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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& e+ G$ U+ j0 f; O8 G
1. predict_fun.m为主程序;# p- i. x: X2 D: Z# \
2. timeseries.m和 serie**pan.m为调用的子程序% x% @0 i8 W. ?+ J
$ {5 V1 C, H+ O! X; O
function ima_pre=predict_fun(b,step) f9 }/ {% m) i& S
% main program invokes timeseries.m and serie**pan.m6 e% {8 ~9 O$ [( l
% input parameters:
8 B/ D9 T* r; Z/ b9 o( E' T$ O% b-------the training data (vector);2 x3 [) t, B+ x4 T2 N6 T
% step----number of prediction data;
# P! q3 \: ~0 E- Y3 G8 ]" }9 `% output parameters:2 i5 d X! @6 B# ~: B. k
% ima_pre---the prediction data(vector);
7 D- n9 j" v. @" Y% w% rold_b=b;3 C9 V! G" y4 K( x& S; Q) B2 ~
mean_b=sum(old_b)/length(old_b);
1 H8 L$ r: p' C% I: t) ]std_b=std(old_b);
8 G ^& Z5 l& P4 Y. T7 Wold_b=(old_b-mean_b)/std_b;$ o+ I5 b* \5 O+ \
[f,x]=timeseries(old_b);! G: d: a3 g# v
old_f2=serie**pan(old_b,step);, R6 N: {! o2 ]" t
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps; G# P/ f. g% {9 d0 F( {& r
R=corrcoef(f);
# _9 ^' h$ D8 a D% H/ x[eigvector eigroot]=eig(R);
, E) K' t3 E( a1 `1 E2 |eigroot=diag(eigroot); P% [, H% o2 U, {5 j, B0 o1 P* J
a=eigroot(end:-1:1);! Q2 E7 Z9 J; `) C. N' Z; O
vector=eigvector(:,end:-1:1);
) v3 m( K0 [0 D- E: H' x# E3 YDevote=a./sum(a);1 |' Y e+ i) r% F
Devotem=cumsum(Devote);
7 Q( I, K. N; v: P, C# S# F1 s6 Cm=find(Devotem>=0.995);6 V$ B% ?% j& ~* K" g" s2 G
m=m(1);
9 ?7 S; j1 g% u. R) iV1=f*eigvector';
4 | v2 e6 q; P, j; rV=V1(:,1:m);; h, `. J( L! w
% old_b=old_b;7 p( R J9 Y2 T
old_fai=inv(V'*V)*V'*old_b;7 @$ B# h! V% A( n3 X0 l
eigvector=eigvector(1:m,1:m);
- G' v) P" x) Ufai=eigvector*old_fai;
0 y. b- l6 A3 K6 Nf2=old_f2(:,1:m);
* H8 }' o0 m! e- Rpredictvalue=f2*fai;
4 `0 B; e1 H, ?7 i9 Wima_pre=std_b*predictvalue+mean_b;4 X# f0 H, n$ A! R2 n
: `6 |) V; }5 [1 P. j
1.子函数: timeseries.m 1 L: y' U- L0 @+ j$ {& \1 J- ^
% timeseries program%
0 f Y9 l2 j e' h; E; t: ]. [% this program is used to generate mean value matrix f;3 p8 k4 x1 h% W9 C$ j1 p) ]# ]
function [f,x]=timeseries(data)
h- _( m4 C3 i' k: O% y2 l% data--------the input sequence (vector);! n4 x0 k9 P3 H! _
% f------mean value matrix f;
" X/ A6 D4 i( Y; i9 B Wn=length(data);2 R& S. ?1 `4 g: f' I, O( j
for L=1:n/2
" f: l0 @* `7 Y. _# X nL=floor(n/L);1 u5 w( z+ J; f: a9 a/ ~* l: x9 H
for i=1:L
; W9 W7 p: D1 l7 w7 D sum=0;1 B6 f! ?# g4 d$ T' R1 w
for j=1:nL
0 f0 k* v; b7 X$ D! ^- k sum=sum+data(i+(j-1)*L);; U/ l; A5 u: c5 c$ u8 Z6 y
end
3 A* {/ c$ H! O+ \2 o7 E/ I x{L,i}=sum/nL;
, i' x3 ? y( f$ u- S8 N8 m! g end% r5 z# K5 L9 u9 L& K
end3 [2 P2 g( u" g: X
L=n/2;0 y2 N# ?$ `% M% r
f=zeros(n,L);
" f i( x x+ o, xfor i=1:L
$ s* k1 a2 k3 O( a rep=floor(n/i);$ |: v/ i) j/ T& x: J9 L9 V
res=mod(n,i);
: @% }' s# n3 h3 T; r b=[x{i,1:i}];b=b';
% s6 A7 I% T" w& B f(1:rep*i,i)=repmat(b,rep,1);
3 q8 U; ~8 \) y3 x. u2 g6 i if res~=0
. k" I0 G+ Z3 q% C" U c=rep*i+1:n;
; i; n% S/ B4 Z" M0 W f(rep*i+1:end,i)=b(1:length(c));
8 C: \( ~1 {. |$ ? {" p end
& `$ B b' h X* J6 C; X$ |5 lend
% c! j7 a. [% O, ?# q. n( |
/ r0 W4 B; Z0 O0 C! h5 G* x% serie**pan.m
- h; U [" ?& V0 q* V% the program is used to generate the prediction matrix f; 6 f! k' e9 Y. r/ y+ l8 \% a
function f=serie**pan(data,step);
, `/ d" g' @" h) W' [%data---- the input sequence (vector) y$ F7 M& D; {7 d, m/ p( B
% setp---- the prediction number;
! {! G( l8 g* }6 On=length(data);
3 l# ^3 }% e6 |8 I, z: ffor L=1:n/2
/ b' C3 W1 K* d( [ H5 e nL=floor(n/L);, J+ C1 }( T0 {
for i=1:L2 `! t# a8 E2 E2 d, Z/ C. w/ G' A
sum=0;
+ f' f7 i. V m2 V& `5 a for j=1:nL) S$ p" l$ ?+ K1 V+ l5 E- }" Z2 V; }3 m
sum=sum+data(i+(j-1)*L);' s6 q6 M3 X- @1 ?/ P- \* c
end3 Q9 g7 j, U$ U! b! U% ~
x{L,i}=sum/nL;6 w& |4 i1 k/ k: r8 V0 M' {! l
end* h9 W2 n* m- p0 }
end9 }# s: N) D& H r3 l" S
L=n/2;
0 `2 U, v5 b% x( df=zeros(n+step,L);6 m' q7 n g* o+ W
for i=1:L" j0 ` t& T% C. [% Q+ G$ K7 D' j
rep=floor((n+step)/i);
& N$ u% I- A7 L! T/ @& K& A! n5 s" ]0 D res=mod(n+step,i);
1 J* F8 k) s; i7 l: z b=[x{i,1:i}];b=b';
( T' {. G1 p/ }! K T2 [2 s% F8 J f(1:rep*i,i)=repmat(b,rep,1);! q$ r) ?: f# E" H9 P
if res~=0
0 R1 K( U. N3 M) G' ` c=rep*i+1:n+step;. n# L8 X- j6 g$ E% q- c
f(rep*i+1:end,i)=b(1:length(c));
& o$ ^% ^( b4 U5 M2 E5 c; V end3 q% B4 s0 b! ]1 z! l3 `
end
4 w# s: k) q- @5 t& L! }* B8 f/ V4 Z& F
二 最短路Dijkstra算法
* r, D7 P1 Q) ^9 k/ a% dijkstra algorithm code program%6 V V' n; d" {; Q: S- O
% the shortest path length algorithm! n" t: Z- ?* n+ x* L6 D0 T
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)# [; u" W0 U: S# @3 R0 V2 |2 _! k, l
% Input parameters:
2 l# |; M/ z4 v% r% e% Input_weight-------the input node weight!
