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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
$ Y6 x8 ?. q$ Y/ r. L1. predict_fun.m为主程序;/ G1 M" X/ G, w
2. timeseries.m和 serie**pan.m为调用的子程序% h6 N& [" ]+ g b5 j
' @0 T1 @1 m6 {5 Q
function ima_pre=predict_fun(b,step)
4 Q0 Z* E @9 m% main program invokes timeseries.m and serie**pan.m: ^- s- F# Y' b. k4 i9 m
% input parameters:# t' f( }1 s8 N% \
% b-------the training data (vector);
! W9 [1 g& H- R2 p6 o% step----number of prediction data;
( Z/ @& O5 z0 Y. P% output parameters:8 s0 q! c8 j" b h
% ima_pre---the prediction data(vector);# M5 n$ _, ]$ z- V, K
old_b=b;7 i. L% T, E' S8 D( g9 d) ^
mean_b=sum(old_b)/length(old_b);
3 v/ C" q/ D& o# F1 W% b$ gstd_b=std(old_b);
! M0 {8 G" w, qold_b=(old_b-mean_b)/std_b;
d' g" X* O6 a/ n5 H[f,x]=timeseries(old_b);
' q9 r- U" w4 p0 E& K+ Gold_f2=serie**pan(old_b,step);
% o. V G8 j. ]% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;
; p6 V6 u% t2 G1 c" b/ F f! u6 xR=corrcoef(f);
" H/ V# a* F7 h+ P[eigvector eigroot]=eig(R);% o0 x) j; J) j7 a6 L+ v
eigroot=diag(eigroot);0 l+ N' E: s$ F2 o
a=eigroot(end:-1:1);; ~* [' k2 Z0 D* b
vector=eigvector(:,end:-1:1);
$ _1 ~/ _5 |5 ~Devote=a./sum(a);( d) x2 N' _9 B; F% D
Devotem=cumsum(Devote);
$ r" O" o% w- Z0 Dm=find(Devotem>=0.995);1 _4 K: c7 C- u
m=m(1);& y# _) b0 \0 m$ t" F# B: h
V1=f*eigvector';
3 P+ e0 n' }/ u% E8 BV=V1(:,1:m);5 o/ e. q' U3 W( C) c! O1 O
% old_b=old_b;
+ c: C: i: V q" P2 s1 ~old_fai=inv(V'*V)*V'*old_b;/ p Z4 U+ U9 J, h+ h- M" Z
eigvector=eigvector(1:m,1:m);
: g6 T9 @: ~9 A: l0 V+ o( {, C) dfai=eigvector*old_fai;
0 b) \! }6 O9 h0 tf2=old_f2(:,1:m);
; g' I$ N5 v5 g( ]6 b3 wpredictvalue=f2*fai;
& S7 v0 K8 _& f9 p& W" X. P+ jima_pre=std_b*predictvalue+mean_b;
. M4 G p/ |( {* F% ^0 z3 [1 [# x) o. L0 v: \
1.子函数: timeseries.m ' N1 K3 `4 z+ H$ J; a
% timeseries program%
1 I. e" {& B5 @% this program is used to generate mean value matrix f;
! R4 M( F5 Y# g/ ^7 Vfunction [f,x]=timeseries(data) ( K+ i5 W0 n& u# O {
% data--------the input sequence (vector);
2 ~" q, z; g' L/ l5 } ~ x% @4 ]% f------mean value matrix f;
+ ~0 \+ n, }4 ]6 Kn=length(data);5 a0 l% Y5 O7 j5 T, _
for L=1:n/2
( H2 m( C* `5 a# T0 g: O9 u nL=floor(n/L);; x& x+ ?5 L/ `9 e
for i=1:L
/ ^: e. v6 O9 J( r! [ sum=0;4 b) M! M8 N) x9 @1 }1 Z T
for j=1:nL5 v& Y" Q P* a& l, E% @
sum=sum+data(i+(j-1)*L);9 G$ B2 U8 N. w; I2 U2 e
end4 R/ P7 y; o% I2 c
x{L,i}=sum/nL;
# L( d# H9 |) T. v* @; i t end
4 ?3 r% V5 g c; z0 G8 Vend
* E" M0 Z& C/ h @# X1 T* AL=n/2;7 k: y6 x6 }+ l& e( l! p8 G! W3 m
f=zeros(n,L);) j/ @2 h5 B# a& U, Y1 {
for i=1:L
/ @% G2 I4 g& ?' y rep=floor(n/i);6 t v% S0 p; f$ D& F( \9 D
res=mod(n,i);
1 B1 s- g* ^$ e$ K* ]% p) P# O b=[x{i,1:i}];b=b';" k+ B; Y! g' \' X2 Z7 r
f(1:rep*i,i)=repmat(b,rep,1);
2 f; F; A6 H M* {1 \4 z: l if res~=0( R8 E$ G8 \3 p, W2 H1 }
c=rep*i+1:n;
! u3 V1 L6 K0 w5 A6 Q) e5 t% s f(rep*i+1:end,i)=b(1:length(c));8 `: @$ v0 m7 a& a7 m
end
- O9 T1 f$ w7 ]& Y& L1 _) O: k8 iend
! q/ x9 H+ K- V% k: \
% v% L9 j8 h8 [6 _: c% serie**pan.m
9 F' F% g1 `3 _& a2 `/ t0 l% the program is used to generate the prediction matrix f; 2 ?7 `1 ^/ H% N$ {# c1 H
function f=serie**pan(data,step);
0 m- x. g6 w; A( ^%data---- the input sequence (vector)3 H& l! L! k0 v* t. z' G
% setp---- the prediction number;4 Z* N# t( o& {! R
n=length(data);+ }9 T& }! \) u; T% l; H
for L=1:n/2
* n( t" {: |% D! M: p# h! `, D nL=floor(n/L);
9 ]4 K* ]- M9 Q. X7 f9 T8 W% v for i=1:L% x! f7 V, d8 V% e ?8 ~2 p
sum=0;
! E6 J/ ^8 O# f0 `. U for j=1:nL, `# w. H) h6 ~5 h* D' Q
sum=sum+data(i+(j-1)*L);
4 F- d1 P$ d- V) E end
& E& Y# S1 h2 u: W- L- t9 k x{L,i}=sum/nL;
+ u9 Z3 Z' G1 k( u1 B end% A' K! d2 T9 `3 H2 X o
end
& f) u. Q+ P5 C# y0 }0 {1 LL=n/2;# B( f h4 [ _5 f
f=zeros(n+step,L);
! p0 y7 y6 J. V7 e! X, L6 bfor i=1:L
5 k. x. k" o {0 l, @: i' z rep=floor((n+step)/i);. a0 q; o1 N# n! k* H6 J# b% L* k
res=mod(n+step,i); I' z0 x5 H( H+ p* a
b=[x{i,1:i}];b=b';) X; m' A/ v+ P* a: S5 G1 D& k
f(1:rep*i,i)=repmat(b,rep,1);7 h0 b" ]) G! s
if res~=0
& c3 _) L9 ^$ f% ?1 b0 g c=rep*i+1:n+step;
W; d- g( }# h& L) \' j f(rep*i+1:end,i)=b(1:length(c));# P7 ~3 D! n9 o, k" `" z! |: F9 E
end
H+ g, u8 S0 M1 l6 Vend1 Y' Y+ G6 Z4 y: B* B
1 _, {) n( J9 z$ x6 Y4 w二 最短路Dijkstra算法: a; ^" @3 Z! Y7 D# I: P6 G
% dijkstra algorithm code program%; V2 x8 y- p4 ^0 t
% the shortest path length algorithm5 Z4 ~) R& f, O5 s- m3 s% T
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)
& U& W; ]7 n. I" }+ u& T% Input parameters:. M+ v2 ]/ P, `8 r$ d
% Input_weight-------the input node weight!
