* d u# X6 Z5 O. a4 t' q2 X! A%T0=clock4 I3 ^. Z$ Y% Q( Q, i
global path p2 D;' I9 z; R3 z! Y' ?8 c5 m* p4 C* V
[m,n]=size(CityPosition);1 K6 S# I$ g. Y g: t V
%生成初始解空间,这样可以比逐步分配空间运行快一些 ' K M. k' ?. o; Q9 ITracePath=zeros(1e3,m); ' j! D, Y; l: }* L' [$ S- H" Z& uDistance=inf*zeros(1,1e3);) O v, b/ Z1 s) q6 r
9 q1 p, D/ T0 k. I& a/ v9 t' OD = sqrt((CityPosition( :, ones(1,m)) - CityPosition( :, ones(1,m))').^2 +...' c: J F. F9 L$ D. \0 V
(CityPosition( : ,2*ones(1,m)) - CityPosition( :,2*ones(1,m))').^2 );, P3 M/ N; A* ]" [
%将城市的坐标矩阵转换为邻接矩阵(城市间距离矩阵)( U+ S% j8 r% F) e/ v, ]$ o
for i=1:pn3 u+ ^7 h& L. E* I6 `- Y' ^" M
path(i,:)=randperm(m);%构造一个初始可行解. k4 e r- f$ g- W% ?3 Y8 P' W
end , {5 J& J; w* |6 gt=zeros(1,pn); A* i) G% z/ k" M! i- F3 h2 c8 [2 [
p2=zeros(1,m);, N t: d: A V) S; a5 `
( J! k; E% G' fiter_max=100;%input('请输入固定温度下最大迭代次数iter_max=' ); w0 @+ A% u Z2 [m_max=5;%input('请输入固定温度下目标函数值允许的最大连续未改进次数m_nax=' ) ; / q' V! J* V. o# i3 G& B* [%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 S. A6 N! X$ O' Y. |5 \
%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8 v0 d3 N6 J. }& h6 u
%人为的使初期 iter_max,m_max 较小,然后使之随温度降低而逐步增大,可能 5 v1 ^5 ~& _% Y5 @. H%会收到到比较好的效果 5 C% P+ ?& b! {' B5 W9 f/ ^: {7 [5 A. j" U3 L: d
T=1e5;+ M8 j* `) j) W9 W" C
N=1; ( f8 z; `6 ]4 Y7 A: \, ]) Gtau=1e-5;%input('请输入最低温度tau=' );9 o; B& N7 S, o' O5 ^
%nn=ceil(log10(tau/T)/log10(0.9));8 G, _' \' B9 n- L. R: Z
while T>=tau%&m_num<m_max / E+ Q; \: h3 I7 J
iter_num=1;%某固定温度下迭代计数器& Y& `" g, B8 n0 k
m_num=1;%某固定温度下目标函数值连续未改进次数计算器7 F. A+ {, ?' M4 Y2 N2 B
%iter_max=100;5 M ~) K$ v9 v8 j6 C
%m_max=10;%ceil(10+0.5*nn-0.3*N);) |5 f- |/ H$ A0 _' g) n
while m_num<m_max&iter_num<iter_max( T3 x2 p* x, V- `
%MRRTT(Metropolis, Rosenbluth, Rosenbluth, Teller, Teller)过程: & V# k" o% H9 S/ z9 g %用任意启发式算法在path的领域N(path)中找出新的更优解 7 U) A2 G4 E+ k. j" W5 P9 A for i=1:pn , p9 H# u6 k, @6 K2 y% W Len1(i)=sum([D(path(i,1:m-1)+m*(path(i,2:m)-1)) D(path(i,m)+m*(path(i,1)-1))]);6 K. x# T7 D$ T; P$ L, ?
