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升级   48.42% TA的每日心情 | 开心 2016-11-7 00:15 |
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签到天数: 7 天 [LV.3]偶尔看看II
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一 基于均值生成函数时间序列预测算法程序
/ J" Z, q D: s: }% @- z1. predict_fun.m为主程序;
$ c- \6 Z8 F1 r C" I2. timeseries.m和 serie**pan.m为调用的子程序
, a6 P& I& E" {- z
. T" E. q8 E" P1 {. |& u) A: ffunction ima_pre=predict_fun(b,step)
0 I6 A, _; _: G6 k) n$ U% main program invokes timeseries.m and serie**pan.m
- p/ F# Q5 r( I* b: F- Y9 a% input parameters:$ p4 {/ M9 j4 M' ~
% b-------the training data (vector);
$ M4 n' A- j! Z$ f* @4 A7 y3 y: V% X. w; |% step----number of prediction data;
4 H9 a3 K, S+ t% output parameters:# q q; b6 \" a# S) |7 M
% ima_pre---the prediction data(vector);: t9 x8 V' z, H( k& a
old_b=b;
2 b E- a4 ]" F; s" C: _' N2 Q& kmean_b=sum(old_b)/length(old_b);; K1 Q/ c: t! V- ]$ G
std_b=std(old_b);
1 `, B' J# H8 h1 y$ {+ B0 q Hold_b=(old_b-mean_b)/std_b;4 O: R8 N) b2 D5 ~
[f,x]=timeseries(old_b);
& I# j* t+ `8 x1 Y, d& l) |1 Nold_f2=serie**pan(old_b,step);% C. r6 q3 D3 d" \' \1 {
% f(f<0.0001&f>-0.0001)=f(f<0.0001&f>-0.0001)+eps;
( N( D1 |3 G: a+ g7 [( FR=corrcoef(f);
. ^6 c8 V) l% y) R[eigvector eigroot]=eig(R);
& |8 K. W6 h g0 F1 f E$ i5 Peigroot=diag(eigroot);! t: o4 n3 {( ~! ^: e! u
a=eigroot(end:-1:1);; V O7 E0 i! G
vector=eigvector(:,end:-1:1);
9 d R2 Y; J) K# E5 TDevote=a./sum(a);
: e/ Q7 n$ {; N8 gDevotem=cumsum(Devote);
" e0 N+ l `2 w1 A2 N! F. }m=find(Devotem>=0.995);8 M1 l6 ] L. Z, V- Y8 M0 S
m=m(1);
3 O7 K* P4 n: d; C: ^' l, `V1=f*eigvector';; H q& y+ k- C w* {+ h; h
V=V1(:,1:m);
) L" h+ @' r: P% old_b=old_b;& \$ F4 j( L, r$ q9 ?( v3 r: ]& t
old_fai=inv(V'*V)*V'*old_b;3 s8 ]" X6 ]+ V
eigvector=eigvector(1:m,1:m);3 P& _/ C# G% k
fai=eigvector*old_fai;
8 y5 Q7 s- U" Y' R; v3 lf2=old_f2(:,1:m);' n& g# @9 W2 j! W9 U. ~/ x6 j
predictvalue=f2*fai;
& k2 V! c1 T' i0 a% f; Pima_pre=std_b*predictvalue+mean_b;+ z5 r$ V6 ]& u) y
% f% Z) b' D& d1 `
1.子函数: timeseries.m
& l2 N7 z M( ~% timeseries program%1 N( H! T/ N3 Q ?# J, l- A
% this program is used to generate mean value matrix f;$ f0 Q( A5 V* F' ]' w: K' M' l
function [f,x]=timeseries(data)
& D. G, t" n% ] C6 T3 Q% data--------the input sequence (vector);
1 F5 H% h* m/ @/ f- e( j% f------mean value matrix f;' o& n$ f# }( g& q
n=length(data);
0 b: S( T: f- g/ I0 c4 Ifor L=1:n/2, e9 T b9 E; G g& {
nL=floor(n/L);. e* t, U+ p4 q' Y
for i=1:L
z- A7 w/ P1 u1 H sum=0;4 [: }# ~) |, t% @) R7 v Z" D. N) X
for j=1:nL
! ]/ k' U4 f& { sum=sum+data(i+(j-1)*L);: }4 V8 {3 P3 F4 ` C
end7 q1 t7 W! {' {& @ V
x{L,i}=sum/nL;
; h: ^, A% `% U. d3 T( n B end% D* C0 p5 Y7 e* w9 P1 y
end
/ g6 [3 W; |& V* F/ y2 g) tL=n/2;+ l7 I6 y) h- s" F" F
f=zeros(n,L);$ I8 Y; ^* X7 B! t! m& f
for i=1:L8 u4 y$ ?# B$ i/ S# y$ Z$ N
rep=floor(n/i);$ }* M1 i' V4 c1 R
res=mod(n,i);# G2 a6 [+ j# C' M9 {
b=[x{i,1:i}];b=b';
: c0 O4 R9 T2 P) i f(1:rep*i,i)=repmat(b,rep,1);+ p: n* M [6 |/ w: F$ ?
if res~=0
9 A( d: T* _ u- S U3 { c=rep*i+1:n;; m8 U6 j: s7 x }
f(rep*i+1:end,i)=b(1:length(c));* x( n9 v( r8 x% f- p U- n
end+ d% S& O B: ]. A% L9 Q, g
end
3 `- N/ t: A( C' H7 s& f9 r, n3 h4 m" E
% serie**pan.m+ v5 C; @. V3 w: i
% the program is used to generate the prediction matrix f;
2 t' p4 i3 y, ^4 Dfunction f=serie**pan(data,step);, _( X Z, c& j3 q$ P+ U
%data---- the input sequence (vector)
/ D* F# `5 f$ p1 W7 d6 y( s% setp---- the prediction number;
& Q" u& b {! _9 d. @n=length(data);9 O8 c8 }7 Y. U0 ~
for L=1:n/2- v" Z) U k" y {2 E( V V
nL=floor(n/L);
5 r* R" i1 ~$ ~8 { r for i=1:L/ [- ?- ~" U2 v
sum=0;0 u* A; t/ f/ C% n- {1 i) ?
