F0 q+ s
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:0 |& \7 R4 F1 J Y8 U( v g
%用任意启发式算法在path的领域N(path)中找出新的更优解+ b. g4 w6 Q4 t% b$ R1 M
for i=1:pn
0 t% M& |& n% ^& r% ^ Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
" Y p! q, D# N$ ?3 v%计算一次行遍所有城市的总路程 6 r% G2 Y ~, }. K& D
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
6 B$ c8 ]! ], R" q" Y0 }! k Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
7 I0 _+ y0 E( S$ c. x9 M4 S0 E end. F5 D9 q7 M6 r* Q4 R, _5 m% y
%Len1% R1 U; Z; c5 |' k& E* E: p
%Len2
, b5 e4 ^& x$ l2 _% ~ %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
% @6 r- @- Q8 P+ V/ e" Z6 X R=rand(1,pn);
1 A" M" H. ]+ E0 Q& p. j3 ~2 _6 r3 e %Len2-Len1<t|exp((Len1-Len2)/(T))>R9 z2 r2 B; N, |# Y8 h) t& T0 B
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)8 W" x! C$ c# ]4 N C! }0 j
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );! g; b9 T, ]( s, s, j# K
Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));" @% u. ]9 n% O2 l9 f, C# }
[TempMinD,TempIndex]=min(Len1);
' l' P. J8 L$ Z/ v9 J. P7 n %TempMinD
8 B+ l$ ^+ Y( d& n/ L/ R' l$ f0 | TracePath(N,: )=path(TempIndex,: );" [9 E2 c0 M& H
Distance(N,: )=TempMinD;# M1 S$ m0 }" e& E8 _9 ?) n
N=N+1;
1 `: ?& `. Y! d %T=T*0.9
0 v$ y8 @4 J. V1 | c7 {* Q, ^ m_num=0;+ m* _3 u8 a* Y _+ x
else& K! O3 ~8 e. j; [ d0 B
m_num=m_num+1;: M# B7 M g& T$ i5 c$ ~2 j
end" |: G! |$ b1 M" U k9 n, O
iter_num=iter_num+1;
* o" O# S G. X" G! l, B end
5 F0 K5 N2 D# M4 R( _- F5 R T=T*0.96 n# H: D2 p. s, K
%m_num,iter_num,N+ @* ~. R/ f$ {
end 7 J7 n0 {" f* O! _1 L
[MinD,Index]=min(Distance);- i P7 N9 y+ |# m7 u3 |1 J
BestPath=TracePath(Index,: );7 i- e3 V* f& p" |, P0 l
disp(MinD)6 t4 @0 W' E; w; K- g" V/ j# c! n: u: Z
%T1=clock- s1 R1 t* \4 y9 [- {: W
: ~% P+ u8 C: I0 ?. x9 O: H B5 h
' }( S6 z' N; n3 Q" ^%更新路线子程序 f: Z' j7 b, ^
function [p2]=ChangePath2(p1,CityNum) I6 n( \( |' c% _0 q0 M" Y
global p2;
* o* g3 _* Q8 K) g8 `3 kwhile(1)4 }) _5 S9 H, n1 F* V4 ^; i
R=unidrnd(CityNum,1,2);4 j, L8 I0 n: F
if abs(R(1)-R(2))>1/ \) L* Z* e; x* O3 U
break;
/ L9 E& K4 ^2 T7 U; D end% e7 D4 h, t. J( A3 x4 W- F
end( f; a6 K$ b: r0 l- S
R=unidrnd(CityNum,1,2);
* O* L x) j: c( [! WI=R(1);J=R(2);
! P$ Z. s2 O9 Y' |6 F%len1=D(p(I),p(J))+D(p(I+1),p(J+1));
6 C( D- I( ]9 V%len2=D(p(I),p(I+1))+D(p(J),p(J+1));" L/ \0 t7 ]8 A t; C" r
if I<J
, f: b3 U+ m$ J V3 t3 ] p2(1:I)=p1(1:I);; K- M0 A& }, W4 H1 a0 o- g
p2(I+1:J)=p1(J:-1:I+1);
$ R: |$ i/ Y; |3 ]0 I1 q9 |. Q9 F6 K p2(J+1:CityNum)=p1(J+1:CityNum);
3 S# |1 |9 M5 s6 |% W2 {else+ J, n: q$ `& k7 @, A
p2(1:J)=p1(1:J);
; }0 b" D6 _- K1 H p2(J+1:I)=p1(I:-1:J+1);
