一 基于均值生成函数时间序列预测算法程序' N% }9 F4 U; o4 W4 Y
1. predict_fun.m为主程序; % L% z4 |7 W6 D$ @, |1 Q3 e5 `2. timeseries.m和 serie**pan.m为调用的子程序 . Z, V# h1 Q h # `' |' A5 z0 tfunction ima_pre=predict_fun(b,step)$ `) h0 U. m Z6 @
% main program invokes timeseries.m and serie**pan.m& l; h, N3 y% k! s
% input parameters: : N4 K+ {% r* I$ U% b-------the training data (vector);6 O0 E! d. I) M
% step----number of prediction data;; n2 p6 N8 F/ S
% output parameters:/ _7 }1 ]& \& i+ Y* J' g* I
% ima_pre---the prediction data(vector);" J m: l5 d* ~8 W J
old_b=b;( K3 {/ i; Y ^1 Z) `3 V
mean_b=sum(old_b)/length(old_b); + i2 Z: w5 m2 Q( tstd_b=std(old_b); / x- c3 i1 j' dold_b=(old_b-mean_b)/std_b; ) R( b2 [; D) V8 n' P' X3 R0 x[f,x]=timeseries(old_b); 1 {& Z- o) ~( ^4 _6 v- Pold_f2=serie**pan(old_b,step);: |1 L9 u3 u, [
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;3 t" {: I) X: `! @: `0 j, s8 N
R=corrcoef(f);# V: v! K2 I8 s& @ S
[eigvector eigroot]=eig(R);" ?7 Y$ h9 |' y# _$ n$ r
eigroot=diag(eigroot);+ f& z) D n) r4 {* z) V' S
a=eigroot(end:-1:1); 7 p; B6 Y/ ?; `: r9 Mvector=eigvector(:,end:-1:1);* O4 y0 @0 S4 a
Devote=a./sum(a);4 v: [8 I0 A, r# r
Devotem=cumsum(Devote);! }2 g6 ^2 Q. j% ]
m=find(Devotem>=0.995); 4 X, }% W! G5 ?* |+ I2 em=m(1);) t5 t; M0 g/ M4 _* ]
V1=f*eigvector';9 @# b) m4 o! F% a. [2 |
V=V1(:,1:m); 2 ?6 A: \1 C/ y! l; A% old_b=old_b;* f; t# Q! f1 ^% X
old_fai=inv(V'*V)*V'*old_b; 3 M6 Y; n2 |) m: B; reigvector=eigvector(1:m,1:m);) P$ w: p! p4 k; P: n( ^- ~8 J. ]
fai=eigvector*old_fai;$ `. Q. |6 Z8 q+ O
f2=old_f2(:,1:m);# r; [8 w% E2 Q3 Q
predictvalue=f2*fai;! _' h) i! \$ [& q' n
ima_pre=std_b*predictvalue+mean_b; 1 ^) P6 h$ i$ R( Z" C/ r: y 4 J, \+ @) Y2 d( X' _8 y V1.子函数: timeseries.m 8 T+ d) ~1 ]: X+ |3 S# E0 `
% timeseries program%/ k* R- {2 S3 p) a7 Z" ~! ?* _
% this program is used to generate mean value matrix f;7 j: I- w* Z8 R4 Z
function [f,x]=timeseries(data) : H5 G* J) _6 H& {; y
% data--------the input sequence (vector);6 Z, \. X2 x' M
% f------mean value matrix f;* _- c) `% x) F) T+ F/ t$ W
n=length(data); 4 n8 X- _6 ^$ R, B+ C1 O' @for L=1:n/2 6 b# W* j! t. P( A' K3 D nL=floor(n/L);3 e+ e h. d6 x. w6 [ F
for i=1:L 3 ^1 x( o! t$ j4 e: G sum=0;4 X7 m: Q/ P6 V P% K% }# J
for j=1:nL6 J2 P0 D1 y1 A
sum=sum+data(i+(j-1)*L); 4 L- x# z( b. F9 s$ B$ G end ' n- |, R1 U9 ]$ E4 _0 r+ D x{L,i}=sum/nL;6 y- ]9 L5 q# V" [* M% {. @- F
end / L. f# N0 B- P9 F6 m9 F" Q$ c; g6 j" |* Jend " ~8 c/ U3 M8 H3 l0 p CL=n/2;& i) `; f+ O0 ~4 S7 P1 S: z- _
f=zeros(n,L);. f: \, c y0 F% ?
for i=1:L ) [7 X' A' W$ w0 \2 x rep=floor(n/i); ; O& T! ?1 h$ O$ q! o) I res=mod(n,i); , o) J' g, w/ b, R, e/ b b=[x{i,1:i}];b=b';- Y5 f) t5 g) J% F9 X
f(1:rep*i,i)=repmat(b,rep,1); 8 Q) I: a7 B5 v$ J9 i$ c if res~=0( y$ w5 e4 Y; K4 y7 P7 W& b
c=rep*i+1:n; 0 C9 h* l# g& o; ~. J f(rep*i+1:end,i)=b(1:length(c)); : C5 K& e& g" c, U8 [! x- |" F) R end / G$ K9 c P6 q, D& F: nend % _: P ` g% r- Q3 K8 V a' Q! K+ J6 W" a; j# R% serie**pan.m& O4 f2 v+ C5 C- B7 ?* e8 b
% the program is used to generate the prediction matrix f; , j4 v" C) p+ [8 r- O: Ufunction f=serie**pan(data,step); 6 z& \$ s0 v7 j%data---- the input sequence (vector)& z/ Y9 s$ e! e/ R* s/ u8 L$ {
% setp---- the prediction number; ( Z0 z' X# H; S% w G7 nn=length(data); - `. w/ ? S( k5 k/ Vfor L=1:n/2 6 Q" s9 T) m1 o8 h: o" ~ nL=floor(n/L); $ k0 L, c6 ^8 R. i7 w* D/ ?" A& t for i=1:L3 g2 |, I0 d& M. ~2 I4 t
sum=0;3 b8 d4 R7 P( k! q4 a% ^6 g( [$ ?
