一 基于均值生成函数时间序列预测算法程序 . ?2 {1 L, s5 w; V8 w1. predict_fun.m为主程序; 3 s/ M- |# J B7 S2. timeseries.m和 serie**pan.m为调用的子程序 . I4 Z1 s. k8 t& y6 x" i+ e B8 o2 P* D) t$ P
function ima_pre=predict_fun(b,step)! b( A! }* G6 A* O
% main program invokes timeseries.m and serie**pan.m % s# r. x! U" o9 I$ _/ _3 O% input parameters: v% e: G* p% \/ J$ P2 ?1 e* ~
% b-------the training data (vector); # e; q0 ^- K) f9 x0 l5 T% step----number of prediction data; % ^4 f. P) G# T+ t% output parameters:4 F* t. E% i- d* ~' }6 y+ P
% ima_pre---the prediction data(vector);$ ~% [! x. i! h: Q2 z
old_b=b;0 P2 p- I2 V5 c
mean_b=sum(old_b)/length(old_b); : N# m _, A+ l; |7 Q! o2 E4 ystd_b=std(old_b); - l4 @" C$ G( S" ^& {8 G4 s1 [* X4 Dold_b=(old_b-mean_b)/std_b; # r' E3 \! n' Y. l[f,x]=timeseries(old_b); " w. i6 [+ ]' h3 E5 q+ J! ~6 [3 kold_f2=serie**pan(old_b,step);; s! j# B( d. k5 }+ j8 j
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;- ~0 W: S- x0 F' F# S
R=corrcoef(f);& d- O4 ]# [0 P" C4 b: e! _, H
[eigvector eigroot]=eig(R); 0 Z( m- r; a% ` W8 |4 Ieigroot=diag(eigroot);/ n6 x; c' U( M9 Q+ e q/ U: I
a=eigroot(end:-1:1);, E2 G+ U _" S, f3 U
vector=eigvector(:,end:-1:1); ! K$ H$ }, {1 q' O$ P( ^2 Y$ EDevote=a./sum(a); 2 X8 X- f3 k) j* U* s. c/ EDevotem=cumsum(Devote); b2 D# z' G) u* R- ] O4 km=find(Devotem>=0.995); 0 N% w8 l1 j$ v7 s Om=m(1); , a7 {7 K, D }4 l1 p& iV1=f*eigvector';" f1 t$ F% j2 ~& Y( Y
V=V1(:,1:m); 6 h8 K7 }* ]# @) ^ t% old_b=old_b;: u0 ?- g, M; ^+ l! Q3 D% C( {: |0 ~
old_fai=inv(V'*V)*V'*old_b;% R, y# @8 j6 E; u4 [$ N
eigvector=eigvector(1:m,1:m); ! k& H; b; D$ k% Gfai=eigvector*old_fai; d6 V2 v6 M1 t2 S4 wf2=old_f2(:,1:m);3 e% G S E1 P" G5 p4 r) {
predictvalue=f2*fai; " Z: J6 ^5 @ r& zima_pre=std_b*predictvalue+mean_b; $ u k$ k. D( M0 }, {% j; p 9 p, T) a2 L! ^; a5 t( |1.子函数: timeseries.m + O% v7 A- _: Z0 e
% timeseries program%+ {4 k( ]) Q: z, g( ^& E
% this program is used to generate mean value matrix f; 7 J+ D' h. [, N$ E$ t+ G) Efunction [f,x]=timeseries(data) 1 V. i, T/ K4 E- n& i% data--------the input sequence (vector); , m' h0 q z4 @% f------mean value matrix f; / o. p0 s/ |1 Wn=length(data); - O8 K2 t2 L; C$ ]# u3 m' ?for L=1:n/2 1 d! i' g7 y/ E* E4 u nL=floor(n/L); 0 D; H# J9 {& F# c* S% { for i=1:L% m- W$ G3 O0 u( ]" A% x: ?/ n
sum=0; 3 D3 W. [8 O$ F9 V6 R for j=1:nL ) H* B$ a$ c7 @5 L+ Q sum=sum+data(i+(j-1)*L); ( D9 [/ m4 p8 U* a/ M P+ i5 ` end 5 H, |5 p0 K( v" y+ T x{L,i}=sum/nL;" t+ q* {1 ~8 R
end / l. b% O, l0 z1 E" Wend 9 W# R: \" j u5 A5 pL=n/2;# y9 _0 \1 y6 w, x" O3 [
f=zeros(n,L);. V4 Y" G3 a" M6 N6 j1 J" h6 I
for i=1:L 6 G* _- F2 L" v/ n4 p. C' d rep=floor(n/i);6 s( A, c- v7 R: ]8 {
res=mod(n,i); ; p" t5 J$ |$ o# W. r: T: e b=[x{i,1:i}];b=b'; : ^ x; }0 f: r& k f(1:rep*i,i)=repmat(b,rep,1); + b+ ~0 H5 g8 l) Z4 M if res~=0 M4 `3 p% ?5 [$ D3 G c=rep*i+1:n; . V" ~5 y! }9 e f(rep*i+1:end,i)=b(1:length(c)); h* d9 r5 e# N" u end3 p7 |9 D. {& k5 n
end/ a& K. P) ?) F# S2 C0 i
' Z- F9 X0 c5 \% serie**pan.m9 K2 J$ e0 K" f
% the program is used to generate the prediction matrix f; $ r! j7 o* X0 W5 N9 _ I, M" V
function f=serie**pan(data,step); 7 p3 D* K$ E& j% b& T" ^* W+ m%data---- the input sequence (vector)6 V/ F/ J: e$ T4 [- |0 ]
% setp---- the prediction number;* o- ~0 I5 M. l/ c6 O. P