3 a' T( J3 Z z( W7 U% start--------the start node number;; K2 L& t; _) q1 B
% endpoint------the end node number;" X4 H- }% R6 T N7 h
% Output parameters:
, j- E* p2 v; Y5 D) p" S4 w% path-----the shortest lenght path from the start node to end node;) s. P6 L$ z. f9 ]
% short_distance------the distance of the shortest lenght path from the
; o* H. n" U% q; j% start node to end node.
1 h0 k3 g: k: `, P9 r[row,col]=size(Input_weight);# v' V, p# T" i, ]4 q
+ ~( ]% T% L4 a. D! g%input detection0 J O" n, O! x3 P' G* \
if row~=col
# C2 K: r" T/ f- e error('input matrix is not a square matrix,input error ' );
' d$ }& V) m6 w! T' k8 H! m" D+ pend
: W" h8 }( s% I ?+ l" nif endpoint>row
6 d5 E( e$ k1 u& d6 n( w error('input parameter endpoint exceed the maximal point number'); [$ C: R/ ?8 q- r! n
end5 p5 M' e) w: h" x! d
) u! N# i# x, d% U% T%initialization' [* Y9 o6 U4 V( b' A
s_path=[start];
8 e8 B/ w3 {" ]) t+ F1 e; @distance=inf*ones(1,row);distance(start)=0;
8 H3 T" p6 N- f% [flag(start)=start;temp=start;
0 u6 [, T# q t, ?- R7 |7 V w1 T0 d+ ]2 ^3 T
while length(s_path)<row: q$ r& [1 H3 m7 W( h
pos=find(Input_weight(temp, : )~=inf);
2 v& @, @7 w7 [ for i=1:length(pos)
0 j% \7 n5 |/ F$ P0 p7 |+ _ if (length(find(s_path==pos(i)))==0)&1 p7 Y: N5 p. ]: _+ C
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))
2 g. E3 G6 v. c& Z- Y9 O2 `! f distance(pos(i))=distance(temp)+Input_weight(temp,pos(i)); P2 r- Q3 N" a, f. X
flag(pos(i))=temp;
; U( U( O' N' G' D7 }* q end# q3 g4 v( H. I) |: M
end3 H. t" Q) H6 _: m1 ^; p8 z
k=inf;/ ~1 w) Q, `# ^- B" \' ?$ E7 X6 z
for i=1:row) Q) r, Z7 X% M3 C' C. Z& |& A
if (length(find(s_path==i))==0)&(k>distance(i))
5 w# e8 J x( ^* O1 H8 A% J% S k=distance(i);4 V' a m% T+ j* ~6 A2 s
temp_2=i;5 A C" }0 b& W
end% }2 ?% r) I4 f* E7 `5 x
end
$ V4 a% A/ Y9 A! o% J4 T& t. K s_path=[s_path,temp_2];! q0 z: ~2 N' K, a$ w3 S i' W
temp=temp_2;; }- v: l. w1 u( y
end
+ l6 n5 A/ L ^# r: t: _
; `# l" {0 U$ k! J$ u! C9 ?%output the result' q2 y# r- b8 _- |
path(1)=endpoint;! Z1 q* O; _- K3 n$ g- ?
