一 基于均值生成函数时间序列预测算法程序9 l. z( _/ @2 _& k& I1 w
1. predict_fun.m为主程序;6 t- ]/ J6 G1 I1 z5 ]
2. timeseries.m和 serie**pan.m为调用的子程序 * y2 I9 a6 k' Q3 I; ` 5 i, j/ L" H2 x$ i9 Dfunction ima_pre=predict_fun(b,step)# C9 W+ V8 s6 n Q
% main program invokes timeseries.m and serie**pan.m4 w2 \# c4 [& ~ F
% input parameters:8 `& j2 d2 I2 [
% b-------the training data (vector);. @3 R% K6 j) R1 f
% step----number of prediction data; ! d. `2 D: E8 f M# h1 \, J% output parameters:. {2 Q' d0 V6 J7 A: K
% ima_pre---the prediction data(vector);" W; e- M' t0 I7 X* k6 E# J
old_b=b;4 W. Y$ ?+ U3 u& j4 M& l
mean_b=sum(old_b)/length(old_b);: h" ~5 m7 [% w# h1 P/ A% l6 s
std_b=std(old_b); 5 [ T- }- G6 W1 _1 Rold_b=(old_b-mean_b)/std_b; * v: I# g. u6 B3 ]$ P1 _8 P[f,x]=timeseries(old_b); 8 f6 G9 |8 L. m9 f$ c; ~: e, Dold_f2=serie**pan(old_b,step);0 X* S4 b& Q& U- b# W5 A
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps; ! {6 w0 \$ N8 k& sR=corrcoef(f); + |# D" s+ J* Y) @0 k[eigvector eigroot]=eig(R);4 _: Z( K. t- @
eigroot=diag(eigroot); * b- U. C0 e* s+ O- p& c+ ?. r/ ua=eigroot(end:-1:1);3 z Y: A0 v7 p6 c9 x& k( O
vector=eigvector(:,end:-1:1);& A3 A4 ?' _% d
Devote=a./sum(a); & U9 M5 D; M/ z. i9 p* [7 ADevotem=cumsum(Devote);; j s; H. k) b( e- ^% w' W; u) l
m=find(Devotem>=0.995); * P4 u3 ]! H) R; b) [m=m(1); . |# H, \; P3 @; z N- pV1=f*eigvector';* R$ m+ J* _2 N- v) D& L, O5 V2 i
V=V1(:,1:m); 3 X# A4 X3 @: F: N2 {% old_b=old_b; : Z8 W' f7 F& | `old_fai=inv(V'*V)*V'*old_b;4 t6 v( b3 z' V/ @/ X
eigvector=eigvector(1:m,1:m);. q1 l& T6 L# [) @
fai=eigvector*old_fai; ) s1 n V0 C! B( `2 Cf2=old_f2(:,1:m); * |+ @6 u$ n1 P$ M7 c! l2 o2 Ypredictvalue=f2*fai;6 P( x3 m( F$ h, ~
ima_pre=std_b*predictvalue+mean_b; 1 ~6 Q# g5 h8 w& u" N5 B/ @4 B& S F0 P0 u/ F& k) o
1.子函数: timeseries.m 4 p% g' m# q% F7 d% f5 Y) G4 \% timeseries program%1 E1 J; ^6 X1 A! v
% this program is used to generate mean value matrix f; / f( @) r! R% O5 D1 h4 O) Rfunction [f,x]=timeseries(data) ( e" O! u2 v( c( N' K4 r% data--------the input sequence (vector);9 v% c( g P' o; i- N& K
% f------mean value matrix f; * X- V7 `2 i8 }/ Cn=length(data); 0 @% q: a% a7 v" {- g, U0 yfor L=1:n/2 w3 r, A4 }8 X
nL=floor(n/L);4 O4 d- P' o# I$ c( W
for i=1:L . _ W7 P6 R4 d" z sum=0;2 N# X+ ^- W/ I9 h2 e
for j=1:nL + M+ M, Y9 ^$ {4 W) W, g sum=sum+data(i+(j-1)*L); / o6 k4 c6 _3 [ end * V. Q6 f2 w' u2 d( ?) K x{L,i}=sum/nL; 2 u' I& _1 }) g$ y! ? end8 P) M8 \' E* e! X$ P
end / B/ `0 i9 a6 j) R* A, tL=n/2; # N9 g( k8 S/ B" K9 S) }' Sf=zeros(n,L); \& W4 Z8 t" q5 ~for i=1:L # f) L' F: @9 V rep=floor(n/i); & n! N- j2 |! u' j/ g; \% x# G' C res=mod(n,i);9 z! r/ y& F) u- j r& ~
b=[x{i,1:i}];b=b';9 `6 u+ S. y# u) ?7 p, P( P
f(1:rep*i,i)=repmat(b,rep,1);( d, K# ?& h- _: ? D0 X4 f
if res~=0 9 G: E: s. n6 W% P c=rep*i+1:n; & X1 }. j0 o9 I$ F$ |, } f(rep*i+1:end,i)=b(1:length(c));! ^6 O- L7 g' i
end- w3 o4 W* c8 I5 y9 p( e! U, b
end; T" L) Z: [; f
0 E. u3 o' u' n) B9 w; Z
% serie**pan.m! |& F" E1 a. z) m0 L
% the program is used to generate the prediction matrix f; , O. W( K! ~8 X. `6 k$ Z$ w, z( p. o
function f=serie**pan(data,step); c! } p$ j+ V5 F6 b5 y* f* s
%data---- the input sequence (vector) $ C. `( L2 f7 M9 g2 ]% setp---- the prediction number;7 x O# x" W: d6 _- F
n=length(data); 8 n) E9 i5 f9 ~* V* \% efor L=1:n/2 1 i9 r# K6 L! T nL=floor(n/L);) B8 {' l8 Z- Z
for i=1:L o8 ]0 P( ?+ s sum=0; ' Y$ S; X- V0 g6 K0 j for j=1:nL5 w, A! D$ ?, i( {' g& I2 A
sum=sum+data(i+(j-1)*L);& f; M' F4 k; x7 n+ y
end . e' U5 t- s( R0 F* n x{L,i}=sum/nL; 3 h5 f8 @. d9 L end : M! F, S+ ^- d; k% dend " I, T6 l' ^- l: l% z5 T* IL=n/2; / x: P0 y, H3 M. nf=zeros(n+step,L);: ^: F6 ^8 a% ^8 W4 ~% {6 a7 B