7 D9 j! V( U8 y: p% A% start--------the start node number;
& \$ E$ G+ u% M* f. c3 r j# |% endpoint------the end node number;7 l- B- l3 i4 C
% Output parameters:
$ Z; [4 v+ T* S& A& l& P) a% path-----the shortest lenght path from the start node to end node;
0 Q. C% Q$ g/ c; c$ U# R. p% short_distance------the distance of the shortest lenght path from the2 Q* T6 ^/ }( Z& q( A
% start node to end node.
. _: [/ t9 v$ m' ]. S; E% @[row,col]=size(Input_weight);
0 \/ _7 H' H/ h e! p# L
% A; D9 }. ]2 ^% w; N%input detection U# u. Y/ q/ j! e5 L7 [5 k+ |
if row~=col
: N1 w4 q e6 M2 s, w error('input matrix is not a square matrix,input error ' );" {& g5 H% O4 }7 U2 S
end+ @2 T+ G1 C z+ w
if endpoint>row m/ Z6 y; A. i+ y& H. N5 c
error('input parameter endpoint exceed the maximal point number');
6 o7 Z. b9 a! U6 s2 R& `0 Dend. F z8 J& P. C% k9 |
7 n J/ U, a5 G+ j ~%initialization- P" t T8 u3 M- A5 z
s_path=[start];3 `* d( ?9 @, T1 ~- f, B6 Y$ T; g/ L
distance=inf*ones(1,row);distance(start)=0;
( V3 Z- _' R) d3 \flag(start)=start;temp=start;2 C7 r U. Q& E+ |& u- ?
* P. z. p9 C& c; O0 C. `6 {
while length(s_path)<row Q$ u8 Z' `8 | n
pos=find(Input_weight(temp, : )~=inf);7 H4 \- Y$ F" D0 V5 O
for i=1:length(pos); C: K# ]9 W/ h% w
if (length(find(s_path==pos(i)))==0)&
1 j4 @7 p8 c- v3 s(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i)))): G: l5 j) h) @# S3 j- M! O
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));; r# Z; W f# \- m+ C( e; i2 y3 k
flag(pos(i))=temp;
" U/ y6 u4 b' Q end
" g/ W) [' ~6 r* K end
; @8 b7 d: Z( i; ? k=inf;" H: |& ]4 n/ K& j1 N! `; T
for i=1:row
+ D. ~8 P' \# h$ n if (length(find(s_path==i))==0)&(k>distance(i))
- \" i) `2 L/ S8 e& t- R: @9 K8 o! V7 L0 S) | k=distance(i);% m2 D7 q: y* ^" \9 J, M
temp_2=i;2 c2 y% l+ p/ N5 r% h9 m
end
& u. N- G$ _ p+ t! ~ end
' }2 T3 p# l6 E( y8 q) O s_path=[s_path,temp_2];
, i, j2 T6 Q# e% j temp=temp_2;
( c) b# v7 ^& ~4 n5 u) bend) w/ u/ e* y9 V" _
& s1 r, T' t4 D
%output the result w" N( b$ ?! f" e. h0 W2 `
path(1)=endpoint;6 |* I% }, v* P$ y- k: r! X$ r! R& D
i=1;) D. L# F0 S+ p2 @
while path(i)~=start
1 O# i0 @2 m+ j6 p$ }+ |9 B2 P( B path(i+1)=flag(path(i));
4 ]/ i& A/ t, c i=i+1;1 T2 o; J0 C( ?' T$ D7 _
end
. p+ a9 T% u+ W& ^( S6 Tpath(i)=start;
# R! G2 Y" b1 u# C" r/ {$ bpath=path(end:-1:1);+ I0 `- L* g! C$ J* {" h
short_distance=distance(endpoint); H6 P0 t* A* [) N P
三 绘制差分方程的映射分叉图
! B# E. n3 e! n# v: [( h
^5 o$ v$ `! P. D: \5 G: ^function fork1(a); # x0 C2 }* y; h2 B" l
' d' O# Q/ `0 b8 K; J- z% 绘制x_(n+1)=1-a*x^2_n映射的分叉图 g1 q8 q+ Y0 t
% Example: , k& T1 q4 E4 U: V. E. u& g; Z
% fork1([0,2]); & A4 \7 q" c, W. J# g3 M
N=300; % 取样点数
$ z. n8 k: N+ l, h. nA=linspace(a(1),a(2),N); - n6 q6 N) J& C* P
starx=0.9; * L% P* s$ M/ U
Z=[];2 ?1 ?+ h5 P: C: Z& j; h' I; z( u
h=waitbar(0,'please wait');m=1;) e0 I& |! C( g7 _8 ?/ D' b6 I* g
for ap=A; / V" F( e: {9 ?3 R
x=starx; , @0 ~/ o1 E" o7 [' a3 Y% w
for k=1:50; / Q Z7 f2 F& T( L
x=1-ap*x^2; 7 P2 m' y- F5 t, a0 A( a
end
0 P8 m& j- i( @ r- h for k=1:201;
* v0 Y/ P4 |" Z. F; B& Q x=1-ap*x^2;
1 I a7 h# x8 K6 l7 Q Z=[Z,ap-x*i];
. |# O, L( [9 Y) j end
% H# I. r' M: h2 o; ~( W! F+ H waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);
: p9 x2 x" u( ?. z9 @" A b m=m+1;
1 i5 l+ _ M$ K/ Nend
6 S9 w+ ~; J6 Fdelete(h);! @# {) o4 U& J! N2 `! A0 R
plot(Z,'.','markersize',2)
, _# U6 n: f% ^( Z1 j6 w; o7 Lxlim(a);
; i1 Y7 z; W: m5 G( W$ t# u1 g. f- K8 I+ R6 t/ h/ x
四 最短路算法------floyd算法' ~+ i9 R* s, Z [+ Z5 n
function ShortPath_floyd(w,start,terminal)
9 t9 w" C: R1 E8 r' u%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
& K. j/ v5 t' [0 K$ e% Z5 p%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];& e7 K ?) H* H1 S! }4 b
%start-----the start node;
4 O. N$ M+ m) n$ z2 f%terminal--------the end node; / Z7 ^6 A4 ?" @, z- Q( x9 M! U$ }
