【回归预测-ELM预测】基于樽海鞘算法结合极限学习机实现风电场功率回归预测附matlab代码

1 内容介绍

风电功率预测为电网规划提供重要的依据,研究风电功率预测方法对确保电网在安全稳定运行下接纳更多的风电具有重要的意义.针对极限学习机(ELM)回归模型预测结果受输入参数影响的问题,现将樽海鞘算法优化算法(SSA)应用于ELM中,提出了一种基于樽海鞘算法优化极限学习机的风功率预测方法.该方法首先将数值天气预报信息(NWP)数据进行数据预处理,并构建出训练样本集,随后建立ELM模型,利用樽海鞘算法算法优化ELM中的输入权值和阈值,从而建立起基于NWP和SSA-ELM风功率预测模型.对华东地区3个不同装机容量的风场NWP数据进行实验.结果表明:该方法的预测精度高且稳定性能好,能够为风电场功率预测以及风电并网安全可靠性提供科学有效的参考依据.

2 仿真代码

%_________________________________________________________________________________

% You can simply define your cost in a seperate file and load its handle to fobj %您可以在单独的文件中定义您的成本，并将其句柄加载到FOBJ % The initial parameters that you need are: %您需要的初始参数是： %__________________________________________ % fobj = @YourCostFunction 你的任务 % dim = number of your variables 变量的数目 % Max_iteration = maximum number of generations 最大迭代次数 % SearchAgents_no = number of search agents 搜索动因子数 % lb=[lb1,lb2,...,lbn] where lbn is the lower bound of variable n %其中lbn是变量n的下界 % ub=[ub1,ub2,...,ubn] where ubn is the upper bound of variable n %其中ubn是变量n的上界 % If all the variables have equal lower bound you can just如果所有变量都有相等的下界，那么 % define lb and ub as two single number numbers 将lb和ub定义为两个单个数字

% To run SSA: [Best_score,Best_pos,SSA_cg_curve]=SSA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj) %__________________________________________

clc clear all close all

%% 加载数据 global indim hiddennum outdim Ptrain Ttrain load Speedwendu load gonglv %训练数据和预测数据 input_train=speedwendu(2:2001,:)'; input_test=speedwendu(2252:2302,:)'; output_train=gonglv(2:2001)'; output_test=gonglv(2252:2302)'; %选连样本输入输出数据归一化 [AllSamInn,AllSamIn] = mapminmax(input_train); Ptrain = AllSamInn; [AllSamOutn,AllSamOut] = mapminmax(output_train); Ttrain = AllSamOutn;

% Evaluating Sample测试样本

%% BP网络训练 %网络进化参数 net.trainParam.epochs=100; net.trainParam.lr=0.1; net.trainParam.goal=0.00001; net.trainParam.show=100; net.trainParam.showWindow=1;

%网络训练 [net,per2]=train(net,Ptrain,Ttrain); EvaSamOutn = sim(net,EvaSamInn); E = mse(EvaSamOutn-Ttest); % 决定系数 N = size(EvaSamOutn,2); R2=(N*sum(EvaSamOutn.*Ttest)-sum(EvaSamOutn)*sum(Ttest))^2/((N*sum((EvaSamOutn).^2)-(sum(EvaSamOutn))^2)*(N*sum((Ttest).^2)-(sum(Ttest))^2)); EvaSamOut=mapminmax('reverse',EvaSamOutn,AllSamOut);%反归一化 error=EvaSamOut-output_test; errormape=(EvaSamOut-output_test)./output_test; % 绘图 figure plot(1:length(EvaSamOut),output_test,'r-*',1:length(EvaSamOut),EvaSamOut,'b:o') grid on legend('真实值','预测值') xlabel('样本编号') ylabel('风力发电功率') string_3 = {'测试集预测结果对比(BP神经网络)'; ['mse = ' num2str(E) ' R^2 = ' num2str(R2)]}; title(string_3) %Draw objective space 绘制目标空间图 figure semilogy(SSA_cg_curve,'Color','r') title('Objective space') xlabel('Iteration'); ylabel('Best score obtained so far');

axis tight grid on box on legend('SSA')

display(['The best solution obtained by SSA is \m ', num2str(Best_pos)]); display(['The best optimal value of the objective funciton found by SSA is \n ', num2str(Best_score)]);

% This function initialize the first population of search agents此函数初始化第一批搜索代理 function Positions=initialization(SearchAgents_no,dim,ub,lb)

