matlab 高階演算法程式**彙總
% renkou1=renkou(:,1);%年末常住人口數
% renkou2=renkou(:,2);%戶籍人口
% renkou3=renkou(:,3);%非戶籍人口
% shjian=1979:2010;
%以上資料自己給
x0=renkou2';
n=length(x0);
lamda=x0(1:n-1)./x0(2:n)
range=minmax(lamda)
x1=cumsum(x0)
for i=2:n
z(i)=0.5*(x1(i)+x1(i-1));
endb=[-z(2:n)',ones(n-1,1)];
y=x0(2:n)';
u=b\y
x=dsolve('dx+a*x=b','x(0)=x0');
x=subs(x,,);
yuce1=subs(x,'t',[0:n-1]);
digits(6),y=vpa(x) %為提高**精度，先計算**值，再顯示微分方程的解
yuce=[x0(1),diff(yuce1)]
epsilon=x0-yuce %計算殘差
delta=abs(epsilon./x0) %計算相對誤差
rho=1-(1-0.5*u(1))/(1+0.5*u(1))*lamda %計算級比偏差值
%以深圳人口資料得到**模型及**誤差相關資料
lamda =
columns 1 through 8
0.9741 0.9611 0.9419 0.8749 0.9311 0.9093 0.9302 0.9254
columns 9 through 16
0.9245 0.9278 0.9442 0.9376 0.9127 0.9148 0.9332 0.9477
columns 17 through 24
0.9592 0.9445 0.9551 0.9562 0.9594 0.9461 0.9469 0.9239
columns 25 through 31
0.9140 0.9077 0.9243 0.9268 0.9312 0.9446 0.9618
range =
0.8749 0.9741
x1 =
1.0e+003 *
columns 1 through 8
0.0313 0.0634 0.0967 0.1322 0.1727 0.2162 0.2641 0.3155
columns 9 through 16
0.3711 0.4313 0.4961 0.5647 0.6380 0.7182 0.8059 0.8999
columns 17 through 24
0.9990 1.1024 1.2119 1.3265 1.4463 1.5712 1.7033 1.8427
columns 25 through 32
1.9936 2.1588 2.3407 2.5375 2.7499 2.9780 3.2194 3.4705
u =-0.0665
31.3737
y =-472.117+503.377*exp(.664533e-1*t)
yuce =
columns 1 through 8
31.2600 34.5876 36.
9641 39.5040 42.2183 45.
1192 48.2194 51.5326
columns 9 through 16
55.0734 58.8576 62.
9017 67.2238 71.8428 76.
7792 82.0548 87.6928
columns 17 through 24
93.7183 100.1578 107.
0397 114.3945 122.2547 130.
6550 139.6324 149.2267
columns 25 through 32
159.4802 170.4382 182.
1492 194.6649 208.0405 222.
3352 237.6121 253.9386
epsilon =
columns 1 through 8
0 -2.4976 -3.5741 -4.0540 -1.6983 -1.5992 -0.3594 -0.0826
columns 9 through 16
0.5266 1.2824 1.9183 1.4262 1.3772 3.4408 5.6352 6.2772
columns 17 through 24
5.4417 3.2222 2.4203 0.2055 -2.4047 -5.7350 -7.5924 -9.7767
columns 25 through 32
-8.5502 -5.3082 -0.
2192 2.1651 4.3395 5.
7348 3.8379 -2.9086
delta =
columns 1 through 8
0 0.0778 0.1070 0.1144 0.0419 0.0367 0.0075 0.0016
columns 9 through 16
0.0095 0.0213 0.0296 0.0208 0.0188 0.0429 0.0643 0.0668
columns 17 through 24
0.0549 0.0312 0.0221 0.0018 0.0201 0.0459 0.0575 0.0701
columns 25 through 32
0.0567 0.0321 0.0012 0.0110 0.0204 0.0251 0.0159 0.0116
rho =
columns 1 through 8
-0.0411 -0.0271 -0.
0066 0.0650 0.0049 0.
0282 0.0058 0.0110
columns 9 through 16
0.0119 0.0084 -0.0091 -0.0020 0.0245 0.0223 0.0027 -0.0128
columns 17 through 24
-0.0251 -0.0094 -0.
0208 -0.0219 -0.0254 -0.