n=size(w,1);9 Z" w0 Q) C( N+ n/ b3 r
[D,path]=floyd1(w);%调用floyd算法程序
+ W8 L s C4 D( {8 C; S" M" M+ X+ }6 h' R# n |3 O; x8 `
%找出任意两点之间的最短路径,并输出$ @1 E/ k. B9 q; o( b7 M& t
for i=1:n
* f5 u3 S- j! l9 ]8 [6 }. x for j=1:n) p) m: Z) P) @8 g+ }4 ?' l0 d9 F3 {
Min_path(i,j).distance=D(i,j);
* B" p( K* `' E4 C, ~ %将i到j的最短路程赋值 Min_path(i,j).distance4 u0 W( s6 R. j7 C- H
%将i到j所经路径赋给Min_path(i,j).path
9 K6 M( l+ Y1 q' t6 | Min_path(i,j).path(1)=i;
3 _2 G C3 Z" R6 |1 Q k=1;
* ~' S8 c2 y. N9 X. V7 W1 |) r% y; h1 \ while Min_path(i,j).path(k)~=j3 y+ b# U2 z1 U
k=k+1;
; _* W9 C% c" F1 x& o* ] Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);8 |5 N' `: u( [. N8 G! A$ w
end
$ ~' | K( `& Q5 k, f end; I) K, w9 z! [
end
2 h; `: g9 G) Y/ Us=sprintf('任意两点之间的最短路径如下:');; n0 A: D1 ~' W) L& T: j
disp(s);
' l, x! R( w1 c; V4 yfor i=1:n
6 M! i4 ]' L; f# {* U for j=1:n: p% Z* ]9 E. B8 \/ ?
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
~! K' \$ ~1 |) p8 l+ P7 Q1 o ,i,j,Min_path(i,j).distance);) n6 p: z ~- Z& z- x
disp(s);- z$ p2 z- P- R4 |% g! V; @
disp(Min_path(i,j).path);* \% P4 b5 Z8 B
end
7 q! @. O) @4 t# R, ^5 d* Hend( s+ k; B& V& b ] i
: A' m1 W i! ]
%找出在指定从start点到terminal点的最短路径,并输出
0 M5 |3 j; I4 n+ Estr1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...
, \- }- T- u& l) A5 t- g# w start,terminal,Min_path(start,terminal).distance); r- Y. E$ U; \0 M1 t
disp(str1);) k9 Z. [1 T G, c
disp(Min_path(start,terminal).path);0 t8 v: f; e% ~2 f2 l( V
& ]2 ?2 H3 x% U; u* ?
%Foldy's Algorithm 算法程序5 g( D- a/ h' ]; H. Z/ I
function [D,path]=floyd1(a)
( x3 f6 Y9 @# f9 x) F$ r. n) ln=size(a,1);
6 {$ C8 d! ~7 _% o& C0 {, A! fD=a;path=zeros(n,n);%设置D和path的初值8 _! b1 w8 n. e$ i7 {2 u: I* {7 ^' m
for i=1:n- [& G t- K' c1 _ L
for j=1:n! N2 e) X/ N. W: I
if D(i,j)~=inf6 f9 } g. W( o. T
path(i,j)=j;%j是i的后点
$ d/ B, f; f7 V- p end
8 b' y* v8 o) Y8 p" S" c* d end! B9 a2 x0 q0 l
end) h8 H% p) I' J1 q$ o0 _3 S
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
; L0 q6 f4 r3 e+ ^ K* Q/ ifor k=1:n
9 K9 ~5 O& ^! _, O( W9 {; l for i=1:n; O7 D% J# \) M2 c, P
for j=1:n
2 H _( Y5 h, {, h$ n if D(i,k)+D(k,j)<D(i,j)" s- U' F0 `; l4 }' k( k
D(i,j)=D(i,k)+D(k,j);%修改长度
, i9 }7 @, J7 N$ g7 H path(i,j)=path(i,k);%修改路径
8 x, i7 V* y7 \/ U$ _$ y end
% y2 Z: v! f! w& I: Z7 X& t; u end/ g2 }4 X, {. q7 {1 \6 ~7 ], A0 h; E: ?5 X
end' C+ u9 D9 V5 Y5 Y, d
end o! g! v, G0 }* c1 t1 J
& `. i9 S& ]- C- N- z五 模拟退火算法源程序
& b0 y/ L3 ]" N8 A9 B3 tfunction [MinD,BestPath]=MainAneal(CityPosition,pn)1 I; u1 K0 R! h- P; q5 D0 c
function [MinD,BestPath]=MainAneal2(CityPosition,pn)
! l1 u) h5 C: 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
. w8 m9 [' K0 w+ X( r% B# h%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...3 C% X# b! ?! j! m1 }$ B( `
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
6 ]$ ~9 A8 \. f/ U9 S' [/ x3 d% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...+ L' d, ], y8 S& X T
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...- @! m. ^- h7 p
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];% B1 w" Y1 T5 n1 Q( c$ J& }
2 j3 ^; J/ L5 k" q8 s%T0=clock
) t5 u1 X) U' j& {" f3 dglobal path p2 D;: I1 o$ W. [& U2 C
[m,n]=size(CityPosition);% g( ^" J1 G- B. Y0 @% \) T
%生成初始解空间,这样可以比逐步分配空间运行快一些% a9 r# Z! d* f5 O
TracePath=zeros(1e3,m);
; T& x- a5 S/ i: K( XDistance=inf*zeros(1,1e3);* A+ e9 _. R. P
, S7 J' _8 _; k5 XD = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
' C6 F/ s$ @, X- X6 I (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
2 y2 X! i; o j9 h6 \1 o%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
- G0 X; O* \: a1 u5 v8 k; \0 {+ Z4 jfor i=1:pn( @' x: V/ c! \/ y
path(i,:)=randperm(m);%构造一个初始可行解' N3 @1 ] H9 a9 G
end2 I+ a3 K0 x W) x
t=zeros(1,pn);
& i9 Y# x/ k0 [1 zp2=zeros(1,m);, J7 u1 }. I8 B6 e' o: H. w; Q
' O* o9 B' H6 N2 B