i=1;( N- P/ ~" A; l; \$ \& y
while path(i)~=start
; V2 w% N% |* z1 B path(i+1)=flag(path(i));4 F. z' O0 x, }& X
i=i+1;
- V' M) G! v, |" {end
1 p1 T+ V, W- q% ]; b1 @! Apath(i)=start;, f, A$ X3 G! x+ o
path=path(end:-1:1);$ n+ {* ?9 S1 w
short_distance=distance(endpoint);
) L2 J: `$ i) l6 }三 绘制差分方程的映射分叉图4 O3 z1 _4 o* X$ r9 l7 l7 a b
- U& B- S' |2 |9 a+ i# J# tfunction fork1(a);
" i0 L" ?2 L6 P L- L$ G: y" l1 H4 _. n9 {( j5 w
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
4 I& Y. {7 X" E2 f) V# c# f% Example:
5 R q, q' W) A* r0 v" F/ \% fork1([0,2]); 8 m# S" a2 S& ?: K6 B" u/ j
N=300; % 取样点数
+ F) c" }) W( U/ jA=linspace(a(1),a(2),N); + k# s( \) f, k. x
starx=0.9;
2 R g) d8 W: B; `Z=[];
8 u4 L. a+ K$ W" u( Yh=waitbar(0,'please wait');m=1;
7 t6 _4 c2 z! z, ~' a7 s. Mfor ap=A;
0 [- s: r- W( k+ N x=starx; 1 G) V: d# |0 f l3 ~, n' O3 j" \
for k=1:50; . U% ^* x$ n8 n
x=1-ap*x^2; + O' M, f5 I9 L x1 d3 \
end & [+ o+ g8 o3 x9 O2 W& {% R
for k=1:201;
2 H) } \; A3 H7 p9 T9 Q x=1-ap*x^2;
* T2 F7 n% H- n0 n) U Z=[Z,ap-x*i]; : G. }; M, F B2 f" n( A* {( U
end 2 q' p: ?6 q( l! [- I
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);9 m3 O0 Y9 m# K: L4 L$ [- b2 V
m=m+1;
$ k$ a. e% v9 q. Xend " D9 G, Z5 q k* `% r- M; G
delete(h);, ? i4 [1 |: s2 j- ^
plot(Z,'.','markersize',2)
7 C; J' \( R p. f3 ~+ l9 i, Jxlim(a);% K$ E1 r: L0 D6 p; \
& L) d5 ^" h' M+ U5 K3 ^7 Q
四 最短路算法------floyd算法
) e0 U5 W% L0 v* }function ShortPath_floyd(w,start,terminal)
, j) T0 w! ~* Y7 y8 |( K%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;
% _6 B2 i1 z" ^1 }; h%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];
0 r6 l, H% ~0 m9 v# L# a, x%start-----the start node;% T; r7 q5 c( i7 R
%terminal--------the end node; . L+ m Z$ z3 \, Q+ V% a& x; F* L
n=size(w,1);1 h/ o5 ~6 h7 { }4 e- e: j
[D,path]=floyd1(w);%调用floyd算法程序& X. R; r# p! L l/ ?: h u: z ^
4 [- t& N6 d/ ?9 L
%找出任意两点之间的最短路径,并输出
0 ]- U. Q( I. l9 A0 s. b1 Cfor i=1:n$ n) Z9 w: E$ S* h3 ^/ |
for j=1:n _& |: K1 R/ w0 k" S! n" @
Min_path(i,j).distance=D(i,j);* o; |4 f* I4 }6 M7 k' `9 q& y
%将i到j的最短路程赋值 Min_path(i,j).distance
0 e }$ C1 c* d) f+ S* ? M %将i到j所经路径赋给Min_path(i,j).path
9 c) v9 Z8 g9 Z: F7 F9 x& @ Min_path(i,j).path(1)=i; @/ `$ b$ X$ O& ]3 Q
k=1;1 ]6 B- Q$ p" K& C# y
while Min_path(i,j).path(k)~=j6 |; g& d! A# f' `& t
k=k+1;
$ u! R+ I" e1 q! |) M Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
1 e1 l; k4 u( `8 | end! A! e0 o# U- \2 E* Y1 y1 O* K
end
- D, R! l4 M2 X# Send- Y4 g' c# H) Q# Q
s=sprintf('任意两点之间的最短路径如下:');- v( n; s+ Y" \) t& }% C
disp(s);, C/ [. r. z& F" Z9 T, u
for i=1:n3 Z1 ~* @7 e0 K6 c* l8 z2 P
for j=1:n
8 J$ p! O3 x. R- c( y4 E s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
6 }$ {- @& J4 ~/ P7 H2 n! L3 ^ ,i,j,Min_path(i,j).distance);& j8 H; n3 t6 ^
disp(s);' i' T2 r. k/ y; \, C! `0 t- s4 a
disp(Min_path(i,j).path);2 U, Q( W- R0 ^, G: G% o( k# j
end. ]/ r5 m8 _& k R7 U! u$ k
end1 C' a! {3 T4 D H
) g( R% u' L) R; Y, \
%找出在指定从start点到terminal点的最短路径,并输出7 _4 P: z/ {* j f8 i! W6 t* P/ ~
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...) D" R; u& I! S: N' |; E
start,terminal,Min_path(start,terminal).distance);
1 C. ^3 r8 @7 n5 G% C; A1 ~disp(str1);
; o1 D) N! Z- [5 |, z4 d- Sdisp(Min_path(start,terminal).path);, H- o/ P3 S1 n" @ _' E8 P( w( m
( K- D- \+ m r/ _
%Foldy's Algorithm 算法程序/ I4 Y7 P+ O3 B
function [D,path]=floyd1(a)
4 n4 c% {# F1 K" Qn=size(a,1);
9 H: h2 y) b7 l2 I, wD=a;path=zeros(n,n);%设置D和path的初值1 c% Z, j4 F4 M7 B' u/ E
for i=1:n7 @2 }$ o$ r6 i3 P& z& z
for j=1:n% L2 L, y% p9 j- V L p
if D(i,j)~=inf' Z0 h# |) N, x; f8 f5 u
path(i,j)=j;%j是i的后点( L" C4 ?% w* B4 e+ O! Q
end
7 |. a3 @$ {& D9 j( j h end$ O; P$ ^; @: y/ @8 v3 J! b0 p
end" q# {; M( ^0 R7 r
%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
9 |7 W; Y% I4 M! F* pfor k=1:n
. b( k& n( d$ B& J8 `- f% P4 v for i=1:n1 G) }7 o$ ]5 {4 K, S1 k: ]. F3 [2 O
for j=1:n7 x: |7 T2 G; ]( N$ }; ]
if D(i,k)+D(k,j)<D(i,j)7 T! t, r; d O8 e q: m- S
D(i,j)=D(i,k)+D(k,j);%修改长度( f G: q z" z! |! o7 d6 b" X4 Y
path(i,j)=path(i,k);%修改路径
. }+ Y8 } P+ r end7 c$ {8 P9 M5 ?# S
end% Q% h7 r0 k' I# Y7 v
end/ K# a7 w% `( R* Z
end
2 |0 `9 H6 h4 B- f
2 T9 ~# g1 F) o" b' J7 s五 模拟退火算法源程序
& W6 G. X8 i: Q" \6 N! xfunction [MinD,BestPath]=MainAneal(CityPosition,pn)
' g$ \1 M# v z% n+ w7 `function [MinD,BestPath]=MainAneal2(CityPosition,pn)" t; [8 e' y G
%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, z' K* Z; I; y0 W$ O% _0 T/ i
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...8 S/ p& D3 L" G/ Z; ^
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...# C h4 h, O% B! j6 k/ j1 }2 x6 i
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...& U4 ~0 E* D9 {- ~: `* L- N