for i=1:L ; E4 o1 J l% C/ s rep=floor((n+step)/i); & m/ r5 h! i6 R res=mod(n+step,i);7 }: {2 T+ q3 k
b=[x{i,1:i}];b=b';! T, M7 u r5 B9 [8 H$ p' U
f(1:rep*i,i)=repmat(b,rep,1); 4 C/ x: z( W, q: X: s3 }4 G4 O- j if res~=0 8 L4 y1 t U5 |& ?5 t8 [/ g$ E3 h c=rep*i+1:n+step;% \5 X7 `& Y! P2 U. S
f(rep*i+1:end,i)=b(1:length(c)); % p6 u% l* g" h- C end + z2 T- o% o# ^, R2 x0 A) x3 zend # W3 u0 \* o/ x! f; g1 |2 } 9 V1 f( g2 |4 @$ I* `7 y4 J二 最短路Dijkstra算法3 L: z; y/ b: L0 ~. E) |
% dijkstra algorithm code program%, [+ G6 t3 `. A( ~( S
% the shortest path length algorithm : \ ?6 h u) v1 }& hfunction [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint) 4 w. b* ^ Z; O# s/ l2 G# D& v% Input parameters:) R* |* c( u3 P% _
% Input_weight-------the input node weight! 2 C( ]5 j8 y# K6 y% start--------the start node number; * V% q4 V% {7 V$ v3 o5 N: e4 _% endpoint------the end node number; 2 i' A. t' W5 A% Output parameters: ; V( v. A8 @2 y9 l/ J U6 c% path-----the shortest lenght path from the start node to end node;3 \% P( \. Z0 [2 I
% short_distance------the distance of the shortest lenght path from the7 g, u" X# |6 e- \+ G& c/ u
% start node to end node.3 e3 w: q3 S, l" l8 o4 u N. y& `4 b
[row,col]=size(Input_weight);$ K# M' T& k* E3 k
6 f- \& l% n, p* Z" ^2 O1 K%input detection 3 x+ P4 D( q& I8 }! J( {; e r+ Sif row~=col ; K5 R4 x$ ^# O: H3 _' J! Q error('input matrix is not a square matrix,input error ' );. t& j. `6 T+ r; o- M
end 2 l0 \; A2 }; u. f! B9 A8 pif endpoint>row8 V) w# J% X2 ?9 n# \
error('input parameter endpoint exceed the maximal point number');. C& X1 J3 Z5 }% o
end ( d: W# H. i% C. l 7 x; W; |5 { c9 r0 q6 t%initialization 3 _7 L6 _7 `3 N* S& l6 Y! @s_path=[start]; " d6 V. F- Y+ s! `( X$ ?0 Y: n& fdistance=inf*ones(1,row);distance(start)=0;$ ]3 h5 @/ {/ [- c ~# Q4 z- c2 `& t
flag(start)=start;temp=start; 2 u7 k2 \* X9 s Y2 x8 F Z" t- R$ u. [9 b: _5 B4 ]8 q
while length(s_path)<row Z6 y. Y' g! \6 l$ h& d9 z pos=find(Input_weight(temp, : )~=inf); , `5 \; p/ I' H( Z7 w% @8 v for i=1:length(pos) . {+ j$ _8 o {; [1 V2 ^/ X; y! Q if (length(find(s_path==pos(i)))==0)& & t- [6 ~+ i* v" z(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i)))) $ g/ N) \, X* T# _$ V distance(pos(i))=distance(temp)+Input_weight(temp,pos(i)); m. @, E. d6 d* T5 n
flag(pos(i))=temp; ! W. S. H5 O5 c9 M2 \+ |$ i end5 ~$ `! h. R1 s3 T( U- ^
end / Q: \. z1 w$ ?( L* j4 r9 | k=inf;% w/ @; y9 ^: [2 l! g' C
for i=1:row1 k8 B7 [9 t8 e6 P* h7 L
if (length(find(s_path==i))==0)&(k>distance(i)) 0 e2 M- n' K' Q k=distance(i);8 E2 K% @$ {& _% a
temp_2=i;5 n& m8 U3 t$ Y% `
end0 N! l5 Y' J5 q
end 7 m8 |. c# O( g s_path=[s_path,temp_2];. u7 q; H. c# ?
temp=temp_2; . [) W/ F; Y: Nend . j- @+ K4 G/ S0 y$ m& R: y8 N# D( s5 N2 m! W
%output the result8 H2 ] G' @4 h6 d
path(1)=endpoint; 5 n! v' E% D- \: D1 l: W( N3 _i=1; ]& p- R8 Q# g- { K2 Rwhile path(i)~=start" ]: `2 s; e# _6 j% Y
path(i+1)=flag(path(i));0 m8 G$ g7 X r+ ~8 }; a
i=i+1;0 b2 b: g8 y; p0 _8 z9 M
end , P2 I, \2 G: b8 x" ^path(i)=start; 7 ?/ f4 T4 x* F1 T& Q: }. q. apath=path(end:-1:1); & z! p# {# T- g) |. O" c- fshort_distance=distance(endpoint);! h7 ~$ L2 m: I+ \1 U9 Q; c
三 绘制差分方程的映射分叉图 6 T, S2 V2 \9 K5 M @3 @* D 0 l2 _, B; m& g" _$ N/ `& vfunction fork1(a); 2 d$ M5 _2 d7 M& a& Z: A
) a" y) b8 J3 i( R- y$ F* t2 b- _
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图 " q& Z8 w+ B% j7 o4 p- |1 b5 ?/ b% Example: % u. V1 M2 K" C& M# W" ^/ i
% fork1([0,2]); - W6 u3 B2 O, q% I) V3 l; SN=300; % 取样点数 ' U; }/ d5 e* w/ T5 ?; x1 IA=linspace(a(1),a(2),N); 9 M! L" k) {7 _& X v$ \starx=0.9; 0 A- f% E q: r X" xZ=[];; v+ p: Q! Q- d# ~
h=waitbar(0,'please wait');m=1; # y8 z+ A* U& L( G+ dfor ap=A; 3 T( G; Y* r2 ?. m x=starx; $ t2 q+ e+ p/ d! K+ n) p0 A4 q0 ?