for j=1:nL% I& }' u0 W( r6 e
sum=sum+data(i+(j-1)*L);
4 E7 J% C" b' u: q- g6 s/ ? end7 X/ _% x% ?5 z7 o o: L r
x{L,i}=sum/nL;6 G3 W6 Z2 s \' t: }0 m: U
end" L) ~/ X+ Q8 X. W
end
9 ~& T% m( @. F9 v" ~# o- UL=n/2;
( _4 S7 Q8 k' H: A: A$ b& df=zeros(n+step,L);
+ L* W' D1 I f4 W k) p, N, Qfor i=1:L
1 R' G* n( a( O- C rep=floor((n+step)/i);1 H. ^# @0 ~( G) z* D+ O" Z; m G
res=mod(n+step,i);
- w1 ?, B1 S$ s$ b, y b=[x{i,1:i}];b=b';
8 o( r% C% I# Y. _: P0 n f(1:rep*i,i)=repmat(b,rep,1);
8 M4 ]. V, [8 d8 V n/ l6 k if res~=0
, R5 g! c- F" i. B7 X) T/ l c=rep*i+1:n+step;0 L8 U1 Q9 j0 m |
f(rep*i+1:end,i)=b(1:length(c));
+ t/ W9 x" N- ~3 _2 U' t/ l end
% ]: h: V' Y2 g# n8 }1 t* K* G% zend7 A9 b. @+ n, U, u9 O" Z! T
" j8 g+ U3 ~9 _/ i. Z9 b
二 最短路Dijkstra算法% ?4 O$ l; _" U$ ^
% dijkstra algorithm code program%# q% t6 s8 G7 d0 ^' C
% the shortest path length algorithm
1 K) J* S, U) \. Xfunction [path,short_distance]=ShortPath_Dijkstra(Input_weight,start,endpoint)9 w9 y: ]6 O5 i. P/ {
% Input parameters:# z) `, b+ C6 M5 A
% Input_weight-------the input node weight!
- L1 F6 J8 i. B! V# G; ]7 w% start--------the start node number;' @( P; u2 w4 f7 h( U0 e
% endpoint------the end node number;
- y4 S$ F+ @0 J7 E$ \( w8 _% Output parameters:
: p+ H1 _4 @" E% path-----the shortest lenght path from the start node to end node;
' c8 x+ c! S" D) u8 X2 n% short_distance------the distance of the shortest lenght path from the
1 t. N4 E) e/ j) w! {" ^% start node to end node.# S; o5 F* ]/ @4 ?( ^; |; i4 l: F
[row,col]=size(Input_weight);2 o. Q/ E5 O7 S' ^$ {4 v* g
2 z+ d% U0 ?% h2 G' k/ x
%input detection4 |0 o$ W. g# E# ]( v
if row~=col
5 D/ D6 l6 q! C3 n: \* d3 K: E error('input matrix is not a square matrix,input error ' );
! _* g2 N4 ?2 G' k$ x5 ]: oend
8 j4 x" G4 X) @' N& Jif endpoint>row/ b" m4 T6 V, a# _3 y4 j% K1 z/ R1 Y
error('input parameter endpoint exceed the maximal point number');% H8 F5 E9 n( L5 S' W# O
end
" M' X0 ~9 u0 U! e# g {" v9 C6 t( R, p4 I# [- a
%initialization
7 }& }. G0 t- H4 ps_path=[start];( Z! y9 I, l$ e0 ]
distance=inf*ones(1,row);distance(start)=0;
5 N4 r- d5 h Z1 @, iflag(start)=start;temp=start;
# F8 o: R# J1 C& ?$ A0 k
/ Q* A: b7 E. c. P' o, X4 I! Lwhile length(s_path)<row
! ~$ ?/ [, f6 O- [- a, n pos=find(Input_weight(temp, : )~=inf);
6 v9 P( [5 c8 s' A' r for i=1:length(pos)
& u$ ^+ g/ \, }. |/ i: B: ? if (length(find(s_path==pos(i)))==0)&4 }6 d/ s" A* h% {% a4 C
(distance(pos(i))>(distance(temp)+Input_weight(temp,pos(i))))% z, j3 I# _% y2 \8 W. Y1 Q
distance(pos(i))=distance(temp)+Input_weight(temp,pos(i));
% b, `: V$ U4 x5 E6 ^ flag(pos(i))=temp;; c& \, G( H% V, q
end9 Z# g7 V# D B5 A
end0 I* S. h! W: r6 f
k=inf;/ g5 h, U- h$ l- K1 k* |
for i=1:row
' m q9 J: u' z2 m6 B/ r if (length(find(s_path==i))==0)&(k>distance(i)). e- x2 }8 i; C7 z7 ]
k=distance(i);* M. L7 K3 k8 i" {+ F, `# |5 Z
temp_2=i;( I% I8 ^* T; b- S& t
end
; V" O7 k* y6 f( s- `7 t! H5 k end
4 f2 S' n$ x. Z# A7 A, k s_path=[s_path,temp_2];
6 H3 S! J3 C9 O7 \# P) c! y2 w temp=temp_2;/ [; `' m* I4 |0 }+ g$ w
end
9 u0 j3 S! ^/ c
3 Q2 n3 I3 }" {( x2 h4 n%output the result
- t7 c, X# {" W) vpath(1)=endpoint;
% w- R, x% l: _i=1;
8 l4 ?6 A5 f- L9 u# P+ j3 q6 d' P2 ]8 A% ywhile path(i)~=start, O- @' i9 _# ], S4 k% S9 r" t- W
path(i+1)=flag(path(i));
2 V, Y0 ?; \( L9 ]/ L- X i=i+1;
7 h+ E: q: Y8 Xend
# A$ W z! Y. V8 tpath(i)=start;
3 k7 n7 G0 T$ O+ Ppath=path(end:-1:1);
) N' J' g8 K3 q6 k# sshort_distance=distance(endpoint);
3 _8 `1 D5 c& U* p( f9 `三 绘制差分方程的映射分叉图
! A* V* j) L2 P
" l8 ?' b* @7 ^% s2 f' z5 afunction fork1(a); ! ^/ m9 i2 _2 T# b6 w
) X' [$ I! h% Y) ~% K8 Y% 绘制x_(n+1)=1-a*x^2_n映射的分叉图
- k+ r$ z7 g9 l$ E% Example:
1 _ F! m: z) l' e0 B( O; C( m% fork1([0,2]); & S, v4 O- B5 h; f0 Y3 P
N=300; % 取样点数
8 Q2 K& U5 Z( e% x. D8 ZA=linspace(a(1),a(2),N);
4 E- S+ I8 {, Q. l- I3 Cstarx=0.9;
& g* p7 ? ?: }: D# mZ=[];
3 W: X t; w" z( w4 j5 Ih=waitbar(0,'please wait');m=1;; n' i9 u7 p) V' g5 F
for ap=A; 1 |# l3 m R. X1 n( z" k
x=starx; ! W/ D$ @ ?5 P; T* z6 B. m7 _
for k=1:50; " k, C# ^- z* @2 X5 U8 X- ?