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
: E: a8 w! J( D/ W% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];
) z# v* R: W/ ]7 e' \# U
# v" A3 z) r% J" I! u%T0=clock
: m- X2 K; J: M6 `4 Z# Rglobal path p2 D;
. V7 F8 c; P/ [1 k[m,n]=size(CityPosition);. U( c8 h8 T0 _5 }% p
%生成初始解空间,这样可以比逐步分配空间运行快一些
; J8 R, o9 l0 P, }: ?1 h$ d! WTracePath=zeros(1e3,m);
# B8 ?+ I8 B* J3 ]Distance=inf*zeros(1,1e3);
: M% B! r1 \1 G" t) F: J; X: i: N5 }) a" @
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +.../ p& X2 C" D5 V- h
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );
" R% \! l3 q+ p- F%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
4 `6 c6 C5 O( H2 T9 F; lfor i=1:pn
7 B9 B2 }; u! L5 q- n. x/ ^# A path(i,:)=randperm(m);%构造一个初始可行解& P) a5 C+ H/ a6 d7 z8 M1 b+ _
end5 n1 t3 ~3 z+ W3 J5 l. Z/ B5 V
t=zeros(1,pn);6 j( X7 d) y6 ]5 `" E) h
p2=zeros(1,m);
+ e* k, s7 i3 k ^
2 k/ g% j( A4 fiter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
" b; }; T: L$ w7 ?m_max=5;%input('请输入固定温度下目标函数值允许的最大连续未改进次数m_nax=' ) ;; j P( E0 e# Y3 B' ]( y
%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) Q7 O- w% C0 Z
%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& w- B) V; k* {1 P+ A% g' d
%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
' ~! [8 {: |2 _/ _# G5 X%会收到到比较好的效果9 ?! J5 J/ C u7 |% H
0 } E$ {9 P* Y T: x8 c0 \
T=1e5;: Y: |7 t" t) @: C+ w# w4 t% D
N=1; ]% R& f# D2 s/ {
tau=1e-5;%input('请输入最低温度tau=' );: J( `! M' q& S& f$ E
%nn=ceil(log10(tau/T)/log10(0.9));
& u7 X$ q/ j+ @5 p' _2 Owhile T>=tau%&m_num<m_max
5 P8 I, @* I! Y* J, O iter_num=1;%某固定温度下迭代计数器5 e* @3 B _; N, l; w
m_num=1;%某固定温度下目标函数值连续未改进次数计算器6 T7 ], D7 l, x
%iter_max=100;: p; O' E5 m2 W) U5 O+ W
%m_max=10;%ceil(10+0.5*nn-0.3*N);
( I# W/ o2 \( v9 p+ K) z$ Z while m_num<m_max&iter_num<iter_max
' u- Z$ N; O3 a %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:6 k i, a% k8 J& h% p M. ]
%用任意启发式算法在path的领域N(path)中找出新的更优解
* H! @* ^8 z7 ^1 u5 M/ h for i=1:pn
& o2 T& I( x! B5 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))]);
: K3 e6 V" x, W/ }0 X%计算一次行遍所有城市的总路程
/ @' Z8 v% X5 X: D [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
6 \6 t# ?% u/ K n/ C2 z Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
3 E3 n9 _/ u% Z* M1 h- t! @; X5 v end7 S9 s) T$ Z, A
%Len1
! ?1 E* V" s' Y; ^- K" t %Len2- z5 q# V! O( r# V3 N
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand
6 O* T+ F3 Z& a6 l4 M2 s& M R=rand(1,pn);9 x( `1 D. r9 C% H
%Len2-Len1<t|exp((Len1-Len2)/(T))>R
2 m" ^9 C; T9 r+ h* q2 \% [: T8 n if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)
( T2 ^5 O6 f5 c$ @9 J) ]# O path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
$ } @+ [" n, l5 Z7 R Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));
2 l' f# j8 K* m+ X# X3 k8 B [TempMinD,TempIndex]=min(Len1);) D9 M0 c% u- d- k5 x- D
%TempMinD$ J, w% m/ p, ~. O9 ^
TracePath(N,: )=path(TempIndex,: );1 W" v- b! M- K2 M. B. }0 o
Distance(N,: )=TempMinD;4 ^3 q; [; n' f1 q Y( J5 Y9 C
N=N+1;
' \2 H6 e! `0 L6 `' r6 p5 M- e %T=T*0.9
; T. S; q$ l% A1 E% i0 ~6 F m_num=0;
$ R: P0 |- K6 d+ Q else9 K/ v% I2 w8 J7 z1 z. v
m_num=m_num+1;
! z# ~3 m: U( e+ k end3 ~4 p2 q& M' n0 h. @9 K
iter_num=iter_num+1;2 A( i! I0 L; p. p( {! A7 K- y
end( Z' L& T8 Y" V8 j9 v2 J: g0 \
T=T*0.9
, N1 _- I: F& s8 T& T%m_num,iter_num,N& `" z1 b% l' Y
end
/ b9 C3 n0 b- E" `0 j[MinD,Index]=min(Distance);
2 R7 V# R0 V$ _. u B, eBestPath=TracePath(Index,: );
# X) ?6 S9 b* J! Jdisp(MinD)
% A0 Q3 r d" g+ ~7 _%T1=clock- j6 G1 L( A0 H
! e2 h a/ i2 ~! k1 S
: v* Z7 _) Z. i C8 v# B- y%更新路线子程序 % [9 Y1 {# l( ^4 G V
function [p2]=ChangePath2(p1,CityNum)+ c8 l y4 s& f# F
global p2;
+ `. m* ~) ^; I twhile(1) P9 V. g4 ~/ d' J2 s& s5 B T
R=unidrnd(CityNum,1,2);
4 y1 h( z* _' ]( _ if abs(R(1)-R(2))>1
! O. Z# S. L2 P U4 U! f break;
2 L! ]; W' H' {, p( \8 ]1 W! g) A end
& A" H; \. b. s# H7 G, A; qend: _" X( z D8 B
R=unidrnd(CityNum,1,2); j3 v% i" Q$ u1 |) e% {: ~
I=R(1);J=R(2);
) F# j, r# Z0 m3 B%len1=D(p(I),p(J))+D(p(I+1),p(J+1));7 D# Y S7 \! {* O2 e, ?0 X4 B
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));: x, }* w! E B" c
if I<J
/ C+ j! ~0 \9 g5 v& u" t- e4 P% Q p2(1:I)=p1(1:I);
& N/ a6 p8 o4 Y! q0 c! M2 O p2(I+1:J)=p1(J:-1:I+1);5 H8 t" ^$ |) U( C- N, _/ A: I
p2(J+1:CityNum)=p1(J+1:CityNum);* ]8 @( t0 T& ]; H: `1 \8 b
else( O5 a/ J7 J; E9 p! P$ [9 L* K2 H% X
p2(1:J)=p1(1:J);+ _# K) e+ M U+ @( h* ]1 |& e
p2(J+1:I)=p1(I:-1:J+1);
3 z6 d& p4 |+ O v p2(I+1:CityNum)=p1(I+1:CityNum);9 w! ]' b/ ~, @; c' ~/ P! g4 S
end6 }: [0 H+ R: P% \! b. X
2 k4 I |! n* Z六 遗传 算 法程序:9 n V$ Y! S" [5 ]
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!