for k=1:50; 6 ], A. X: _" a/ k
x=1-ap*x^2; 8 s2 b5 E/ h8 B, w. d. I
end 9 ]( Z2 N' J) ~& e% Y for k=1:201; ) [2 i! z' \; n& G1 g$ v$ W$ J
x=1-ap*x^2; + r: R1 o4 o- @4 A+ U% `7 w Z=[Z,ap-x*i]; 9 d. `- i. z8 z, O- E; w$ A1 K8 I end ! p8 Z" W8 Y+ J2 M6 ~
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h); I$ ~, e' X! H) M" L
m=m+1;- @' q. Q+ T8 {
end $ ?; F, M' p7 ^9 M fdelete(h); 8 V5 `1 m& s" c* }7 w% S* `plot(Z,'.','markersize',2) , C/ D+ F j5 G: ?2 }7 v. r
xlim(a); & t' L* R- D2 {0 C5 \ ' x# [/ ?; P" a; o四 最短路算法------floyd算法; L. x' e$ m! E% U& L6 I8 Y
function ShortPath_floyd(w,start,terminal) & Z( [/ P; W( Q%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;$ t/ @* F5 |3 R0 m& i% F
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];. e& X4 ~2 O: N& L& b
%start-----the start node;: [) v* G% u3 z1 f6 M& b
%terminal--------the end node; & l* W% N" y$ X) C' j2 Kn=size(w,1);% k2 v$ Q6 r" l# p' a2 p! z
[D,path]=floyd1(w);%调用floyd算法程序 7 l9 u) [8 `# d4 P5 G4 L% `3 }7 g6 ~6 H3 j/ _
%找出任意两点之间的最短路径,并输出 ; S8 ?/ I. f" |for i=1:n ; e! g$ ] [3 I! V3 [ for j=1:n+ ?6 I3 M4 v% E! [1 A
Min_path(i,j).distance=D(i,j); M0 ~3 f" D4 l$ s u- o
%将i到j的最短路程赋值 Min_path(i,j).distance 8 ~5 h2 B- x! X! ?# B1 n; B/ E$ e! G %将i到j所经路径赋给Min_path(i,j).path * L0 r: z8 B0 f5 Z* J# F Min_path(i,j).path(1)=i;1 ]( Q' C% W2 @9 ]1 V: b" N
k=1;1 j. r G0 D/ F6 t" }; \
while Min_path(i,j).path(k)~=j# F6 i7 e! U" Z% u
k=k+1; 2 G# ~! k6 L7 Y, [9 @! Y; i: Q( M/ Z Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);* e- C4 r7 Z* U( J
end ; @! Q/ {' T! v0 V end* @, L& y8 {$ u+ K2 q" X7 V( A: _* d
end r1 ]* R$ g; r4 F7 U
s=sprintf('任意两点之间的最短路径如下:'); 0 `% N$ r9 y0 @, f$ ldisp(s); 2 v1 t6 ]5 `, d' w1 d. T( w7 ffor i=1:n% O7 h& h; y Z
for j=1:n/ r8 x) y2 \3 ~
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'... ' s% D# w7 h* g- P/ s ,i,j,Min_path(i,j).distance);% _6 W: C5 b3 e1 J" N& O% X+ T- n
disp(s); . C/ a) ^! l {+ d. N" B2 p disp(Min_path(i,j).path);$ y2 x& ^0 u5 s0 f
end 5 M0 P: W K& L7 Xend$ U' X! e2 J# J$ w
6 R& Q/ ~ N# |; a1 F! c%找出在指定从start点到terminal点的最短路径,并输出# W/ `7 I1 v) ~$ ]
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...; [4 N* V [6 r7 Z* d
start,terminal,Min_path(start,terminal).distance);5 Q# O2 P; C% _- b
disp(str1);$ }" B3 e# z! G
disp(Min_path(start,terminal).path); - Z% m1 N7 \$ O, Y$ t- c. N* Z* D + j s' X9 v L* ^3 P5 F- \% q( \%Foldy's Algorithm 算法程序; x* u) N' k8 G
function [D,path]=floyd1(a)8 P" }) X. C) E3 y: ]
n=size(a,1);6 g8 M( ~6 e3 M6 l7 `
D=a;path=zeros(n,n);%设置D和path的初值: k6 c- u3 \4 l( \* A$ g. h
for i=1:n3 O o+ t# f) x6 F( y* u
for j=1:n : i1 Q. Z. }3 c) q if D(i,j)~=inf7 X3 Q5 T- R0 r2 R6 O
path(i,j)=j;%j是i的后点 " j! q) \3 m( N# o' {/ B end+ P8 b( w6 }- R
end 8 z. d1 l; } C3 V# q( K, wend - B3 G- V4 K! O: x1 W$ t%做n次迭代,每次迭代都更新D(i,j)和path(i,j) 0 g3 \7 a# \+ Y8 |; q# R* Tfor k=1:n 2 o7 v- G V% a for i=1:n 0 `* G) P g( c: C9 Y' v for j=1:n6 K1 }8 H( w2 z0 r
if D(i,k)+D(k,j)<D(i,j)( N; ]% h- H/ u- t. k! F, t3 S$ h
D(i,j)=D(i,k)+D(k,j);%修改长度 a7 b2 T& w- r! \$ E6 Z4 @ path(i,j)=path(i,k);%修改路径! g# w ~9 R# u
end 8 m$ ~+ r! h. z( F& _/ ~2 B9 ? end # p, P) z; O+ f- D# {4 Z) D7 G' j end* Z$ `9 f9 }6 J7 d
end 0 l' x6 K& Z7 c, q: p8 |) U8 a: U: a' n7 |
五 模拟退火算法源程序# [. L& h F! z5 i- w- g7 K) Z
function [MinD,BestPath]=MainAneal(CityPosition,pn) , p0 `1 P; z+ J: D* _9 g$ D/ Vfunction [MinD,BestPath]=MainAneal2(CityPosition,pn). F5 {. S; \& @5 h; @
%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 5 b2 z! e3 R4 Y6 C%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...* b' w! b% c+ ^+ Q) V. } y, V
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;... 0 r( q5 A; w. q% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;... ) I. a+ `4 J& \" _% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;... ! M8 m- k4 a1 N1 _% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];! U: p6 D X: ] i& R* B; L
4 r+ ]3 R) D, m! p) q( Z% U%T0=clock- }7 X7 R% X; ~ }8 d# _% s
global path p2 D; $ S9 n6 m4 H1 V o$ w[m,n]=size(CityPosition); : D4 V# W# O+ [; z1 d* c) B7 `%生成初始解空间,这样可以比逐步分配空间运行快一些1 w" D/ N# @0 @. j- w