%计算一次行遍所有城市的总路程 7 t6 N' ]: p4 S( _
[path2(i,: )]=ChangePath2(path(i,: ),m);%更新路线 5 e3 A9 c' j1 t! 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))]); 5 i# I$ P( n) Q; z2 R. n% n$ G end: h8 l( ^ d* Z; G" N8 r3 t2 L
%Len1 p \$ q+ N- ~& l% D& h) z+ b7 N %Len2 7 m3 c% L Y/ s %if Len2-Len1<0|exp((Len1-Len2)/(T))>rand 6 q; U* @5 J# d3 }. { R=rand(1,pn);. B0 z6 E Q. r$ d
%Len2-Len1<t|exp((Len1-Len2)/(T))>R( y! z8 ^+ ]0 y2 t$ {$ _& l
if find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0) 8 C/ b2 B; q2 @ path(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : )=path2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0), : ); 5 P, u" U1 {/ V* b! ] F9 J Len1(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0))=Len2(find((Len2-Len1<t|exp((Len1-Len2)/(T))>R)~=0));" [" j( S* ~. ?$ N7 D
[TempMinD,TempIndex]=min(Len1);& I- ]( z4 z+ b J# h# q& T% f4 j" o
%TempMinD 7 @+ f8 ?( v3 ^ ]' w- } TracePath(N,: )=path(TempIndex,: );2 V: W8 Q: @1 \: [. f- g% ?
Distance(N,: )=TempMinD; * K3 O1 R' D3 B% |, k0 Y N=N+1;% a. v+ U% L& j
%T=T*0.90 v$ X1 u% r" l9 M5 O7 U; l
m_num=0; & K; }) r% c. G" i; Y: e* A else ' \5 }( i2 f6 C1 f* C m_num=m_num+1;0 [5 i9 r# Q* Z: p$ S7 Z% J2 Q
end2 C# v' ^% U" D/ a
iter_num=iter_num+1;4 V( H% n# G6 V7 h
end ' v+ D% e6 m& T6 _* @. m T=T*0.9 / [8 O. `+ q$ a; s% C' j%m_num,iter_num,N8 q3 P0 ^; C+ x. d E4 v! Y- m
end & ^- R8 I" i- B9 b9 Z[MinD,Index]=min(Distance); " n! o" y9 z0 f' g# F; Q7 x8 A0 N ~BestPath=TracePath(Index,: );$ R) N+ _; l* O* a
disp(MinD) , p M6 S: s/ S+ i%T1=clock % \) M3 b) v* a / [( Z' H; u. h; ?4 M, ^
4 \1 t* ~) O% { v6 `+ `% S
%更新路线子程序 , D" V" O5 B7 ~# K' M
function [p2]=ChangePath2(p1,CityNum)' }6 Q/ B" E( A9 w- w& b
global p2; 2 m3 B" e0 W: v4 r& Swhile(1) 8 P5 U& o" e- w ~ R=unidrnd(CityNum,1,2); 5 p, D. T/ O) G9 m# E3 F" l e6 O% Z( B if abs(R(1)-R(2))>1- D% c$ [, v; E ]
break;+ ?. e" O/ P% l$ {& F
end & l( H' y% w: D yend . y! i% c; v+ `; k" h7 {; ~R=unidrnd(CityNum,1,2);2 T$ s" y, W8 z. h i- x
I=R(1);J=R(2); 9 B. v! s4 v2 s%len1=D(p(I),p(J))+D(p(I+1),p(J+1));( `) K: _0 j, @
%len2=D(p(I),p(I+1))+D(p(J),p(J+1));- |1 y$ d2 S$ h6 D
if I<J & k4 l0 y8 y( {1 [( E p2(1:I)=p1(1:I); + x' I) C7 A$ v* Q3 t p2(I+1:J)=p1(J:-1:I+1); , d3 w. ]9 Q& i4 M) a9 {' m& ` p2(J+1:CityNum)=p1(J+1:CityNum);& D; h! @: w; M; n
else' g$ \& p# W1 D6 V0 P
p2(1:J)=p1(1:J);1 a0 c- J- ^" P6 n$ v+ o
p2(J+1:I)=p1(I:-1:J+1);) x% I# R) g7 l% S _' p C. ?