for j=1:nL ! C* \8 O, |& W! n2 X4 A sum=sum+data(i+(j-1)*L);# T: U3 @, k6 Y2 @3 v f
end # Q% q3 `0 ~% O( c. A x{L,i}=sum/nL;4 @4 s1 V7 h; `% n( J, d- D
end# D3 p) R. o% ]# Y
end ( g# b9 n5 r4 W' f- P* _) BL=n/2;, D, B* |0 X1 ]- i5 B) B8 O
f=zeros(n+step,L);/ k- t. y: o2 {
for i=1:L / ^- Q9 V- n2 `8 B3 H' B* `0 j rep=floor((n+step)/i); 6 Y9 U, }( L- h/ ~ res=mod(n+step,i); , C, |) S* h7 P8 t4 k b=[x{i,1:i}];b=b';+ ~/ L+ `) I6 n* N
f(1:rep*i,i)=repmat(b,rep,1);. x1 f- b+ b2 E' d4 a% i7 S2 E) l+ M
if res~=0 4 p% E2 {) D0 O8 g3 }8 ~! O$ @ c=rep*i+1:n+step; ! A& F; ]% d* |6 ?+ }: V5 t f(rep*i+1:end,i)=b(1:length(c));9 v( p0 ~7 f; H+ q! L8 |
end/ D1 Z/ m, ]+ a. E" z7 \
end% b F1 ~2 Q) @/ T5 {
5 J1 |! @& F8 o* i% E二 最短路Dijkstra算法" U. c0 _$ x3 K& V# K
% dijkstra algorithm code program%$ b9 j# P7 e) d9 M# U( ^0 L6 s' _ Y
% the shortest path length algorithm# k# |( a5 X" q* Y& T% z: {
function [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint): r) }, o& t4 v ]& s& u( F
% Input parameters: ) R1 c7 m6 l. S, x% Input_weight-------the input node weight! ' l) m' ~# |( v" U3 P& q% X, @% start--------the start node number;! }7 V# x0 R8 z6 V3 w
% endpoint------the end node number;. x8 G( G C; h: N7 z; ]; W
% Output parameters:. u8 A" b- b, b3 E* e; t
% path-----the shortest lenght path from the start node to end node; - D# j5 Z+ o G' H' e% short_distance------the distance of the shortest lenght path from the 3 p' h0 w* t& l; t E: e% start node to end node. $ B. b: k) v% i2 Q) _4 y% P* d. q[row,col]=size(Input_weight);2 X# Y7 T' i9 q6 x) X
0 i* @0 s1 a/ b" v3 Y) y/ q& q
%input detection / ^8 e* {- |8 s6 jif row~=col ' |: `% s2 i; j8 p8 [- u; @6 _ error('input matrix is not a square matrix,input error ' );3 i. | d9 ]% @+ k9 d- }# R
end+ m# b; E$ U7 s* x% T
if endpoint>row: L \7 i, U4 I# u
error('input parameter endpoint exceed the maximal point number'); ' l; j } c, G; c" D) W& Jend & ?' Q- T- e% w) U3 b0 n# M1 f1 P' o# f& @& H' |
%initialization 3 G3 _: b% c& s. w; Gs_path=[start];$ c: X, Z; m" Z$ K
distance=inf*ones(1,row);distance(start)=0;: V% i* F3 j( {3 y1 l8 j
flag(start)=start;temp=start; 9 w8 i. X8 F: D4 `1 [4 t' x9 M, k r% o1 V0 Z% u% f) s3 J/ ~
while length(s_path)<row0 w: I9 ?3 P+ }4 s! J# m; Q# G! N
pos=find(Input_weight(temp, : )~=inf);" |+ Z# g0 O. u" I& |! \" k+ z
for i=1:length(pos) A% Y! Q8 [& u3 ^5 o3 Y3 k if (length(find(s_path==pos(i)))==0)& 3 D# w- O. v; {' b2 w(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))- B3 v4 x( n; L2 M
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i)); ; Q- @6 D, M. `( L flag(pos(i))=temp; & z( i" F- D% ~- d end9 R: a _6 N: t! n
end % c4 S) z! U9 y0 {' H& c5 g9 F( b k=inf; ) C( O2 T+ M. z8 X5 a! E% q for i=1:row ( Z3 f8 g3 l) |; f5 ^/ [) x& p5 U' e; X if (length(find(s_path==i))==0)&(k>distance(i)) m/ `1 Q: b' d8 ~ k=distance(i); ; _: e& h! A: k/ e temp_2=i; I; S8 E% C; ^9 |5 q& \. \% B5 F end . f! w& F o1 K0 D end ! D$ V X; K; E1 W, b6 J s_path=[s_path,temp_2];* ]$ v4 ^2 K8 j5 M" N) U
temp=temp_2;* k3 F8 L6 p+ V) S2 A9 {; g7 J8 o
end / \* Q" Q( }( u2 ?+ ]) n. {* z6 o% \5 o& B; i
%output the result6 z, U/ S, j. \" ?& e
path(1)=endpoint; : [! i o' W( g' I% |# b' ei=1;) }+ K4 B) _5 U5 m; n" m* _- T
while path(i)~=start 8 m1 `+ C; Q( [3 J s( p- y path(i+1)=flag(path(i)); : m7 d( e& o1 P+ O4 K i. g" |4 @; f i=i+1;8 W4 ~5 J$ T' @" ]: n& }* c; G
end4 Z& U' x' q9 M' a' Q
path(i)=start;9 K% \( b2 m# u5 @
path=path(end:-1:1); 8 Y8 G: L! r& L8 H# Y& oshort_distance=distance(endpoint);" o7 [3 S9 X# s
三 绘制差分方程的映射分叉图* O3 K9 R( A- T+ d) S* n# d
0 i9 O4 k+ V; E8 E6 g- o6 p9 Nfunction fork1(a); % d* _8 p1 s9 A& @/ U
/ a# j( V$ s8 k
% 绘制x_(n+1)=1-a*x^2_n映射的分叉图 ( n1 E% \# E! G6 a6 |$ z% Example: / x9 o4 W1 A+ b B
% fork1([0,2]); $ q- L: ~0 w6 @, O5 B. U; t; C' eN=300; % 取样点数 ; r5 L; t8 a1 D$ o/ j
A=linspace(a(1),a(2),N); 5 S$ c: d5 ^% N# `! L6 H% v, p
starx=0.9; 1 N4 i* r: o# M: y7 I9 T" l
Z=[];- ?1 }6 X1 U& [- r0 u5 a' M
h=waitbar(0,'please wait');m=1; u' J' z. [0 ?# T* Afor ap=A; 4 n9 H* l% {+ G# F- L7 S
x=starx; ; ?+ Y" M% n/ Z$ z9 C
for k=1:50; 3 `# M( S- v% Q5 C
x=1-ap*x^2; : V* w! Y# ~( R k+ S
end * r' x9 u# V" p' A