, m. H8 F' }" H0 q% a; \+ r
/ C. W/ f0 x4 }) sfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
6 F/ e Q( {% [0 _% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
6 f! p9 U' V. N& |3 \) m% Finds a maximum of a function of several variables.# n' p2 c& d6 U( |& E A0 X
% fmaxga solves problems of the form: 9 k! E1 \; A" K4 s& W% z# `" ?
% max F(X) subject to: LB <= X <= UB
2 b/ G, v9 H6 @( |8 l& h4 i% BestPop - 最优的群体即为最优的染色体群; f1 V0 s3 T6 j9 B$ n/ o$ N
% Trace - 最佳染色体所对应的目标函数值
& D' k; x, A5 [* ?3 I& r/ b% FUN - 目标函数3 x7 o, m7 t4 ~! Q9 D' W% K
% LB - 自变量下限
1 v3 E+ F5 Y3 X" m% UB - 自变量上限$ |' E; Q, F8 S4 w' D, |8 |% h* g2 F
% eranum - 种群的代数,取100--1000(默认200); i! I( n% r# q. Q( `9 P' ~/ e( U# ]
% popsize - 每一代种群的规模;此可取50--200(默认100)
/ f6 ^5 w9 S+ j% [% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
! Z: r' ?5 V! P* I. m% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
# W7 L/ G5 e9 S- X5 P+ F: F5 }% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
" u6 L8 P9 w4 {/ p% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编 R+ C( X7 T, o: e% t
%码,option(2)设定求解精度(默认1e-4)3 n4 S+ p& Z3 Y7 ~& x
%# N8 {) t2 w, o$ G, O4 A
% ------------------------------------------------------------------------
# n4 t$ `) X1 L. |0 p! M3 H) A* j) |$ A3 @; d/ [
T1=clock;$ n9 P3 Z) G9 }+ \1 f
if nargin<3, error('FMAXGA requires at least three input arguments'); end& l0 q/ \. ~& l7 _
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end# @% x3 S9 p+ ]$ b6 h
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
" m. h3 r: K, |5 E3 n; p# ?if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end" W' {* B% k% ^2 p) d' f
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
2 _* G l6 ~6 I5 i, O: [5 s Jif nargin==7, pInversion=0.15;options=[0 1e-4];end
( u, z8 h0 i( Q+ aif find((LB-UB)>0)
" g* ]7 A! x/ D0 g' {5 _ error('数据输入错误,请重新输入(LB<UB):');
0 j, }/ X* {4 ~% u) m' `, |end D6 V4 `% J6 }, `
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));+ A0 X6 @3 a4 {* P: ?: V
disp(s);
?* n, o$ e# ~3 s1 D4 a
* @: S) p7 J# V; H- @7 j: Nglobal m n NewPop children1 children2 VarNum. u8 y7 V7 M4 K' M& G
" N: z. y' T' r" n+ F
bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);: S" S- K' Z% b: Q: ], F
precision=options(2);%由求解精度确定二进制编码长度0 p' T4 l$ ?9 D) s0 z( m: s8 u* v2 t
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间7 V |- a- P; ]% a" @/ d4 h! s
[Pop]=InitPopGray(popsize,bits);%初始化种群
6 \: d8 _: {) X Q: p- R[m,n]=size(Pop);
; c/ a# J9 t5 V% N& T+ X1 FNewPop=zeros(m,n);
) }$ p& o9 z. r0 Schildren1=zeros(1,n);
' f7 ]4 [# D4 k) V& Echildren2=zeros(1,n);
, ~* h1 E& n; ^3 R; Qpm0=pMutation;
$ u$ F2 u2 q/ ~0 p( V8 ZBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace' W" B) B' p/ }7 x4 B8 E8 J
Trace=zeros(eranum,length(bits)+1);
% R. Q8 x4 ?0 O. C3 `5 ?i=1;
8 A# H2 H( B9 v; Q, K& pwhile i<=eranum
) x; j D- Z% e0 p; p ~, s for j=1:m4 l! M; z/ o! K9 F% l: B( G
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度) X, Z' Q G* L- Y) q/ Y
end( b* `" t$ E4 X6 M4 M! f) x0 U
[MaxValue,Index]=max(value);
; B8 o* h. }, z t: |% n BestPop(i,:)=Pop(Index,:);
9 t5 ` Z5 v ~ Trace(i,1)=MaxValue;% P. x' h7 q( b! c7 j/ y9 l$ s4 O s
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
; c9 y, i! h+ n: c5 h [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择6 D9 [8 a f9 U5 W M/ c4 }
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum)); v& ~: d# d* M6 p8 O" S
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率1 \* q- I! q" D) y, L1 a) Z
%round(unidrnd(eranum-i)/eranum)
) X3 {. w9 O: {" _% F [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异7 _3 V8 M/ R& M, @( l. c
[InversionPop]=Inversion(MutationPop,pInversion);%倒位; R( U' [ }% _' ~
Pop=InversionPop;%更新
& }8 T- |6 U" mpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); ( }' B% q2 r/ h7 a. k/ T& Z
%随着种群向前进化,逐步增大变异率至1/2交叉率