x=1-ap*x^2;
( M/ `6 G" q# q5 S @ { end 5 G" ^" ~- R" N4 b0 O/ x( L7 d. q. P
for k=1:201;
( y( P# K4 Z4 J D- ^% s5 a. a x=1-ap*x^2; 8 b& W* E% e9 R! z
Z=[Z,ap-x*i];
6 S; P/ O/ u6 x9 ~& R. A end
2 s+ o8 t" ]5 S& e+ T5 A r waitbar(m/N,h,['completed ',num2str(round(100*m/N)),'%'],h);% S, P9 n+ a# C P( P
m=m+1;$ x0 n; P3 ~4 O' S6 A; M
end
- n0 Y) L w. M/ sdelete(h);3 P: N$ l" z( ]+ F% X
plot(Z,'.','markersize',2) , o& ]9 O( P9 E, U
xlim(a);
7 t3 g. I) x2 X* h/ F/ |
" J3 _3 b9 T+ ?) e7 t& X' _7 S四 最短路算法------floyd算法
3 K7 o8 ]$ n* J9 ~/ ifunction ShortPath_floyd(w,start,terminal) * U- S1 W7 I+ G; Y% ]% q
%w----adjoin matrix, w=[0 50 inf inf inf;inf 0 inf inf 80;$ E! I1 M6 ~5 `2 y. p+ t
%inf 30 0 20 inf;inf inf inf 0 70;65 inf 100 inf 0];: Q( E- C! |$ T/ U; g
%start-----the start node;6 g& r0 P! C: m8 f8 @1 M
%terminal--------the end node;
$ U! K0 Y( H1 @, nn=size(w,1);+ u& e7 i! Z7 Q( H, j" F$ b/ t9 E
[D,path]=floyd1(w);%调用floyd算法程序
L' t: [* f) _5 w. ^/ M9 d) O
+ X! H2 A- I8 T' t$ P: U%找出任意两点之间的最短路径,并输出
" u! r$ i' V: q8 O% gfor i=1:n9 A% ?! I' | k3 e
for j=1:n- q6 [+ n2 G- U
Min_path(i,j).distance=D(i,j);
/ ?6 `( e! s( w4 T3 D %将i到j的最短路程赋值 Min_path(i,j).distance
* V0 x! ~7 |* i. s5 \! Y6 P' d %将i到j所经路径赋给Min_path(i,j).path
. b P; R6 t, l( N r3 _ Min_path(i,j).path(1)=i;
5 E# i1 G) U; ~& c$ H7 x k=1;
' i( A7 E" C% C9 n while Min_path(i,j).path(k)~=j
; B, ^% c i( D# N! \/ y k=k+1;3 P' B( B% T$ S" d# z8 ^' Y
Min_path(i,j).path(k)=path(Min_path(i,j).path(k-1),j);
3 k8 ^! a% O" {' ?% ` end$ [! e, T+ _2 f
end0 p: f* z2 O7 m
end
) _" \7 l1 }7 h4 v3 D6 W# G% bs=sprintf('任意两点之间的最短路径如下:');" s7 j. D4 N& `
disp(s);" e$ d) K5 O, t" k& X. a
for i=1:n2 t8 `: ^, P2 o2 z/ c6 m
for j=1:n. ]' a* H! h( `
s=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:'...
1 o+ }: l9 G( N6 w9 ~+ m ,i,j,Min_path(i,j).distance);4 u: \9 g; q2 O
disp(s);6 |& o' e9 ]6 O% a( f8 r
disp(Min_path(i,j).path);
% K: k8 `6 A( X3 w end( J3 o$ {. H6 ~. Q) A8 n
end; d, W6 p2 w1 }" } _1 M
# K8 B, x$ O) a# E) X, X" V
%找出在指定从start点到terminal点的最短路径,并输出 r& t) M: S* t4 P- ~6 [" \
str1=sprintf('从%d到%d的最短路径长度为:%d\n所经路径为:',...8 @( f$ y: K; ~- M9 G
start,terminal,Min_path(start,terminal).distance);
; f+ y; @( f; c5 ]- Gdisp(str1);
5 |' ~- r2 J; V2 pdisp(Min_path(start,terminal).path);* c% y: d' h% m9 j- _+ m8 j/ F+ w7 ?: Y
2 o6 K. w% m U1 Q%Foldy's Algorithm 算法程序
; W% n' K& a9 d. ]0 {function [D,path]=floyd1(a)- r( A8 [1 R0 l# R( |
n=size(a,1);
( S% r: V6 U9 [4 |0 o8 uD=a;path=zeros(n,n);%设置D和path的初值2 @/ C' t1 x2 P& S1 _+ \5 O6 k! R
for i=1:n
- Z6 S" ~% G; q" m8 L; S* X( U for j=1:n
3 S2 e- q/ G$ }" f6 D if D(i,j)~=inf
% {, V( K9 C6 _: V4 c2 H. m path(i,j)=j;%j是i的后点3 w1 Q% W0 N* m& b
end
7 Q2 D, [* t6 J2 b) y k end
# j o" G k0 ~) B5 {& G; p& {; o! Wend
0 s7 S6 v" [% s: e%做n次迭代,每次迭代都更新D(i,j)和path(i,j)
/ E; k; y: b V7 c8 _! h7 `. f Afor k=1:n
5 I0 ^. Q' l) B v/ M- i4 | for i=1:n
' L# L9 {& H% M0 B* U: K# J& C for j=1:n
4 o) c1 k4 N3 b* E! S if D(i,k)+D(k,j)<D(i,j)
7 d% d9 O4 N6 r# ^! F D(i,j)=D(i,k)+D(k,j);%修改长度
- F' @4 p9 F3 m! d: U3 }5 V+ O3 y. i; |1 } path(i,j)=path(i,k);%修改路径9 n) i, a& z; ^$ q8 J( @
end6 S3 G2 A5 b6 F5 U; {$ v# v( i
end# F7 }' T( u* B, \) m- }
end8 d4 c5 ]9 ]& z( S
end" Q' O$ Y/ r3 m8 P5 s
8 C. r8 ^( p! @
五 模拟退火算法源程序8 O$ R& q5 X/ a1 N: h: y
function [MinD,BestPath]=MainAneal(CityPosition,pn)
% ?0 w5 Z* r" A+ Sfunction [MinD,BestPath]=MainAneal2(CityPosition,pn)
3 l, L, ^. o1 Q( j+ A%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" q" i. S, T/ d. t
%CityPosition_31=[1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...% @* ?% R( ]& a5 |5 s
% 3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
1 \$ d& Q; a7 k4 J9 Z% 2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...* f& v& A) O" c; r5 y
% 3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...% e/ I& y s, W9 {
% 3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;2370 2975];& e) R( \, G& G& ?