p2(I+1:CityNum)=p1(I+1:CityNum); ( `2 V2 A) l$ b8 r z! [end 9 Y; Z, R7 T; U# h% a& Y3 |4 D% f2 _2 c1 ~4 Q
六 遗传 算 法程序: 9 a1 I9 n% O+ e' J, u6 |( q 说明: 为遗传算法的主程序; 采用二进制Gray编码,采用基于轮盘赌法的非线性排名选择, 均匀交叉,变异操作,而且还引入了倒位操作!# h" f/ x: \8 [( N9 z. F4 l+ d7 w
7 ~# Z7 i; [( Z; q8 wfunction [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options) 4 ]" T' t2 v, |/ y% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation) ; z1 i. Z: i U! t! K% Finds a maximum of a function of several variables.- Y+ Z. D1 V$ c( @
% fmaxga solves problems of the form: ' ?! T6 B- Y. P& @ j b
% max F(X) subject to: LB <= X <= UB 1 \$ a7 J8 e; b
% BestPop - 最优的群体即为最优的染色体群8 _0 {0 @, a/ n
% Trace - 最佳染色体所对应的目标函数值( N) ^2 {* t( V; H5 k
% FUN - 目标函数 0 Y+ d2 V- n- P, e" b% LB - 自变量下限 - X7 {* M. \1 `& F% C% UB - 自变量上限 % u- |+ {4 _: X9 P! M3 {4 c: m3 J% eranum - 种群的代数,取100--1000(默认200)* R @ A& @& f# g# Z( l) R# L# j
% popsize - 每一代种群的规模;此可取50--200(默认100)$ ?' v1 K9 J, Y, o3 v3 X! U
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8) u0 S" `- I+ y6 D
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1); T. y+ P+ }# @9 \, i8 Y8 x
% pInversion - 倒位概率,一般取0.05-0.3之间较好(默认0.2)9 C( c. B/ C# z0 @
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编 % Z' _. N. l( s4 d+ l%码,option(2)设定求解精度(默认1e-4) ! J3 C- K) C1 A& z0 g0 ?% - l1 S9 l' G: t ~0 R# W% ------------------------------------------------------------------------ ! F6 `) D1 r% g# L' d& ]% M , y, j" _4 b6 Q' Q |2 eT1=clock; 5 ]% f9 a2 }3 T, e. ^if nargin<3, error('FMAXGA requires at least three input arguments'); end 5 b# c2 j. E7 v: j: Q) Mif nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end 6 Y% U8 g) \. r; O% S5 Rif nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end& m5 l2 p9 m2 D( O/ d+ h5 l
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end 9 R! }4 d1 m6 I5 ~# @& M: q( Cif nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end, g1 B! |5 D* X3 Y
if nargin==7, pInversion=0.15;options=[0 1e-4];end3 H# Y5 c) w) o# m$ G8 S
if find((LB-UB)>0) 6 n) {1 z4 |' }5 h1 | error('数据输入错误,请重新输入(LB<UB):'); # c2 T B. x+ v6 X' S# hend/ a+ G" C7 h. I4 o* B7 \8 Y
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));% S/ o3 c$ [# F, T& _! M/ |
disp(s); h- {, H6 R# S% z
0 b9 _3 B/ C6 Z% M4 r+ }/ Y! U
global m n NewPop children1 children2 VarNum 6 l, s0 O" j& ]' k & d) N6 {0 z" a: m \bounds=[LB;UB]';bits=[];VarNum=size(bounds,1); 0 E/ P+ j+ T/ {, [2 A- x2 @( mprecision=options(2);%由求解精度确定二进制编码长度 9 [: c# |+ E* G, _4 ]& cbits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间 / O2 }/ \# U9 C" E* |8 r[Pop]=InitPopGray(popsize,bits);%初始化种群) H7 }( \9 x* @* H: D: d7 x, e9 h* x2 T
[m,n]=size(Pop); 0 @2 S+ A6 ~" U1 u% t0 T/ k/ \. TNewPop=zeros(m,n);) N/ m; L! Z) m; x, H
children1=zeros(1,n); % p5 `+ O8 B" @* mchildren2=zeros(1,n); & C2 [( Q: n- N1 ]pm0=pMutation; % I2 r* r) {% H/ B5 E, d# _BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace " S* I5 D4 [# |; \! l `0 n6 v4 B+ NTrace=zeros(eranum,length(bits)+1); ! g: B' L. R4 w6 ei=1;$ Y) L' d% \. Q; Y( B7 g- O0 k
while i<=eranum( x. A- ]% @5 b. d
for j=1:m+ f$ t: D5 {; F) ~: y" G
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度 " U, |6 ? R; m- k end ) l/ e: }* o% `; [( w [MaxValue,Index]=max(value);0 l( n+ T/ K; o5 k3 ?