Boundary_no= size(ub,1); % numnber of boundaries 边界数

% If the boundaries of all variables are equal and user enter a signle如果所有变量的边界相等并且用户输入一个符号 % number for both ub and lb if Boundary_no==1 Positions=rand(SearchAgents_no,dim).*(ub-lb)+lb; end

% If each variable has a different lb and ub 如果每个变量的lb和ub不同 if Boundary_no>1 for i=1:dim ub_i=ub(i); lb_i=lb(i); Positions(:,i)=rand(SearchAgents_no,1).*(ub_i-lb_i)+lb_i; end end

%_________________________________________________________________________________ % Salp Swarm Algorithm (SSA) source codes version 1.0 % % Developed in MATLAB R2016a % % Author and programmer: Seyedali Mirjalili % % e-Mail: ali.mirjalili@gmail.com % seyedali.mirjalili@griffithuni.edu.au % % Homepage: http://www.alimirjalili.com % % Main paper: % S. Mirjalili, A.H. Gandomi, S.Z. Mirjalili, S. Saremi, H. Faris, S.M. Mirjalili, % Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems % Advances in Engineering Software % DOI: http://dx.doi.org/10.1016/j.advengsoft.2017.07.002 %____________________________________________________________________________________

% This function draws the benchmark functions此函数用于绘制基准函数

function func_plot(func_name)

[lb,ub,dim,fobj]=Get_Functions_details(func_name);

switch func_name case 'F1' x=-100:2:100; y=x; %[-100,100] case 'F2' x=-100:2:100; y=x; %[-10,10] case 'F3' x=-100:2:100; y=x; %[-100,100] case 'F4' x=-100:2:100; y=x; %[-100,100] case 'F5' x=-200:2:200; y=x; %[-5,5] case 'F6' x=-100:2:100; y=x; %[-100,100] case 'F7' x=-1:0.03:1; y=x %[-1,1] case 'F8' x=-500:10:500;y=x; %[-500,500] case 'F9' x=-5:0.1:5; y=x; %[-5,5] case 'F10' x=-20:0.5:20; y=x;%[-500,500] case 'F11' x=-500:10:500; y=x;%[-0.5,0.5] case 'F12' x=-10:0.1:10; y=x;%[-pi,pi] case 'F13' x=-5:0.08:5; y=x;%[-3,1] case 'F14' x=-100:2:100; y=x;%[-100,100] case 'F15' x=-5:0.1:5; y=x;%[-5,5] case 'F16' x=-1:0.01:1; y=x;%[-5,5] case 'F17' x=-5:0.1:5; y=x;%[-5,5] case 'F18' x=-5:0.06:5; y=x;%[-5,5] case 'F19' x=-5:0.1:5; y=x;%[-5,5] case 'F20' x=-5:0.1:5; y=x;%[-5,5] case 'F21' x=-5:0.1:5; y=x;%[-5,5] case 'F22' x=-5:0.1:5; y=x;%[-5,5] case 'F23' x=-5:0.1:5; y=x;%[-5,5] end

L=length(x); f=[];

for i=1:L for j=1:L if strcmp(func_name,'F15')==0 && strcmp(func_name,'F19')==0 && strcmp(func_name,'F20')==0 && strcmp(func_name,'F21')==0 && strcmp(func_name,'F22')==0 && strcmp(func_name,'F23')==0 f(i,j)=fobj([x(i),y(j)]); end if strcmp(func_name,'F15')==1 f(i,j)=fobj([x(i),y(j),0,0]); end if strcmp(func_name,'F19')==1 f(i,j)=fobj([x(i),y(j),0]); end if strcmp(func_name,'F20')==1 f(i,j)=fobj([x(i),y(j),0,0,0,0]); end if strcmp(func_name,'F21')==1 || strcmp(func_name,'F22')==1 ||strcmp(func_name,'F23')==1 f(i,j)=fobj([x(i),y(j),0,0]); end end end

surfc(x,y,f,'LineStyle','none');

end

% This function containts full information and implementations of the benchmark %此函数包含基准的完整信息和实现 % functions in Table 1, Table 2, and Table 3 in the paper