$ S1 R& V. l1 A% Y
%T0=clock
& V6 K. }+ Q; W. x5 Aglobal path p2 D;
5 {( K" r! u8 U$ V! j( k) [* f[m,n]=size(CityPosition);$ q7 V0 c9 U7 s: Z
%生成初始解空间,这样可以比逐步分配空间运行快一些
8 }' x* y& P( r* E, kTracePath=zeros(1e3,m);
; Z9 v+ S$ X" d( W) l: W7 m! SDistance=inf*zeros(1,1e3);
* S' k4 r. h. W l* _; E
) A9 P$ C/ c, G& FD = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...
/ {; M) X# }/ Q( v (CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );! o. u2 x7 \; @. ^0 g& T
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)
& q3 V5 W/ _, M* [/ }5 Z d6 sfor i=1:pn5 P" d1 s! y @8 W
path(i,:)=randperm(m);%构造一个初始可行解6 m) x0 S7 D/ l6 H4 W
end
4 D4 a& R: }% w, ?4 g* C; Y, v" Tt=zeros(1,pn);, f% D0 m, p# ]: z
p2=zeros(1,m);# s: E4 o% o4 G1 r9 f
; a" @/ y7 R: I- q
iter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' );
) R- q+ m6 N8 R9 Ym_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=' ) ;
! a9 Q7 j5 z% |$ ]" T4 k2 ]%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
( z- Z6 X* X* {, C) p: x6 J%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 _ X. J* I3 _5 m
%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* b1 W) c/ W5 l, y( l0 g7 s: {
%会收到到比较好的效果
% l7 `+ S8 \! H4 m6 O
. } v, h. A; F9 S* bT=1e5;. I2 O8 }5 @& F
N=1;
" L- u- E, F0 {: O6 qtau=1e-5;%input('请输入最低温度tau=' );
! w! N6 K3 o" N4 u, B, [( ]1 \" [%nn=ceil(log10(tau/T)/log10(0.9)); U# U3 j. p6 k9 u$ l* ^" c
while T>=tau%&m_num<m_max
& k. ?5 w+ r+ S9 L6 _! D iter_num=1;%某固定温度下迭代计数器& O! z! y( o2 z+ B7 b5 K* {& 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
3 s" g0 ^' i2 N9 F- Z %iter_max=100;& d; W0 D$ \0 h8 O" ~
%m_max=10;%ceil(10+0.5*nn-0.3*N);" j8 k R# z: I9 c5 H5 D
while m_num<m_max&iter_num<iter_max
" q$ H! b; [, i2 d/ E %MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程:8 n! T+ ^1 P4 ?( v3 x
%用任意启发式算法在path的领域N(path)中找出新的更优解) v6 P5 j* t3 \) C8 T( o
for i=1:pn. i1 F5 G5 l( z% Y5 A9 J t/ R7 d* m
Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);0 }1 O) G4 g, ~* G6 D1 s
%计算一次行遍所有城市的总路程
9 Y i8 z4 u8 K [path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线
/ q0 W# f7 ]) R4 m* E; z4 \) D Len2(i)=sum([D(path2(i,1:m-1)+m*(path2(i,2:m)-1)) D(path2(i,m)+m*(path2(i,1)-1))]);
/ c* m/ Q6 x3 C0 i, d* P end( t: a9 a1 u, _' j+ w% m
%Len13 P4 k0 a# s3 _; O, @
%Len2
/ }2 f. x: X; d9 l %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand$ N- d/ d' g) B' p( }1 E% v
R=rand(1,pn);' U; x6 U' F4 @# \ X5 Y# V" |
%Len2-Len1<t|exp((Len1-Len2)/(T))>R5 v0 y+ f1 _0 |1 K
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0)( Q$ t, Y Q; {# Y
path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : );
3 Q/ |$ X2 d# s% |8 v/ f" ~ Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));' \7 v$ N; J- {2 `" ~& g
[TempMinD,TempIndex]=min(Len1);
" r$ M) d) S9 t3 D2 b %TempMinD
: |% X5 [0 U) ?( X" { TracePath(N,: )=path(TempIndex,: );* c- X7 Q5 y+ f
Distance(N,: )=TempMinD;1 m: n z$ ^/ r7 q
N=N+1;+ E) p4 x" b7 ?1 b& u3 a
%T=T*0.9
4 j3 F! A4 l" p; f m_num=0;5 l5 r# s6 H! H7 E8 E
else7 N, Y7 o- I) ^' V
m_num=m_num+1;9 [: M4 I. O! X. ?/ |2 l+ V) q5 I) b
end7 l: w1 j5 G# m. q, z
iter_num=iter_num+1;
2 n, D6 O" D% I& Z- t- B6 B3 n. i end3 m$ B$ ^( W3 d, Q
T=T*0.98 t& Q% I; t7 E) w1 O
%m_num,iter_num,N
; Q. G3 W' `: w2 F4 P% Tend
& B9 o3 D3 [9 g4 Z$ Q) S% u+ L+ G[MinD,Index]=min(Distance);
: Q* O, B3 D. M. q- b8 ]BestPath=TracePath(Index,: );
3 a# W% |3 F* G% K; V$ L$ V8 ~ @! idisp(MinD)3 H/ k$ c/ \7 H4 V% N6 S% r
%T1=clock
, @; T2 x* G+ K8 r0 q " F" I9 B+ S4 @
5 ] }* r2 V. L, Z: v
%更新路线子程序 1 Z: @4 ?- n5 \4 E, @7 Y$ i
function [p2]=ChangePath2(p1,CityNum)* v7 P: C" Q3 u8 j! G! N
global p2;- N# ]% l( c7 W
while(1)& U- ~+ P/ W+ m0 l4 h4 B+ I. w
R=unidrnd(CityNum,1,2);
9 g. P: P0 b+ N" h' h$ R! e( d) [( i if abs(R(1)-R(2))>1
) h8 j* {, b! L' T break;. g# ?% N5 W- p4 W" q, ` ]" o
end
7 G6 Y2 p4 i* `+ c5 u/ ]) J$ t; F7 N7 Fend0 F5 N0 K8 K( n _+ W9 T
R=unidrnd(CityNum,1,2);
1 @3 r7 u' e2 V' c3 j* RI=R(1);J=R(2);5 c# [8 j9 L0 q
%len1=D(p(I),p(J))+D(p(I+1),p(J+1));( ^6 ^2 ?$ `) k6 x
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));0 l3 P/ }$ i5 e- s8 c
if I<J
9 ~% y' v. `$ r% u; u& U. Z2 E# t p2(1:I)=p1(1:I);3 ?6 C; {1 K. {
p2(I+1:J)=p1(J:-1:I+1);% n, H( F/ o9 g* C8 U; i
p2(J+1:CityNum)=p1(J+1:CityNum);
7 v M+ F! r! ~. V' Nelse$ p1 \, {/ w% Z- f- @
p2(1:J)=p1(1:J);. n: T' g8 A: h+ B" g
p2(J+1:I)=p1(I:-1:J+1);2 N: Q& S9 _) ~9 X: d1 G) N% x
p2(I+1:CityNum)=p1(I+1:CityNum);
4 V, k V: j+ Vend8 |/ T7 C1 z$ S; `! W% M
3 H9 U1 o R0 P* W
六 遗传 算 法程序:
" T& T6 `, [" ^ W8 f, h 说明: 为遗传算法的主程序; 采用二进制Gray编码,采用基于轮盘赌法的非线性排名选择, 均匀交叉,变异操作,而且还引入了倒位操作!