for k=1:201; 6 b& Z( u: \: B d+ K
x=1-ap*x^2; / t+ E3 h' f o# t
Z=[Z,ap-x*i]; ; l# n/ t8 ^% D" L/ S+ t' r end 5 o4 n& s/ E3 B, N: B: X' N( w
waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);# a$ W1 D y) z$ R8 l% G' v
m=m+1; `3 Z: ^( O; {+ i) l
end ' P/ m2 a$ V7 V% i, ^" O# A8 ]; K4 odelete(h); : f! u3 [, W# ~. }plot(Z,'.','markersize',2) / ^# a$ B: r( ~4 C2 U: L
xlim(a); 9 @3 q! V# ?) C4 l4 N + ]# u7 L% N5 _8 C- N1 V四 最短路算法------floyd算法 7 ?* @) |: `5 D- @; k( p) Vfunction ShortPath_floyd(w,start,terminal) 5 _% k Q$ f8 u5 z4 S, K%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;) m/ e9 y2 N9 O6 T; h7 v3 _
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];$ k) i! |3 h! x+ l! b
%start-----the start node; " D& m/ Q# k8 u%terminal--------the end node; 3 ^# U& r/ c! r# C0 ?; Jn=size(w,1);* ]9 L& o+ W" R2 O5 ]. y) }
[D,path]=floyd1(w);%调用floyd算法程序 & N# q I- e$ b: W' Z- y8 r. C0 v8 {, ]+ v+ h7 Y
%找出任意两点之间的最短路径,并输出 8 }7 u. F B- B4 e$ c, pfor i=1:n$ C$ j O. D& r) l1 r! d
for j=1:n . h, T: B- k$ S+ @4 q+ N1 q Min_path(i,j).distance=D(i,j);1 B4 X# L7 e; ~7 a4 r, }( g
%将i到j的最短路程赋值 Min_path(i,j).distance3 `* v( I! Y$ g' k5 a
%将i到j所经路径赋给Min_path(i,j).path& @. |/ I9 O) a- _, s1 Z
Min_path(i,j).path(1)=i; & D1 j- X" Z6 f7 Q k=1; 4 G7 l3 p; n; K$ k; u8 V/ E while Min_path(i,j).path(k)~=j 8 g$ ^: w9 [3 W3 R; I3 V+ i k=k+1; ! m }: I4 D1 m+ U! s& \, w3 {0 h Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j); 8 J) p( A6 `# D7 ]- T end" ^) X/ I* |; V$ u2 ^" z# U1 z8 L
end7 H$ B4 O6 F' V& D
end" ^4 M( b+ c' Q3 U
s=sprintf('任意两点之间的最短路径如下:');, p% L6 ^6 L- o4 D/ V" X
disp(s); 6 J; d, `1 m) m5 g; E* efor i=1:n0 a* G: n e; q- B; X
for j=1:n7 N! Q4 V& H1 q
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...# l4 I, {5 T, M a& P' C; B3 {5 v
,i,j,Min_path(i,j).distance); ; J1 T p% p% ^0 i$ ]0 C t' N disp(s);4 J" C5 Y4 n7 I3 h$ e& r
disp(Min_path(i,j).path);4 c+ e4 M+ ?1 R! V/ F* V) q4 P9 N
end+ r5 i6 y% _3 ?5 b3 D
end ) h! R4 k0 E; }3 _; N+ n* Q) N! h 0 C9 T6 P; U4 C4 {! f+ o%找出在指定从start点到terminal点的最短路径,并输出1 \" L- P; i" n+ {3 R' _$ r
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...) \+ x1 r1 Z: N# v/ C: A4 @
start,terminal,Min_path(start,terminal).distance); $ v. X. [7 E/ jdisp(str1); : m. E$ | a3 T) cdisp(Min_path(start,terminal).path); 8 w6 y: ~1 o# q2 j8 ^4 {7 l9 h, ~1 F
%Foldy's Algorithm 算法程序 7 E- z( X/ t' B- Ifunction [D,path]=floyd1(a) : U- V* V2 ~0 ^4 _0 dn=size(a,1);- E- F. @. w+ l0 e$ j& S+ x
D=a;path=zeros(n,n);%设置D和path的初值 0 M1 K" b( V/ `1 l, Wfor i=1:n 3 j8 s' W+ E" B. p, t7 a3 ] for j=1:n$ q, b! ^/ r- y
if D(i,j)~=inf5 Y3 O% [- @ U8 B* b
path(i,j)=j;%j是i的后点0 s ?+ \" ~# c z/ @7 _
end & L, ]+ Z; \ {% k* s end; ], c% V0 ?: _- _& [9 B
end * K' ?: f* `; O) V8 G$ {( K%做n次迭代,每次迭代都更新D(i,j)和path(i,j) 2 r% o4 y: G6 V3 S: d Ufor k=1:n & t5 {+ d6 p ]% r+ p$ f for i=1:n 2 z' H5 Z; r2 H" @5 O$ v for j=1:n 7 |6 w5 f2 v* V2 G9 g if D(i,k)+D(k,j)<D(i,j)& }; X# D, ~, A$ Y0 n( F
D(i,j)=D(i,k)+D(k,j);%修改长度& ~# o# o" D& s/ U* {7 E
path(i,j)=path(i,k);%修改路径) T. @2 u8 C* q b5 l
end 3 Y% K a; z3 w4 j/ L end# j6 e$ |! m" c8 I- N( C
end3 e( i, A) Y3 M- j
end* |. ]+ Y4 _8 E& H) N2 U v: b5 \
( U6 [. Q1 {$ G. C: ?) L五 模拟退火算法源程序6 s! [8 V& o% T! n- w/ ]: v5 o
function [MinD,BestPath]=MainAneal(CityPosition,pn)& q# }5 b5 ^4 T- I) I; }
function [MinD,BestPath]=MainAneal2(CityPosition,pn) 2 r% ?9 `; e! l0 C; 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 . x8 U5 t1 S! a, }) g9 D4 Z%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;.... m: y% I. J/ A. K
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;... - v. Z, w. ~& u" T3 e( O% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...) c- m% ^( O0 w5 t+ [7 f3 A
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...* X( M0 I$ Y O
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];9 d1 U& _) N% D
* K3 [( v# @! x, E6 q9 _
%T0=clock # N- z& ^8 V# t. pglobal path p2 D;2 w9 N" v7 Z' \9 _) d% E0 {6 D l
[m,n]=size(CityPosition);7 v' o \: c% T t0 E+ F4 g& n
%生成初始解空间,这样可以比逐步分配空间运行快一些 , X3 S D- u) B3 p( F5 q4 RTracePath=zeros(1e3,m); $ \, q$ M& g8 e6 Y% hDistance=inf*zeros(1,1e3);9 `4 B" }1 m4 k; c3 ~3 H. E8 U
5 N' C6 s. G3 o& e9 ~& h( O. d
D = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...7 a) T1 j, D+ S! n' g0 ~& v
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 ); ( C ~. F' ]* w%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵). @. I: n( G q& F2 y
for i=1:pn . d7 v: @( A& a/ V9 r path(i,:)=randperm(m);%构造一个初始可行解7 [/ l2 s5 p) o8 y
end( N+ Q9 W% d, J* K0 f4 C
t=zeros(1,pn); & ?. D( G0 Y: }7 P; J8 C+ r; f5 Cp2=zeros(1,m);3 c( c2 P9 y4 ~' s
9 Z2 M& C$ B' n. V7 {" ~8 j4 N
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' ); ) K Q% ^) h) M9 J' L5 _' }2 om_max=5;%input('请输入固定温度下目标函数值允许的最大连续未改进次数m_nax=' ) ;: E' ~) v1 B: b2 h# u
%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 $ k; J# f: V2 s%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$ h+ F5 H9 C7 G3 w4 B/ O/ c: f! U& S
%人为的使初期 iter_max,m_max 较小,然后使之随温度降低而逐步增大,可能' H$ q+ [# R" Z' F/ k, K8 l2 n j
%会收到到比较好的效果 2 h1 x1 H6 T" y( A* ?& X- g1 M 5 t1 z! F. R4 qT=1e5;. R& ]7 X% e2 ]" W' h
N=1;% r8 V d9 w( @5 G0 d, m
tau=1e-5;%input('请输入最低温度tau=' );8 ]( `5 w( u+ R3 z* g
%nn=ceil(log10(tau/T)/log10(0.9));9 A& e/ w5 o X, d' w! y6 U7 v
while T>=tau%&m_num<m_max * P) v& Q9 n1 Q7 ~/ B1 M) W# ] iter_num=1;%某固定温度下迭代计数器 5 D$ B' l. F0 V' f" m3 L, G m_num=1;%某固定温度下目标函数值连续未改进次数计算器/ Y7 f$ z3 p6 D4 x2 W
%iter_max=100;3 O* O4 [, ]* c9 r9 Y3 n& W
%m_max=10;%ceil(10+0.5*nn-0.3*N);& y4 B# M/ U1 Z4 E: q- ]
while m_num<m_max&iter_num<iter_max3 I/ \) F/ E. v# a" {
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:3 D! J* }# X9 E4 ?' Q5 ^/ B
%用任意启发式算法在path的领域N(path)中找出新的更优解 * o" U' S: P# P for i=1:pn # M+ a0 W: Y @* X. x Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);/ k' A1 }+ f2 i" N y) }. s* R# Y8 ~: T
%计算一次行遍所有城市的总路程 9 I* C( @. f* q& ]: M G$ p9 ? [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线+ z- T3 I" C6 G! X8 g( j1 f
Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);, G6 W7 J+ U- m+ b
end 5 C. {1 [( v" W6 L %Len18 B) }% b4 E4 j+ _
%Len2 2 `: f0 U/ |# F) }0 D8 w2 Z %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand1 H& C, y9 p d9 g q- Z1 |: D
R=rand(1,pn); # x+ w* r2 J1 u; N$ [# I, L %Len2-Len1<t|exp((Len1-Len2)/(T))>R' h) i, b' Y; D- w5 K
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0) 5 Z9 L! u4 x) S6 T0 q6 Y5 O path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : ); ) m0 ~, S9 ]+ ^& b Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));* u& U( j- [+ Y3 S( \8 m
[TempMinD,TempIndex]=min(Len1);* M( f$ W, ]- O) o" a
%TempMinD' V" n/ C8 K$ f- H( _. j
TracePath(N,: )=path(TempIndex,: ); 9 ?7 i% H U7 d: m Distance(N,: )=TempMinD; 4 M5 k' T& J' v! L+ G+ x N=N+1; @/ G) n: V; Y" K; w9 |9 ?4 L
%T=T*0.93 N( f' d7 g0 R1 _$ x
m_num=0; 5 ~& r+ v: D% P! _. | else ; o/ S& a/ ^) p; \5 ?" N% N m_num=m_num+1; 8 n3 R5 A5 L' r! d end : D7 b' E0 d! u3 c! _& i iter_num=iter_num+1; + E3 Z) J: G+ Y) n/ ^2 L end : Y+ `; D- T u5 u% | T=T*0.9/ B0 j3 l u" e
%m_num,iter_num,N & ?) V `* W1 ~, Tend , m) E4 b7 o1 b# b t[MinD,Index]=min(Distance);& X: E: Z" n2 _! \
BestPath=TracePath(Index,: ); ! b% W5 X! A K6 V9 Sdisp(MinD) . \9 u- F6 N# l) J%T1=clock ' ?. Q2 B( Z7 E3 } 3 H6 [, P: M/ I9 Q% q; k
+ L p, V, H/ v$ [3 D# c
%更新路线子程序 $ [8 ^: O' w+ t, V4 ifunction [p2]=ChangePath2(p1,CityNum) 6 p3 D4 R3 t1 k# G5 X3 ~global p2; ' r* J9 t/ h" w) m* [while(1) ?. b }, e" A. e* o; w
R=unidrnd(CityNum,1,2); 2 o0 i' p U/ x3 U/ w# E+ R if abs(R(1)-R(2))>1 0 T$ u5 L2 M7 q- v. n break; 3 ]- `4 V& C3 c8 t: K8 b8 n3 {9 e end 1 C+ g' c' X/ S: _+ \end' N: f* c5 K3 B. `, z
R=unidrnd(CityNum,1,2); # M: f" n; j- o) L4 r \+ AI=R(1);J=R(2);; u' U/ T4 w3 x
%len1=D(p(I),p(J))+D(p(I+1),p(J+1)); 2 B' @, a7 u5 a) o$ w; C) L%len2=D(p(I),p(I+1))+D(p(J),p(J+1)); + \. h2 Z1 r. ?- a, zif I<J 8 P5 G9 _3 O9 _( i p2(1:I)=p1(1:I);6 o$ w4 g9 R6 C5 |* Z/ u
p2(I+1:J)=p1(J:-1:I+1);+ n9 l6 E' U d* v9 p
p2(J+1:CityNum)=p1(J+1:CityNum);& k% h# M8 `1 F; }
else8 N' T* m' `4 X
p2(1:J)=p1(1:J);8 q( d7 V; S; f4 W% S+ K$ [4 |
p2(J+1:I)=p1(I:-1:J+1);) }, s6 S* _2 J
p2(I+1:CityNum)=p1(I+1:CityNum);0 N7 l! o# u% |
end 1 r+ t( Y' e3 {$ S% U0 v# P" f8 D7 n' `) L
六 遗传 算 法程序:& s2 w3 W7 y% c$ t
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! ; }8 h9 ^: _, n* T# e$ R, D1 C7 \* T( ~