% lb is the lower bound: lb=[lb_1,lb_2,...,lb_d] % up is the uppper bound: ub=[ub_1,ub_2,...,ub_d] % dim is the number of variables (dimension of the problem)

function [lb,ub,dim,fobj] = Get_Functions_details(F)

switch F case 'F1' fobj = @F1; lb=-10; ub=10; dim=121; case 'F2' fobj = @F2; lb=-10; ub=10; dim=10; case 'F3' fobj = @F3; lb=-100; ub=100; dim=10; case 'F4' fobj = @F4; lb=-100; ub=100; dim=10; case 'F5' fobj = @F5; lb=-30; ub=30; dim=10; case 'F6' fobj = @F6; lb=-100; ub=100; dim=10; case 'F7' fobj = @F7; lb=-1.28; ub=1.28; dim=10; case 'F8' fobj = @F8; lb=-500; ub=500; dim=10; case 'F9' fobj = @F9; lb=-5.12; ub=5.12; dim=10; case 'F10' fobj = @F10; lb=-32; ub=32; dim=10; case 'F11' fobj = @F11; lb=-600; ub=600; dim=10; case 'F12' fobj = @F12; lb=-50; ub=50; dim=10; case 'F13' fobj = @F13; lb=-50; ub=50; dim=10; case 'F14' fobj = @F14; lb=-65.536; ub=65.536; dim=2; case 'F15' fobj = @F15; lb=-5; ub=5; dim=4; case 'F16' fobj = @F16; lb=-5; ub=5; dim=2; case 'F17' fobj = @F17; lb=[-5,0]; ub=[10,15]; dim=2; case 'F18' fobj = @F18; lb=-2; ub=2; dim=2; case 'F19' fobj = @F19; lb=0; ub=1; dim=3; case 'F20' fobj = @F20; lb=0; ub=1; dim=6; case 'F21' fobj = @F21; lb=0; ub=10; dim=4; case 'F22' fobj = @F22; lb=0; ub=10; dim=4; case 'F23' fobj = @F23; lb=0; ub=10; dim=4; end

end

% F1

function o = F1(pm) global indim hiddennum outdim Ptrain Ttrain for i=1:hiddennum x2iw(i,:)=pm(((i-1)*indim+1):i*indim); end x2lw=pm(hiddennum*indim+1:hiddennum*indim+hiddennum); x2b=pm(hiddennum*indim+hiddennum+1:length(pm)); x2b1=x2b(1:hiddennum).'; x2b2=x2b(hiddennum+1:hiddennum+outdim).';

IW1=x2iw; IW2=x2lw; b1=x2b1; b2=x2b2; error=ELMfun(IW1,b1,Ptrain,Ttrain,hiddennum,IW2,b2); o=mse(error); end

% F2

function o = F2(x) o=sum(abs(x))+prod(abs(x)); end

% F3

function o = F3(x) dim=size(x,2); o=0; for i=1:dim o=o+sum(x(1:i))^2; end end

% F4

function o = F4(x) o=max(abs(x)); end

% F5

function o = F5(x) dim=size(x,2); o=sum(100*(x(2:dim)-(x(1:dim-1).^2)).^2+(x(1:dim-1)-1).^2); end

% F6

function o = F6(x) o=sum(abs((x+.5)).^2); end

% F7

function o = F7(x) dim=size(x,2); o=sum([1:dim].*(x.^4))+rand; end

% F8

function o = F8(x) o=sum(-x.*sin(sqrt(abs(x)))); end

% F9

function o = F9(x) dim=size(x,2); o=sum(x.^2-10*cos(2*pi.*x))+10*dim; end

% F10

function o = F10(x) dim=size(x,2); o=-20*exp(-.2*sqrt(sum(x.^2)/dim))-exp(sum(cos(2*pi.*x))/dim)+20+exp(1); end

% F11

function o = F11(x) dim=size(x,2); o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1; end

% F12

function o = F12(x) dim=size(x,2); o=(pi/dim)*(10*((sin(pi*(1+(x(1)+1)/4)))^2)+sum((((x(1:dim-1)+1)./4).^2).*... (1+10.*((sin(pi.*(1+(x(2:dim)+1)./4)))).^2))+((x(dim)+1)/4)^2)+sum(Ufun(x,10,100,4)); end

% F13

function o = F13(x) dim=size(x,2); o=.1*((sin(3*pi*x(1)))^2+sum((x(1:dim-1)-1).^2.*(1+(sin(3.*pi.*x(2:dim))).^2))+... ((x(dim)-1)^2)*(1+(sin(2*pi*x(dim)))^2))+sum(Ufun(x,5,100,4)); end

% F14

function o = F14(x) aS=[-32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32;,... -32 -32 -32 -32 -32 -16 -16 -16 -16 -16 0 0 0 0 0 16 16 16 16 16 32 32 32 32 32];

for j=1:25 bS(j)=sum((x'-aS(:,j)).^6); end o=(1/500+sum(1./([1:25]+bS))).^(-1); end