n=length(data); 4 |" o; F* v2 s' t! afor L=1:n/2 # Y7 X( n, B3 _& R8 i; y nL=floor(n/L); ' U' D9 [- o( V5 h. z) W$ n- w for i=1:L 7 J8 j1 i2 _- N" G' m) K+ j0 Z sum=0; ( [2 c! M$ [, A; B6 ]) @+ q for j=1:nL 0 k C, p a7 e @" ~; u) H/ [+ [ sum=sum+data(i+(j-1)*L); 3 h9 P" ^, n. _' I7 R: ] end$ E2 O' L/ x9 G! v# |# V5 |
x{L,i}=sum/nL;% a) ^. `" f5 i1 L% {" j
end- B0 p/ g1 L& d2 X$ |1 W5 V. L2 _
end8 B/ ?$ R A% Z" C$ s, H) w: w
L=n/2;- |# e) ~3 j: p4 d7 ?% x/ ^0 o
f=zeros(n+step,L);, z0 ^; z, _1 Z- ^/ N2 _
for i=1:L9 {! C1 d3 @, Z' z6 u' C
rep=floor((n+step)/i);9 N# G% L4 o9 h; `- {4 U: l
res=mod(n+step,i); , x9 }6 ^2 j1 s9 h b=[x{i,1:i}];b=b';8 P, L$ F0 t0 Y0 g) ~
f(1:rep*i,i)=repmat(b,rep,1);$ w% e' T: [6 T
if res~=0 7 x( }* v9 i* a+ u; `" W c=rep*i+1:n+step;# }. K" L. w% i) ~- Z3 ]
f(rep*i+1:end,i)=b(1:length(c)); ! }5 s# ~; w5 S" C( e5 W* p end $ X; J$ _/ {+ g- Kend * _: s6 o- [ I6 e* l5 O8 \2 O5 v; m6 o" V! t
二 最短路Dijkstra算法 $ `# W+ l2 t* |; h: ~% dijkstra algorithm code program% 9 ]$ U7 r! q) h( e. a( U- X% the shortest path length algorithm ' L* B! Q& r$ z. [function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint); ` I3 p1 G4 a- L: x! a, R
% Input parameters:& {# Y& A0 A% w1 O, c7 Y
% Input_weight-------the input node weight!+ _. C! ]+ {# k
% start--------the start node number;2 \9 D* L) ~9 T- `+ X9 A
% endpoint------the end node number;' }9 w6 n, G4 c8 A% C! y
% Output parameters:4 u5 h* a0 \4 Z6 i! \
% path-----the shortest lenght path from the start node to end node;0 ?6 C4 K. t. X' A$ j: D1 [/ T8 o
% short_distance------the distance of the shortest lenght path from the ; a' l7 ?8 y% z/ \6 w% start node to end node. & D$ q$ m* h& y* j: N- J[row,col]=size(Input_weight); 0 |; ?. O& p4 i5 d1 U' n* n) C2 z- ]4 w! Q
%input detection % Q9 q* ]8 S, k, mif row~=col. ]2 s ?( ?' ~" u$ h4 ]
error('input matrix is not a square matrix,input error ' );% r" v0 f. H' q
end ! a' ?3 a/ x9 T5 q9 r, Wif endpoint>row- S; |4 u' @6 H/ k% o
error('input parameter endpoint exceed the maximal point number');: R3 A2 q# E8 W# j( m( j, ?8 @9 x
end ) ~% P5 [6 c- L$ p5 v + T7 y+ }/ {. S& f8 t. |%initialization" f) E" l# z3 l4 q7 t$ l
s_path=[start];" X8 x' S) H$ q
distance=inf*ones(1,row);distance(start)=0;* ?/ Y! _& U6 ?
flag(start)=start;temp=start; 2 M$ ?; w3 g; ^. G! \! t6 H9 c! `: K, z/ {; N; y6 [$ ?
while length(s_path)<row5 i" I4 `5 |# e2 O5 {
pos=find(Input_weight(temp, : )~=inf); ! V- B e4 D7 |, J6 K3 M* P* M. j for i=1:length(pos), a: k5 g" A2 \7 ^# M# p# y* D
if (length(find(s_path==pos(i)))==0)& . T% T7 {! N! d0 M3 ~, y. v$ s(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))# I% I! J. p- X6 Q; x, E! F
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));- i6 k4 ~1 V6 f1 c/ Z$ ^
flag(pos(i))=temp;! a' a% t! N6 z; ~8 P" X
end/ t; s5 o1 P% o1 i7 |
end : A/ {2 s; ]2 a1 k% a7 | k=inf;& \" p# _) V- \2 w
for i=1:row " R {4 Z5 z) V3 E; ? if (length(find(s_path==i))==0)&(k>distance(i)) ; Y3 K* D: m0 C# X( @2 M4 h3 y& Y k=distance(i); . [$ z5 e3 ~2 P- }, V' z temp_2=i; * A m) R4 ~- L/ q* y end- e9 Y7 v7 y( c: r2 R g/ N2 Z
end1 w% ?) Z& w5 |6 [; b: U7 R
s_path=[s_path,temp_2];& N5 e* f) |: {+ o6 H
temp=temp_2; # d3 x; v9 W7 J9 f Aend( J6 k: Q/ S5 }2 @3 q/ |
# }% O# L5 c( n1 Z8 \! L, r
%output the result- p3 C' C. i. V. Z# v( r
path(1)=endpoint;( g7 [4 n6 ^- ^# w
i=1;, }& U+ k, e7 Q- j3 M5 p
while path(i)~=start, \$ W1 K; k% N$ h* B
path(i+1)=flag(path(i)); % }0 x+ v& V/ I* |& l8 [, v i=i+1;% ?; O3 V2 K7 a- O Z+ R
end }% q+ u. A% {- y0 ^4 l" [3 e% L" Z1 \
path(i)=start;1 N. ]- Q/ y* @" g4 ?