B* p& `+ I1 |! A |7 q p2(I+1:CityNum)=p1(I+1:CityNum);0 E$ z9 g( U& a5 b9 j
end; m6 `4 S0 T. }+ ]# V3 {
0 T+ y9 ]7 m, s六 遗传 算 法程序:
! o# r8 G. G8 W% S 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!4 U% B! F: c( Q$ _' l& ]
. m4 d0 h& t# T% w% Sfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
2 \* V+ k- V3 c2 E0 S' M( ~% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) ' E9 @( W2 Y; l& V4 i- e
% Finds a maximum of a function of several variables.5 P0 {4 M1 u3 q4 T1 g" i* I1 y
% fmaxga solves problems of the form: ' u8 G" c* E5 ?) X! Z( R4 v
% max F(X) subject to: LB <= X <= UB
) Q. o- r6 ~( e$ \9 V+ A J& c% BestPop - 最优的群体即为最优的染色体群
( T9 t' P# V) ~1 U- H% Trace - 最佳染色体所对应的目标函数值
3 V% n( B4 }$ T& y7 t% FUN - 目标函数. t2 o( O0 K7 u" h e8 ]
% LB - 自变量下限1 q8 d6 Z1 [* A4 |
% UB - 自变量上限$ y0 T0 u. t0 x2 ^: j
% eranum - 种群的代数,取100--1000(默认200)+ X) e2 w6 `" q! M3 O7 v! i2 {
% popsize - 每一代种群的规模;此可取50--200(默认100)$ S9 v1 D8 ], z- T6 S
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)2 O+ w% f) F! q1 I+ N
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1); W- s( Z& l/ t& |& Y
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
5 M$ L" a9 p! z% |8 j7 A% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编$ F3 Y u$ j2 o
%码,option(2)设定求解精度(默认1e-4)
! n! f! g" I& N! h! _1 t%
3 Z, [- J. r+ p ~% ------------------------------------------------------------------------
2 [8 B, R) O# P! Q$ k7 n$ ?# Z$ o; J
T1=clock;' i5 f6 k0 P& \/ K
if nargin<3, error('FMAXGA requires at least three input arguments'); end7 J1 w. r# x+ j. `
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
9 W n/ n* `4 g4 V/ b; iif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
; P) }4 h" C/ {( V/ `9 a k2 Wif nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end3 C) w! i5 u8 W4 _
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
4 K& O5 Z0 \6 h& O8 v7 f( v. }0 {if nargin==7, pInversion=0.15;options=[0 1e-4];end" [: |, p8 z1 s! `
if find((LB-UB)>0)2 F4 q6 \; L; m3 @
error('数据输入错误,请重新输入(LB<UB):');
1 \4 U% R; o" m1 ?8 |) f2 A* Send3 {7 a, O! V$ _& {1 J: W, N. e
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));9 J6 R9 k( J! T+ q# f
disp(s);4 i# R. ~# o+ v7 d6 q+ }' k; h7 }( h
$ H& W' \7 G+ [0 pglobal m n NewPop children1 children2 VarNum8 t# M# M5 t5 n/ W+ B
& Q5 U* Y& s( Y' F d( H
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
' x) F: y9 T$ v% i5 C+ t5 Vprecision=options(2);%由求解精度确定二进制编码长度
9 ]' Q- [# }- o( n$ w2 m: i5 Bbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
( \9 @1 Q! J) T# p[Pop]=InitPopGray(popsize,bits);%初始化种群
{ k8 X9 z' O; z6 d[m,n]=size(Pop);3 B* c, k2 q3 S9 M
NewPop=zeros(m,n);: B7 f/ `) u9 E. X! a