function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)/ D( }+ F6 N/ m4 v! e4 m, S' d( w
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) : ^" m% e+ M* t, N# l b9 O
% Finds a maximum of a function of several variables.6 ^+ O5 w8 O3 P9 ?$ S# h7 B* i" V
% fmaxga solves problems of the form: $ c' n. n( k- b
% max F(X) subject to: LB <= X <= UB ) l( _' o3 b# Z O3 P& Z% q( ]( |% BestPop - 最优的群体即为最优的染色体群 % n; V' w$ ~; ]# Z% Trace - 最佳染色体所对应的目标函数值* w. n4 |% V/ ^# B, N
% FUN - 目标函数 + U) t e% v) ~4 P" w" h8 \; n2 ^% LB - 自变量下限 4 M! q2 N: w7 H$ v7 O% UB - 自变量上限0 k0 d2 B( H/ w( e8 B& S/ ]5 P
% eranum - 种群的代数,取100--1000(默认200) ( n7 @& ]& ?9 V+ |9 N7 D% popsize - 每一代种群的规模;此可取50--200(默认100) , n3 ^9 U) l! d9 H% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8) + }7 D3 w& L( ^! E0 g" ^ Y3 S+ q1 v) m% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)- W g( S! ?& J
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2); y- _- ^$ ]. T6 S w
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编 % ~% ~3 f9 e. H4 q6 v v9 [%码,option(2)设定求解精度(默认1e-4) " L& a- k) i! Y. B5 L% ; N1 G+ P4 I# I# v6 N1 |% ------------------------------------------------------------------------- K0 l( L0 s' y- X( W
; d# a. ] s" U( i! V! P* F
T1=clock; & [; }" A$ t% ]; A8 ?$ _8 W0 Dif nargin<3, error('FMAXGA requires at least three input arguments'); end" g- b) L+ q$ f8 L2 ?$ B
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end : a0 A- h+ Z5 |6 c1 s% ~if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end4 F, C, d8 M. V5 e$ r2 `
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end % ^* ]+ U2 E' S9 ^if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end3 B/ P& [6 U1 z% C3 w- |1 z, U9 H
if nargin==7, pInversion=0.15;options=[0 1e-4];end' Y# \; U% a! S) v& P2 {
if find((LB-UB)>0)# Z9 Y8 z8 G: W K) J9 A$ E- p1 v
error('数据输入错误,请重新输入(LB<UB):'); $ Y, O/ w) M! t u2 o* Oend 8 O& C( D: H( Q: P! E, S, E' [s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000)); + z2 c" R' |6 Y2 V; fdisp(s); / O A U) k& C# {1 |( g5 c3 B) b4 b4 z, O
global m n NewPop children1 children2 VarNum( y' E4 f( G5 d3 p$ V: {* R
7 o2 c5 l1 K ~" wbounds=[LB;UB]';bits=[];VarNum=size(bounds,1);. t! R8 }$ S; L% I2 N- r
precision=options(2);%由求解精度确定二进制编码长度( \& W6 @! Z+ l4 x& }! _
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间 2 j, J+ P# R. T) J& F$ Q: Z[Pop]=InitPopGray(popsize,bits);%初始化种群( f& Z% ~, v2 A U
[m,n]=size(Pop); H& v9 a3 k: A5 j# }- f. W: FNewPop=zeros(m,n); 0 V5 m2 L6 p* _- S' e8 H' ]+ y0 `. cchildren1=zeros(1,n); 6 J: p. G4 j. q# ]. Schildren2=zeros(1,n); & ^( L+ x% t" P, k: K! _4 h' ~pm0=pMutation; 7 g n" h3 f' o: ZBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace 2 X! R# `5 c. `1 c* cTrace=zeros(eranum,length(bits)+1); ; \, T9 e7 I5 @8 oi=1;. T& ~; e! I5 B1 g- a
while i<=eranum 9 X% X, l; H) l/ l2 O; ^# }7 r4 i for j=1:m 0 J' z% B4 O- |* d+ _, a value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度0 Z4 F9 m+ O u% _3 u
end4 t% m2 x/ b- A
[MaxValue,Index]=max(value);9 u ?1 j0 i/ O4 l+ r
BestPop(i,:)=Pop(Index,:);% Q$ {6 w2 ^7 s& ~7 L3 p1 i, I
Trace(i,1)=MaxValue;4 C1 d) O5 B$ w/ Y4 |; E' W4 P
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits); * Z7 n* k9 T; {& s( _2 L [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择 w8 {' Z' Q* B; g( Y/ I[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum)); 1 D+ \' I" l& Z3 Y/ A%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率$ {! {5 ]$ l: [* _5 V0 I3 J, G7 J
%round(unidrnd(eranum-i)/eranum)6 `) U! H5 n, i( J" D. P
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异 * t0 c3 X% q3 s; q! p5 A! [9 R& I) Z [InversionPop]=Inversion(MutationPop,pInversion);%倒位* Y0 B# }) d( j0 H5 f, @/ f' }& g
Pop=InversionPop;%更新2 S U; O( U P( r" }6 d: Y n, R
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); & b6 o$ U; S: D0 f" k- M
%随着种群向前进化,逐步增大变异率至1/2交叉率* O- T1 z0 ^' d9 D d5 h
p(i)=pMutation; ) v7 W9 r5 U( x d7 F0 O- k. T$ o: P- Q i=i+1; , ~% F7 x/ E. e" V* Q' b- V. s1 xend ! V) f* J) K Z$ Xt=1:eranum;# x1 M5 J3 G& Y! }- a* s/ c/ ~
plot(t,Trace(:,1)'); . s9 \( @- U1 h. s* B! Dtitle('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)');# F% z# k D% J. O) {8 n