path=path(end:-1:1);$ [ L! Y8 f4 L+ i+ o) Q
short_distance=distance(endpoint);8 ~% N1 {( o! [/ C
三 绘制差分方程的映射分叉图1 ]7 m) ` d& [2 O) p
% M/ o4 g# E; q0 ~ |
function fork1(a); . N# T3 e/ I# |8 w7 M% d- v, W) q
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图 9 k2 w! u, x! ?3 O7 A) Q% Example: ' O1 a* f4 H( Q' B& `4 W9 K
% fork1([0,2]); * J+ R& {+ o2 t3 T1 O- a: r
N=300; % 取样点数 * W2 O8 n; t% eA=linspace(a(1),a(2),N); ; |6 `* e) t6 l. C& V3 c
starx=0.9; 0 V3 ^. Z9 V/ b
Z=[];. t8 {" W" d! p! U. R
h=waitbar(0,'please wait');m=1; 2 z" I0 Y' A" p. W- Afor ap=A; . X" \+ J" \, _8 J/ z
x=starx; + P5 |6 N1 m. s8 [/ M) r
for k=1:50; % L# n: _" Z" k; G u# c x=1-ap*x^2; ; l' O D6 Q: t2 U# v end 1 j% f& T O2 l4 b5 v* V4 T* K for k=1:201; " P& J+ P& ~- ?6 J0 F
x=1-ap*x^2; . ?$ x( x6 M! E Z=[Z,ap-x*i]; 5 b1 e7 S' b; U% L1 g! T+ K
end 4 Z+ i, ^0 T8 j0 l7 |" e waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);5 W' @ D: |6 [2 ]; ?% R
m=m+1; 9 i/ E& d9 A) {! V2 A5 `end * f9 }- J* n) F
delete(h); 0 Y' L( f& @# t/ Y: O/ T1 u. wplot(Z,'.','markersize',2) # S+ l! Q( S; {( X$ P4 e& L |# E/ I
xlim(a);( t n- R; [) C. L. O$ @
* C$ ?, Q, }, L" Q四 最短路算法------floyd算法; r, H7 q4 }9 Q6 y2 Y4 C
function ShortPath_floyd(w,start,terminal) & T0 ]- F1 Z7 t5 F%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;" z3 r1 @2 I* w9 a' U
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0]; 4 a* ^3 L# U! Y% Z2 D' z- Z%start-----the start node;& X K4 \& ]8 e. m
%terminal--------the end node; l) m2 m7 s% H3 b) C& F( k
n=size(w,1);* | O! u$ D, u3 f6 O
[D,path]=floyd1(w);%调用floyd算法程序/ R/ H% b ^# a+ l
' X- a% l9 M# ^; \! j- c( X3 O3 S
%找出任意两点之间的最短路径,并输出 % v) L5 t- O6 Bfor i=1:n3 G9 d3 H) n% O
for j=1:n) b! j( h6 J9 G' A. S: s, h1 d
Min_path(i,j).distance=D(i,j);. m; o- i3 Q/ n6 v
%将i到j的最短路程赋值 Min_path(i,j).distance m2 s. Z" V9 x* H
%将i到j所经路径赋给Min_path(i,j).path0 ?4 A3 C8 E& ~! l: F
Min_path(i,j).path(1)=i; $ R/ L: W# o3 C9 t* C k=1;0 v( ^$ @* N; x+ h2 c- Y* G$ s' `
while Min_path(i,j).path(k)~=j" S. U+ `% G ^7 U. b
k=k+1;7 M% @ ^! }6 k# i
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j); 6 x& \7 K' i h$ h& S! C2 P3 F1 _ end% Z3 s" V) O% O; N
end ' |, |$ H/ d( k7 d# Y8 o. lend2 j. L& z, D n
s=sprintf('任意两点之间的最短路径如下:'); 9 }+ L! s8 C2 x& t. kdisp(s); A" Z2 t; I# p2 x# ^3 {for i=1:n ( j6 f9 A+ m* H6 G l9 } for j=1:n# \! D, F. t. H
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...+ ~& j7 m* L0 Q+ E0 [* J
,i,j,Min_path(i,j).distance); 1 [; {( q. ?7 o! L disp(s);" Z& W. Q9 w' Z' I
disp(Min_path(i,j).path);+ A& O: @) U9 Y. k; c
end3 ^" z# |& |' \$ j- V
end& A; S/ \. K4 ~6 p7 c
/ P$ P+ Z! ^% l) @- \% {%找出在指定从start点到terminal点的最短路径,并输出5 Q f+ m# ~2 ^- E- T
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...& w5 D- f. n- [- g5 S. } ~, H
start,terminal,Min_path(start,terminal).distance); $ {: e+ T3 w& _6 _- Xdisp(str1); # J7 B" e# s) r' m' h0 S! w+ }disp(Min_path(start,terminal).path);8 D3 _" _* c0 v" o4 \" S
2 f- F4 ^, O- A m4 e4 M2 j
%Foldy's Algorithm 算法程序8 W% z) u6 C1 z+ ?6 j
function [D,path]=floyd1(a)/ I6 J; o7 i0 e3 a& a
n=size(a,1);. `' Z' D+ t7 M. Y1 K" v
D=a;path=zeros(n,n);%设置D和path的初值 ) A% c9 i% l7 }# { x% x, Ifor i=1:n ( y# |2 h# g5 e for j=1:n : y5 i+ b" G0 Q# t# q& s if D(i,j)~=inf" o ~1 Y% r1 ]+ v
path(i,j)=j;%j是i的后点6 O: \) @3 z* I) K0 _
end9 Z# f+ O% c4 z" B3 l2 y
end 2 C' _9 ~; L i4 b# i' m* X7 }) bend " Y, m, [6 Y; D/ }* W) j%做n次迭代,每次迭代都更新D(i,j)和path(i,j)/ l: m& t2 m q: L! S
for k=1:n / J/ D% j) g; P0 r for i=1:n0 N1 R, I1 T, }( Q4 M
for j=1:n * d+ d% Y, X3 R% ?' a# Y( i' S8 [ if D(i,k)+D(k,j)<D(i,j)4 }5 r7 _- l9 H+ l$ i9 A X5 A
D(i,j)=D(i,k)+D(k,j);%修改长度! p- X2 D# P1 \* Z6 S
path(i,j)=path(i,k);%修改路径 8 `, v+ l. s1 ]9 s end) Y- | S Y! D1 `
end- K% P% |8 ]4 ^" U: b
end6 m9 I% O% W- d
end! g0 R- Z1 c, x. i
. P% M x+ L# k: I) y. ]五 模拟退火算法源程序7 D1 @2 T( U+ O) C" W# M
function [MinD,BestPath]=MainAneal(CityPosition,pn) * q2 M1 U! r3 A' z' U0 \1 k: D& X5 ufunction [MinD,BestPath]=MainAneal2(CityPosition,pn)- u0 C! R6 N6 u" Y
%此题以中国31省会城市的最短旅行路径为例,给出TSP问题的模拟退火程序- S. G$ ^- w2 {2 M$ X
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;... 6 U) o m3 R1 j% w) ?' Q; X6 Z6 b6 k% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...( h: ~3 P* j2 f* o5 N
% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...+ H* s' f7 m' N# O: k8 m0 g) m1 y% x
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;... 3 o' u4 b' m( F0 Y% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975]; 5 G6 n3 J$ x& K 0 W: Z- v+ Z+ v- `- o- D%T0=clock6 V9 [8 f6 a4 l3 ?, h
global path p2 D;! \- h0 u. e3 z, x. v% s0 d
[m,n]=size(CityPosition); # ^3 H8 W( s$ f' b2 B+ `%生成初始解空间,这样可以比逐步分配空间运行快一些 / M' U. d0 h, u7 i0 `TracePath=zeros(1e3,m); 4 u5 z* |! k/ ?- e8 V9 sDistance=inf*zeros(1,1e3); . H, G0 s/ U( P2 [* j; G, L# K; E; I- K
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...' k) f: L& A3 B L
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );, M* H2 i: s* h
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)$ W- A9 g: u/ m
for i=1:pn % d, R) ?" [+ ~4 O: u path(i,:)=randperm(m);%构造一个初始可行解, y. G; y4 a1 X4 r$ g; ~
end * A) x9 h0 E( U* M7 g/ bt=zeros(1,pn); i# y9 x$ o3 Q7 x
p2=zeros(1,m);9 f; x5 {$ R/ Z3 y! R$ G Y
4 w# Z8 \4 @, C% l% e7 p1 i: m8 I
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );0 e, @5 Y+ L- v) }' _5 c2 S& z
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=' ) ; 7 \2 G. E4 j" v%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 3 _' ]' r+ U4 `) Q; D3 O%而随着降温的进行新解被吸收的概率逐渐减少,又难以跳出局限% a3 ~) z6 b4 x# \; b- w5 u
%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5 B: v& {* }5 W$ {6 S
%会收到到比较好的效果' F. F& H5 L; Z' ` Z6 ~0 I
6 k0 u* M" r s( Q! k. rT=1e5; " k& Z/ a3 _/ D) D5 PN=1;( I& @' ^( G9 J# d& J' c3 u1 ^
tau=1e-5;%input('请输入最低温度tau=' );* x" e+ k T9 ~6 E. A
%nn=ceil(log10(tau/T)/log10(0.9)); ) }- W& V; {: M }while T>=tau%&m_num<m_max ) P( Y1 M$ J* A* k3 R( K/ E" F
iter_num=1;%某固定温度下迭代计数器9 Y( D9 n' f& L6 z8 c: F
m_num=1;%某固定温度下目标函数值连续未改进次数计算器$ g2 T {5 E/ T; q C& m2 m$ @
%iter_max=100;% d: B/ n( Q' U" ]6 k9 k& z! y
%m_max=10;%ceil(10+0.5*nn-0.3*N);' n) _( W% E: e* Z
while m_num<m_max&iter_num<iter_max / w1 L: R0 G& L' f( b3 y/ g %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:2 Z4 D9 ]) _5 X1 p( _; P# U
%用任意启发式算法在path的领域N(path)中找出新的更优解# _" V8 b* L: F& v8 r
for i=1:pn 9 q1 e$ }$ p& v- V+ e Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]); " J- Z1 B4 m/ m%计算一次行遍所有城市的总路程 1 d- M# f& U8 o) Q) u) z5 c [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线9 T0 j+ A% [% V- a' u
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);, [6 E5 x! B( K' {" c4 W
end* Q+ m3 {& ^, U
%Len1 ; q6 W. Q; c! B+ w %Len2/ A! n' K( a/ H2 i0 z/ V; ~6 H
%if Len2-Len1<0|exp((Len1-Len2)/(T))>rand 4 H( n8 O, p3 ] R=rand(1,pn); ; t5 Y. ?/ w7 Z %Len2-Len1<t|exp((Len1-Len2)/(T))>R$ N d0 t4 ~& L0 |6 y
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)3 x! l; ^4 R# p9 x/ [7 x" H2 h- a
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : ); * ^2 d% D+ N# Q) d4 _1 ? Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)); 4 r; M! P1 R1 H5 K" J' h; s$ i [TempMinD,TempIndex]=min(Len1); 2 A' K) a; T8 p+ c5 b `# d% E %TempMinD ! m* s& U. z7 K4 C TracePath(N,: )=path(TempIndex,: ); / w" u* N; N i* y: ] x) B+ u8 M U Distance(N,: )=TempMinD; . N' m( e: E7 v" K& J' N6 v N=N+1; % Z# K) l4 H2 C6 h %T=T*0.9 , P& B; Q4 D7 ]' m9 ?* s m_num=0;. l. F$ q3 E$ }" \$ K
else2 R5 j; v2 C G9 O
m_num=m_num+1; + ?9 Q! Z2 [6 j3 |# M! U end5 O9 x0 m% S+ A; H: p3 i2 i' Q1 Y0 c
iter_num=iter_num+1; - t1 G2 ^7 q+ [6 U end" l9 q3 P7 w( M% Z, C
T=T*0.9 - [6 e# @5 k8 Q! t6 C%m_num,iter_num,N9 ~3 m/ z! m1 M$ f% q! K9 m
end ! \5 V m7 u6 P* l) F
[MinD,Index]=min(Distance);" M* H3 [* O% E4 l! k
BestPath=TracePath(Index,: ); $ g3 [. A- E) C0 q: U; @disp(MinD)" Y( l% r: [7 i1 B, b$ n
%T1=clock# Z2 [% h# r, I) M/ x
& Y. b$ h0 j/ {) E ; H2 K* e6 [: I- }- b8 T, C
%更新路线子程序 1 s3 V, l" `$ |
function [p2]=ChangePath2(p1,CityNum) ( r0 f1 m4 ^1 F: E) aglobal p2; 9 ]2 U N$ Q! F- twhile(1)+ J6 o9 O/ r) }% j v2 V1 y( m$ I
R=unidrnd(CityNum,1,2);' r4 h: z8 X G$ y6 N/ O
if abs(R(1)-R(2))>1# h8 }/ }7 e" w# X. a8 o0 N+ z
break; 4 x/ N. M' N* y E* e9 L end W. k6 h3 S, z3 W0 r. K. V2 hend 1 T& C. w2 P9 j$ J3 K1 Z, HR=unidrnd(CityNum,1,2); " ^( H: u8 b) I! ?% a4 T+ zI=R(1);J=R(2); ( W6 ?- o6 U" @+ y& d: _2 D+ @%len1=D(p(I),p(J))+D(p(I+1),p(J+1)); + |* u1 ^6 e. ~+ K0 b/ g& ^%len2=D(p(I),p(I+1))+D(p(J),p(J+1));' Z: X: d% T$ z( R% D
if I<J3 e* U# _3 G3 B; u% K: }% i% ]7 s) w