BestPop(i,:)=Pop(Index,:);7 m9 ]* w. R' }( H/ R8 }% F2 l' |( h0 |
Trace(i,1)=MaxValue;: R1 Y: |. W8 \" [- P
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits); $ P$ r! \, `6 X+ _" C8 J [selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择6 q4 n$ ?! A# `7 b: ^" \9 g
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum)); 0 {0 l1 Y# u0 x% U, T%采用多点交叉和均匀交叉,且逐步增大均匀交叉的概率, _, f, A: e5 T" n5 S1 H
%round(unidrnd(eranum-i)/eranum); k& \4 u# e% _
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异 7 Q8 T- u' G7 n6 a/ ` [InversionPop]=Inversion(MutationPop,pInversion);%倒位' e% A& R% I3 G: h# e) ^7 ` h8 d' f
Pop=InversionPop;%更新" i/ F% w z1 j0 a8 a; d# @/ y. _! s' g( h
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4); & a) t: { L' r% j+ P
%随着种群向前进化,逐步增大变异率至1/2交叉率1 t% i+ |. ?. `4 X
p(i)=pMutation;4 T! U/ o/ w( D6 O/ v8 a
i=i+1; 5 p$ h, s+ D* @# m4 L- F6 ] {' Send 6 ]: m1 l+ A. \% `, m( J+ T# r2 Gt=1:eranum;) W5 }' ?! v' r
plot(t,Trace(:,1)');4 w4 O4 N# C& Z
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)');* \2 w6 }5 {3 o& `1 `
[MaxFval,I]=max(Trace(:,1)); - i3 A' }+ s9 q0 ~X=Trace(I,(2:length(bits)+1)); ! N/ h2 Q5 g7 I Qhold on; plot(I,MaxFval,'*');4 a/ g+ n' U9 H7 u# J
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]); / Y# Y$ i' C3 A9 b$ Ystr1=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,:)));, ?: \5 E* d1 o+ J
disp(str1);$ I/ T$ Y. M8 @5 P F9 D
%figure(2);plot(t,p);%绘制变异值增大过程 S/ Y. [: ?( \1 y
T2=clock; 3 r3 `" I9 N) i/ z! C* g5 t! lelapsed_time=T2-T1;9 Y" W( `( S* G) d8 ~- D* R
if elapsed_time(6)<0 ( r# l& }' U8 ^9 `" @9 t7 ~8 p" h elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1; 8 A+ C8 d* `$ s- Kend ) V9 N& m* @2 S* d! k; xif elapsed_time(5)<0 " N4 s, V7 Z( H; a elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1; l# U* I" I1 t4 j$ y' Y" |, I0 l0 r
end %像这种程序当然不考虑运行上小时啦, A k9 ]9 o: s" L, [
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)); % v+ }! F# p! e9 Y: Mdisp(str2);( `0 v+ G; W; i8 ?% \
2 K' n9 l7 {% S6 s: C& l3 x
: e$ b1 [. U7 \% u+ U
%初始化种群 * Z( u' O) e1 y* l' ^% g%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 ?2 O# v5 \4 y: I- ^function [initpop]=InitPopGray(popsize,bits)! U# ?- N8 @$ B. P3 P& ?8 s# B6 @+ }+ L, N
len=sum(bits); 6 h% \$ e L2 F8 K9 T( {& Ninitpop=zeros(popsize,len);%The whole zero encoding individual3 Z7 j' P& G! c0 [7 I7 ^& m