children1=zeros(1,n);' v0 R) ~ S/ I) ?6 M( Q
children2=zeros(1,n);
" v" k+ M& K: a% }pm0=pMutation;4 ?+ w; {; e0 R
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
5 k- \, i$ G, |) F- aTrace=zeros(eranum,length(bits)+1);7 b9 m1 D$ V W' ^# D0 o
i=1;
( w5 ~2 j! K1 i9 @! ~9 L2 Pwhile i<=eranum2 g' Q) m8 F+ }4 n n4 t
for j=1:m
) v! l0 r" R3 G' d value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度5 K6 G5 Q: f3 `
end
1 [% u4 ?" @% H' k4 y& Y/ U# L [MaxValue,Index]=max(value);
' B5 {4 ^8 B( e! t3 a BestPop(i,:)=Pop(Index,:);
3 {: N" w* Y& e& H/ n6 W6 W Trace(i,1)=MaxValue;9 \! C g6 a! ~0 V% |2 l) \
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
1 P5 U% G3 y6 O0 [) D [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
5 _. g: H- u4 J* k% G# ?[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
) k' j: U" u+ n1 ]9 L%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率
+ I& g4 l- B5 M/ H) A& w/ q+ F7 M6 r' H %round(unidrnd(eranum-i)/eranum)
9 t+ g$ G5 K, x [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
7 M. z3 h$ N" X [InversionPop]=Inversion(MutationPop,pInversion);%倒位
3 p g' g2 V" R' W0 R& x) D Pop=InversionPop;%更新
9 w, Q0 S/ h( d0 w$ J( lpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
: V x" p9 P, W; l%随着种群向前进化,逐步增大变异率至1/2交叉率: G# k- D/ {. `
p(i)=pMutation;
7 ]$ R; X+ S9 b* }: M# n i=i+1;
/ }: s+ e* a. ]5 ]end) U! z; O e0 J4 c: s( P2 Z
t=1:eranum;, s. C8 @" y) s( F) U, ]
plot(t,Trace(:,1)');
, F' N& {) z# E1 R: f! d7 A7 [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)');
% A3 p9 z/ o- @5 j, N8 F' _$ y[MaxFval,I]=max(Trace(:,1));
0 C- U& `* @$ G/ Z# i0 G% G/ S TX=Trace(I,(2:length(bits)+1));1 Q- T5 r0 V% j O6 ?8 H2 X
hold on; plot(I,MaxFval,'*');" Q( s. p- Q% T% _
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
/ P6 P9 e- T$ Q, t- ~& a7 tstr1=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,:)));/ T; C. V& U/ p+ S6 w; l$ L
disp(str1);
- C% K) ]! W, q/ W2 Q7 d%figure(2);plot(t,p);%绘制变异值增大过程! E% Z% w0 t! h. y4 Q' n
T2=clock;
% J, O d# J3 f5 g# C" y1 \elapsed_time=T2-T1;5 D9 T- O9 v. ^7 W% r
if elapsed_time(6)<0. o8 A. }4 s I+ v$ r
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;* F% A* x; e8 M: U5 _) m" t: |' c. H
end3 C# ^% i) z/ B+ {& ] ]
if elapsed_time(5)<04 W$ Z$ g& b5 e4 @
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;/ \' D1 @- T, L) K
end %像这种程序当然不考虑运行上小时啦
9 p1 z' V s, U Astr2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));
; ^( l) l+ [7 V! c* v" Q0 q% Udisp(str2);
$ I" A) ?! M3 s( Q4 W; x8 L- r8 R6 K5 b
7 q* l6 {. b# t5 p9 z% o
%初始化种群. N) K# ]5 M8 H- z' F# {
%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