TracePath=zeros(1e3,m); 6 a- j1 n- d) N2 w/ |! uDistance=inf*zeros(1,1e3);! x2 g [; e1 h4 N
4 z. i2 y1 N9 g) c U6 \D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +... # |1 B4 B' r7 f' Y+ z8 X8 L (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 ); ; N1 j; z7 Q1 a) F3 i# q' S%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)1 a: J+ l6 X# }$ X! C8 {
for i=1:pn ]; X) @, R8 u2 {" s9 i
path(i,:)=randperm(m);%构造一个初始可行解 8 m0 o! C' u2 @* l/ yend & L: J( a/ j, ?! }( wt=zeros(1,pn);3 J6 c5 R5 I# \, c/ r3 Y4 x
p2=zeros(1,m);$ |9 Y5 r+ z8 W/ T" x0 W
& ] W* \7 U$ t! F3 Q* {1 I
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' ); " n9 K0 z" L' O4 `6 hm_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=' ) ;5 K9 ^2 s6 {7 E
%如果考虑到降温初期新解被吸收概率较大,容易陷入局部最优2 ~/ ?$ o" z( f, X x
%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 0 Y* b# Q# T. H7 X, Z%人为的使初期 iter_max,m_max 较小,然后使之随温度降低而逐步增大,可能! ]3 l/ T3 _& y) T% z9 d
%会收到到比较好的效果 9 _, s9 s! K0 l: d3 O! K + {! _; q# P" aT=1e5; & ~" S/ `. Z. {; j* i' }N=1; + G# e3 a4 b' J5 B, W: vtau=1e-5;%input('请输入最低温度tau=' ); . ~: G0 t: Z' M* R5 } G0 @%nn=ceil(log10(tau/T)/log10(0.9)); : s! R0 { A) H+ y! Z0 u7 nwhile T>=tau%&m_num<m_max # `4 S4 ~/ P) p
iter_num=1;%某固定温度下迭代计数器6 ?3 I; |; G) J& C T" @7 i% G7 X
m_num=1;%某固定温度下目标函数值连续未改进次数计算器 9 L& `% J; M; J- o) w %iter_max=100;8 i! T- I6 V' v6 d, W: E3 L
%m_max=10;%ceil(10+0.5*nn-0.3*N); 3 F/ h7 \8 k) b; g' O7 G while m_num<m_max&iter_num<iter_max 2 W1 p* Z/ {( |' Y" }' T* s/ ?0 L %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:5 b3 e2 d9 V+ o
%用任意启发式算法在path的领域N(path)中找出新的更优解4 P8 K, a0 v4 {! Q: R
for i=1:pn W6 @( h/ J, \. _. G9 o. k
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);7 O- o' n* Z* k+ i
%计算一次行遍所有城市的总路程 5 Y. D9 C1 f0 m" w' c1 L [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线 & k* a, M% }/ ~. i) C Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);" B* Z! [- K) `
end) w& k, R, M" T; {7 v7 X' v
%Len1 % c# y; o" u: Z9 c+ d; k5 H: u %Len2 ) {. @1 h! F% ~0 {7 u; _9 z %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand4 l7 v7 j2 `' L* }
R=rand(1,pn);6 E' Q" k- }3 M+ I4 M0 {7 O
%Len2-Len1<t|exp((Len1-Len2)/(T))>R' F/ P3 K% c6 F( z
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0) 5 R& v4 f$ P# G. i9 C& K path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : ); l$ G: K" Y& v/ i) [' T4 n( H: T& H Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)); 2 ^- k4 o9 P9 H; y4 r5 u+ F [TempMinD,TempIndex]=min(Len1);8 |. f( z, v9 T- p, d- x
%TempMinD & l# v7 N6 {4 O+ V TracePath(N,: )=path(TempIndex,: );* E8 c }7 _& m# M {( B
Distance(N,: )=TempMinD;0 A9 q% w6 S4 u" s* A7 _
N=N+1; # }; ~( C a. m& y3 @ %T=T*0.9, f# @% R3 R8 U* ]& O+ {
m_num=0; / t# E$ X. d: }1 d: e) L9 { else $ Y" g! A4 {& d, ~8 d m_num=m_num+1;+ W4 L: v7 L e- {1 j7 e
end/ A' T; N8 q+ E8 d
iter_num=iter_num+1; + B2 p3 r: j, x end3 j" B& Q9 y+ E# o# e
T=T*0.9 0 ~! }7 l/ C2 }$ F# z% B! T1 T%m_num,iter_num,N / R/ M' p$ v/ C' H7 c5 y% yend % n4 @/ U5 x) r$ B
[MinD,Index]=min(Distance); ; F9 C1 E5 c: \5 r- cBestPath=TracePath(Index,: );3 m, N/ ?; }6 r$ W
disp(MinD)+ y/ A0 h# y& b# @+ Z' u
%T1=clock! ?- w; m) }: C5 x7 w8 e0 r) }
- } g+ R8 h" X3 I) Y* |2 l
* I$ V% t& h' [8 Y
%更新路线子程序 4 m9 Y9 J5 A( c9 o3 F. @function [p2]=ChangePath2(p1,CityNum)! S9 j3 N. k( K' L% X
global p2; * e6 R; r5 C8 A1 e) m. }! Mwhile(1)! _/ Q" H" _. K8 }3 r& p. l9 d( U" m9 U
R=unidrnd(CityNum,1,2); 4 Q2 c( t4 I9 T* B6 a# M if abs(R(1)-R(2))>1 ) j. Q. O: G4 ~ [8 q8 ^ break; ' {* r" b5 N7 @- X( {# |1 y end0 G |& }$ p# S3 F# J# x
end( F4 a/ \. Y J# m; P, H
R=unidrnd(CityNum,1,2);. K" N0 d+ W7 P- E0 n! Y* Q7 C
I=R(1);J=R(2);1 F) q9 R9 j# C4 W0 l1 P: s
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));7 t0 G& _! I# L6 q
%len2=D(p(I),p(I+1))+D(p(J),p(J+1)); 7 ^9 y1 c' j; J' |) Y/ Aif I<J1 x* H" Z0 Q( K: S( z: A: t
p2(1:I)=p1(1:I);) M" b y) S- }$ S" e% z9 C
p2(I+1:J)=p1(J:-1:I+1); V# z' F9 D0 m) E6 c3 } p2(J+1:CityNum)=p1(J+1:CityNum); 8 P0 x" J$ ^, }else % Q5 f- B* G, ` P# Z6 g- { p2(1:J)=p1(1:J); ; _8 Z; V, i! Q7 T3 ~ p2(J+1:I)=p1(I:-1:J+1);! ? c, e# u# _1 W5 b