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );' R$ S* g, k" @. M' U3 k; p
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=' ) ;
) v$ [, `" O( V( Q( ^- F%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# v7 p$ L0 S2 h1 c# L6 m
%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
' U0 x0 w/ e8 U) M. i7 T3 l9 v( ]; R%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
$ H! z7 z1 _ A; O%会收到到比较好的效果- N# ~" }; O K- ^. [% m
- c1 v' r* c# z
T=1e5;# i% g: {! r7 X$ c- T
N=1;
" W* ^* @3 Q3 A8 n$ `) s; M9 Vtau=1e-5;%input('请输入最低温度tau=' );
# Q, F3 e, R1 e; p- F% H5 m%nn=ceil(log10(tau/T)/log10(0.9));$ r- S! v: B$ @) _" t' n9 S
while T>=tau%&m_num<m_max
* ?0 m: R6 j, j* s: K iter_num=1;%某固定温度下迭代计数器& |& F; O/ }8 o7 V4 g l
m_num=1;%某固定温度下目标函数值连续未改进次数计算器4 U$ f, ? _3 D: l/ g1 B
%iter_max=100;( T" S' j) c. _- o
%m_max=10;%ceil(10+0.5*nn-0.3*N);' u2 C& ~. r" K8 c, m, O2 o" e
while m_num<m_max&iter_num<iter_max
' W$ h( W5 k: m. U7 L; S; _ %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:
/ Z+ k4 x8 ~$ ] %用任意启发式算法在path的领域N(path)中找出新的更优解
6 `" h; t# f H8 Y2 o for i=1:pn& Z! B. ]/ K. x- J, M
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);
6 e$ L; A1 D9 X* y o1 U/ C; k%计算一次行遍所有城市的总路程
$ I( X# t2 n+ e( k9 ~ [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线7 L! @% q: V: G% y/ G
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);1 T) U3 Z7 {$ E$ j8 F* s
end/ m7 Y% M+ `* Z# r/ Y4 ~! x
%Len1
& R% p+ T. |' c %Len2- c6 u8 }' Z) R' X& _* H; I4 g8 u
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
1 ^! f5 m$ a# W$ F) k R=rand(1,pn);
5 _( {/ t' O: d %Len2-Len1<t|exp((Len1-Len2)/(T))>R
, O% m6 N9 ^1 {% x' ~5 p if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)# Q/ }6 Y3 i' c" C4 C9 b# R9 M! a0 A$ u
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
8 d3 w" L" m2 x1 q* u5 `3 I Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
% ~4 M+ C+ d( ` [TempMinD,TempIndex]=min(Len1);
9 l# w1 @; d9 {8 u- l %TempMinD4 v% K# _9 q+ e6 k' L" ? e+ R
TracePath(N,: )=path(TempIndex,: );
* U. K: u0 a; f Distance(N,: )=TempMinD;% |' C) c7 o" c
N=N+1;
6 ~1 V& e9 o s, h( I1 m: y %T=T*0.9
; {$ v: ]( T# s; ? m_num=0;+ R( K. ^/ J) n
else* M! o* m3 H% n$ x: _( ]1 ~
m_num=m_num+1;
. o) o9 s- c/ l5 v D" ? end
. X: J- @7 W) e# M% B9 u iter_num=iter_num+1;8 P9 C- N: t* q7 [& q1 K
end
^: `" W4 x4 `0 u" b4 d; K9 o( E: U* ~ T=T*0.9# p2 Y1 y! v$ J4 V+ W
%m_num,iter_num,N
0 |! J9 f+ c# d8 [9 Y1 yend 1 j8 S6 b0 T1 ~/ P6 {5 J" S3 j/ A
[MinD,Index]=min(Distance);
5 L. L, X: U k& V) \ cBestPath=TracePath(Index,: );2 P, z) {3 u# e0 z1 P, _- f9 `
disp(MinD)
% H5 @' L: _5 Z6 O* ?4 o# W c%T1=clock% z/ o J' K/ j* h" ^5 ~# C
1 @/ i' y* e) v n* I! E ! U6 h0 V* `! r# ^4 m- o1 {+ L
%更新路线子程序
& U3 t. |% _* J* m% m' kfunction [p2]=ChangePath2(p1,CityNum)
8 ~9 n1 C9 c4 V* u( _global p2;3 k6 w" M6 h! ?0 v- K2 p- m
while(1)
I. m0 ?- z! p3 R: w. L4 F* L3 I R=unidrnd(CityNum,1,2);$ f! F+ V3 d6 J
if abs(R(1)-R(2))>1
. `6 o9 S+ @+ h# P4 q$ m6 z- z break;
6 U- r. P1 P! {9 d end
7 n4 _# |+ v! B+ G+ W$ S7 Q9 tend- D0 Z8 V0 }: \, O a2 }
R=unidrnd(CityNum,1,2);. O' R7 S- i8 r1 y) e# V
I=R(1);J=R(2);- ?" |/ O) E6 R5 s& _( E
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));+ l) W9 |/ `% C
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));9 C- l3 J. b( ?5 A8 R& z) @
if I<J
$ k9 R7 W& I. m0 N p2(1:I)=p1(1:I);
& H8 e0 U; }7 x6 M4 o! w, j' Q p2(I+1:J)=p1(J:-1:I+1);
, x! Y! t5 G/ C3 k5 Z* g p2(J+1:CityNum)=p1(J+1:CityNum);
3 U; z7 T' q' ~& D: |else
# B9 ]* P, _/ R5 C! L% K& ^ p2(1:J)=p1(1:J);& v# w( G1 V i% B' Q+ e
p2(J+1:I)=p1(I:-1:J+1);# _- u; ]! m- D* ^5 y d% Z
p2(I+1:CityNum)=p1(I+1:CityNum);
. t0 e/ r, f& I2 `end
+ k3 ]3 B' h" i& {. j
* `1 P0 \ N/ I! _0 g4 K六 遗传 算 法程序:8 u- b" B! O- b$ t6 h
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!