% F15

function o = F15(x) aK=[.1957 .1947 .1735 .16 .0844 .0627 .0456 .0342 .0323 .0235 .0246]; bK=[.25 .5 1 2 4 6 8 10 12 14 16];bK=1./bK; o=sum((aK-((x(1).*(bK.^2+x(2).*bK))./(bK.^2+x(3).*bK+x(4)))).^2); end

% F16

function o = F16(x) o=4*(x(1)^2)-2.1*(x(1)^4)+(x(1)^6)/3+x(1)*x(2)-4*(x(2)^2)+4*(x(2)^4); end

% F17

function o = F17(x) o=(x(2)-(x(1)^2)*5.1/(4*(pi^2))+5/pi*x(1)-6)^2+10*(1-1/(8*pi))*cos(x(1))+10; end

% F18

function o = F18(x) o=(1+(x(1)+x(2)+1)^2*(19-14*x(1)+3*(x(1)^2)-14*x(2)+6*x(1)*x(2)+3*x(2)^2))*... (30+(2*x(1)-3*x(2))^2*(18-32*x(1)+12*(x(1)^2)+48*x(2)-36*x(1)*x(2)+27*(x(2)^2))); end

% F19

function o = F19(x) aH=[3 10 30;.1 10 35;3 10 30;.1 10 35];cH=[1 1.2 3 3.2]; pH=[.3689 .117 .2673;.4699 .4387 .747;.1091 .8732 .5547;.03815 .5743 .8828]; o=0; for i=1:4 o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2)))); end end

% F20

function o = F20(x) aH=[10 3 17 3.5 1.7 8;.05 10 17 .1 8 14;3 3.5 1.7 10 17 8;17 8 .05 10 .1 14]; cH=[1 1.2 3 3.2]; pH=[.1312 .1696 .5569 .0124 .8283 .5886;.2329 .4135 .8307 .3736 .1004 .9991;... .2348 .1415 .3522 .2883 .3047 .6650;.4047 .8828 .8732 .5743 .1091 .0381]; o=0; for i=1:4 o=o-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2)))); end end

% F21

function o = F21(x) aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0; for i=1:5 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end

% F22

function o = F22(x) aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0; for i=1:7 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end

% F23

function o = F23(x) aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0; for i=1:10 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end

function o=Ufun(x,a,k,m) o=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a)); end

1 内容介绍

2 仿真代码

%_________________________________________________________________________________

% To run SSA: [Best_score,Best_pos,SSA_cg_curve]=SSA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj) %__________________________________________

clc clear all close all

% Evaluating Sample测试样本

%% BP网络训练 %网络进化参数 net.trainParam.epochs=100; net.trainParam.lr=0.1; net.trainParam.goal=0.00001; net.trainParam.show=100; net.trainParam.showWindow=1;

axis tight grid on box on legend('SSA')

display(['The best solution obtained by SSA is \m ', num2str(Best_pos)]); display(['The best optimal value of the objective funciton found by SSA is \n ', num2str(Best_score)]);

% This function initialize the first population of search agents此函数初始化第一批搜索代理 function Positions=initialization(SearchAgents_no,dim,ub,lb)

Boundary_no= size(ub,1); % numnber of boundaries 边界数

% This function draws the benchmark functions此函数用于绘制基准函数

function func_plot(func_name)

[lb,ub,dim,fobj]=Get_Functions_details(func_name);

L=length(x); f=[];

surfc(x,y,f,'LineStyle','none');

end

% This function containts full information and implementations of the benchmark %此函数包含基准的完整信息和实现 % functions in Table 1, Table 2, and Table 3 in the paper

% lb is the lower bound: lb=[lb_1,lb_2,...,lb_d] % up is the uppper bound: ub=[ub_1,ub_2,...,ub_d] % dim is the number of variables (dimension of the problem)

function [lb,ub,dim,fobj] = Get_Functions_details(F)

end

% F1

IW1=x2iw; IW2=x2lw; b1=x2b1; b2=x2b2; error=ELMfun(IW1,b1,Ptrain,Ttrain,hiddennum,IW2,b2); o=mse(error); end

% F2

function o = F2(x) o=sum(abs(x))+prod(abs(x)); end

% F3

function o = F3(x) dim=size(x,2); o=0; for i=1:dim o=o+sum(x(1:i))^2; end end

% F4

function o = F4(x) o=max(abs(x)); end

% F5

function o = F5(x) dim=size(x,2); o=sum(100*(x(2:dim)-(x(1:dim-1).^2)).^2+(x(1:dim-1)-1).^2); end