[MaxFval,I]=max(Trace(:,1));* G9 {/ s6 w8 f' B, O7 M( G
X=Trace(I,(2:length(bits)+1)); k. f8 ~0 O) m3 s$ q
hold on; plot(I,MaxFval,'*');8 d; i( M5 h+ `" g c
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);5 H* u$ b. y& ~1 p P
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,:)));$ P7 E; x- V9 Y0 ~: @3 [: ?8 Q
disp(str1);2 t# l" H) v. ]) p p ?1 A
%figure(2);plot(t,p);%绘制变异值增大过程 ; W0 Y/ L, U+ X# x& Q! B2 N$ ~T2=clock; # C' K$ }, b& Q, V2 H5 uelapsed_time=T2-T1;' [! ?' O! S% m3 L. @4 l
if elapsed_time(6)<0$ M( o8 W8 m; `# X _ r
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1; : J! b) F- ^) \" r) j, i7 Wend , _6 U! F0 r. ^2 F4 T/ gif elapsed_time(5)<0( ?, ]6 n6 z! V- j8 k& z
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1; 2 ?" D' ~; X+ s; q% ^1 _end %像这种程序当然不考虑运行上小时啦" B7 O) y+ J* M+ t( n
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)); " a6 ]! S( f2 v, Kdisp(str2);/ [+ K1 }3 H% j# ?" B& P
8 f+ n9 f6 Z9 s9 L& R + E) [4 a! V2 t3 o+ [: ]%初始化种群- J+ \+ x$ [4 U
%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- k' O, m3 _* y% ~# {" i: e V* _5 {
function [initpop]=InitPopGray(popsize,bits)8 a& H9 }/ ~) y% a/ L7 {: s
len=sum(bits);8 o; D$ w' {/ C2 J' F7 R( L
initpop=zeros(popsize,len);%The whole zero encoding individual }2 z% G ~. v- N1 v7 G, ifor i=2:popsize-1 6 F7 }3 ? L) g) h k0 a0 J pop=round(rand(1,len)); , \+ k3 X& m3 ^8 N% w pop=mod(([0 pop]+[pop 0]),2); 9 C- f4 ]+ R9 B0 Q- x. p %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2) % W7 X; Z9 ^2 |8 l7 a+ @' D7 G %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)2 q5 N6 |7 V7 j
initpop(i,:)=pop(1:end-1);/ |* G) r! V* t; e
end: E: C* b$ j3 R+ r- ^8 c. R2 \
initpop(popsize,:)=ones(1,len);%The whole one encoding individual/ }& W0 ^* L& N) g2 q/ M- _
%解码 D3 g1 g3 B/ c" N* c! b. a
8 K) q0 D' Y4 c3 ^& sfunction [fval] = b2f(bval,bounds,bits) 4 V+ O! L/ I0 _% fval - 表征各变量的十进制数0 ? Y2 k4 A8 O
% bval - 表征各变量的二进制编码串1 T* B: J: c- ?7 E
% bounds - 各变量的取值范围 / V5 l# F9 g3 {, l1 R% bits - 各变量的二进制编码长度; U2 V) k* G& E4 ?2 m3 x
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables 4 U! {% u$ ] Q, D9 b$ _0 g) TnumV=size(bounds,1); & z- d8 l3 m f) X6 e( ccs=[0 cumsum(bits)]; ' D: T$ z- ]& b5 j! b
for i=1:numV ( A% z) n# s# y! L a=bval((cs(i)+1):cs(i+1));! [9 c4 y$ j' r8 ]* q1 U1 Z4 f
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1); l" M# x1 ^, `1 ^( f& n+ V4 Y Z
end1 V" @! ^) |- Z9 y% Q# d- r
%选择操作 ! N2 f. u% U3 z& I%采用基于轮盘赌法的非线性排名选择 4 P5 h* [% s. n8 P" ~% x%各个体成员按适应值从大到小分配选择概率: # u" P* T7 P: d8 ?%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1 : u% R& G7 x# Y& E9 L0 N0 p0 y" A- S4 \: ]
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)' k$ f. R# O1 y4 B: j2 z
global m n ( T4 s S9 Q/ ^' U% bselectpop=zeros(m,n); & N9 t& E" a4 C U- yfit=zeros(m,1);8 @: V. m2 z6 Q4 i- L
for i=1:m$ M/ T4 X# ?6 r. {, d1 ]
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据 7 y. Q) t; M ~7 @) U( L6 Bend 5 ~: \5 A& J, _- i2 R7 qselectprob=fit/sum(fit);%计算各个体相对适应度(0,1) ! U+ q" q. S6 `: u. `q=max(selectprob);%选择最优的概率 7 Z; t s( \. k6 g. M3 [ V3 sx=zeros(m,2);' e. ]/ o6 s: r8 Q
x(:,1)=[m:-1:1]';* }+ u7 O" g. t$ L# e
[y x(:,2)]=sort(selectprob);6 A+ s* ~3 z9 l
r=q/(1-(1-q)^m);%标准分布基值% U/ F* \1 F# M( W$ S, R
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率- ]. q' B6 h& B& A5 Q% {0 Q/ o0 X
newfit=cumsum(newfit);%计算各选择概率之和$ V) m& @2 ?- C* `0 W
rNums=sort(rand(m,1));: L% V# ~+ c) K0 d/ `
fitIn=1;newIn=1; 6 H1 F2 }+ t+ t6 k ?, Bwhile newIn<=m 1 J: c2 c' t$ E: U if rNums(newIn)<newfit(fitIn), u+ e# U' K5 Y0 t( \
selectpop(newIn,:)=pop(fitIn,:);" F- Y8 {, M% n+ C8 \# P9 z1 o$ x
newIn=newIn+1; $ c6 x) @8 }& g2 X4 {7 Y else7 e+ r3 F- q$ w6 |
fitIn=fitIn+1;. c6 h; e0 o3 s3 T+ r0 {
end# _3 {; b$ v8 r7 F4 o3 k
end 8 L; ~( r) }7 o- W l+ P%交叉操作 + ]5 \& z) U9 `; C: D- r* A4 Rfunction [NewPop]=CrossOver(OldPop,pCross,opts) 7 t4 {4 B! u: o! }3 e%OldPop为父代种群,pcross为交叉概率% @# \5 A) _; A2 e/ ^. Y
global m n NewPop , A8 p( ?% H% s% j! s1 ~8 L- wr=rand(1,m);8 A3 g# r3 Y/ E% G
y1=find(r<pCross); 9 S: @$ D( [" o7 `y2=find(r>=pCross); 7 u c4 Z; ?3 qlen=length(y1);" g) t1 A* o8 z& ^& ?