; b5 X" I, u6 |3 efunction [initpop]=InitPopGray(popsize,bits)) m! A2 V" J- S4 B/ G5 Y
len=sum(bits);
9 u+ w5 L3 g. I* z/ ~5 G1 ^initpop=zeros(popsize,len);%The whole zero encoding individual
' a" j8 U7 I8 ^; D) v& }for i=2:popsize-1" l, b. Q' ?9 u' S) B- S
pop=round(rand(1,len));" y; }/ e; E, Y* M# A3 }7 K
pop=mod(([0 pop]+[pop 0]),2);
, j) P) j4 f( f2 f7 h* l %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2), s- ~/ |) ?. e0 Z
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
K7 f5 A5 ]1 C$ n7 b, [ initpop(i,:)=pop(1:end-1);
. C% z1 h0 O: U! _end; w& e. `( y- [8 ]
initpop(popsize,:)=ones(1,len);%The whole one encoding individual
- o- _) g" F3 }6 q%解码
, E/ X+ B1 r; j3 r- N) H6 O0 U4 e! m
1 o% N8 o6 X! {function [fval] = b2f(bval,bounds,bits)
+ ^6 \& q& B7 g5 n, ?+ ]% fval - 表征各变量的十进制数% @/ u! f! d% U( b7 U' d
% bval - 表征各变量的二进制编码串5 d& I8 b3 M8 ^8 X( Q7 @7 _
% bounds - 各变量的取值范围9 u/ z4 L- b9 M3 \3 `6 X
% bits - 各变量的二进制编码长度
+ J- A( S) p% G6 G) r; mscale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
2 L5 {9 f# |2 r0 x0 JnumV=size(bounds,1);
w4 J7 \5 E D0 o4 P8 n( ~cs=[0 cumsum(bits)];
4 ?7 K- P; x! gfor i=1:numV
8 b/ Q# f, H* O: c2 E& [. l a=bval((cs(i)+1):cs(i+1));4 z/ u$ M. S/ L* i1 q
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
) i. N+ v) ^4 ]0 g4 }/ yend
' D; [$ N( b) b% w; U%选择操作
! q8 U% w# T! d# y9 G C" Z* Z! l0 _%采用基于轮盘赌法的非线性排名选择
' V0 {" K- R9 p%各个体成员按适应值从大到小分配选择概率:
: ^/ t1 X- J. E/ ~%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1. Z: |, H8 a+ o# x* A& U3 [8 T
) r4 e6 B: o; l4 Afunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits); J' Y( ^+ ]& s# I2 w* R" H
global m n
: V9 S9 D/ { _selectpop=zeros(m,n); O9 d- ?- y4 O H& u
fit=zeros(m,1);
8 I0 \4 y! Z! D' G Z) H% h( H1 afor i=1:m5 r2 V0 _) \! f' A I; }+ n8 y% m
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据* i% t" V0 q8 x- O9 ?1 }9 c
end
2 o, y, X+ t- F8 ~selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
3 U, B! O) B6 w: ]4 U9 ?9 Bq=max(selectprob);%选择最优的概率
" M$ t. g/ i1 G' Cx=zeros(m,2);
! I9 u! O) K( ?0 D. ix(:,1)=[m:-1:1]';5 i, K. O9 o0 W' d8 K. c
[y x(:,2)]=sort(selectprob);1 ^' Q' C& b; B
r=q/(1-(1-q)^m);%标准分布基值
* r$ Y! ?# b6 E( ]newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率+ Z! B; ^. ~ q( U2 X) F
newfit=cumsum(newfit);%计算各选择概率之和
+ t. e( s8 `# C J* a$ G( l- I/ zrNums=sort(rand(m,1));: r6 m0 T' r& d! `
fitIn=1;newIn=1;
4 R3 w! T' v5 L! |: swhile newIn<=m
+ ?9 g j5 G5 q% {# A0 L E if rNums(newIn)<newfit(fitIn)
0 I; P4 H1 X; k3 Z# t3 v selectpop(newIn,:)=pop(fitIn,:);
! R0 ~1 j9 d) h% h) G2 \ newIn=newIn+1;
# c+ ]0 n% n% _) P5 V/ G else
, Q4 j$ c7 @' x4 I) y7 ~ fitIn=fitIn+1;