p2(1:I)=p1(1:I);( Z6 j# A0 T, H3 n- ~
p2(I+1:J)=p1(J:-1:I+1); " P3 u* A' S, H p2(J+1:CityNum)=p1(J+1:CityNum); 2 W4 X) K3 ^+ I8 s3 G7 belse 8 _. `9 H" G( V: u; `. M: k+ m: k p2(1:J)=p1(1:J); 5 T+ ?2 o1 m( ? p2(J+1:I)=p1(I:-1:J+1);5 O( @2 k. y" T* Z
p2(I+1:CityNum)=p1(I+1:CityNum);! u& B/ Z( {4 n6 R
end 9 s# Z: }+ U0 T* }" p/ U0 n9 {0 U
六 遗传 算 法程序:7 X8 `3 `( y0 ]4 S+ W1 Q
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! . [ D' {9 B8 Z4 ]: X ! X0 W9 I) o8 p3 cfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)- U* M1 d6 K6 H+ d+ g
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) " ?7 ^# `1 X, |; C4 W
% Finds a maximum of a function of several variables.& X4 v5 p: s' `' N' S( T
% fmaxga solves problems of the form: - Z: } l* U2 E6 ]8 J( ~5 X
% max F(X) subject to: LB <= X <= UB 3 i& {+ a7 Q2 w2 i& q9 N* ^5 a
% BestPop - 最优的群体即为最优的染色体群# \1 n$ y6 x% @
% Trace - 最佳染色体所对应的目标函数值4 G: f; n8 g6 r( Q1 n
% FUN - 目标函数+ P; O$ X- B& c2 W7 t1 P6 T
% LB - 自变量下限/ {- J" N( ?1 k5 k2 R0 @5 M7 d
% UB - 自变量上限; m9 M1 ~+ U2 |% k; X% ?! K$ U( ^
% eranum - 种群的代数,取100--1000(默认200)/ D, t: E: I: I0 P
% popsize - 每一代种群的规模;此可取50--200(默认100) ) E" Y4 O& N* z6 V% V: X6 K: R% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)6 j7 X5 v6 x2 ` I% r2 p% v& p
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)& E0 E( d+ b F7 R4 K$ c
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2) / i! {) V" c0 j% V% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编 9 u! Y. E% E& U) ]3 U) a%码,option(2)设定求解精度(默认1e-4) , T/ G3 `1 w, L! [% . h% F6 g, W+ j% ------------------------------------------------------------------------ ) S, Q( m9 T& {) j0 i/ v- ~0 c$ [9 r" l7 g& t9 P) y. ?$ m
T1=clock;. ]# q0 q% O+ B8 ?& U' m
if nargin<3, error('FMAXGA requires at least three input arguments'); end4 k& o2 j7 @' l5 ~' K& z
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end 5 l! X* a- P6 o8 l1 A. q- @3 Wif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end, C3 K" V' r, A' D+ U+ j
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end 2 w5 k I( k Q a7 Z3 H f3 xif nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end! D) ^3 p5 r& a1 h
if nargin==7, pInversion=0.15;options=[0 1e-4];end1 g- T; u3 y7 A
if find((LB-UB)>0)6 t2 G) ~* ]: l4 x# f
error('数据输入错误,请重新输入(LB<UB):'); % a0 X+ w; j6 o- Dend ; ~! Y4 W' F. ~- Y: Es=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));/ P& M7 \; J: n ?1 q0 ~
disp(s);1 p, S/ n* _9 {6 y2 X- o
6 d" b3 v1 i2 C- A; h5 |3 T
global m n NewPop children1 children2 VarNum# P! a. Z% s; h
' r7 c' ~8 b0 l- A: bbounds=[LB;UB]';bits=[];VarNum=size(bounds,1);9 U; `5 S6 x5 b( @. `# e
precision=options(2);%由求解精度确定二进制编码长度 ' u& ~6 T/ N1 a+ ]bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间/ Y3 {3 N+ O- C6 E0 n- X
[Pop]=InitPopGray(popsize,bits);%初始化种群 , Y6 i+ X- E/ R: ~[m,n]=size(Pop); 0 U: v" v) S0 @: R4 f" k7 fNewPop=zeros(m,n);% [1 @/ ^9 \6 F4 E* W0 m/ X7 {
children1=zeros(1,n); * D& \1 w" {7 x }children2=zeros(1,n);- y! A1 W" u. _' L
pm0=pMutation;, {2 y0 r1 h* ^0 ~) [- s
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace4 c! r7 Y2 c. D i, g
Trace=zeros(eranum,length(bits)+1);; _7 H! j5 |9 n+ G. ^9 e
i=1; " h% ]! B; B* Jwhile i<=eranum $ A, W; i; ^; U$ d8 Z3 J- @ for j=1:m7 Q, A7 h) ^ V3 T
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度 9 r% m( G+ Q* v' O end ?5 Y7 H' P: x& |0 y
[MaxValue,Index]=max(value);+ e" ~4 e) q" ^/ Z4 X1 P
BestPop(i,:)=Pop(Index,:); & y' G8 b! d( n8 n Trace(i,1)=MaxValue; ( Z# P+ d1 i3 h Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);! c+ C4 @& s) h2 u6 j/ y, D
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择 3 }# k) `. R. K& S7 f* ]. w( q[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum)); r6 \3 Y$ U; w( a0 A( d3 y%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率6 v) a+ ^5 `9 U: X; e8 N
%round(unidrnd(eranum-i)/eranum) 6 G+ a; ]6 d+ g% v [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异0 h' P) B- m& K1 x/ R
[InversionPop]=Inversion(MutationPop,pInversion);%倒位& d4 _7 K$ _* b+ n7 g
Pop=InversionPop;%更新) e0 W# l8 v; w9 R1 L7 ?% [
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); 0 J% o9 H+ y7 S7 b%随着种群向前进化,逐步增大变异率至1/2交叉率 - s, y) v) O! B p(i)=pMutation; # n8 |; @- Y/ F% I( I/ C/ K1 O i=i+1; 4 q3 t: M5 a& n' }0 _( U! ]end1 }" f0 T0 F* F3 m+ B