p2(I+1:CityNum)=p1(I+1:CityNum);! i- Y* a: O4 S4 y% ^
end( X9 n7 w; M9 k8 O
' j: |" Y7 X% n: C
六 遗传 算 法程序: - O9 i3 `2 L o 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! ) p$ p' @4 V- G6 o / Y5 i. [9 d! G, S- {4 }; F9 X7 k/ Gfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options) 8 Z p9 C$ l2 R/ n% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) 5 T0 Z2 i1 [# Y% Finds a maximum of a function of several variables. - D; D/ K W" z7 a! _% fmaxga solves problems of the form: 7 S" w" A( Z/ z3 ~) @% max F(X) subject to: LB <= X <= UB ! k( U# q3 N4 t, X$ R5 `% BestPop - 最优的群体即为最优的染色体群 ; o5 |% p* l; _8 z% Trace - 最佳染色体所对应的目标函数值 7 l# ~) i- Z+ W& I3 z% FUN - 目标函数 4 |, U5 b" {0 k" P% r- ?* [% LB - 自变量下限4 t/ |) Y1 [, s$ A1 }9 p( q
% UB - 自变量上限 9 O* K# E* |$ o7 [' F, r9 p" c% eranum - 种群的代数,取100--1000(默认200)( o+ _1 b m- P, M; s3 I( R" m$ U) a
% popsize - 每一代种群的规模;此可取50--200(默认100)/ o1 F, k4 E. {0 _! t; r
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8) 4 ^) O# b# M0 \' T% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)/ ?, p3 z0 U" u6 B# `0 M& z. q6 t
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2) ' C' c; F V1 y5 v* h/ I4 Z% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编 1 c w0 C, ^* M. h%码,option(2)设定求解精度(默认1e-4); ~6 r) x1 h& w. _: ]
% 6 l/ J8 `. O" x% ------------------------------------------------------------------------9 {" n; z k# D! N) q
' z0 f% a# g4 `, CT1=clock; 6 I; }4 m6 p5 Z0 z+ Iif nargin<3, error('FMAXGA requires at least three input arguments'); end! a0 Q' W9 g D6 `1 p
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end. g6 Q" E8 H, d
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end 5 m o6 f( G7 \ t! `if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end 6 m q _6 ^- I9 O! }8 u: dif nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end$ z% }( b9 Y+ b- Z% V7 G( t
if nargin==7, pInversion=0.15;options=[0 1e-4];end ; e+ \$ E1 Q2 B. d$ gif find((LB-UB)>0) + Y% T1 ?. I* i, f$ U$ m0 h+ ^! T error('数据输入错误,请重新输入(LB<UB):'); * S _% I1 O& {end 0 G! g* Q) R( ~# M" B, Es=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000)); % r4 Q7 N: s6 Y3 Hdisp(s);9 U3 G P7 y- L% v
2 L6 Q) T& c* R: W2 \) o
global m n NewPop children1 children2 VarNum ) q, k+ t3 f& A" U7 U. u/ f : V( B% ~. ~7 [& e6 }: \bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);4 O" k- Y% K5 h/ N. p3 s$ Z
precision=options(2);%由求解精度确定二进制编码长度 & `8 o1 H; Q* [' d$ J8 \bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间- a; Q6 n! @. W( N3 r H) ^
[Pop]=InitPopGray(popsize,bits);%初始化种群 9 m& b9 N1 ?+ e0 ]1 A8 s/ E[m,n]=size(Pop); 8 }4 w1 e1 m x+ @, ?6 ]/ \2 x5 UNewPop=zeros(m,n);% x9 E; A9 e' A8 i
children1=zeros(1,n);( s% F9 v( \# _/ E+ ^; p9 w( h
children2=zeros(1,n);+ j" \5 I6 ?0 K( ?, S, p
pm0=pMutation; " u) I: i: g& r, N8 rBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace$ L9 o3 n" P* y" G7 y
Trace=zeros(eranum,length(bits)+1);' i8 _5 c+ y# K6 A! P N1 H
i=1;/ ~ ^' n4 l, M- {) \% j
while i<=eranum ) Y, M2 b! ?3 T* l" J7 o for j=1:m ( T9 f! u0 E f; n) z. T6 P! R value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度 / @ E0 b/ Q$ j: {) u end " S5 Y; q' ?# a5 Z( f [MaxValue,Index]=max(value); , d% X! c" X2 } BestPop(i,:)=Pop(Index,:);/ N+ Q( ~: u& b+ k+ p' p
Trace(i,1)=MaxValue;1 T3 B5 K) T1 x) S. [8 o1 |. H, f
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits); , q0 p2 q3 c& K6 i4 e [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择 # J1 m3 b3 ?; s6 b[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));% _3 t4 o* d) S9 S
%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率5 ^% g" h: b! y% P& Y4 o4 X
%round(unidrnd(eranum-i)/eranum) * v# R7 f/ |- N% j/ v1 h [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异$ f/ E5 G3 T: a6 N; X1 ~
[InversionPop]=Inversion(MutationPop,pInversion);%倒位 |5 d7 N5 k2 A/ t6 r Pop=InversionPop;%更新2 h) I/ y1 c- J5 t8 v2 _" A6 l
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); , h+ C, [4 u0 o& y. X) ^, ]0 }0 h. [, U