$ ^% _1 H" [) h$ r0 S
! z7 l3 [$ {( B5 {' z1 B4 ~function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
3 {6 Q- k6 `+ N# B# N% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
/ G) @0 ^/ |* M" Y' V% Finds a maximum of a function of several variables.$ ?# I7 ^7 |2 q7 A$ g; B
% fmaxga solves problems of the form:
. t# \3 @5 Z+ O% max F(X) subject to: LB <= X <= UB 8 W9 ^8 L R! s- w+ x
% BestPop - 最优的群体即为最优的染色体群& q2 ?( W+ i- H8 {: r, {9 N
% Trace - 最佳染色体所对应的目标函数值
; g/ _9 w! c6 |& E( U% FUN - 目标函数$ t' |6 f3 _ i3 T4 I+ F1 n9 b. o& v
% LB - 自变量下限
( \* A9 l! T1 ]6 d$ |* u) `: p% UB - 自变量上限
9 a5 y8 o1 \' o! b9 `3 z% eranum - 种群的代数,取100--1000(默认200)
) A% V$ K& O. G% popsize - 每一代种群的规模;此可取50--200(默认100)
5 V/ g) ^4 H2 m" B7 g- [# U% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)3 e% o) x; g: e5 E; p# S
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
' b6 {% ?3 Z; K' p% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2) s5 J C) G' C8 \; _# Y4 Z
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
0 n1 p; V( q- I. v7 [) p%码,option(2)设定求解精度(默认1e-4)
/ p$ F! T' v( a8 Y D%# K7 ^1 E: K3 q2 A
% ------------------------------------------------------------------------% I; C0 ?. d, z- D0 @1 X
6 C# [4 M/ ^$ r$ ]( mT1=clock;
2 o3 |( u$ w2 `4 _% wif nargin<3, error('FMAXGA requires at least three input arguments'); end
- \3 v' F. Y! c7 _& }. s5 [/ ~if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end3 n9 g' J6 u% Q& N1 y9 \( N# e
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
1 T5 v; z* b2 K2 j$ ~2 g$ tif nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end0 b0 H5 R! y* d. t7 p
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
, E3 e% Z- Y f" S8 b$ P+ cif nargin==7, pInversion=0.15;options=[0 1e-4];end" k8 V+ R0 n9 a
if find((LB-UB)>0)
3 X& J* F; Z$ m; ~ error('数据输入错误,请重新输入(LB<UB):');
! }/ \" d4 C; F! |end
5 [5 E/ c& o1 V8 _# ks=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));5 e$ P8 h$ J, ^$ p. c
disp(s);- L; o5 O2 O# H& T, G
3 i. G2 w1 r# p9 G# _$ v# c- d2 x8 i
global m n NewPop children1 children2 VarNum
: y$ }9 q# a# J
" s! `$ M2 Y+ ~# gbounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
: K( i; v7 V ^' }$ Z) j% n/ u: Cprecision=options(2);%由求解精度确定二进制编码长度
1 [3 E' U1 k0 c S6 N4 Obits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
7 w; i4 _; M0 O L[Pop]=InitPopGray(popsize,bits);%初始化种群
# M5 Y$ X( C% j+ Y# s; O }[m,n]=size(Pop);: @: r D K( y- d
NewPop=zeros(m,n);; F5 i8 w; L6 s2 w( p
children1=zeros(1,n);1 S. Q* m+ R, U b6 a) D) `3 z
children2=zeros(1,n);
; q( j# g9 A" P2 epm0=pMutation;
& S8 i9 G; U+ \BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace, v h- U, _5 [/ V) ]
Trace=zeros(eranum,length(bits)+1);2 ^7 X: Q! q/ w( Y
i=1;/ U# O* I4 H `2 R0 V# {* F
while i<=eranum7 w0 s1 K' A* {0 }6 r
for j=1:m2 y* U2 n, m+ r1 {5 t
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度9 w) s6 o' F" @+ S2 N
end
: W& t3 X* @, r& I Z! f [MaxValue,Index]=max(value);4 C# @9 m/ L% m! y2 b9 ?* H( m7 }" b
BestPop(i,:)=Pop(Index,:);
- ?. K4 e9 F5 @! D+ K# X4 [; | v Trace(i,1)=MaxValue;: H6 l) n4 l4 |0 J( c6 d' F+ Y
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
0 @/ z) M7 S9 i [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
* l9 s, C9 t" d) s" g. X/ @[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));! N. A6 k( n! d- ^* T- X8 @4 ^
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率4 o+ }" q7 `% a2 K; } b
%round(unidrnd(eranum-i)/eranum); q/ P E8 a' u1 S
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异! l( i; G; G& u d1 o" }( S! r
[InversionPop]=Inversion(MutationPop,pInversion);%倒位
8 x5 p+ a7 Z' m Pop=InversionPop;%更新
1 e, s; d+ D/ EpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); 5 I4 `3 o+ \; d# M
%随着种群向前进化,逐步增大变异率至1/2交叉率/ t2 ~4 k1 u5 R( Y- S7 M7 O
p(i)=pMutation;
; v- f5 n' \1 K5 r i=i+1; o/ l' p* |, ~6 ^; Z! ?! k7 p
end
* D9 D7 |3 w' e, l Wt=1:eranum;
/ b$ @4 \+ Q% yplot(t,Trace(:,1)');
0 ?' V. B$ N" K0 Ititle('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)');" ]6 x; j- C5 U% C2 K M$ k
[MaxFval,I]=max(Trace(:,1));
- ?" D) ^) @# ]8 u" n, |X=Trace(I,(2:length(bits)+1));7 M* O0 w. a7 z# S, L1 C8 i
hold on; plot(I,MaxFval,'*');; ~8 X% f& ]6 A( R; `' ^4 ^- ?