% c, H- q) {' u8 q6 C0 b p(i)=pMutation;
4 A" q1 c; T" U5 ~+ \! @, G& B5 I i=i+1;
8 v0 B( f6 Q, c) | gend
) j4 q7 p9 y6 e+ n2 d5 L. gt=1:eranum;( t( C+ m0 ?6 m5 L' o
plot(t,Trace(:,1)');- K, Q( v H+ X- ~! ^: y9 I
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)');
( i. l. E& c* [1 |! {[MaxFval,I]=max(Trace(:,1));
: i9 ^8 u, y/ ^1 N9 w* E0 vX=Trace(I,(2:length(bits)+1));
. a5 K2 \. z# D6 d x# lhold on; plot(I,MaxFval,'*');8 E a9 ?0 b2 j2 o" p
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);$ q& G- h( s+ C3 s
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,:)));/ a6 Q( | n1 t: F0 ]8 n; I. ~
disp(str1);2 T9 b5 P, L8 u N( ^! D* B4 X
%figure(2);plot(t,p);%绘制变异值增大过程
$ h* y0 q$ v" }0 X! B! JT2=clock;3 C* ]( g& p+ F( d
elapsed_time=T2-T1;
) [4 I5 D& U, fif elapsed_time(6)<05 _* Q; [( y1 c5 k( p( g+ j/ {
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
" p' Q. |+ P" ~& {4 U2 ~end
2 r, B0 Z# Y* I7 q6 q$ x3 _6 [1 V1 Q8 Cif elapsed_time(5)<01 V* t& z+ a" \, o8 \. m( @
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;8 `( @( @" t9 d: H( T1 M) i
end %像这种程序当然不考虑运行上小时啦
$ z; G" i" R' q; G8 ?2 ~7 ~. Gstr2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));
0 ^5 g& U$ T7 j z+ a' @8 l* ]disp(str2);0 r2 }, u( f+ ^( I/ c& _
' d1 }$ r5 u) ]' o
% }8 k( @& R$ |0 B* ^%初始化种群
6 m# A7 D, Y4 w+ ?' l$ q1 o%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9 Z( ]4 N; d' L7 ~/ F X! H- j
function [initpop]=InitPopGray(popsize,bits)" p3 Y4 u) }; f7 ~& l. d
len=sum(bits);
5 N! v7 k. ?. ]initpop=zeros(popsize,len);%The whole zero encoding individual
6 q, w3 M/ f; Q3 }for i=2:popsize-1
8 v4 j% K0 j! F2 \" m pop=round(rand(1,len));2 a {$ L' ]% ~3 d6 W4 Y
pop=mod(([0 pop]+[pop 0]),2);* d' p- ~3 u% W1 w9 H/ B, H4 T
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)5 O$ H" S1 H, }
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)$ [; L( x' Z3 o2 R
initpop(i,:)=pop(1:end-1);8 |( a3 A( t1 r1 i+ |2 z/ L
end( r# R$ V2 {$ s Z7 H/ E4 ]
initpop(popsize,:)=ones(1,len);%The whole one encoding individual8 K* R2 i+ M" \% D2 K8 b8 Q
%解码 c+ [/ M# W- U* R5 K8 j- v6 s: k
1 n- Y) F0 |3 l
function [fval] = b2f(bval,bounds,bits)
( Y# p$ e: C9 z# @3 l! ]% fval - 表征各变量的十进制数/ S' m5 z1 a% @6 R
% bval - 表征各变量的二进制编码串4 e ]( x7 ?! @4 w3 N; \7 E
% bounds - 各变量的取值范围
! z% a1 d$ M3 c, b% bits - 各变量的二进制编码长度& z8 F8 [) d+ @
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
* b6 F# L& G- u* q8 e$ s$ `2 rnumV=size(bounds,1);) ?6 u9 \4 r u. S V
cs=[0 cumsum(bits)];
8 M3 \7 _" ?( K0 cfor i=1:numV, s( j- H( u: `
a=bval((cs(i)+1):cs(i+1));
# ]. ~2 L8 n3 m7 C- J/ l fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
W" G: C! i- F0 v, @0 uend
. |) } q' |6 j1 @" U% {+ x%选择操作' K x2 [' W& M/ U4 `( A' ~
%采用基于轮盘赌法的非线性排名选择 \* Y R8 d+ i! |+ R
%各个体成员按适应值从大到小分配选择概率:
% ]3 w9 x5 ]- Z- [; l%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1( i' l/ h& N1 f' Q
8 |2 b1 H' r) Z/ G
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
. a6 Q$ n3 Z7 W3 X# U( cglobal m n
2 U7 z5 Z- J3 g; v H; L; }9 Aselectpop=zeros(m,n);: N6 E# w8 W8 Q6 y
fit=zeros(m,1);
$ M+ }* L% v+ m, K2 ~6 Yfor i=1:m5 U* W- ~( r% J E3 [
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据# L4 o% {; u1 n9 I3 V& I
end+ ], `- p" A* o* g: s& k
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)0 p) C" p' u5 V" h: }
q=max(selectprob);%选择最优的概率. m' P4 T3 @7 `7 [- }* X( E
x=zeros(m,2);5 d( O* x/ X8 B$ h+ W' [2 j
x(:,1)=[m:-1:1]';
; ^/ G7 Z1 {/ I- ]# o[y x(:,2)]=sort(selectprob);
; ]1 F+ \3 l7 a K% Q5 Or=q/(1-(1-q)^m);%标准分布基值
: j i3 x' R8 ^. g d! X0 } Wnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
2 ~. B9 J8 E! g* O& x. Knewfit=cumsum(newfit);%计算各选择概率之和
. \$ Q9 D; s0 W- o( BrNums=sort(rand(m,1));9 D9 \9 O6 r" P
fitIn=1;newIn=1;$ ?# x4 a/ v( H7 s: {
while newIn<=m
7 L$ `! h/ P: b- k, s2 K if rNums(newIn)<newfit(fitIn)