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& h7 D8 f" R1 C' d; J/ E( ]
y2(length(y2)+1)=y1(len); % k5 P, n$ L' | y1(len)=[]; ]; W/ E3 N$ _3 U% ]0 T; D4 W
end9 ?7 J6 C1 a5 X7 j L ^
if length(y1)>=2. m0 C1 K1 w& c1 S6 x
for i=0:2:length(y1)-2 1 D; k, _7 H7 O. g, y$ U/ P" ] if opts==0 , A$ |, l& [) f$ V5 Q2 _ [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:)); 8 v# y' S; g+ w s. s; R else% N) O/ _# O# B2 X9 w: z% c
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:)); ! Y, m9 p% n. T5 L end$ T d$ \* s+ Y5 o
end 8 A' h/ I }) d; L* D
end " V+ ^1 d1 F8 J9 h8 cNewPop(y2,:)=OldPop(y2,:); H6 L/ K1 }6 k1 c: J; y" b' _- i; }; w
%采用均匀交叉 ; J' M+ S8 l2 Vfunction [children1,children2]=EqualCrossOver(parent1,parent2) ( G8 a' Y ?" \( I" K( U0 `$ F* l: B) J. w8 g1 ]
global n children1 children2 9 J1 H3 ]4 }3 }7 B. E* L- s- ?
hidecode=round(rand(1,n));%随机生成掩码 7 Z$ w& I5 T. ?6 }: o5 w3 x1 h6 Tcrossposition=find(hidecode==1); 9 m3 _: ^+ }- a0 L( O+ A" Lholdposition=find(hidecode==0);2 n$ b+ z) P @' p; S
children1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因" }8 @( }7 {# K% c1 ^
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因& J& s; G# E' ^
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因( Y' s7 l, @, W3 Z9 A9 k2 }' i
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因' c8 i6 v# k' B% ^: [' E4 O
* N( g! A, [9 ~7 @" r% y! Q%采用多点交叉,交叉点数由变量数决定 ' o+ B I6 V( x0 X( _) z6 s. `6 E1 Q8 P* K
function [Children1,Children2]=MultiPointCross(Parent1,Parent2), h1 t5 R. ~; w% D1 g9 @- g: d
( m3 a' B2 p$ x$ l/ Y4 v* ]) Nglobal n Children1 Children2 VarNum1 }4 s. @4 ]. @; A. r6 M
Children1=Parent1;7 I7 X. f X# @3 o% m8 \+ h
Children2=Parent2; 1 |8 A8 S0 p' j6 BPoints=sort(unidrnd(n,1,2*VarNum)); 9 p h5 Z. ]9 o' afor i=1:VarNum: A3 @5 W9 N; q7 e" B
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));4 }: r) r5 u7 E1 d: h0 \
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i)); * g& p* f/ n6 L/ n8 _$ `7 U- s9 v% |end ( s* {+ @7 u9 E 3 M3 V- F7 k, Y8 R/ X. |%变异操作 # G0 f. L U3 k( u; N0 Afunction [NewPop]=Mutation(OldPop,pMutation,VarNum)" f. K2 P& U, ~
& e5 z& {( z: i" z- H0 v
global m n NewPop' f. f4 n/ X! E8 E/ r& K; c p
r=rand(1,m); ! }. z; ^" L! _5 }: d* Q0 U# O/ Tposition=find(r<=pMutation); " j" c% }! y( \5 Q( z" `len=length(position);( @: }5 Z T1 ~# s
if len>=1# N; U6 r& ]; A- P6 H% H4 j
for i=1:len4 ^+ O1 @! N$ l# L D) c ?
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点0 a% d! L- W* i- V# C0 X2 E
for j=1:length(k) : C! h5 P: z7 ? if OldPop(position(i),k(j))==1 / O: C7 j! X+ }1 M* K1 H1 M OldPop(position(i),k(j))=0;7 K9 _: A$ H5 o+ w+ f
else0 A* q6 l I3 ~) z
OldPop(position(i),k(j))=1;9 Q2 j( m9 `8 `) {( l
end # @" R: f) P$ v/ u% R end! u0 q' V2 K! V( y/ _" \
end 1 \# K- b2 H |8 X/ c1 g! ~/ Cend 3 ~/ X( t4 G" b, w7 LNewPop=OldPop; 9 ^3 ^# W$ C( q. _5 y! ~; w0 j1 O$ R
%倒位操作 1 q7 D7 |+ `2 g+ B0 p2 G) v4 m* S4 \$ F( ]* S3 S4 m
function [NewPop]=Inversion(OldPop,pInversion)/ P" k& @. ^: I( a4 v
% F2 A, J# Y) W& t- m$ _
global m n NewPop. h9 O( {' L7 ^: n! C) X. p
NewPop=OldPop; / E/ o6 j4 k1 [4 q9 Y6 d* C1 Z9 Ur=rand(1,m);# G4 q% ?- W. |3 [' ]4 w: k8 G! e
PopIn=find(r<=pInversion);* W5 B6 T J0 n# C4 ]3 N
len=length(PopIn); % X- H3 a: K& u. v( m5 Dif len>=1& Z. {& E& `" e( l4 q
for i=1:len 2 B1 C" S" l* u2 c a d=sort(unidrnd(n,1,2)); , U( x% p" y) P( ~2 a if d(1)~=1&d(2)~=n/ Q0 k$ A6 d3 [4 M5 N. O! G
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);0 e0 E' U: Z0 Z/ ?