%随着种群向前进化,逐步增大变异率至1/2交叉率 k. f$ I v- T# A2 `3 [* y p(i)=pMutation; 1 ]* z% x W# g' u i=i+1; ( W" r: f( ~3 ^* v1 Y; d* n2 F& nend & |" Q& l4 U" ~0 pt=1:eranum; 3 l# F# W1 t7 b7 ?: k1 ~plot(t,Trace(:,1)');: ^: Z0 G- l1 P9 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)'); ; D) g2 W2 W: g2 \# L, H[MaxFval,I]=max(Trace(:,1)); ' j0 X$ Q2 }& h) {X=Trace(I,(2:length(bits)+1));- T& \( m6 @/ L s* p/ _
hold on; plot(I,MaxFval,'*'); - Y/ _) E. I' u! ?) M6 }6 ]text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]); ; A$ S# n# V- R6 p! vstr1=sprintf('进化到 %d 代 ,自变量为 %s 时,得本次求解的最优值 %f\n对应染色体是:%s',I,num2str(X),MaxFval,num2str(BestPop(I,:))); 1 ?* R! m$ W6 y: Zdisp(str1); - E" O, C2 \) P) }%figure(2);plot(t,p);%绘制变异值增大过程 7 ?( w* m9 c7 ^. g Z, d) cT2=clock;+ r8 L3 C+ F" Y+ M
elapsed_time=T2-T1; `; G9 h3 \' A) c( F- n; z! Pif elapsed_time(6)<0 # W0 X# R& e: u: F. ^ elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1; 1 U3 V. I0 G K- m& U8 I) `end5 k h5 f$ Z( m0 y/ }
if elapsed_time(5)<0 5 s9 y- G5 v9 V: G9 _ elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;3 d( ~! }2 S( |' }3 ]! b
end %像这种程序当然不考虑运行上小时啦1 k( b* G$ R( B
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));' X/ ^( K, b! n+ Z% x
disp(str2); 8 \) F7 f- \+ S; j {8 P6 I/ i ^9 p* W# L" \; ?
* j+ @+ X- ^& L1 h5 V* x5 X8 x D
%初始化种群7 [& T* { G& H! P& 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 , [4 B% Q+ J. z/ afunction [initpop]=InitPopGray(popsize,bits). ^! q" V% J% u. O# w. `6 ~! `0 f. k
len=sum(bits);# m z7 b) S7 K$ \9 |, k/ j7 q. t5 w
initpop=zeros(popsize,len);%The whole zero encoding individual% m6 F" P) O& s _
for i=2:popsize-1 7 e2 i0 g$ x* r7 s3 O pop=round(rand(1,len));/ e a) ?" ]: c6 c& B3 U# Q( u
pop=mod(([0 pop]+[pop 0]),2);9 N9 x& V2 X* u: b5 {
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2) 8 R3 F; h- i; G8 j. H %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)) [$ l# q* T- f3 t0 j
initpop(i,:)=pop(1:end-1);/ S4 q/ ~5 c' z
end& w8 ?5 C8 V8 h* V& M0 g' v6 k
initpop(popsize,:)=ones(1,len);%The whole one encoding individual1 J5 N# U& M5 h7 B+ f4 }/ {% E# d# ^4 R
%解码 N! b J5 d3 s c O" k9 m8 ?4 {5 ?9 j0 ?* I1 y
function [fval] = b2f(bval,bounds,bits)9 `0 y$ v; X0 E% \7 F% T9 x
% fval - 表征各变量的十进制数 ; @2 N! E9 M# B5 \: Z5 E3 M% bval - 表征各变量的二进制编码串 2 g& [5 @) B3 L) B- X% bounds - 各变量的取值范围 , O0 i8 w. K _9 Y& z% bits - 各变量的二进制编码长度 ; z3 b* _+ S& _7 _5 D- G M8 bscale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables ' m; H [+ N5 L6 F& r3 unumV=size(bounds,1); , S+ O( K ]7 N }cs=[0 cumsum(bits)]; " q6 p( r$ C- H
for i=1:numV1 @- W" [! o( d, W4 I% m. s
a=bval((cs(i)+1):cs(i+1)); E: g7 q/ J0 B9 u
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1); ' P3 @% C$ V( r+ ^3 z( T5 tend7 k" s8 E2 H( q' |4 F4 K
%选择操作" k1 b* C4 ]8 E8 x8 R& V$ i# R
%采用基于轮盘赌法的非线性排名选择5 }) A S/ ?) \% m1 R, F. J; W
%各个体成员按适应值从大到小分配选择概率:: S+ A+ e- \% E0 p$ }# q* c) ^7 t" [
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1& l3 H- ~$ x1 Y$ E) N) G
1 a: r2 n' H2 F( q* Lfunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)* _( Z$ P5 _' g2 _ w
global m n % @9 I& U' W: `: a. V2 tselectpop=zeros(m,n); / `+ i3 u* t( `7 Gfit=zeros(m,1); . N* r$ x7 k/ N; }* [3 \for i=1:m ( x- Z1 E" w$ b* ?. x fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据 x$ @! J( V G3 ^end2 X+ g+ W* @' W
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)1 r, B4 r* O$ ], t1 Z- k
q=max(selectprob);%选择最优的概率 % h/ S6 V. ?9 ], ?2 U# A8 G5 N8 Ox=zeros(m,2); 6 ?6 b* \9 H. l" J" Y0 Zx(:,1)=[m:-1:1]';! o9 L' J {& B2 ^5 m
[y x(:,2)]=sort(selectprob);2 }! k. n4 o u9 g9 Z' U
r=q/(1-(1-q)^m);%标准分布基值 / A( v4 A2 C6 m8 rnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率 ( z3 l' t) B$ p/ Q" Q; tnewfit=cumsum(newfit);%计算各选择概率之和 5 e5 A. }' [% O1 ~( mrNums=sort(rand(m,1)); * u3 D0 v1 y! ^1 D. o' [1 {fitIn=1;newIn=1; , Y5 f8 x5 n& q( t$ u; ^2 \while newIn<=m/ I" T o: s% b% D7 W
if rNums(newIn)<newfit(fitIn)8 {3 k- N p7 d9 T
selectpop(newIn,:)=pop(fitIn,:);& ~6 X2 x9 G2 N& `2 m6 u9 \
newIn=newIn+1;" I) m6 m$ I. U& G. R- T# k
else 2 I) V+ v4 C+ s/ G; { fitIn=fitIn+1;( ^5 O8 ~( Z+ U% [& J7 \1 e* x; M% W
end# ~1 g* X! e' |$ v
end0 Y- O0 Z; U' \1 k' K+ a% ~