for i=2:popsize-1 # J4 X& f! o7 r1 _- h% i pop=round(rand(1,len));1 @! H0 ^1 S) P: ?7 M; j9 f
pop=mod(([0 pop]+[pop 0]),2);9 Z3 m% o1 k( X
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2) 5 Z5 @$ z) Z+ Y1 c- a %其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n) 7 p9 r) @- X, f- K) S. o' C9 k initpop(i,:)=pop(1:end-1); `4 t% |! `- Q* Z1 S3 N
end0 }; m6 [; b. B$ h) x
initpop(popsize,:)=ones(1,len);%The whole one encoding individual1 k$ ?" a& P* E2 ~& U
%解码 : L# Z' x) e5 |, O0 I5 c$ n2 R 4 L# ]/ o% H6 F: V5 v- m; lfunction [fval] = b2f(bval,bounds,bits) " _9 e! i& K0 H$ r/ U# ^' V! B( }% fval - 表征各变量的十进制数6 f# d4 l* Z5 z y6 z% I
% bval - 表征各变量的二进制编码串# Y. Z) O8 U7 |. `
% bounds - 各变量的取值范围$ V0 H3 y- X& g
% bits - 各变量的二进制编码长度 $ P$ L! \3 ]$ z, S4 [: c" yscale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables. i& l' V o; E
numV=size(bounds,1); 5 t9 _6 g) |3 f, g! Y! kcs=[0 cumsum(bits)]; * g2 k- ]; F8 J9 x3 rfor i=1:numV 8 s& i$ h# X: D7 V+ B' a a=bval((cs(i)+1):cs(i+1)); & P. C/ G& }1 B$ s# ~- M fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1); ; M# @( Y6 b) | Xend: ^+ h7 i% `, [3 Q9 v3 _3 T
%选择操作 / [2 V* n/ W0 p/ n# o2 N% U1 x* o%采用基于轮盘赌法的非线性排名选择! n( T9 Y8 B6 I7 J: V4 y
%各个体成员按适应值从大到小分配选择概率: . c& U g1 W" s( h( @- T" u- r%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1& M3 I b1 s/ a
T; \/ w8 ~( _
function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)4 d1 [ V, T0 x2 l7 s$ y" f
global m n+ R% p5 w# e- x0 ?# K. E
selectpop=zeros(m,n);5 Q* {7 l4 w, [& e+ C, |, h; Y
fit=zeros(m,1);0 U' G7 w6 z4 @2 @* Q7 Q
for i=1:m 5 ^! Y' b: |/ G2 i8 T fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据 / F- `3 a/ u; Y9 _; x1 n; Send. I* n. c( c5 r' |$ |7 @' H
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)3 _: a2 R$ G, P8 g V6 m* i
q=max(selectprob);%选择最优的概率 % W9 f x% X% `* m+ o7 E0 Qx=zeros(m,2);" ?# }3 F$ m2 Y; K# }
x(:,1)=[m:-1:1]'; 8 h" `/ P5 W9 @; i[y x(:,2)]=sort(selectprob);4 M8 ]; r: z4 j/ A
r=q/(1-(1-q)^m);%标准分布基值/ G" ^3 q; q# D" w9 c
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率 0 z5 v8 e: r# pnewfit=cumsum(newfit);%计算各选择概率之和. E1 r: j) ]+ Y3 X
rNums=sort(rand(m,1)); 1 p3 U, l1 G4 @5 J+ m9 m9 H! KfitIn=1;newIn=1;2 T3 _/ F0 g: {/ f. |( }. K0 T
while newIn<=m 4 m& N4 {" V3 e { if rNums(newIn)<newfit(fitIn)6 d6 e5 f0 I8 t