$ j# ?& N5 L4 }/ H selectpop(newIn,:)=pop(fitIn,:);
* c0 g5 H& y3 V4 S newIn=newIn+1;- j' `9 X0 x) I- s: z( L& h
else
. Q# P' D+ H W) [* Z fitIn=fitIn+1;& ?5 x9 Z0 u; _* j' C, W# A6 V
end
6 F& i1 W# k' H+ oend
3 D* T$ x' A7 c8 V; i3 y' o+ v%交叉操作
) A! z1 s( J0 P( s2 t! Ufunction [NewPop]=CrossOver(OldPop,pCross,opts)9 o$ \8 b* e% R/ |& p0 m
%OldPop为父代种群,pcross为交叉概率
6 L+ N: {" r; Q& y! bglobal m n NewPop
- `3 C2 j: L, H8 w5 _ dr=rand(1,m);
7 S; e& H, p7 t. h: |y1=find(r<pCross);
$ \# I' U: L M2 gy2=find(r>=pCross);
/ L) s0 K6 a$ b5 dlen=length(y1);3 u4 F$ B# D: _0 T$ G. D9 c% k& K# X
if len>2&mod(len,2)==1%如果用来进行交叉的染色体的条数为奇数,将其调整为偶数& [' U- M" \, \3 t& S
y2(length(y2)+1)=y1(len);
) W' _' O5 r6 `- I y1(len)=[];$ d* k: N9 {8 _, y" Y- o1 l
end
3 l& V' R+ n/ f% D% S% O! Rif length(y1)>=2, w+ N6 o7 [; T% n9 a
for i=0:2:length(y1)-2
# d& A$ k9 g# {* \6 o( N: B: E if opts==0
* g% {# G8 s! X7 P D, R7 I [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));" p. {2 \! @- {" y3 `
else% Y7 M0 _& C4 K' Z
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));5 i9 W# D! W G( X/ K
end
0 b6 _: d, H5 X* J0 y# u3 d% s3 ] end 1 u6 _# \1 s. T
end1 g# {, o. S% G3 u
NewPop(y2,:)=OldPop(y2,:);$ h! u( K- I( q" C
& z# U' r& s9 |%采用均匀交叉 2 L9 y( ]4 V E) P# e
function [children1,children2]=EqualCrossOver(parent1,parent2)
: `4 D) ]5 K9 m. Q6 |$ r9 F7 S- f+ K; ~/ k" `7 H
global n children1 children2
- b1 F& {% g1 L& Rhidecode=round(rand(1,n));%随机生成掩码
; u R/ A: G! C- r9 C; b4 scrossposition=find(hidecode==1);
4 A( {- t* \, I% |' C3 Wholdposition=find(hidecode==0);" n$ ^/ U4 f3 X( M# I8 A" b
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因% `: n& q5 } e1 m* g8 g& [1 _. R. y, |
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因
2 B' }+ Q# d; ochildren2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
% }* {3 p2 K7 _+ i0 p! |6 f/ q- }children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因
0 N6 z' u* _; f7 m2 B5 r3 V# S' v) H) c2 s
%采用多点交叉,交叉点数由变量数决定6 B* |! O) e7 b: M' G, [
! Q- R! o# R, V( H, J; n, i. xfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)
9 P: @6 |3 V' E9 c- |' s9 }2 d
" }6 N1 i0 c/ y) fglobal n Children1 Children2 VarNum; ^% X: U+ E; a) [
Children1=Parent1;
1 k0 Z2 r4 I( h) ?; kChildren2=Parent2;
# F( @# Y3 z% L, U" z: L8 q. ^Points=sort(unidrnd(n,1,2*VarNum));6 l( I! Y2 u, @
for i=1:VarNum
& w3 B, n- L. Z# j Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));; C1 Q$ o% P# g3 Y+ T
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
3 ~' D; t; G8 H3 C; f/ [end- A9 f& @9 D! E5 L; ~! _4 `% U
/ A4 Q2 M- X7 L, b3 k; Y" R5 E%变异操作
" W u- S+ L/ Q& O" f4 [1 |6 dfunction [NewPop]=Mutation(OldPop,pMutation,VarNum)
" o7 R1 b2 n ]- q8 D" F0 _
6 A% q; Z9 H: Z7 b( `8 |- `6 g% mglobal m n NewPop2 _, O0 U3 m+ H$ y3 D, Q
r=rand(1,m);* P0 p8 k/ b9 a5 H9 @* N
position=find(r<=pMutation);
: r ~! x9 s' Qlen=length(position);
2 A( ]$ q+ ] Y3 n( v b+ F6 Zif len>=16 O4 u `$ `) l# k$ }
for i=1:len6 B. P8 T1 u# W, B* I) n a: M9 c
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
7 s% U& O: ~: z6 w1 J2 P for j=1:length(k)
) r* o; E, [* U0 n8 X+ Z if OldPop(position(i),k(j))==1
3 W, p1 W7 Z# L OldPop(position(i),k(j))=0;
) X, o o7 a% B1 P7 X- b8 o else
1 O+ t- c7 h% b* @- F" _, | OldPop(position(i),k(j))=1;" a1 s( J/ v( v" O! n
end
8 @; Z' s! o- e% F" X% B! H end* P& c2 ]6 b: P. M
end" t! h3 o9 G6 t' J
end
! `1 H! n' M- }8 |) x& r' q; qNewPop=OldPop;5 o# C3 ?/ V0 o
. |. Z" a( g& W
%倒位操作
1 m4 }7 A$ F' J6 T3 W) q. m2 \4 i6 n8 b& G0 f- Z( R
function [NewPop]=Inversion(OldPop,pInversion)$ D1 f1 o3 }; d6 `
2 a" u4 m6 H. I9 t6 w" Yglobal m n NewPop0 K; N- {9 \) h d: r: c
NewPop=OldPop;6 ^4 h- H, }. J4 [2 _
r=rand(1,m);
) G: S/ v- w$ Y4 L! C$ rPopIn=find(r<=pInversion);3 z* O7 z8 M" t. I& N
len=length(PopIn);
" u8 J9 ]* [ W- I6 Mif len>=10 g) C; e8 M. M( N9 @: O: f7 Y7 i
for i=1:len