%交叉操作 8 g1 l9 w3 p0 @: O1 o" }; W8 Xfunction [NewPop]=CrossOver(OldPop,pCross,opts)7 {8 G! I* P+ m) I
%OldPop为父代种群,pcross为交叉概率! R, b) h5 O7 {7 _$ H
global m n NewPop 5 \1 Q* V" s# W$ vr=rand(1,m); % h5 O; i& T, Ty1=find(r<pCross);+ ^3 i; v* O0 P d9 n3 O* T
y2=find(r>=pCross); , e1 c$ v {; E$ s2 vlen=length(y1); ) u8 \% Q4 {( J% W) n) B; pif 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& m# [+ X' K) l# f( R
y2(length(y2)+1)=y1(len); % |7 U# Q3 A0 s/ U4 Y: } y1(len)=[];7 m3 X; O; ^* S; e* a3 c- d
end+ b% }8 }# r1 ~; E& g+ j& s! M
if length(y1)>=2( `8 m4 ^6 ?) b% E
for i=0:2:length(y1)-2 & \+ a% U9 O/ Q if opts==0 3 [! o% l# E3 p% U) H6 D [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:)); ! v6 c% I, M( `9 n2 g/ E, f else2 D1 c' m9 [+ @9 @6 M$ _
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:)); 7 L& h1 P2 x" g; L& e0 ?! I+ A end " \8 J& W7 ]& h0 o8 y) T end ! a2 w! s# m1 j% p9 l+ g
end4 I+ Y# ~; f0 |- Y/ m8 H# k
NewPop(y2,:)=OldPop(y2,:);( l; z; X% L6 X5 X8 f
+ ]! r( S1 c7 b4 y; |% ~. ~; ^%采用均匀交叉 6 G' R6 ^. R! ]5 z* s$ z, l
function [children1,children2]=EqualCrossOver(parent1,parent2). l$ t3 l1 Z6 d+ q
0 ^+ S, F7 c) ~( W* X, jglobal n children1 children2 * a: K% M3 m3 U- p f
hidecode=round(rand(1,n));%随机生成掩码8 v7 @0 V2 P& [% n) n
crossposition=find(hidecode==1);7 B2 O) S( e3 I8 X8 A
holdposition=find(hidecode==0); % V! A" {" y5 w2 @children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因. e% z+ J. u9 g1 p6 z+ ~/ c
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因1 H8 C! e) F. R& B) o
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因' j2 K9 k+ _3 v; i& P/ S
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因 8 w, V4 _( I7 I% v d- s9 ^+ y1 [( a
%采用多点交叉,交叉点数由变量数决定 6 @& Q7 o6 Z0 S* }$ T; E) Z+ x) E ; m- `! D8 |- z. M/ v* rfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2) 4 B5 j1 m4 o/ k 9 p9 H3 R' H; n3 S, F; s# `global n Children1 Children2 VarNum , U7 d" `+ v; o: E/ nChildren1=Parent1;2 ]7 \8 H- U( c; U# u
Children2=Parent2; R0 F# i0 t: U3 w3 D' k$ Y IPoints=sort(unidrnd(n,1,2*VarNum));2 @8 r: w; M) s
for i=1:VarNum 5 \* n# q% v9 I* f ?9 a Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i)); 9 M" K5 Z8 o6 A* j Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i)); 3 v- F/ K; \8 v: B4 G' \end# n% q& K. t+ M# a+ X0 e
8 y2 ~9 x4 C+ `0 I%变异操作) I5 p* b0 A0 a" I
function [NewPop]=Mutation(OldPop,pMutation,VarNum)+ g1 `; p7 s9 ^6 K0 _7 ^. q
# n, o; C2 G& ?% \: ]6 H C2 v
global m n NewPop 8 D( O9 }( y& I0 nr=rand(1,m);4 c/ R# ]1 H; F5 r# o
position=find(r<=pMutation); ! q u1 q6 e+ c+ c* i. D1 \; y) X2 flen=length(position);; a9 [, t$ E) d" R6 S/ v) w5 j
if len>=1' Z: s: H5 r. T" @8 q
for i=1:len . h' J b/ `0 C2 ^0 B. Q k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点2 E- u B3 F( P$ A. F5 ^) {
for j=1:length(k) $ R9 w5 u; i7 J' _3 d% ] if OldPop(position(i),k(j))==15 u) T$ }( c& }; x& ~7 R
OldPop(position(i),k(j))=0;3 H6 |0 O# a7 N/ M" y" `
else0 O& X7 {9 D7 X; k& F2 P; Q6 o
OldPop(position(i),k(j))=1;1 p2 Q$ o2 x4 _; w% F% W& h" j
end( Z$ q Y& B4 P3 d$ z
end . \ X2 c) M( B7 v end9 ?3 F6 n% h \5 v5 z& @
end) ?3 p1 M9 n0 [5 W
NewPop=OldPop;6 b5 L6 m; z2 [' B$ d1 z9 h
* F8 }2 e* k0 V. _%倒位操作 9 c( X& ]2 d% S" c% f0 Z$ p! ^4 X5 @8 ]) x6 }( E
function [NewPop]=Inversion(OldPop,pInversion) ( E! |* O0 f! O/ j& t8 a) U2 `$ X* R7 |
global m n NewPop 8 M0 N( a' B- l8 o( k. p JNewPop=OldPop;4 S4 H* M2 B; Y+ z& b
r=rand(1,m); * Z! J/ c$ l$ b. }- s1 `PopIn=find(r<=pInversion); 5 ~- s3 O7 U* h$ ^. Z0 t# G' dlen=length(PopIn);' G8 U/ p, |" s$ F: ?1 N
if len>=1" O4 i( s ^$ {9 N! |6 e w
for i=1:len * I! m' w# [ V: F3 q d=sort(unidrnd(n,1,2)); 8 O* @1 I% R8 D" G' J; U if d(1)~=1&d(2)~=n6 b1 x6 H3 _0 b8 p
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);5 R( y* F. k3 _/ L5 m+ n! ~
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));, o R) k( k$ o/ [3 j
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);: p6 e- L' V n( w2 F8 y
end M \8 P/ g) J- t
end % T) P3 d) `" N% E3 `% uend 5 M7 h1 S1 p6 \ L ( E- ?' O- l, Z/ X6 I七 径向基神经网络训练程序 - d- A: w% t# M( P1 j6 U ) }9 r8 R: r/ U8 T8 k$ \1 N) Vclear all;, {* v# z$ v0 w; A/ @; } ?