8 a F7 \- X: E& L end
1 J. N7 y) a1 c) Z+ nend; H7 F: [# D/ @$ N1 b' L
%交叉操作/ C% I# y+ e+ j
function [NewPop]=CrossOver(OldPop,pCross,opts)
& G* o& F4 r4 K%OldPop为父代种群,pcross为交叉概率5 J* s ~* q6 E5 n8 V" L, e$ Y
global m n NewPop
- z2 E; R/ J% Ar=rand(1,m);
+ N0 O7 T& g+ y6 wy1=find(r<pCross);
" _6 |8 @& g, }4 O# Z; I7 i4 Iy2=find(r>=pCross);( g& c2 T- ^) F, l; ~6 @* I- r
len=length(y1);) P1 [/ E4 [( V' n7 B% c5 O$ D; F
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7 q S1 S) x: I+ m" C
y2(length(y2)+1)=y1(len);
( I' P" X: {* i" D; s/ H$ F% X% @: O y1(len)=[];
0 j4 w% f7 O8 S M9 Yend
" T: F/ t- n! E0 J* sif length(y1)>=2
5 J8 @# A5 ?5 q) M8 H! f for i=0:2:length(y1)-2
3 q/ u f$ L) }$ ]8 } if opts==0
/ w& p [% x( q- E9 I [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
* T# e: a8 z, {% A: f. v else
& I3 }1 R+ o$ j% ]* b2 B9 z. c [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));. I$ q. z- P$ i- \: J! ]1 s+ }
end6 j x" [" X( y) R$ }: h6 a
end 2 \" X/ A, H8 a
end8 b v: R6 W4 Y$ b2 F
NewPop(y2,:)=OldPop(y2,:);
4 i& c! B( u# A/ C$ `* ~
9 `9 x8 W: g9 W- s%采用均匀交叉 $ v: A) [( f& F" Y T R
function [children1,children2]=EqualCrossOver(parent1,parent2)% [4 g1 L) {9 ?8 w' ~
% }6 W, h# o* G
global n children1 children2 * X1 S4 F: Y0 ]- d0 q( R5 S
hidecode=round(rand(1,n));%随机生成掩码
0 L( j; g" L* ^ h; e9 Scrossposition=find(hidecode==1);
( T& |+ a4 _( O) m; tholdposition=find(hidecode==0);
( G* |. M5 h; X4 i3 U0 l1 schildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因2 e& N2 S1 J" x1 x4 T( u
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
( z3 F9 K( S6 e4 m; Zchildren2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因: J7 y& _+ I6 H/ j
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因% T+ W/ E0 V4 k' `( @0 [
% S h9 d$ x1 J; d
%采用多点交叉,交叉点数由变量数决定- f4 Q9 O$ d4 |+ @# T7 T
4 ^) G9 a/ u W! @3 A Z1 y4 lfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)0 W# N4 C6 g' ^- w0 ~9 h
- |' Z( G" J3 T4 n: U( k
global n Children1 Children2 VarNum
7 }2 U. E3 p2 R+ ?Children1=Parent1;& n- N% ]0 Q, C5 F% r6 S
Children2=Parent2;
2 M9 F h' y+ f8 }; D0 TPoints=sort(unidrnd(n,1,2*VarNum));
& O+ G5 `0 I# _8 t. E; wfor i=1:VarNum
; s; ?( y7 f$ S1 `) f7 ~ Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));) c3 D9 I6 L. M( g
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
$ b6 w9 f3 [# {4 g8 Q0 Rend) p/ o [6 G6 l4 J5 W. x4 y
, a. K& a# M/ J3 H
%变异操作
2 \: z0 G5 S; b- O6 m& |( vfunction [NewPop]=Mutation(OldPop,pMutation,VarNum)2 ^. A0 g' S' j% t7 ]8 F I0 t
' v8 m2 ?& a8 [$ m; K* u
global m n NewPop: K6 N! q7 c: S9 N5 O( E6 L
r=rand(1,m);