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);0 w3 z* l6 `$ T$ x$ s) o2 g+ z
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,:)));
# U4 H3 V- ` ?( A& g3 K. {- n8 C6 h9 Gdisp(str1);/ }- E! ^4 o, l+ z& Y! ?
%figure(2);plot(t,p);%绘制变异值增大过程
( V% U$ M" X3 T1 t mT2=clock;( S# S+ D6 T: J# ^+ l
elapsed_time=T2-T1;5 C7 L: b, o( E( }+ g6 t
if elapsed_time(6)<0! \0 J' u @; F' Y9 ~5 N0 Z
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;4 K7 |- T" b/ c2 M6 K
end$ Y# X0 h6 N- R
if elapsed_time(5)<0' r. G2 G9 E0 ]$ V0 E, i" M
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
4 |7 R+ |! m( b5 [ Q& Qend %像这种程序当然不考虑运行上小时啦' B) Q4 j$ i. M
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));1 C0 |# A, |; z1 q; r, n
disp(str2);
, d% g" Y# {3 x0 s% U8 q' r( a4 Y- f# }. a( m U% \
% v9 ^, P) o7 S7 u
%初始化种群2 P" M; }" y; S' D1 Y) B
%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* C! w- ]- j1 X1 c2 E. r
function [initpop]=InitPopGray(popsize,bits)
7 Q3 j: p" V0 z H8 J9 Xlen=sum(bits);
/ y; v; ]. _4 k \1 ]! Qinitpop=zeros(popsize,len);%The whole zero encoding individual
+ u4 f, i! C8 I+ m, V& o+ Afor i=2:popsize-1
1 N! e7 S @* e9 g9 i pop=round(rand(1,len));( @. j! C( z8 F3 D4 O/ P
pop=mod(([0 pop]+[pop 0]),2);+ L( q( |; m6 g
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
9 w1 S; l, t% |& V# V %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n), l2 \2 }+ o8 j
initpop(i,:)=pop(1:end-1);
$ I) ?- P) W0 R' I) j: I* zend" o! x6 n5 u3 n u/ T) t! x. Z
initpop(popsize,:)=ones(1,len);%The whole one encoding individual
7 Y% j- r& }6 G5 B+ M%解码
6 H9 U5 g, V; D' @$ J6 h
# [, |2 A- }: e9 D( J" cfunction [fval] = b2f(bval,bounds,bits)( r; y" u" Q# B( w
% fval - 表征各变量的十进制数. b+ W8 H }0 \7 s
% bval - 表征各变量的二进制编码串 g3 K+ }+ A2 S( [6 d
% bounds - 各变量的取值范围1 b- b) ^" s' A& q6 a9 w
% bits - 各变量的二进制编码长度
; P/ B( E: y6 U: V( a. uscale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables7 U5 c* W* [2 k; H, u$ n9 @" B$ w
numV=size(bounds,1); t) V4 N! l& M% z' [& e/ X% i
cs=[0 cumsum(bits)]; + {& [' b, m) M- x9 }, R% o6 U
for i=1:numV
7 @ `1 q$ v" Z) p a=bval((cs(i)+1):cs(i+1));
2 I: ^3 W+ n( x; ] fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);0 t8 s+ l# P* [
end. [6 T5 R5 r, ~( v, l; v F, y
%选择操作
5 i K, I6 b; t, p8 k%采用基于轮盘赌法的非线性排名选择- ^# d* c! o+ C2 S% E
%各个体成员按适应值从大到小分配选择概率:
2 B* J' m9 c, V: i%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=15 ~9 F9 t0 G0 V$ O' j3 M
1 z+ D8 B/ V4 o- j- K3 W% X
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
1 V% v q, }6 m% @$ z. z2 jglobal m n
5 f f$ g4 q- F+ d/ ^selectpop=zeros(m,n);. Z5 `) P4 z$ b- y8 Y$ S# _
fit=zeros(m,1);
0 q% c* J3 D7 z }+ d$ O& I: j0 {for i=1:m2 B0 r2 ~! ~3 g7 f
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
3 Z, U0 |3 u0 L& ~6 v. @end
# O$ ~. @6 x! u+ z' g, H/ U% e5 l5 \selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)* v1 `/ W3 o8 E& k1 O
q=max(selectprob);%选择最优的概率2 Q; g) E2 y0 y8 F
x=zeros(m,2);( e. v Z+ l' Y3 [" O6 f
x(:,1)=[m:-1:1]';
! J6 j5 t# g- E( H7 N) |, D0 W; o[y x(:,2)]=sort(selectprob);
2 h8 q4 a" Q# o/ b( P- E" Lr=q/(1-(1-q)^m);%标准分布基值
. y4 {- g# X5 A* K* `newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
4 c$ O2 \, i! @! A7 l$ J- _& O9 n5 Znewfit=cumsum(newfit);%计算各选择概率之和
& |6 ]- O7 c8 S: _, M: ArNums=sort(rand(m,1));
; Z' r! K( s2 p& c9 \3 C- XfitIn=1;newIn=1;
O$ F+ \% T; \* \0 ~- ?while newIn<=m
. f" t; V' c9 a$ _ if rNums(newIn)<newfit(fitIn)
4 o M V) p1 ~9 ` selectpop(newIn,:)=pop(fitIn,:);) Q9 l- O: N3 @0 I0 \" I) j! u
newIn=newIn+1;' k/ n% Q: ?: h: g+ k# M( ?4 I
else
/ p0 n/ ?; s( l; D7 q* D+ ~7 F% ~) M fitIn=fitIn+1; H7 H! A( b1 i" l0 |+ c# w
end9 L |) y2 X, D& t: ]+ F
end9 m9 y; Z2 x' b+ h