& O4 Y& C% k; w! f5 Y
9 E/ n5 |: j' \ ~function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)" o0 r. G3 V4 y: z
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
' |. e! x( B2 r' S% Finds a maximum of a function of several variables.4 M; j4 V% T5 V R$ ~1 r. B
% fmaxga solves problems of the form: 1 i! @* t0 A& ^/ U* d
% max F(X) subject to: LB <= X <= UB
. Q6 n& Q o M# S' \% BestPop - 最优的群体即为最优的染色体群
% b& `1 g- \ F' C% T% Trace - 最佳染色体所对应的目标函数值6 B" `$ Z+ f; u$ X0 O
% FUN - 目标函数$ _0 ]4 Z _ o4 R
% LB - 自变量下限( f# r# p8 y; }& `
% UB - 自变量上限
4 S! c4 Y+ o5 M! ~0 O9 k# P% eranum - 种群的代数,取100--1000(默认200)# I2 |3 t/ j4 a( i) f6 }
% popsize - 每一代种群的规模;此可取50--200(默认100)6 T& f& D0 S7 s- U2 h# ?
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
/ E4 I. U0 J: n/ K- @- o+ b% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
& l" j8 [. D' Z& h' V0 d/ P, h% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)
* x0 G6 x" L; g9 P; d+ i; _% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编6 z6 \6 a5 L. ^2 g
%码,option(2)设定求解精度(默认1e-4)
( g# Q! R6 b/ N; A- K" S8 O%1 ]4 W% T& a3 z5 c9 L
% ------------------------------------------------------------------------
9 c) K0 g) H! q; U/ @9 A. @7 S* [4 c9 Y! w& L: h
T1=clock;- ~0 y! y# w/ ?( x4 C+ M$ \
if nargin<3, error('FMAXGA requires at least three input arguments'); end2 \1 e8 _. y1 A% O8 q" d. {
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
: D6 u/ `9 S; k2 @8 pif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end! X0 A5 [' _2 u9 d- C
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end8 ^! }2 X/ ~9 \" p N
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
! [4 Z# Z& A3 w* i. U: }, \if nargin==7, pInversion=0.15;options=[0 1e-4];end6 i' a# }8 K, r8 `9 @) ]! H! Q1 \/ x/ ]
if find((LB-UB)>0)* W% }9 y" Y9 D$ I& y6 W7 E. k
error('数据输入错误,请重新输入(LB<UB):');- L& h* F) y* h# J- W- `3 P
end
+ k# P# O7 S7 V5 Ws=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));* p& Y0 R% A; S% u0 x) p
disp(s);2 L" O9 t1 y2 m) m0 @" e
, U. d4 M1 W& [2 s; ~global m n NewPop children1 children2 VarNum0 I4 p% W; N- Y% O
# P3 k0 X- x7 H" S; G8 Wbounds=[LB;UB]';bits=[];VarNum=size(bounds,1);" F2 ?7 r+ Y/ _. ?/ e1 U
precision=options(2);%由求解精度确定二进制编码长度5 ^0 ?$ O! l( y9 v. Y6 \# L5 H/ D
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
4 W' v% Q( r- g. b3 s) B4 G[Pop]=InitPopGray(popsize,bits);%初始化种群7 O1 E% v% K+ j
[m,n]=size(Pop);
; Q4 }% X/ h" i1 O* YNewPop=zeros(m,n);
3 v6 r# J0 ]$ i" K; w* B1 V1 f5 Bchildren1=zeros(1,n);! h, J6 O' d* P3 B
children2=zeros(1,n);' S! Y) r7 \3 f1 D
pm0=pMutation;
# F" w! V7 X7 t& _# y/ z% u1 hBestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace4 `" r: M3 t+ I* b5 M" z# U2 w
Trace=zeros(eranum,length(bits)+1); v$ d0 E! c. ^! ^5 @3 N2 A/ q$ C
i=1;9 i1 v O$ R Y) ~% y4 X- y) U
while i<=eranum1 _4 M3 ?% q# u7 \4 a. ~- E
for j=1:m4 s( t% N2 k8 L' O3 ~ K- E
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
( a8 W6 ^; W$ r: @4 F c7 h) T end" Q1 a2 M% O, t1 L
[MaxValue,Index]=max(value);$ H, C w# d( G4 P
BestPop(i,:)=Pop(Index,:);
4 u2 K( ^. x' W4 k4 i6 H Trace(i,1)=MaxValue;# z8 K5 \: M- O7 n
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);" f9 Z0 g, _( w7 t* \
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
$ U1 h8 p$ v$ j3 y! H! a: d! k* ^8 E[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
P/ g* Q3 `4 N1 {/ ?0 H%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率+ g( p. @0 T) l! ~/ g& F7 p O
%round(unidrnd(eranum-i)/eranum)
$ p0 V d$ S5 p [MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
7 J7 ^2 y3 C; n& F6 h( W* p [InversionPop]=Inversion(MutationPop,pInversion);%倒位
6 B* f6 y3 E# w1 d* h4 U. V Pop=InversionPop;%更新
. f4 [5 X4 _) l+ gpMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