% v: E0 J; x; r5 {$ l) kposition=find(r<=pMutation);, \3 ^, ~3 K2 C9 t3 X+ M. ]
len=length(position);
. s+ U( J. ^3 _' V. j$ r# \2 M+ F, zif len>=12 P& m) W: w+ t) }! Z
for i=1:len
: H" J$ B8 \ S# V$ P k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点( H3 @# E6 c% W$ M _6 h
for j=1:length(k)
! D6 N6 x1 Z% E( O1 Z: j if OldPop(position(i),k(j))==1
9 g$ c* V4 J0 Q6 _( A; A$ k* ` OldPop(position(i),k(j))=0;
3 I7 l% [7 t. ^! o' y else3 P( P! K9 l; E2 k' L
OldPop(position(i),k(j))=1;
; m* _" a8 r( n/ ~$ ] end' `# ?1 X3 v6 K$ l
end# z* S7 J( a& } s, X% e. M
end
* I6 P) }! g6 [1 M7 O: X9 F! lend# c" R' [0 y9 {/ u* y+ p
NewPop=OldPop;
$ r# c- L4 U* X
: X% H; U' B( S4 b7 u%倒位操作
& d, ~/ A0 q& S9 j( p( k+ Y5 n, C% Z# E4 d* P/ ]
function [NewPop]=Inversion(OldPop,pInversion)" N: ]0 W+ r4 w
: d1 \+ r9 u" d5 d6 ^5 F# k
global m n NewPop
8 l) h+ E" w& x4 iNewPop=OldPop;
9 @2 S0 ^( _. ir=rand(1,m);3 Z( p w9 n6 j
PopIn=find(r<=pInversion);
' T# r. S& L4 |) B2 U$ Slen=length(PopIn);
! v8 D' u$ J" L/ g5 H- Hif len>=13 {6 w; h" G, F! n- F
for i=1:len( g2 J( u3 v2 G0 H, @" N# Y
d=sort(unidrnd(n,1,2));
2 A9 k: V2 l* p if d(1)~=1&d(2)~=n: F4 K2 D' Q6 Z$ Z" K
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);. F P2 \9 Q+ D- b V* R
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
7 J7 N( s) c6 ` NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
& w1 D( A4 D% c7 [1 t8 _' `6 ~ end
# X, i% X' `2 ~ y end- }# V4 Z1 p1 t# I" j3 R+ h
end
' _) i6 z& S0 F a5 U0 _& u" q/ P5 o' k8 @
七 径向基神经网络训练程序* V. C( ?5 U) p: z3 W6 q" i
% k/ [" C( n7 I3 P* T* i
clear all;8 |# W2 H' D$ i5 n$ R- T' l
clc;
$ h& X v O$ t3 o+ ?%newrb 建立一个径向基函数神经网络
) ]( n% [. _$ C) ?2 ^3 Vp=0:0.1:1; %输入矢量
( @3 A( v: T( o# u8 h2 `t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
) s" Z' j9 z- C: @2 P! vgoal=0.01; %误差
" H1 w" \' t: b# v' y) V) Fsp=1; %扩展常数1 N7 t& `& _2 e5 g9 d- m5 z
mn=100;%神经元的最多个数
5 m; i# q9 _# k* _! Jdf=1; %训练过程的显示频率
0 _: t- P" _. L6 Z; G' S/ N[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
' J2 K& M8 \1 p/ W! y1 v& }; [) O% [net,tr]=train(net,p); %调用traingdm算法训练网络+ `3 K! o5 @& D8 s
%对网络进行仿真,并绘制样本数据和网络输出图形' G( j3 _9 ?) j3 F, V2 ?
A=sim(net,p);
+ o- K6 }- }$ B7 O) I. AE=t-A;
( D; W- S6 B& V% z" y1 R2 A9 |* J# osse=sse(E); ?) [8 `* C6 t5 V
figure; / O, u2 {% ?! ^5 l y7 d9 b
plot(p,t,'r-+',p,A,'b-*');
3 e$ D; ?4 I' o' E' r' ulegend('输入数据曲线','训练输出曲线');5 @3 d0 |5 v6 o
echo off N! P. B8 V1 D5 I. q& Y. I6 g. J
3 C# B* N2 Q* g" @* x* U2 _说明:newrb函数本来 在创建新的网络的时候就进行了训练!7 b; |. e& i0 Z- j ~# 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,
( \! e' o1 l. T8 \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!