selectpop(newIn,:)=pop(fitIn,:);7 K% E: X0 Q" j. w% ^+ b2 p
newIn=newIn+1; $ {. T, M4 f& f% k7 l9 I else 0 Z' S% v( ^# G9 R fitIn=fitIn+1; - r6 Y1 X. g6 I$ g* Y/ ^ U. O& D end m |7 B8 Y9 [ T* t
end) d' y3 \- c* s! ?" \, Y k+ \
%交叉操作 ! u$ |; ]6 n7 r0 x" x E ^4 afunction [NewPop]=CrossOver(OldPop,pCross,opts)4 p! U( x0 x% ]* [ ?/ A0 c% |9 ]
%OldPop为父代种群,pcross为交叉概率 : c" a1 ~2 F1 @; q3 Rglobal m n NewPop $ g8 i' b$ z+ q; \7 E6 N. m, R
r=rand(1,m);+ y. z. z, f( {: x
y1=find(r<pCross);% S7 y( H T3 L- q5 j8 i( Y
y2=find(r>=pCross);! {6 F$ Z9 e7 p+ v
len=length(y1); 0 _" L4 y _) D4 v8 p7 A7 _( ]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 2 A/ h ?$ k: C0 U& R y2(length(y2)+1)=y1(len);9 s( U5 Y1 ]+ o
y1(len)=[]; . k* C5 T7 e! zend8 y6 ]* A: x( L$ W# U( w
if length(y1)>=2 8 t& x: t. R. ]+ Q for i=0:2:length(y1)-2 & z; g6 h7 y; g9 T- d v if opts==0 ! o9 t+ s8 l/ k( _: u [NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:)); % j" ]3 _. A Q* P: Y6 V$ W else- U7 z4 T; r. I* z
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));+ v" W2 x- [: a, F
end 1 h3 L, l! [. }6 ] end 7 J: ]8 P( z# d0 P C6 |* Wend8 q" a4 K+ e! Y5 B: t! C
NewPop(y2,:)=OldPop(y2,:); . S) Q0 r1 t4 h$ X0 Z3 M+ `% s |6 J* ]( {+ }
%采用均匀交叉 7 R, [- S3 N8 D8 {4 _
function [children1,children2]=EqualCrossOver(parent1,parent2)$ y1 i+ b4 ^# D
- w8 g# {; B" T7 N0 y! T5 Eglobal n children1 children2 ! P R1 a* i9 H& [/ C' ^
hidecode=round(rand(1,n));%随机生成掩码5 x) c' A8 [" r# G: ~
crossposition=find(hidecode==1);$ v; O/ D% J3 j/ i
holdposition=find(hidecode==0); 5 P8 ]- g' S/ i' W# D+ _1 Mchildren1(crossposition)=parent1(crossposition);%掩码为1,父1为子1提供基因 " p4 m6 L$ l# \3 B. @children1(holdposition)=parent2(holdposition);%掩码为0,父2为子1提供基因8 j; _ V0 Q$ p; D( f2 R6 p/ {* o
children2(crossposition)=parent2(crossposition);%掩码为1,父2为子2提供基因7 A2 A9 B0 _2 i( a/ A$ k
children2(holdposition)=parent1(holdposition);%掩码为0,父1为子2提供基因7 w# X1 G' B1 w. Q8 T
& [( a& y4 @/ L4 o4 R
%采用多点交叉,交叉点数由变量数决定 " {( Q. S$ Z# j7 C. q w) X9 Y. M2 p8 N+ j Z
function [Children1,Children2]=MultiPointCross(Parent1,Parent2)& U. N: r9 Z+ u6 q4 e1 s
M& O: }2 t5 P6 e! {& Y# i2 k aglobal n Children1 Children2 VarNum 0 b+ C0 q, H9 j* H0 oChildren1=Parent1; + o, E$ {: C$ Y4 Q: c6 T+ L4 _Children2=Parent2; ! G9 r y7 G% [5 m) hPoints=sort(unidrnd(n,1,2*VarNum));3 V9 Y/ Y! j: g0 q) O, }