0111 -0.0119 0.0126
columns 25 through 31
0.0232 0.0300 0.0122 0.0095 0.0048 -0.0095 -0.0280
% optimizing a function using ****** genetic algorithm with elitist preserved
%max f(x1,x2)=100*(x1*x1-x2).^2+(1-x1).^2; -2.0480<=x1,x2<=2.0480
% author: wang yonglin (
clc;clear all;
format long;%設定資料顯示格式
%初始化引數
t=100;%**代數
n=80;% 群體規模
pm=0.05;pc=0.8;%交叉變異概率
umax=2.048;umin=-2.048;%引數取值範圍
l=10;%單個引數字串長度，總編碼長度2l
bval=round(rand(n,2*l));%初始種群
bestv=-inf;%最優適應度初值
%迭代開始
for ii=1:t
%解碼，計算適應度
for i=1:n
y1=0;y2=0;
for j=1:1:l
y1=y1+bval(i,l-j+1)*2^(j-1);
endx1=(umax-umin)*y1/(2^l-1)+umin;
for j=1:1:l
y2=y2+bval(i,2*l-j+1)*2^(j-1);
endx2=(umax-umin)*y2/(2^l-1)+umin;
obj(i)=100*(x1*x1-x2).^2+(1-x1).^2; %目標函式
xx(i,:)=[x1,x2];
endfunc=obj;%目標函式轉換為適應度函式
p=func./sum(func);
q=cumsum(p);%累加
[fmax,indmax]=max(func);%求當代最佳個體
if fmax>=bestv
bestv=fmax;%到目前為止最優適應度值
bvalxx=bval(indmax,:);%到目前為止最佳位串
optxx=xx(indmax,:);%到目前為止最優引數
endbfit1(ii)=bestv; % 儲存每代的最優適應度
%%%%遺傳操作開始
%輪盤賭選擇
for i=1:(n-1)
r=rand;
tmp=find(r<=q);
newbval(i,:)=bval(tmp(1),:);
endnewbval(n,:)=bvalxx;%最優保留
bval=newbval;
%單點交叉
for i=1:2:(n-1)
cc=rand;
if ccpoint=ceil(rand*(2*l-1));%取得乙個1到2l-1的整數
ch=bval(i,:);
bval(i,point+1:2*l)=bval(i+1,point+1:2*l);
bval(i+1,point+1:2*l)=ch(1,point+1:2*l);
endend
bval(n,:)=bvalxx;%最優保留
%位點變異
mm=rand(n,2*l)mm(n,:)=zeros(1,2*l);%最後一行不變異，強制賦0
bval(mm)=1-bval(mm);
end%輸出
plot(bfit1);% 繪製最優適應度進化曲線
bestv %輸出最優適應度值
optxx %輸出最優引數
%declare the parameters of the optimization
max_iterations = 1000;
no_of_particles = 50;
dimensions = 1;
delta_min = -0.003;
delta_max = 0.003;
c1 = 1.3;
c2 = 1.3;
%initialise the particles and teir velocity components
for count_x = 1:no_of_particles
for count_y = 1:dimensions
particle_position(count_x,count_y) = rand*10;
particle_velocity(count_x,count_y) = rand;
p_best(count_x,count_y) = particle_position(count_x,count_y);
endend%initialize the p_best_fitness array
for count = 1:no_of_particles
p_best_fitness(count) = -1000;
end%particle_position
%particle_velocity
%main particle swrm routine
for count = 1:max_iterations
%find the fitness of each particle
%change fitness function as per equation requiresd and dimensions
for count_x = 1:no_of_particles
%x = particle_position(count_x,1);
%y = particle_position(count_x,2);
%z = particle_position(count_x,3);
%soln = x^2 - 3*y*x + z;
%x = particle_position(count_x);
%soln = x^2-2*x+1;
x = particle_position(count_x);
soln = x-7;
if soln~=0
current_fitness(count_x) = 1/abs(soln);
else
current_fitness =1000;
endend%decide on p_best etc for each particle
for count_x = 1:no_of_particles
if current_fitness(count_x) >p_best_fitness(count_x)
p_best_fitness(count_x) = current_fitness(count_x);
for count_y = 1:dimensions
p_best(count_x,count_y) = particle_position(count_x,count_y);
endendend%decide on the global best among all the particles
[g_best_val,g_best_index] = max(current_fitness);
%g_best contains the position of teh global best
for count_y = 1:dimensions
g_best(count_y) = particle_position(g_best_index,count_y);
end%update the position and velocity compponents
for count_x = 1:no_of_particles
for count_y = 1:dimensions
p_current(count_y) = particle_position(count_x,count_y);
endfor count_y = 1:dimensions
particle_velocity(count_y) = particle_velocity(count_y) + c1*rand*(p_best(count_y)-p_current(count_y)) + c2*rand*(g_best(count_y)-p_current(count_y));
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