t=1:eranum; & D9 x* B3 H" D7 |# F8 V wplot(t,Trace(:,1)');3 W3 {0 L! G; @) T" Y
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)'); 0 d7 F6 s& H: N: T0 [[MaxFval,I]=max(Trace(:,1)); / w4 H5 w3 T6 W& ~+ ~X=Trace(I,(2:length(bits)+1)); c' e+ Q5 e6 ^; q& ^hold on; plot(I,MaxFval,'*');. t0 \2 V* p J7 G1 c- B, J/ T
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);9 I; J: n3 P4 b! L
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,:)));+ }! O, x" b# W" V" W9 S) {% V
disp(str1);# {0 r" i% ^, W$ t' l
%figure(2);plot(t,p);%绘制变异值增大过程 ! Y: ~; j# i1 D* H3 J' f6 nT2=clock;( T! g" [( \1 ~+ y9 |) f0 r
elapsed_time=T2-T1;5 b: X" q& @* W: A
if elapsed_time(6)<0, i- U* I D3 n8 Q' h E4 Z5 Q4 C% n
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1; * M: z( o8 K/ u& p( {2 Dend + y; g# k2 o( j6 @; t& C0 x/ @0 tif elapsed_time(5)<07 X2 V, z6 {" H: Z* O! A
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;, C* V" K2 q) R5 N
end %像这种程序当然不考虑运行上小时啦5 ~, l5 t( w5 z. M5 U u% e
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));! b' i$ a! @) U2 m+ {& ~9 `' o3 R! q
disp(str2);7 x5 D# U; j% F
$ b: l% S* R6 @. M4 k( r }2 w& V) j$ _%初始化种群 0 C9 s5 i, ]1 g o2 i: u7 |- J%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- g+ L# Z$ P% K+ P
function [initpop]=InitPopGray(popsize,bits): ?7 i& y6 l: m+ S
len=sum(bits); 4 y) ^9 m! {* H7 G: T* {initpop=zeros(popsize,len);%The whole zero encoding individual 8 q. m i/ {0 kfor i=2:popsize-1 7 N( G% B4 M7 h/ r* A, X# A; m pop=round(rand(1,len));% G7 B7 o4 S+ n/ \7 N
pop=mod(([0 pop]+[pop 0]),2);, [- H. }' z! w( `" h9 c8 J& Y5 E
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)+ s& w; c0 m% p, A: B. b3 \
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n) + {2 T! B% h# r3 E! B# L# l1 ^ initpop(i,:)=pop(1:end-1);+ n F6 a& h W7 M+ r$ t: a7 s
end. Z; ?0 }& J& V/ V% ^! j
initpop(popsize,:)=ones(1,len);%The whole one encoding individual 8 P) `, M, ?; d% e% s" ~+ C3 i%解码 8 N; ^- d7 D2 A% X6 m' P1 C. b , f9 @- V4 [1 g( L. Tfunction [fval] = b2f(bval,bounds,bits) - F% N9 k* g. O. J# ?# _% fval - 表征各变量的十进制数+ {- t4 _; Q9 p) r& u
% bval - 表征各变量的二进制编码串6 `0 W' h2 V4 Z
% bounds - 各变量的取值范围 o- ^) b; @! Q$ m! {, E- k% bits - 各变量的二进制编码长度 : @0 \/ h+ F: c0 W5 `: uscale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables' P. J5 I F+ }! l
numV=size(bounds,1);2 A2 U: _# y# T0 }( b) E
cs=[0 cumsum(bits)]; 7 A5 U4 P+ A0 I0 Y7 N+ Z5 @: Nfor i=1:numV, @2 H0 t, z$ L# Q# m4 F8 J
a=bval((cs(i)+1):cs(i+1)); 4 `& W- h% K) }* E1 N b fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);& A# k$ J$ i0 {7 I
end: N/ V" \: d0 h9 l6 A0 E0 s7 ?
%选择操作 ! H [* O/ l4 N6 O%采用基于轮盘赌法的非线性排名选择 3 l8 l$ x8 G& b2 L! k6 z; u3 L1 ~%各个体成员按适应值从大到小分配选择概率: ; U/ K" S2 B" P0 t1 z8 V+ \" S%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=12 t9 t! T$ q' W
# O) g* B; x) L4 o/ Xfunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits) 1 U# m! a9 ~' h* s( A3 qglobal m n8 e; r! `* q: K; H. A$ r% M$ k* X7 U
selectpop=zeros(m,n); + i# f x) k3 k2 q6 bfit=zeros(m,1); ! s7 u; L5 R0 \4 T3 |for i=1:m, P. E: K7 s1 M U$ N5 |! b
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据 6 { X7 q M, E2 n- G4 uend* }' p7 |, H9 U0 S; M% _5 A
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)4 A I* s( @+ m8 p
q=max(selectprob);%选择最优的概率 # y5 ^0 d. \4 M2 w- y& C0 T5 Ox=zeros(m,2);$ X9 d0 L7 j V( }& l
x(:,1)=[m:-1:1]';. j, a6 L& _& U: P+ r$ D
[y x(:,2)]=sort(selectprob);7 `% G; J9 H1 w; t% M
r=q/(1-(1-q)^m);%标准分布基值% B R0 I: k7 m8 B; {
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率 + d6 P& a" W2 S+ i1 Ynewfit=cumsum(newfit);%计算各选择概率之和 , o! P3 j. h8 @7 L& N) irNums=sort(rand(m,1));) f) D, }; [$ ]: _' X/ q
fitIn=1;newIn=1;7 l6 O+ B; o- f3 Z; b- W1 [* K
while newIn<=m & W' ~9 D! i* x: O if rNums(newIn)<newfit(fitIn)& `$ d8 Z: o- i4 p: V
selectpop(newIn,:)=pop(fitIn,:);, i% p7 ^; E# }' T0 l
newIn=newIn+1; , c$ P+ s# V7 Q8 T5 T else4 [8 J3 h3 S3 M: B$ v
fitIn=fitIn+1;# C l- p0 R- H; O" ^* o
end 3 l) s4 u, @6 t3 M; V) }end R( e( D1 u) O/ P( \
%交叉操作 r' c# c b' x S, qfunction [NewPop]=CrossOver(OldPop,pCross,opts)- Q/ E. l: b8 N- B
%OldPop为父代种群,pcross为交叉概率 - M" w" S M. o7 Y1 D5 w5 nglobal m n NewPop 2 q( U! G9 i7 q: N% ?