for i=1:VarNum n. H3 g- V4 \. M; f$ x5 H Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i)); 4 ?/ R! G2 v1 W6 x% g# C) \0 f. v+ X Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i)); ' w3 P l+ p7 q; c, j% Z/ j# Vend+ G6 f3 P8 D2 G {: I
; q) W4 B8 s' F" d5 g, v
%变异操作 & j% v1 w- L& y" {! |0 hfunction [NewPop]=Mutation(OldPop,pMutation,VarNum) 5 L3 y# W( X/ v% f0 D 2 X: L" S* H) S4 n" \$ }global m n NewPop! B {: Y: b: d" R: v' t7 M
r=rand(1,m); 1 x$ C5 K. v; \position=find(r<=pMutation); 0 g6 C2 L) F3 }+ Dlen=length(position);# h* V$ x) b- o- F
if len>=12 x, A2 j$ q2 K6 M: [4 N0 V
for i=1:len$ X6 f" {: g' H2 P W
k=unidrnd(n,1,VarNum); %设置变异点数,一般设置1点 - x" \3 V, O D/ N for j=1:length(k) 6 [8 p5 e3 p" `* L B+ m if OldPop(position(i),k(j))==1 1 Q0 E- w4 Q) C/ g- T OldPop(position(i),k(j))=0;1 B" F) w/ K' t
else 9 r3 S0 x: t K6 V/ u2 k8 R1 X4 \ OldPop(position(i),k(j))=1;7 b$ L6 d, O# a4 M5 z
end 9 ^; o1 T6 K) b( ?+ w end & H# x; ]( Z' ?) P end" E2 C; ~; t$ n" M1 l: V h v3 N
end i% h9 ?9 D# [+ d) D9 hNewPop=OldPop; 1 k' o( V/ r R9 v7 ~0 u4 l+ r& X8 Z; n; d1 j6 \8 n9 l- x
%倒位操作 . B5 R O, F: o( e 2 Y# U0 S, V. `& Sfunction [NewPop]=Inversion(OldPop,pInversion)! x5 B8 K8 m& ]+ c' I9 v- d; @
& e3 t1 k. x" ]: A/ d) Mglobal m n NewPop# ]; H; H/ B0 C4 T$ r3 S+ l
NewPop=OldPop;& H1 Y$ u9 S1 k, e5 _# N
r=rand(1,m); # u5 _$ ?8 ]4 M, Y0 aPopIn=find(r<=pInversion); % `: c7 L6 z7 t, w! ]- D* n& u' hlen=length(PopIn); 1 v9 p$ R! `0 n0 \if len>=1 ! i2 N- M0 C1 W9 [6 K$ c0 i for i=1:len % Q ]- `* z2 _. }" K d=sort(unidrnd(n,1,2)); 9 w1 V8 B) `+ f1 w) U if d(1)~=1&d(2)~=n7 n! m8 Z' H' l% l# q
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);: j2 P; X2 F6 _' M* G! @4 y2 l
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1)); 8 b3 k1 b) H6 f" {* \( m# N: s9 s# i NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);# c) R) n; E& [" |: z
end; Q2 M; C; ~/ W
end1 {1 d% E# W) B, _0 p
end 5 @) s- s8 n; q( k0 v! G& v' l7 ~ # l3 }4 p5 K) z0 C/ H Y q七 径向基神经网络训练程序 5 N4 f: b2 E) e: n" d" ?. O( {$ R. A3 q$ \9 h
clear all;& T* s+ J; u1 F, {) e/ q0 b
clc;6 }1 r! ]' k# g1 ]0 O0 }5 l
%newrb 建立一个径向基函数神经网络% W: Q L9 x) |( K& Y% {
p=0:0.1:1; %输入矢量/ s2 G7 C/ F; k, ^
t=[0 -1 0 1 1 0 -1 0 0 1 1 ];%目标矢量" {7 v6 U( Z7 j4 A, S K5 l
goal=0.01; %误差 ' y8 ~+ ^7 n, c) C2 _sp=1; %扩展常数- w2 x8 J2 }$ T
mn=100;%神经元的最多个数# [ j7 a7 `7 o5 D* ?