# L& _6 j! S" E& Q/ P%随着种群向前进化,逐步增大变异率至1/2交叉率/ g) P. W/ s! p7 @" U6 B
p(i)=pMutation;
N5 w7 U8 r/ {- D. Y- ]2 o4 S Y' W i=i+1;. P- j. {7 [3 n
end( h/ `# f/ o G
t=1:eranum;
% Y/ o/ b" Q7 m5 |' T& i1 B7 Yplot(t,Trace(:,1)');6 e$ X: L6 \# e# W9 Q6 t
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)');8 O) y' E* S: G) R6 k- K7 y
[MaxFval,I]=max(Trace(:,1));- g4 u9 J$ o H) b0 C( Q. n
X=Trace(I,(2:length(bits)+1));: O2 h5 @5 ~1 h4 \
hold on; plot(I,MaxFval,'*');# ?3 i* ?/ |' z+ _: C1 j7 [
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
1 B+ i6 L/ d8 B5 {* I0 Tstr1=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,:)));
* ^( j5 {# w+ b( ]" p. E9 C; K3 |disp(str1);
' f+ S0 ?1 }0 k( U5 l r7 S8 }%figure(2);plot(t,p);%绘制变异值增大过程! ]/ c R& {4 _0 ~* K2 o1 B3 @. t
T2=clock;. _/ [" [0 k4 G8 K& u# H# S
elapsed_time=T2-T1;
, O( t+ n6 Z: B* X1 f* R" U1 D) |if elapsed_time(6)<0
: z. J k" B! ^8 S5 p$ @5 J elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;6 O/ |# X2 f& [$ @) ?: J. k! _
end
& C, { ?2 S5 ^3 v- Q; L* N) rif elapsed_time(5)<0
: t/ t- w. ]5 { elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
. k/ E. [1 a! a( [end %像这种程序当然不考虑运行上小时啦: Q1 r: s! Z) \6 e# y* ], {6 N% 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));; L0 c" e6 N3 C3 P
disp(str2);( Y3 }9 E0 f. n- @. X
7 G0 p. ^$ k" k, ^+ @+ \& U, j
8 _* Q0 [* l3 B: G" R" t
%初始化种群
% T5 V4 ?- @7 `7 F7 G1 Y% s%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
; X* R; O1 Z5 ~$ N7 v$ ?function [initpop]=InitPopGray(popsize,bits)
5 @$ ?8 Y1 g, q" }/ I" Ilen=sum(bits);9 x1 w' u& x/ z
initpop=zeros(popsize,len);%The whole zero encoding individual3 ^3 e, t4 `/ G9 h/ W0 H- d3 M( ^! K4 P
for i=2:popsize-1
. D, ^& |. s8 T: o8 J1 c pop=round(rand(1,len));* x) C& J' C8 U1 ~4 h8 r' I( y
pop=mod(([0 pop]+[pop 0]),2);
1 O/ Y8 U7 y+ G8 m# R0 B %i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)8 c) Z: U# x7 i( L% u8 y; d
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)9 r( E2 l& M( {+ `
initpop(i,:)=pop(1:end-1);- a; O/ C1 _6 ]+ b3 [! W1 g
end# Z3 J! Q3 t e6 K; B
initpop(popsize,:)=ones(1,len);%The whole one encoding individual6 J6 `1 j4 `6 F
%解码
. d* K( ?' Z. ?# b o _! o+ A8 L7 f7 _) }
function [fval] = b2f(bval,bounds,bits)4 g- J" V6 U5 v
% fval - 表征各变量的十进制数/ }; q9 S% o! F8 f9 o( M
% bval - 表征各变量的二进制编码串: n9 ^5 x5 H$ }; x' L5 ~0 G
% bounds - 各变量的取值范围/ X8 x @1 R0 m
% bits - 各变量的二进制编码长度
8 v$ d1 A9 v# `. J2 G8 Nscale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
& _( p4 h4 t4 \$ _4 x, v+ inumV=size(bounds,1);! X1 c8 n& r( c; h; O' u
cs=[0 cumsum(bits)];
2 N- A+ s; L6 _) K; ~- L7 Ufor i=1:numV
1 j0 D5 V! ?" {8 T6 j; ]9 ? a=bval((cs(i)+1):cs(i+1));: }, b3 o, \+ L. t
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);7 e. N( I9 F9 t- X' l
end2 I# n- v: N8 r; h$ \
%选择操作+ @+ V6 L/ i+ ?# I( Y
%采用基于轮盘赌法的非线性排名选择
) q) U5 y; l. c/ z%各个体成员按适应值从大到小分配选择概率:' Y6 t2 E+ m8 _3 d$ Y
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=15 r! P, a- O% N
6 d t4 ~5 w" c5 efunction [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
% o+ m9 d" \, `! Yglobal m n( c, ^+ V; J* b8 C8 o. @
selectpop=zeros(m,n);0 S9 `/ r; o: P/ S
fit=zeros(m,1);9 L" K5 ^- ^ R5 U
for i=1:m) k/ }# {* E/ \0 \
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据& |: ~8 I, U6 e% D
end3 }1 N0 Z3 X2 [, V9 p! K! _- h
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
- V: W3 W9 p1 l, P3 Qq=max(selectprob);%选择最优的概率* t( T$ D# T0 k8 o0 [4 @/ I, m
x=zeros(m,2);# _) `# X0 d- ?+ ^4 K% @" N% [
x(:,1)=[m:-1:1]';% V# g( Z; f: ^7 b$ ^- B: z5 }) I
[y x(:,2)]=sort(selectprob);$ X6 S3 K4 h( u! }6 m8 c* u
r=q/(1-(1-q)^m);%标准分布基值
8 q; Q; ^8 f8 U+ r9 Bnewfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
. i0 K% R+ o; _# F' m8 j+ Z2 xnewfit=cumsum(newfit);%计算各选择概率之和' E+ {. D3 _- K/ D' f& G
rNums=sort(rand(m,1));- d3 q: H# v7 q8 [) W0 T
fitIn=1;newIn=1;