, _1 W. b; [+ R# p2 H6 I2 X( m d=sort(unidrnd(n,1,2));' G2 X# l* ?1 E6 B$ H
if d(1)~=1&d(2)~=n
9 e' h* w' g$ ? NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
- F7 s4 w8 U% [! [9 L NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));* { r8 y- e9 E; N
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);% ^- @$ ?+ A% z3 X% y1 g5 _, s$ \- O
end Z" x J; g! S3 k
end' D" I* S% [1 [+ t; `
end
* m5 \ l; A# A% Z
# d+ |# u& ?" j) ]# b+ v: O8 b5 x: Y七 径向基神经网络训练程序) Y8 ^8 Y5 `7 V7 I: t
2 e* p5 y/ o8 Z3 A( E
clear all;
8 B% j. M( | o0 O$ s: Pclc;
& V, V% s# q0 X U+ t& s& X%newrb 建立一个径向基函数神经网络; B& q% a+ Z. e3 w1 @; \
p=0:0.1:1; %输入矢量
7 ~! u' g9 L! y V' E: Rt=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量0 I" ^' \# U# [' U( i( W9 D
goal=0.01; %误差9 G3 X/ W$ u- a+ b& Y6 h& H2 X
sp=1; %扩展常数% \$ Y, c4 S4 d6 S4 R
mn=100;%神经元的最多个数* W5 |+ V# s, k8 g
df=1; %训练过程的显示频率; y3 ^. w7 A: G# Y0 S8 H$ w. D
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络2 X5 e) h2 X" R! ]1 I) M
% [net,tr]=train(net,p); %调用traingdm算法训练网络/ b9 L5 z# B7 R# c4 o
%对网络进行仿真,并绘制样本数据和网络输出图形
8 b; A6 A1 {1 @1 B& q3 |A=sim(net,p);
% ?4 y! k! z& T5 GE=t-A;
# L# D; g" U) |7 K) |" H; @sse=sse(E);
T6 ]. [! w: Efigure;
/ _# f; N3 q( f ~2 kplot(p,t,'r-+',p,A,'b-*');+ A8 f+ `0 q6 u% b9 l5 R6 \
legend('输入数据曲线','训练输出曲线');
& V5 Q6 x: Q( n7 qecho off 6 ~ W4 W6 g7 y
0 a# e, t" r& H6 g' [! P说明:newrb函数本来 在创建新的网络的时候就进行了训练!
) p+ j, q5 S5 M( c1 [- X( `+ I3 c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,8 `7 L* ?6 W/ q+ T9 [$ t
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!- J& Z. U/ V% \7 W% w( a+ l2 q
+ l' L( e1 O$ |. J$ a! P
v6 v/ N: l, y
训练结果显示:7 W! e) h5 F5 `, \8 }% V9 Y
NEWRB, neurons = 0, SSE = 5.09735 i1 d# w7 Q# n9 T$ E- X
NEWRB, neurons = 2, SSE = 4.87139! s) e# P. J6 o0 s
NEWRB, neurons = 3, SSE = 3.611760 p5 z- u$ D$ E$ U' J3 S3 ^4 C
NEWRB, neurons = 4, SSE = 3.4875, L. `' m% j, I3 f. c
NEWRB, neurons = 5, SSE = 0.534217
) ^* `, l+ E0 _/ r( V# y2 UNEWRB, neurons = 6, SSE = 0.51785
5 n8 n# r4 S3 ~ T7 e) E# h5 B0 INEWRB, neurons = 7, SSE = 0.434259
8 E! E5 e! y% ]1 u% qNEWRB, neurons = 8, SSE = 0.3415189 \1 s8 S6 j% p9 N2 y: o- N
NEWRB, neurons = 9, SSE = 0.341519# b. v7 ~; I O; y j
NEWRB, neurons = 10, SSE = 0.00257832: n: S: D5 l$ k8 T% |# o
3 n% E q; W9 M& Y2 L0 w! ?2 e* E
八 删除当前路径下所有的带后缀.asv的文件
0 i. v" D1 j+ S6 [说明:该程序具有很好的移植性,用户可以根据自己地9 H# f! [9 x* m `
要求修改程序,删除不同后缀类型的文件!
% p2 h8 C; j: m4 y c0 ~4 G; X Wfunction delete_asv(bpath)
9 d+ q* w% \1 K! h. ]%If bpath is not specified,it lists all the asv files in the current& E0 V9 t4 M% X8 V+ D
%directory and will delete all the file with asv ! i) K# J3 Y. N3 [
% Example:
, K# _" J1 v6 `% delete_asv('*.asv') will delete the file with name *.asv;& o7 y" B( J) U( ~$ \% n
% delete_asv will delete all the file with .asv.
6 S" E {6 [8 |' d+ r# r( P: Y% u
/ y! [& I6 k, `" J/ j; I& q; _if nargin < 1
- W* ?8 t5 |2 S, L$ l4 \' J% N+ X5 Z%list all the asv file in the current directory
$ z/ y9 ^1 f! c! b4 c( h files=dir('*.asv');
5 y; A+ [" J( m. p9 n# m5 @else% G& ]4 M Y3 F9 V% d M- @9 i9 i
% find the exact file in the path of bpath
( b; n$ X. M7 B% c [pathstr,name] = fileparts(bpath);
5 j. E' X0 D6 r% ]0 h" N if exist(bpath,'dir')
( p& p2 g$ `* Z. l/ Q- e1 P% [1 I2 M/ E name = [name '\*'];. N4 K1 I) N. n, e0 X4 `' L3 s
end
. F3 @5 ` I% V6 p ext = '.asv';
) |# U" d5 h/ f+ [; y- s files=dir(fullfile(pathstr,[name ext]));
+ a, h, I, `% ?4 D4 Eend* x1 c$ g0 \3 |; ]! I" e
* u$ {# e( ?: C9 B5 r% S3 e
if ~isempty(files)5 R, g# }2 Y/ t1 v' u. A" t
for i=1:size(files,1)$ |- X/ @2 o% v
title=files(i).name;* @2 w; K% x9 U. I9 F4 n0 l
delete(title);7 J, d/ C; u; d
end
' S; o ?/ E$ f9 T3 T6 Z% Iend* T# y5 C& x+ |3 J, F% `
8 }. R; `3 ?. I7 y* `0 u d0 ?
( g {& L0 [- G+ \4 G$ Q同样也可以在Matlab的窗口设置中取消保存.asv文件!% P$ E7 L& K/ |2 m3 R& L
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