r=rand(1,m); ' b* o* E% l/ i s* N( U6 Sy1=find(r<pCross);) N' M7 |5 b3 |, M% s
y2=find(r>=pCross); 9 c+ I( i: i) e2 Q4 p! K! dlen=length(y1); - k' G' H8 H9 U3 ] |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1 Z0 w& O+ H& U- ]8 }" T
y2(length(y2)+1)=y1(len);% t' k2 V! H$ c" _$ b. ]# T0 H
y1(len)=[]; ; W1 ~+ m* W! ^2 Iend 1 u! h( M0 n9 g/ H$ |if length(y1)>=2 " m! ^8 o( j J0 W for i=0:2:length(y1)-2( M! a+ \' [0 W1 N( {
if opts==0! y$ N. l8 v; R" B, L( I
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:)); + M0 @! v0 S8 k: H ?( f& W: }3 t! h else ; w: {" `! y$ ?) X0 M/ [8 x- p [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));- E5 X( I: i/ T& t: y* p9 H4 z
end 2 z* g+ W3 p B# E6 { end 9 p5 s \( R9 Yend " R2 ^# X$ A1 e: Q9 o9 gNewPop(y2,:)=OldPop(y2,:); ; L% E. o3 r# x1 `. m1 r8 V( Y6 @5 h9 w9 i$ d' i0 W) c4 Z
%采用均匀交叉 ) p/ U2 ^' ^6 E8 D' Bfunction [children1,children2]=EqualCrossOver(parent1,parent2), y2 V. {1 ~0 F% X8 ]1 w
4 g8 K1 i v+ M+ H$ b6 D) h6 W
global n children1 children2 3 K/ v* z# p9 N ?* E5 Ehidecode=round(rand(1,n));%随机生成掩码 # w6 f# r* z5 gcrossposition=find(hidecode==1); : J! h9 w& y0 z( n7 h- y' {holdposition=find(hidecode==0);: Z: p! V Q& L' p% u: ^
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因 ) T) Y) B5 G' w" {$ S1 hchildren1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因) [6 o) Z! F4 @) E5 B
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因/ y* g$ z' u( N5 S+ I+ f" L# R i
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因- {' [1 G/ L4 y
) ]. W4 P: y& M! z4 W%采用多点交叉,交叉点数由变量数决定 8 ~" m1 `- [: U7 f3 b% ?5 Z; Q+ N
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)" U/ {2 p$ K- K d8 l
" T P4 K# u% lglobal n Children1 Children2 VarNum" _) v# p6 l% p% v1 l) V' v
Children1=Parent1;3 ]1 v& p6 q% N1 j! _# ~2 g
Children2=Parent2; # H) @( d- Y) bPoints=sort(unidrnd(n,1,2*VarNum)); - N# a. U8 b5 Afor i=1:VarNum , G* k5 p* D' u Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));- L; @, O& k& l6 y& Y
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));- K* Q1 O& g& N3 e e
end / t+ O2 r4 f+ `( G2 ]- F! U' H+ |! m1 p
%变异操作 7 g* I) N8 U6 X/ Ffunction [NewPop]=Mutation(OldPop,pMutation,VarNum)7 U2 |! ?2 q; J z
y8 J4 q0 P" _2 Z) f
global m n NewPop X8 _6 G9 \9 `$ F4 d& Y: z# L: [. nr=rand(1,m); @3 f4 U" B& \. q7 }7 L2 W
position=find(r<=pMutation);/ Y+ C" |4 Z. w) |* m
len=length(position); / @; b' r8 R. ^! c! z+ Sif len>=1; { _* _7 D: S
for i=1:len ! E+ E2 h2 E( | k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点 & Q" R) W: N0 o* u- n for j=1:length(k)6 i, `3 E2 Y7 V" j! @* l
if OldPop(position(i),k(j))==1& e2 ~( ~7 \, v; L1 s- c- u% q
OldPop(position(i),k(j))=0; f6 t3 @9 }5 Q' c( q: ~
else 2 q1 w0 S% s& A; o( Z) j) s" Y& t9 x OldPop(position(i),k(j))=1; & Q. f$ j9 p' s6 F7 J* a0 E end # Y, J3 w. O2 O( s7 g end ' J. r# o8 X/ H- O: b9 ]' F9 C6 f end : t8 g; B3 L2 ^) jend , G( S! K; M u8 a' {2 {' F/ MNewPop=OldPop; t, a" t5 `9 c4 M$ x P. F% Y 8 v2 z5 d% t; I/ I, r%倒位操作) c# D% g5 z2 L) H
' A+ z. G+ I$ ^! n/ N" Ofunction [NewPop]=Inversion(OldPop,pInversion) 2 W/ r+ ^, Q# C/ e) C }3 D 2 T# f+ t# F: S7 Z, \3 c1 L# t9 Mglobal m n NewPop , B5 D$ U8 l) U/ q/ KNewPop=OldPop;# B# O+ T" o, d. J
r=rand(1,m);$ Y! _4 D- U3 e* H' T
PopIn=find(r<=pInversion); + ^# L% o; H E7 C0 W% Llen=length(PopIn); 0 j& U; L) f8 ?- Pif len>=13 }6 u' G; H5 U$ H- v% y/ p0 s
for i=1:len % m' U# N ]$ V7 w6 q d=sort(unidrnd(n,1,2)); " H" Y1 P" b7 X if d(1)~=1&d(2)~=n/ B2 }: Q( N5 R c+ f