! P8 @5 c$ |5 R9 D2 F+ Z4 p! swhile newIn<=m
; w* ~9 Y, n& y2 Y) N, S6 D5 F; H if rNums(newIn)<newfit(fitIn)) F4 v! q1 u, [# E
selectpop(newIn,:)=pop(fitIn,:); b0 I/ D7 w k
newIn=newIn+1;
2 M8 S6 G1 c! W3 l- Q else
) Q# X' D6 b0 a. @( L fitIn=fitIn+1;; T4 P9 J' @0 ?0 \* [
end
, c N1 u" Q* c& r0 \& o7 Bend4 a, M! N5 R- p. T$ L' I
%交叉操作
6 L# ]1 k5 X$ Vfunction [NewPop]=CrossOver(OldPop,pCross,opts)
/ A# N( r/ W& H+ B! e%OldPop为父代种群,pcross为交叉概率
9 J; L0 Q- \/ J2 z0 `global m n NewPop ( H5 J! S9 S% v; c3 | Y
r=rand(1,m);+ ` @, l) ~8 ?- y4 p* @
y1=find(r<pCross);+ @% C8 i; |0 q L% ~2 I8 o
y2=find(r>=pCross);
/ G. C! A/ [! p1 @- R8 X6 l- ^/ llen=length(y1);
" N F. K3 w& t# u* E. b$ s: yif len>2&mod(len,2)==1%如果用来进行交叉的染色体的条数为奇数,将其调整为偶数, u: R8 y, ~5 z
y2(length(y2)+1)=y1(len);
5 H- e m7 o$ ~& ?/ { y1(len)=[];" K0 {/ y4 u# j& Q
end
$ ]& \8 y9 y5 x" j9 }- Q4 Z0 u9 h: V4 aif length(y1)>=2
1 ^4 Z) @$ K. y! |, H( j! J' A for i=0:2:length(y1)-2
- M; O0 J3 e0 N+ R, E" \+ |$ e1 t, U if opts==0
% \6 ~2 O( Z& V' ] [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));, L7 u9 G4 H4 j1 G
else
5 I8 R u8 k; p [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));- e8 R# b3 ?9 d- Z$ t
end- a# T& c- L9 W; [5 T( Z
end
/ I* V% W& h0 ~, L, r9 xend2 y" h5 X- M1 w! ?& L. P6 T
NewPop(y2,:)=OldPop(y2,:); _( K1 U: p5 J8 |
5 J. J: w, v" ~
%采用均匀交叉 5 M* L2 K) R9 [6 N% r3 O P
function [children1,children2]=EqualCrossOver(parent1,parent2); t, d2 @0 {1 O# {5 p$ c' _2 A3 ?0 |% G
4 N* u: h! A" k$ r4 kglobal n children1 children2
8 J1 W& ~7 }* x1 Q4 Dhidecode=round(rand(1,n));%随机生成掩码
* T1 A. A$ s) I. g0 d3 Vcrossposition=find(hidecode==1);8 k3 L+ K. i( l" e+ {
holdposition=find(hidecode==0);
, P8 u; A( I, [! D7 z `+ Cchildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因1 r" j1 p2 D) @# H* n% J, X
children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因2 F, G0 r) \3 a4 v M ]+ ?" e
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因
, z$ p. P* f' |* q0 Ychildren2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因' w. i1 O" b- O6 _
1 u3 ^# a- @/ C) |2 x6 p
%采用多点交叉,交叉点数由变量数决定
0 _( i- Z/ p' L1 O6 Q; `
1 Q3 D$ D5 B3 @2 y' mfunction [Children1,Children2]=MultiPointCross(Parent1,Parent2)" n! \! ~9 z) E3 x$ S( I( I
4 c! V1 @3 a6 w( Q5 F; \' T2 p
global n Children1 Children2 VarNum
& k6 K. Q0 A# Q/ xChildren1=Parent1;! f( t. H" A P# n
Children2=Parent2;
: y1 w7 s) ?( \Points=sort(unidrnd(n,1,2*VarNum));+ L2 \' N, y$ L2 Q3 x
for i=1:VarNum; s4 v$ U) {/ }+ M$ K/ k- e+ i y
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
7 z1 j9 I3 F6 b Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
; {" [! J F- H. J) H$ O& aend& ]+ q) o8 ^+ _$ L p% b
$ M3 D4 n- l9 T" J4 _
%变异操作0 ^6 D. E/ Y% ~$ x6 j& q0 N
function [NewPop]=Mutation(OldPop,pMutation,VarNum)
& \9 z0 f1 m- C4 G, m4 e. O0 f2 s: R0 t
global m n NewPop
4 r6 [, V; }% sr=rand(1,m);; S$ B- ]7 @$ V4 U. {
position=find(r<=pMutation);
/ H) j/ G. B0 |( _len=length(position);
/ _6 f( c7 W2 g, \) Tif len>=1, e4 I" Q; V/ K' ~# ~0 P
for i=1:len
8 F y8 V4 l# A( H1 I k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点
6 a) \+ d1 s* K, K" |& ^ for j=1:length(k)2 x7 ?$ w9 Z0 k. T
if OldPop(position(i),k(j))==1
: h5 E1 i. G0 E1 C' `, i OldPop(position(i),k(j))=0;1 F6 ?; |7 c8 n4 K9 E
else
9 o# |/ F3 j' B1 n: y# X+ M OldPop(position(i),k(j))=1;
: X" J) F! G& T7 l8 y end, B) @* b8 F% C* N; O6 b, f% J
end
2 e* n+ L- P6 Y/ r7 ^' _3 x5 h end
' t, J3 d( n) }& m0 nend5 a# y1 Y. q$ e: P1 k# |! j+ I
NewPop=OldPop;& d0 y: t: e$ I) t; ^
7 D8 |0 N d- X5 L- u
%倒位操作
`+ [, ~9 j T
& R I& s) o0 b S' E! ifunction [NewPop]=Inversion(OldPop,pInversion); P7 c! Y1 U8 ^$ H' R
1 K7 y3 ^0 e4 _global m n NewPop9 r" J: R p; g, y& Q2 t
NewPop=OldPop;
/ k$ r" r0 G2 C3 D3 {; }5 H1 {r=rand(1,m);
5 \9 @! r$ h! K aPopIn=find(r<=pInversion);