clc; 3 }* I0 r+ F* [%newrb 建立一个径向基函数神经网络, @6 k. r7 _9 g8 W' }
p=0:0.1:1; %输入矢量 J& {2 Z* ~, Xt=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量( F: I5 d) K6 H& _* o
goal=0.01; %误差; Z1 I- w% {' j* I9 v
sp=1; %扩展常数 4 k& P' [9 d" m8 |$ `5 T2 Hmn=100;%神经元的最多个数 4 k; d' {- k' u8 o. f! `3 Tdf=1; %训练过程的显示频率9 ~$ i. z- m) @/ S* N1 j
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络 , y9 \6 F& U! K9 @( E% [net,tr]=train(net,p); %调用traingdm算法训练网络, a7 x8 h$ g5 o+ }- \* w I4 `
%对网络进行仿真,并绘制样本数据和网络输出图形4 }& }6 v3 T1 o6 ?# V& t
A=sim(net,p);1 W( h4 w# `; S2 k
E=t-A;! Q6 x6 o" X; ], v
sse=sse(E);* P/ c, N8 R( T
figure; 8 {) z+ U! t, k# y- X/ b# {# l
plot(p,t,'r-+',p,A,'b-*');8 |( ` A; d1 K) T; B u3 J
legend('输入数据曲线','训练输出曲线'); # ^( G3 f/ {8 R* T$ M6 R: xecho off ' v& U! v X9 A. T! N: f0 w5 E9 x- f( f3 V3 v3 X4 Q
说明:newrb函数本来 在创建新的网络的时候就进行了训练! 0 J# W7 q2 t# F* w+ u l# @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,( i) \) W. U6 M
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! ( ~. S" O% B9 l G3 n1 h: _' I' E9 n
6 q& i+ G# m% Q% h* W; j; l! G8 @训练结果显示:" \3 m% @, u2 G+ {8 e* x8 |4 x& E: K
NEWRB, neurons = 0, SSE = 5.0973 M n6 H4 @% B) I. I; u7 e. pNEWRB, neurons = 2, SSE = 4.87139. j' U$ a3 w' N/ a( B
NEWRB, neurons = 3, SSE = 3.61176/ j' m$ W9 B$ f j" _4 X
NEWRB, neurons = 4, SSE = 3.4875 4 W4 K1 `' t& O% @) H$ A8 dNEWRB, neurons = 5, SSE = 0.534217. ^2 ?# W- x( D/ \" s0 l
NEWRB, neurons = 6, SSE = 0.51785 & ?4 }4 V$ Q3 n& Y% JNEWRB, neurons = 7, SSE = 0.434259$ E( @6 I( ?1 v. u6 O- }, {- n
NEWRB, neurons = 8, SSE = 0.341518 % A) i# p$ v2 S. sNEWRB, neurons = 9, SSE = 0.341519" I8 r: A5 G0 z) L! _% P
NEWRB, neurons = 10, SSE = 0.00257832* I, S0 j5 _: s. W$ z9 w; N
" H+ h; A8 C$ s1 a$ T! ]* p八 删除当前路径下所有的带后缀.asv的文件& P: H3 z9 ^3 ^ Y% L$ q8 R; t' c
说明:该程序具有很好的移植性,用户可以根据自己地) x/ I/ ?2 `: h
要求修改程序,删除不同后缀类型的文件! 2 ]9 V. Q; b+ I+ r3 K" H
function delete_asv(bpath) 7 p! m3 l& O9 p& E& L- C%If bpath is not specified,it lists all the asv files in the current; f+ `$ [$ Q( `7 h2 _, @1 U
%directory and will delete all the file with asv + L$ p& @ X, S9 w( _+ ?7 L3 f% Example: % L5 d( o2 d2 ?% delete_asv('*.asv') will delete the file with name *.asv; , z/ P" f) ^$ C% delete_asv will delete all the file with .asv.3 p4 \0 m: T5 k9 y, _; w) L5 c
, T9 B# G7 w) V* i) q9 d5 \" iif nargin < 1/ B* ^8 |* H; t3 g& A g' ]
%list all the asv file in the current directory+ K S [7 ]( ]$ X- x' c/ }; [) r
files=dir('*.asv');1 ^' D0 [# O4 q
else * D& E9 j7 D% G5 u5 W% find the exact file in the path of bpath # f8 B; w5 [- U8 n; @+ I [pathstr,name] = fileparts(bpath);% M, K( |9 m1 Z! N
if exist(bpath,'dir')$ t, L6 \# K* h B
name = [name '\*']; . I2 l2 G+ w$ X8 R end 0 m6 F; B$ S( s9 G$ V ext = '.asv'; 7 v" d. B( F, \# j3 e files=dir(fullfile(pathstr,[name ext])); 0 ]$ c: Y; [& V) B$ Rend. E# H5 L& G. k: b! N4 k/ g/ Z
9 b+ G! T" f, `+ d; n( rif ~isempty(files) / V+ s7 s' K6 l2 n for i=1:size(files,1)2 ? ]4 o- `2 L
title=files(i).name;5 F1 Z! b" f, x6 r9 \* R/ m
delete(title); + W. \/ h9 ] `8 u, \9 K4 X- }( N- E end ' ^8 T6 h- N& N1 O8 C/ gend5 s R) q D. R/ r# ~) v
2 Y' |) I9 K7 C1 C9 d n% z+ a% @/ Q; M9 R同样也可以在Matlab的窗口设置中取消保存.asv文件!& T3 X! a; |4 S" k8 o0 d1 p