$ ?+ f4 [6 e6 c4 ]3 U' X. @. h9 g8 W5 s
& I7 W4 f+ E& S9 p1 n l* s训练结果显示:7 S0 }8 ^7 [2 B8 t$ v" s
NEWRB, neurons = 0, SSE = 5.0973
7 Q+ m8 r+ q3 |7 JNEWRB, neurons = 2, SSE = 4.871390 f1 ~% `/ c1 a& Y7 M( R5 o
NEWRB, neurons = 3, SSE = 3.61176 z3 ^" P! H% b U" V5 Y) x
NEWRB, neurons = 4, SSE = 3.4875
6 e% i3 x5 {& {% b- E$ |1 {NEWRB, neurons = 5, SSE = 0.534217
/ o' j& N! f `" M7 @7 fNEWRB, neurons = 6, SSE = 0.51785
5 f$ K5 _% A* ^, C; ? _# SNEWRB, neurons = 7, SSE = 0.4342591 Q5 {4 R1 w0 G5 P9 H9 a6 y
NEWRB, neurons = 8, SSE = 0.341518
3 X& v/ Y9 _! nNEWRB, neurons = 9, SSE = 0.341519
" z4 r; i* Y) O0 f3 UNEWRB, neurons = 10, SSE = 0.00257832
5 ?- C3 B8 j) m/ }: e9 ?% x: Q! F5 `8 h: l0 L! ], `' g
八 删除当前路径下所有的带后缀.asv的文件
& s! L4 \% P" B说明:该程序具有很好的移植性,用户可以根据自己地" @/ i! R* i4 e" Y
要求修改程序,删除不同后缀类型的文件! 3 ?, O. H% h: v
function delete_asv(bpath) 6 V! D0 W8 ~4 C7 T o
%If bpath is not specified,it lists all the asv files in the current
: {2 s2 r8 x" A* a, u: h2 I% w9 s%directory and will delete all the file with asv 3 A" |6 V4 f" k7 X; g
% Example:
+ p5 a( n$ L# t6 ~& E% delete_asv('*.asv') will delete the file with name *.asv;
7 j0 P/ E! J; j8 h! F" D% delete_asv will delete all the file with .asv.
$ z* U: Y6 c" U7 b8 w. [5 D+ S- ^8 t1 Y
if nargin < 1: U& V$ ?% u( V* E2 p
%list all the asv file in the current directory
4 U8 K* n2 T5 H9 |% }0 R files=dir('*.asv');' {1 E4 ~ ~& w' U& F. y; a
else
! Q. W) A4 v/ M) { s( O% find the exact file in the path of bpath. X9 B' {! u4 \& C: p
[pathstr,name] = fileparts(bpath);* J4 K g& e( i* V8 |8 H
if exist(bpath,'dir')
) P( A" E, P" Q! S! S0 t- C# ] name = [name '\*'];
+ Q2 C5 |0 f5 U% j; v7 ^ end
N, ]$ ], e) l A ext = '.asv';
$ D! V6 T- _1 [ files=dir(fullfile(pathstr,[name ext]));
' N: m$ L1 Q, T2 Z$ M& u8 Aend
! l3 R% y2 ]4 b: x g
1 O$ Y/ L; l& C+ lif ~isempty(files)
. ^8 d) U1 N3 t% L. b: ~) q for i=1:size(files,1)4 Y/ [" r6 v$ C* q
title=files(i).name;; Y# l5 w3 `7 g: A/ F1 X, K; J
delete(title);
3 j @9 g0 E5 \# i8 s! e6 l M end9 O8 `$ ?8 b4 T2 q% L, H
end6 q; p* k- a T7 ^4 x# o
' r- u: G. N9 x: [
# I% u9 e) v$ l4 S! r4 T. _. r同样也可以在Matlab的窗口设置中取消保存.asv文件!5 `0 T/ Z' _: } u$ Q
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