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));/ p* h, `; H, k) v8 N
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);+ u- w4 u; t! p% ?3 r1 D; {' ?4 t
end- U' g) m+ b8 e& |8 G7 l8 ?
end 7 P' ~. u- H9 b. }) M3 Aend 5 g; w2 _9 X2 J |9 ^, \ 6 F+ l( ?! s4 g. C七 径向基神经网络训练程序 2 m2 c, x I* y6 d# u9 v) G' G: x6 A, G
clear all; 9 S4 W" r ]4 [% p3 sclc; & V" I# J: F7 J4 y, ~9 d. O# ?%newrb 建立一个径向基函数神经网络 ) L# [* `2 G1 d& u/ Qp=0:0.1:1; %输入矢量 & x$ m+ L' P+ Q& ^6 Z; `+ ^t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量8 W" M( D$ r6 e9 w
goal=0.01; %误差 " E+ Q8 ~, g q& W. N+ Ssp=1; %扩展常数 4 _' v* G+ O5 E' Y) p5 Vmn=100;%神经元的最多个数9 E: ^: M: G5 `! n" w$ s4 M
df=1; %训练过程的显示频率) ]( \$ g4 x" Q
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络 * I) T8 K9 ?, t T1 v6 ]% [net,tr]=train(net,p); %调用traingdm算法训练网络 # ^( \8 u2 @# _$ L- n%对网络进行仿真,并绘制样本数据和网络输出图形" F1 d, W6 N4 K4 ^& J! y# W5 L
A=sim(net,p); 1 {$ V- P! c1 j% H& B! t' gE=t-A; 9 i2 S( N- v8 n1 c O) `sse=sse(E);. j; D: X: y1 V, a
figure; ' W0 X) W- c8 I0 d. l3 B
plot(p,t,'r-+',p,A,'b-*');+ |0 d _+ W. Y; t1 { c$ q/ P
legend('输入数据曲线','训练输出曲线'); % {2 N' l7 a5 ?/ o, ?echo off 9 {/ a' Y. j- P* X* g3 ]! W
- D8 ?/ R8 W$ _- F说明:newrb函数本来 在创建新的网络的时候就进行了训练!* V8 T! z: I2 z0 _1 W; S
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, & f, f; x. o& f( J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! & r# o" Y$ ~+ d9 z3 D- Z! n- W/ ?1 F* M ! S" g% d, T9 R( j, L; o h. ]( ^ U$ T
训练结果显示:, B' d' Y& u) Q
NEWRB, neurons = 0, SSE = 5.0973/ F2 d' I& [) V% `+ U# y* D
NEWRB, neurons = 2, SSE = 4.87139 7 H, f0 G& h. J7 K, U- ENEWRB, neurons = 3, SSE = 3.61176 6 E9 E, }8 N: R& r& J) dNEWRB, neurons = 4, SSE = 3.4875) y8 I, Q) x0 X# P, S* u
NEWRB, neurons = 5, SSE = 0.534217 % ^/ n1 `* [2 Z+ V0 PNEWRB, neurons = 6, SSE = 0.51785( w, i8 d/ ~4 n \5 ^6 V
NEWRB, neurons = 7, SSE = 0.4342599 L9 y( o" d# e- K2 `0 d \
NEWRB, neurons = 8, SSE = 0.341518 ; o4 u1 K2 a) W4 k. C. W* uNEWRB, neurons = 9, SSE = 0.341519 * C& b, g: [* A$ y( `NEWRB, neurons = 10, SSE = 0.00257832" s% w' D3 O. h( ^9 v% Y
" e$ V/ ^2 z7 {八 删除当前路径下所有的带后缀.asv的文件2 E+ ~" x7 X+ H& y, O4 Z
说明:该程序具有很好的移植性,用户可以根据自己地# ]0 |+ H( S/ C/ F3 f
要求修改程序,删除不同后缀类型的文件! : p6 ?! i. Q% h' j# Ofunction delete_asv(bpath) 8 |7 O( J F% L; v$ `0 R; o%If bpath is not specified,it lists all the asv files in the current4 N# `+ ~9 \5 E/ E5 n6 L& ^
%directory and will delete all the file with asv ) z1 i7 ^0 v# ~. y& ^+ @! [6 i
% Example: / B! y% T8 i- l7 g/ g, I% delete_asv('*.asv') will delete the file with name *.asv; 7 `0 _# v7 ^. z+ r8 d6 j# H \% delete_asv will delete all the file with .asv. # w/ w8 {- V. p3 U! z& W 6 y- _% ]1 `" [6 ~+ zif nargin < 15 t. e- D4 k4 f$ k
%list all the asv file in the current directory ! z0 w0 ]5 z5 L- G files=dir('*.asv'); 3 T( I; @# `: D+ _( w+ |2 U- Kelse) ?; _4 t6 _' g% L
% find the exact file in the path of bpath- C" ?7 P6 ` J# L# g
[pathstr,name] = fileparts(bpath);% f- h+ y& `3 Y, V4 ^0 }6 @
if exist(bpath,'dir') / y# A% W& [# q) S" p& Q name = [name '\*']; / r5 ?6 t9 W7 u/ C3 y [& c" x6 `+ @ end4 P9 s1 Z. b2 ~0 i9 ~0 W9 f
ext = '.asv';/ K5 y6 G) a: z) l* N3 c" W
files=dir(fullfile(pathstr,[name ext]));, r, I9 T& v7 a' o
end : N+ F3 G* x- y4 a1 N/ F4 T& v% ?2 \
if ~isempty(files)2 R3 V6 |& u! l l, l# a9 G1 b
for i=1:size(files,1)5 L' a% T; R) s) F; ?
title=files(i).name; $ |% z1 l. W# O+ e8 s delete(title);& u+ X- n7 n' k' K+ B5 \
end ! p. P. b+ X7 v5 ?end- X# t! v2 j. V0 w
, o) w+ Q: k- x7 g. j* w# @( P ( e2 F1 l0 o& C同样也可以在Matlab的窗口设置中取消保存.asv文件! ; a2 r+ k: I$ ]7 O3 n& q# C