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1); ) V7 h- ^ j1 T2 {% i$ b NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1)); p3 y6 j3 K2 }& e/ o NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);3 T% q- A3 n7 h" j: }
end 4 b% l7 y' ]- _% S end# V3 V/ I1 Q2 I6 ]9 I# v
end * a8 o0 m5 M4 A0 P + T7 y6 D9 x6 r& h ^七 径向基神经网络训练程序% p5 Q4 ~" b& W5 H; U
9 E+ P+ T9 Z v1 _4 @7 r: F7 Y1 z4 Yclear all;$ H. G" u; m$ N- H" l5 B
clc;' O" H, e1 I" D: D3 Z/ K. A
%newrb 建立一个径向基函数神经网络 ; O" p" k3 G2 s* q5 yp=0:0.1:1; %输入矢量 4 D" ]: | |5 R0 ~' R9 o0 yt=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量 - G- n- M$ L' e5 S+ x8 u4 Kgoal=0.01; %误差- D" v" ?) \0 D% c. n
sp=1; %扩展常数 1 U* N1 z$ x# [) ~mn=100;%神经元的最多个数 / r- F- @5 C6 l# n( Idf=1; %训练过程的显示频率, C% h4 p6 K s8 X7 E
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络" u5 m6 a' H j6 B
% [net,tr]=train(net,p); %调用traingdm算法训练网络6 i0 f& {) }: Q5 }
%对网络进行仿真,并绘制样本数据和网络输出图形8 d1 W0 E2 [6 R+ R: l( }
A=sim(net,p); 8 `, f* S1 V u' cE=t-A;5 [0 t( n4 U7 G w$ `
sse=sse(E); & P- L! E) d! p' O+ ^ T+ N9 kfigure; 5 l( a( n0 ?; u* ]6 U! D- d7 D) Nplot(p,t,'r-+',p,A,'b-*');* d# t2 |1 N$ J5 p6 e
legend('输入数据曲线','训练输出曲线'); . l( ^! ]# }1 ?* D: `4 ]echo off 9 m( D H E& N5 E/ J( H7 G$ ~2 M, G
说明:newrb函数本来 在创建新的网络的时候就进行了训练!, Q; Q0 C9 H4 |9 V& m. I8 }
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,6 N R3 z8 V' t1 i$ i% ? u
那么继续增加神经元,程序终止条件是满足精度要求或者达到最大神经元的数目.关键的一个常数是spread(即散布常数的设置,扩展常数的设置).不能对创建的net调用train函数进行训练!, B7 U* h0 z/ c0 t* ]
6 C$ A# M, w6 o4 S- l
9 q1 {- |7 O- O9 Y1 A
训练结果显示: 5 h; q- y* j6 X4 X1 W! y! u. p) ANEWRB, neurons = 0, SSE = 5.09735 J$ [, }9 A1 V4 [0 s8 o) d% l
NEWRB, neurons = 2, SSE = 4.87139& o4 t, m2 i4 V2 L0 V
NEWRB, neurons = 3, SSE = 3.61176( @& c. v$ C! g% T
NEWRB, neurons = 4, SSE = 3.4875 Z, ^7 p5 f- Q/ t5 S
NEWRB, neurons = 5, SSE = 0.534217 % G" e7 X8 Z8 {NEWRB, neurons = 6, SSE = 0.51785" a$ ]; G2 F. G2 v; A
NEWRB, neurons = 7, SSE = 0.4342596 A2 M5 N4 @5 L0 R) T9 V
NEWRB, neurons = 8, SSE = 0.3415182 f5 s/ R" H7 O
NEWRB, neurons = 9, SSE = 0.3415197 G- d! A8 c+ n$ p4 v/ ?9 \: l
NEWRB, neurons = 10, SSE = 0.00257832$ o) q; l6 L# s
6 b' T9 ]$ I, Z5 G, P8 G6 L八 删除当前路径下所有的带后缀.asv的文件% p) ?4 H8 Q. P$ E7 I% }- }9 X
说明:该程序具有很好的移植性,用户可以根据自己地 * P0 ]7 f6 g! B$ ~要求修改程序,删除不同后缀类型的文件! + v5 K4 h: h+ T2 ^5 M7 ~3 o4 G/ O; }function delete_asv(bpath) ) A1 K% ` G8 Z% H
%If bpath is not specified,it lists all the asv files in the current & Z7 \& L* Q0 r/ B: Y%directory and will delete all the file with asv & H# O" T* G' l e* L5 C& a
% Example:" B1 v4 c% V& f, r
% delete_asv('*.asv') will delete the file with name *.asv;/ K+ I4 B: w: S+ f9 e
% delete_asv will delete all the file with .asv. 9 Y6 j; I7 d4 V1 {: v) D N6 h 7 ~7 }- @8 I1 e; g$ zif nargin < 1 G1 s6 u1 r ~%list all the asv file in the current directory 7 t$ n' A1 X! F M! |0 o8 j files=dir('*.asv');# `: A+ C0 ]/ m. u1 U6 [; f( o' j
else + K' Y' J9 l7 q% h, H: ~8 N% q% find the exact file in the path of bpath ! g0 f0 q2 H1 W& Q9 h! g. @ [pathstr,name] = fileparts(bpath);& v" K- {) N) _3 `( D* |2 @& A
if exist(bpath,'dir')1 _* u5 N w6 S3 K1 C, J' r& k& m
name = [name '\*']; " D! o0 b2 S' F end ' s* p' ]! `4 F; k2 y ext = '.asv';+ S# G( \( ]; c+ Z% O7 E% z, k
files=dir(fullfile(pathstr,[name ext])); ! ^$ a4 b$ ~6 |- Z8 h% n! fend5 F1 x7 N' h2 ?
: V7 u' J1 z+ ~, k
if ~isempty(files)* f/ [/ k2 r: l) P7 X4 R Q- @, v
for i=1:size(files,1) 2 f2 k% @ k' H% J$ T title=files(i).name; 6 d+ a1 P, R5 a9 e* ~1 ` delete(title); 2 N, K% |5 f2 Z) o8 |" L3 W end( I6 Q' X& M4 b; q8 E' ^
end $ U- H4 v* A& s" \" I# I4 m # |! B' z& ^8 A/ s- k; Z3 E( V0 f, ~6 k) J4 A# N# T
同样也可以在Matlab的窗口设置中取消保存.asv文件!1 P* K; S9 ?' I0 e0 l