%交叉操作
' c O" x e; V7 S$ {& sfunction [NewPop]=CrossOver(OldPop,pCross,opts)6 G& S Z- L3 @ w9 p
%OldPop为父代种群,pcross为交叉概率- O3 a3 s r: t9 x5 L) L; _
global m n NewPop 7 T7 [3 V5 e2 X5 l8 W6 E8 z
r=rand(1,m);
$ I$ Q( H0 v" @. L2 iy1=find(r<pCross);
( p5 r- g- S. n: P/ h. A. By2=find(r>=pCross);8 ~ Y/ w3 H& N$ ~" u; t" z
len=length(y1);7 M) u: |: K. @
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
' |! A, @* c* f2 ~ y2(length(y2)+1)=y1(len);3 }1 X' U5 `( Y% f
y1(len)=[];8 M; y( W5 z; Y
end5 |. I5 Z% G" A! L2 ~, K
if length(y1)>=2
6 h* C, u" Y& r" W8 U$ {9 M for i=0:2:length(y1)-2: p, [0 ?: ~! _( i c- e- t
if opts==02 Z6 u0 T+ i- M8 q
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
" C& v. }- \. i6 { l/ w else
" M. J9 o6 [) z0 h# g- \ [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
2 _3 q. ^ s0 J3 o0 T3 d end( a$ l, w- D" r
end : b" K0 U3 y8 _
end1 P1 \ Y, H& @' t* W. z7 U
NewPop(y2,:)=OldPop(y2,:);
2 v: d5 i: h2 L4 m) a+ Q. o/ c% S5 [# A/ K" _; |
%采用均匀交叉
' Y, D8 U4 S7 a# o' |* w0 H5 ]! c/ bfunction [children1,children2]=EqualCrossOver(parent1,parent2)
% U! f1 Y) U+ [" Q6 M+ n
+ I! ]! U' a- m9 m- k' g$ Yglobal n children1 children2 6 |2 \& S: B/ _. H9 C8 {$ Y
hidecode=round(rand(1,n));%随机生成掩码
4 i7 x5 H5 M: ncrossposition=find(hidecode==1);
; p# f2 X7 {6 `3 w( }) F$ [holdposition=find(hidecode==0);" c# D. ~1 W5 |- [1 b+ I
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因
/ v) w/ Y6 c% cchildren1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
# B" b U3 L2 N7 w# p/ Ochildren2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
: p0 b# M) `. Dchildren2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因+ F% v! G7 n& s
7 n* `& {- a2 _) k, \) u; o- n" V
%采用多点交叉,交叉点数由变量数决定" b3 V" a- A8 p$ n/ B
& f; j! G6 u6 _1 ~& d' e5 m
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)* z! D% ~+ Q3 ]9 o
- t3 w, X8 e8 z+ J! q& [& w
global n Children1 Children2 VarNum
+ s& b0 k# |' D: TChildren1=Parent1;! \$ a8 T% `+ Y# K
Children2=Parent2;
7 W$ N6 x! F3 M x1 JPoints=sort(unidrnd(n,1,2*VarNum));* J+ N( H) \; y W5 \$ P' K. h
for i=1:VarNum
9 c3 Y- `* Y+ p& B+ b. O& v Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));0 s G0 i: o7 v* I
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));2 E& ^2 @. t4 R8 Y# s- r0 X7 g& ^. O0 T
end( B. `" S( @2 z& {# l
2 q) [* V1 B( Q1 X J, H7 ]! D; M%变异操作% Y9 n7 e: | M
function [NewPop]=Mutation(OldPop,pMutation,VarNum)# a( N2 h* G6 X. S v
) Z; D v7 T8 k) \global m n NewPop' d4 w+ [) w. f6 [! x2 n9 c* T
r=rand(1,m);
2 o E9 } B- e, l+ _position=find(r<=pMutation);# c- D* F2 e1 q- |
len=length(position);
4 q- j% o6 D: ^$ Y d" C1 ^8 e; p6 rif len>=1: y7 E; ~7 _* \5 D! I1 T! n
for i=1:len
1 V3 j; b2 d# Q$ E# S8 [ k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
" F/ u ~$ ~+ Y d% n* C for j=1:length(k)" b# Q; ^8 C( r& P; a
if OldPop(position(i),k(j))==1
; f5 o5 B. ]5 I( M OldPop(position(i),k(j))=0;$ l% N# C+ `4 t2 X& U) c9 X
else
% u! ?. L3 z3 j: f, k2 z OldPop(position(i),k(j))=1;3 T* P6 i7 h2 J' w' @& v: W3 }
end% X3 x6 j2 G7 Y, Q6 G! q% l. h
end9 L) J/ [, [; i
end* m% M6 P5 C+ O6 w) _$ C
end
?2 l# l. [; FNewPop=OldPop;( z& H G; o6 f6 m- O
( f' |. {5 A: i) F%倒位操作' u, s& P, z+ ~4 b
" ^# g8 h0 X# T4 T8 I6 F; r1 X: bfunction [NewPop]=Inversion(OldPop,pInversion)* ]+ f7 R! u( j* m6 [, u
* Y) H2 Y* i" D0 v' j
global m n NewPop) R3 F9 {! x1 ?4 [& C
NewPop=OldPop;) E4 w5 e/ H2 A' [. L
r=rand(1,m);; e5 d" v0 ~( G4 E& H! }& M. M
PopIn=find(r<=pInversion);( x* D3 |+ y$ l
len=length(PopIn);
! _8 C) K2 p- X. G9 X$ m8 B8 @if len>=18 q* f, A8 U% ^0 |$ `
for i=1:len
% k: V: }6 `1 Z! Z d=sort(unidrnd(n,1,2));( ]1 U& G* t" I- t; h0 e6 w
if d(1)~=1&d(2)~=n& y' q; Z }4 @8 e& ~