& |8 {. ~- B1 C7 s Vlen=length(PopIn);
. j8 ^; E5 W2 Z8 s4 ~- vif len>=1 u. v) l7 M4 g* p" R: _7 j& o
for i=1:len
$ m) g/ O B. n d=sort(unidrnd(n,1,2));
* _, g# {$ F2 J7 } R" Q# v if d(1)~=1&d(2)~=n n# _% U3 Q0 o; x' ^4 N
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
& m& O9 R7 j# y# E: n- T' s. g3 z NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
% ?- n& P+ r$ `& g: s NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
* s5 c& L P$ g5 S end
; h8 }! n9 R f9 {1 b9 b+ y end
; h* L% S9 P, Fend1 {$ T+ z1 ~/ ^1 l
1 v, {% F# g( I
七 径向基神经网络训练程序
6 p1 B3 B. L6 b' Q d7 K, }( F- l4 C$ D9 P* |: O c! m; H6 ]
clear all;: E. ]( H# l I
clc;
& ?4 p/ _: e+ ~. ~$ b%newrb 建立一个径向基函数神经网络' a \5 `- K9 ]" C
p=0:0.1:1; %输入矢量
$ @9 R# Z9 f# h* ~t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量
6 ]/ c5 p+ V7 J# D" c, Kgoal=0.01; %误差7 h; Q) n7 m9 J2 `
sp=1; %扩展常数) X3 S0 {: B3 E( w
mn=100;%神经元的最多个数: W& I7 T; ]! R* _
df=1; %训练过程的显示频率
7 G, t$ ?; D3 n9 Z' k+ ^5 P: H[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络
4 ?" X! h+ i; r% [net,tr]=train(net,p); %调用traingdm算法训练网络
# H/ x1 k! e7 Y%对网络进行仿真,并绘制样本数据和网络输出图形
. }* F4 ~9 u5 IA=sim(net,p);) U; j4 F7 {3 W8 Y
E=t-A;
$ [; x9 ?1 `4 b" k* Wsse=sse(E);/ I' I1 ]/ t/ E
figure; 2 m K+ x- V7 p) b; \/ |, y% p9 D
plot(p,t,'r-+',p,A,'b-*');, {. P( g9 i7 W& ^
legend('输入数据曲线','训练输出曲线');
1 ~2 s$ z6 B, \4 Cecho off 7 p/ a- E( G' c! o" e* R
$ d6 e; A& n8 T4 a; ?" ?说明:newrb函数本来 在创建新的网络的时候就进行了训练!# _. d% s! Y5 ^" Z, w( C; Y, z! A% k
每次训练都增加一个神经元,都能最大程度得降低误差,如果未达到精度要求,2 r1 E' B( t" O1 b" ~
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!
4 Y6 s& x) U. M8 e
( c* |' D% Z5 V: s' `- E7 K
+ W6 R3 f. Z4 r训练结果显示:
4 R6 Z0 J! d2 W, v. { GNEWRB, neurons = 0, SSE = 5.0973
: E- t, k# Z eNEWRB, neurons = 2, SSE = 4.871391 y# _ G a( l6 A% G
NEWRB, neurons = 3, SSE = 3.61176! z, S# Q% \( M* J* Q" f" O
NEWRB, neurons = 4, SSE = 3.4875
+ w" @: t/ N7 B$ a# sNEWRB, neurons = 5, SSE = 0.534217( g" s! V% t# W0 H8 @' R. A. D
NEWRB, neurons = 6, SSE = 0.51785. r* ~& d+ B+ n: G; w- [
NEWRB, neurons = 7, SSE = 0.434259
+ i/ r; P: c1 }' \# BNEWRB, neurons = 8, SSE = 0.341518
& f1 w* H2 W1 x% P+ D3 ?NEWRB, neurons = 9, SSE = 0.3415197 f* i7 q4 G, x
NEWRB, neurons = 10, SSE = 0.00257832
. x( d, C8 ]; z/ r% b/ d; ?, r# i
e+ D6 B/ c6 M9 t八 删除当前路径下所有的带后缀.asv的文件+ K2 Q$ v1 t& F- H% T) V
说明:该程序具有很好的移植性,用户可以根据自己地3 e @* o- A% ~6 L
要求修改程序,删除不同后缀类型的文件!
' F$ i1 z8 W# r- p c2 Rfunction delete_asv(bpath) ! N4 c4 F6 A0 G% i
%If bpath is not specified,it lists all the asv files in the current
, t4 E3 t* i1 B4 D%directory and will delete all the file with asv
, ^* M4 @) ?: I4 d# q% Example:( z) K0 Z4 i/ I( A! B- a
% delete_asv('*.asv') will delete the file with name *.asv;
2 a6 n) s( ~4 U7 P$ r4 }% delete_asv will delete all the file with .asv.
( b/ q& `; M6 O3 j* D+ A
7 e' {. C# s5 B/ a$ Y/ q+ }if nargin < 1
! |9 J0 [3 g# |' s9 ]%list all the asv file in the current directory! v9 w- Z P% F2 w( _1 `' q u6 l
files=dir('*.asv');/ J: w/ E3 e( K
else2 f# {6 u. Q. b7 A
% find the exact file in the path of bpath
* ]7 A2 u" ~7 m6 P' x# B4 X9 e [pathstr,name] = fileparts(bpath);
- _9 V* q9 `/ h2 e if exist(bpath,'dir')& k* |! O }0 o0 Z$ L( x$ ^; \5 M
name = [name '\*'];2 \- U7 Y+ i' ]% |
end% W. D K' l ]: H$ T; P
ext = '.asv';
, J- ]8 p6 a) ?, G' a! V, n4 C files=dir(fullfile(pathstr,[name ext]));
# R2 H1 O/ q4 U+ a# j' tend- {6 z$ m! P1 V1 ]
3 h( D5 h6 B2 I" M
if ~isempty(files)- h- P5 n; v+ G+ c8 b! x: u7 D: {( l
for i=1:size(files,1)- m6 h5 i. R/ O9 N, _
title=files(i).name;: g. T% c8 y: x3 k$ n! I6 J
delete(title);( q8 A8 R8 N I E
end
1 {+ ~7 ?2 S. ~7 bend1 e( k; e; `# \- s9 J+ q8 y" z( ?' \
! S' z5 W9 ~& ]7 }5 R) V. Y, ^
; l0 j* c- A9 s4 d: E6 T; D: H同样也可以在Matlab的窗口设置中取消保存.asv文件!$ C# Z4 L0 _. L1 O8 N
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