df=1; %训练过程的显示频率" X% Y1 ~# Y# {- r7 Q
[net,tr]=newrb(p,t,goal,sp,mn,df); %创建一个径向基函数网络! ?. X- z. Y7 b1 M) T# ~( ~: u
% [net,tr]=train(net,p); %调用traingdm算法训练网络 / P8 [0 Z2 Z9 ` O; I" Z5 i%对网络进行仿真,并绘制样本数据和网络输出图形, F z! c; l1 [7 j* x
A=sim(net,p); / v0 ]- ^2 C$ gE=t-A;4 I8 e: j0 ^7 U; Z- `
sse=sse(E); & j. x2 h8 H2 ^& V' Z' ^figure; 7 ]6 e- d5 W2 N$ Dplot(p,t,'r-+',p,A,'b-*');3 Q$ l" G; }4 w1 d/ ~
legend('输入数据曲线','训练输出曲线');2 A/ W! J! }* F0 `$ T, Y
echo off 5 s, N; s3 z1 I. |0 C. G$ u8 h
2 O# Z* H; ~1 u( M( Z! @4 h( I6 F说明:newrb函数本来 在创建新的网络的时候就进行了训练!6 }. c { g: C
每次训练都增加一个神经元,都能最大程度得降低误差,如果未达到精度要求, $ |5 P. |' g. [8 ^. C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! 9 \6 e% r( e) @- h5 G" O 7 t9 p% f' x3 L* }( a# `: {) k q! q/ x . Q' t' U5 Y2 w c0 t训练结果显示: ) S2 M3 V% f$ \4 _9 x9 F* YNEWRB, neurons = 0, SSE = 5.0973 2 V/ s. G5 k6 I# CNEWRB, neurons = 2, SSE = 4.871390 R. X6 Q' j% x9 F, j- P+ B
NEWRB, neurons = 3, SSE = 3.61176 3 r- ]9 g- c# t' n b6 T" q; A- JNEWRB, neurons = 4, SSE = 3.48756 a4 `$ L6 P) V: X
NEWRB, neurons = 5, SSE = 0.5342175 r- W' x9 F1 L3 R" E& K' P8 j
NEWRB, neurons = 6, SSE = 0.517851 j0 P; F3 v b( @
NEWRB, neurons = 7, SSE = 0.434259 : M4 c- j& [2 _. Y8 XNEWRB, neurons = 8, SSE = 0.341518 & ^; y4 s h L0 DNEWRB, neurons = 9, SSE = 0.341519- q$ B7 S6 k& C- r5 w# O# J
NEWRB, neurons = 10, SSE = 0.00257832& A% p6 ?2 V# Y0 s% |9 G& M2 ]
' I: V+ W: y( o$ M0 B
八 删除当前路径下所有的带后缀.asv的文件 3 \; x5 `2 {0 V说明:该程序具有很好的移植性,用户可以根据自己地 : `# v7 q$ s; Z, Z: ?$ ?# e4 b要求修改程序,删除不同后缀类型的文件! ! ^+ M# S. z0 `5 i. W
function delete_asv(bpath) ; q- r5 [2 X4 ?, z0 L%If bpath is not specified,it lists all the asv files in the current& r6 a8 i, {! z8 @
%directory and will delete all the file with asv ' f1 B6 X4 F+ {4 i4 a* z% Example: $ d: O$ D/ N) m9 |2 A- N% delete_asv('*.asv') will delete the file with name *.asv; 3 E' v6 U) L! O' x. c6 E8 }+ D% delete_asv will delete all the file with .asv. ; j, F- J/ ~/ v6 S0 q* n1 m! a1 i$ D3 `
if nargin < 1' a6 V; v* ~/ W0 [" l+ ~
%list all the asv file in the current directory 8 K; Z2 T) r r2 c( m4 l* t files=dir('*.asv'); + |, X$ @" W4 o7 j% Uelse ; K, L- G: S7 v. x: q @; u5 d% find the exact file in the path of bpath 6 _9 c2 d- d: D# _2 }. c [pathstr,name] = fileparts(bpath);! a4 I/ Z1 `% `/ f2 s
if exist(bpath,'dir')- N5 x7 @+ I2 x
name = [name '\*']; 6 i" E& c J" c! F end }1 {) Q' E$ B( s8 |9 M/ x, Z ext = '.asv';& B; g8 x6 A2 B" O0 o, b
files=dir(fullfile(pathstr,[name ext])); + V+ b2 Q3 v0 C8 u8 {7 _7 k$ gend & V( s" d9 _ }4 `! T* |; V ' O% x: ]3 n9 w' ^8 {: x0 pif ~isempty(files)" D/ m5 `3 } j$ u ^; P: K
for i=1:size(files,1)" R0 E* [* t8 E9 A& V/ m1 ]
title=files(i).name;$ u0 Q" E+ z) d- {, l4 v# d6 ?
delete(title); 5 S6 w5 }* D' E- I @* q# M end . d, t& W. t. y: f( |end1 d9 I( t l( _9 E4 p7 a5 T+ j
$ a. E9 h3 F1 a( n* T* M3 U4 n