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
# x h/ B/ E6 S0 Z- E; W9 }( o! ~7 q6 b8 W NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
3 _- V+ p& J+ r* ?+ R" \' w NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
+ r# @7 X* O5 W7 y( _ end/ _/ P9 Q; a+ t- K5 z
end
1 t' ]5 b8 @$ ]# h+ b; zend9 n5 D" Q5 F8 x! \7 u
* e5 ^% b4 r3 b, t3 ^) P
七 径向基神经网络训练程序. i6 w/ F3 V9 n/ f! y
# ~* Z! M# Q8 R' n# iclear all;& w/ z* [5 Q; ~' C- ?2 V
clc;' t3 a( H+ \0 m5 e
%newrb 建立一个径向基函数神经网络
* U6 H4 y& {( ^2 c& K( x- Xp=0:0.1:1; %输入矢量# ~% l+ D( x5 r: \
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量2 K( B: K2 |' i* D; |! Q+ @1 b
goal=0.01; %误差5 N/ H8 _. }" p
sp=1; %扩展常数
- L) K+ o( t& r2 s4 d" Imn=100;%神经元的最多个数
$ P2 Y/ A L7 G$ t0 e+ j9 ?df=1; %训练过程的显示频率; K+ S0 `1 i' \
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
( ]7 R- R. Z3 L6 G% [net,tr]=train(net,p); %调用traingdm算法训练网络+ d' g! z: O0 Y0 I
%对网络进行仿真,并绘制样本数据和网络输出图形
+ n$ Q3 |$ Y1 Z6 W& u9 qA=sim(net,p);
( I# i0 S4 {! X) [E=t-A;
- }& \) O; Z, Jsse=sse(E);
! o, p7 s4 S8 L/ Lfigure;
& L! h2 C1 _- p0 M: J. f4 l$ Hplot(p,t,'r-+',p,A,'b-*');
( A4 ~7 n. D* R2 ~- m% Hlegend('输入数据曲线','训练输出曲线');
5 y P& `' ^$ K# \' O* m5 h# necho off
% n8 Y" B6 a( c" u% D) j/ K: e, T3 X! J' {( R; [9 Q
说明:newrb函数本来 在创建新的网络的时候就进行了训练!
- d: z8 a& m/ G7 S6 X8 b3 w. u% 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,
2 A' {/ n' R' d, X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! Q. M( ^1 S+ x# R1 Y
P2 n* ?+ L/ C( @9 b# Y% y" {
. T2 N9 H+ h& G$ m2 n# H训练结果显示:
3 }5 @' d4 k2 k8 S, \' wNEWRB, neurons = 0, SSE = 5.0973
$ |+ H4 m9 A1 |! f" C, k( L/ U7 l MNEWRB, neurons = 2, SSE = 4.87139
: h9 j/ Q n& S5 MNEWRB, neurons = 3, SSE = 3.611769 e& L5 F% ?( F' r( D$ X4 F
NEWRB, neurons = 4, SSE = 3.4875. r3 h( @( z- |; J) H( ]
NEWRB, neurons = 5, SSE = 0.534217
2 i* A/ b$ ^6 m+ H( xNEWRB, neurons = 6, SSE = 0.51785( C7 H$ I$ B' u3 I0 i
NEWRB, neurons = 7, SSE = 0.4342598 v9 W+ F4 [6 G9 e
NEWRB, neurons = 8, SSE = 0.3415184 q) T% R7 p# @3 f7 q# a
NEWRB, neurons = 9, SSE = 0.341519- `8 B. Y/ j$ k9 k
NEWRB, neurons = 10, SSE = 0.00257832( B# w$ t1 ^4 g. k* O' ^' w' b3 M
' ?6 h1 W; E( q* s1 @% @: P
八 删除当前路径下所有的带后缀.asv的文件
/ ?# ?5 y! m' F8 F8 i- a说明:该程序具有很好的移植性,用户可以根据自己地: ~. V4 d7 _* D( z! ?* H. z
要求修改程序,删除不同后缀类型的文件!
. T4 q9 k/ W$ h. Efunction delete_asv(bpath)
% q9 l2 L- q* N0 n, r9 {9 o%If bpath is not specified,it lists all the asv files in the current
2 W3 m2 [7 a0 [: Q%directory and will delete all the file with asv
' Z( M, t& Z; }) z. b( M% Example:1 r' Z/ _& Q t2 Z; Y, Y
% delete_asv('*.asv') will delete the file with name *.asv;
' T: J- J m- G% |% delete_asv will delete all the file with .asv.9 d }) a7 m* v. ?9 B: o
* N+ R- S& q, x/ p6 vif nargin < 1! u9 O+ a3 P. @
%list all the asv file in the current directory
& E3 J0 f) F( B9 ? files=dir('*.asv');
/ a9 p5 o+ U' A* Delse
+ @2 |/ ~: t5 P8 ?% X5 }% find the exact file in the path of bpath7 I0 D* N* y2 K3 S2 L# v
[pathstr,name] = fileparts(bpath);
6 ?1 g/ E( P- J if exist(bpath,'dir')
% K+ A3 S" O4 P name = [name '\*'];
% F( k8 R( \9 s3 \' X end& [' i; ~6 q# E; d
ext = '.asv';
& Z6 Y8 V2 }2 I files=dir(fullfile(pathstr,[name ext]));' C' t& t, A+ T: l
end1 p: {: L0 c1 @' ~) N0 s( p
: Q/ d- q' A5 y/ P, u$ U8 y/ U
if ~isempty(files)& Z5 q' ~! ?9 o4 T
for i=1:size(files,1)
" O/ N; ^& B- a, R0 `1 q3 r4 t6 ` title=files(i).name;
1 E3 ?$ Y! Y1 f/ _! [ delete(title);: k$ F4 a8 g" @0 a/ L3 ^3 N7 o4 L6 M% n
end
) r' I9 _3 t% F" z9 E9 P' w5 Rend
! i* O3 c8 W- R- d2 h8 i/ _
/ F7 d* a/ s* P( @5 I4 E0 K" w; @4 p, w) B) m8 g1 J! L9 Y
同样也可以在Matlab的窗口设置中取消保存.asv文件!) t F# d; a! G f% o: n4 G* w8 l
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