% F6

function o = F6(x) o=sum(abs((x+.5)).^2); end

% F7

function o = F7(x) dim=size(x,2); o=sum([1:dim].*(x.^4))+rand; end

% F8

function o = F8(x) o=sum(-x.*sin(sqrt(abs(x)))); end

% F9

function o = F9(x) dim=size(x,2); o=sum(x.^2-10*cos(2*pi.*x))+10*dim; end

% F10

function o = F10(x) dim=size(x,2); o=-20*exp(-.2*sqrt(sum(x.^2)/dim))-exp(sum(cos(2*pi.*x))/dim)+20+exp(1); end

% F11

function o = F11(x) dim=size(x,2); o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1; end

% F12

% F13

function o = F13(x) dim=size(x,2); o=.1*((sin(3*pi*x(1)))^2+sum((x(1:dim-1)-1).^2.*(1+(sin(3.*pi.*x(2:dim))).^2))+... ((x(dim)-1)^2)*(1+(sin(2*pi*x(dim)))^2))+sum(Ufun(x,5,100,4)); end

% F14

function o = F14(x) aS=[-32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32;,... -32 -32 -32 -32 -32 -16 -16 -16 -16 -16 0 0 0 0 0 16 16 16 16 16 32 32 32 32 32];

for j=1:25 bS(j)=sum((x'-aS(:,j)).^6); end o=(1/500+sum(1./([1:25]+bS))).^(-1); end

% F15

% F16

function o = F16(x) o=4*(x(1)^2)-2.1*(x(1)^4)+(x(1)^6)/3+x(1)*x(2)-4*(x(2)^2)+4*(x(2)^4); end

% F17

function o = F17(x) o=(x(2)-(x(1)^2)*5.1/(4*(pi^2))+5/pi*x(1)-6)^2+10*(1-1/(8*pi))*cos(x(1))+10; end

% F18

function o = F18(x) o=(1+(x(1)+x(2)+1)^2*(19-14*x(1)+3*(x(1)^2)-14*x(2)+6*x(1)*x(2)+3*x(2)^2))*... (30+(2*x(1)-3*x(2))^2*(18-32*x(1)+12*(x(1)^2)+48*x(2)-36*x(1)*x(2)+27*(x(2)^2))); end

% F19

% F20

% F21

function o = F21(x) aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0; for i=1:5 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end

% F22

function o = F22(x) aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0; for i=1:7 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end

% F23

function o = F23(x) aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0; for i=1:10 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end

function o=Ufun(x,a,k,m) o=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a)); end

1 内容介绍

2 仿真代码

%_________________________________________________________________________________

% To run SSA: [Best_score,Best_pos,SSA_cg_curve]=SSA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj) %__________________________________________

clc clear all close all

% Evaluating Sample测试样本

%% BP网络训练 %网络进化参数 net.trainParam.epochs=100; net.trainParam.lr=0.1; net.trainParam.goal=0.00001; net.trainParam.show=100; net.trainParam.showWindow=1;

axis tight grid on box on legend('SSA')

display(['The best solution obtained by SSA is \m ', num2str(Best_pos)]); display(['The best optimal value of the objective funciton found by SSA is \n ', num2str(Best_score)]);

% This function initialize the first population of search agents此函数初始化第一批搜索代理 function Positions=initialization(SearchAgents_no,dim,ub,lb)

Boundary_no= size(ub,1); % numnber of boundaries 边界数

% This function draws the benchmark functions此函数用于绘制基准函数

function func_plot(func_name)

[lb,ub,dim,fobj]=Get_Functions_details(func_name);

L=length(x); f=[];

surfc(x,y,f,'LineStyle','none');

end

% This function containts full information and implementations of the benchmark %此函数包含基准的完整信息和实现 % functions in Table 1, Table 2, and Table 3 in the paper

% lb is the lower bound: lb=[lb_1,lb_2,...,lb_d] % up is the uppper bound: ub=[ub_1,ub_2,...,ub_d] % dim is the number of variables (dimension of the problem)

function [lb,ub,dim,fobj] = Get_Functions_details(F)

end

% F1

IW1=x2iw; IW2=x2lw; b1=x2b1; b2=x2b2; error=ELMfun(IW1,b1,Ptrain,Ttrain,hiddennum,IW2,b2); o=mse(error); end

% F2

function o = F2(x) o=sum(abs(x))+prod(abs(x)); end

% F3

function o = F3(x) dim=size(x,2); o=0; for i=1:dim o=o+sum(x(1:i))^2; end end

% F4

function o = F4(x) o=max(abs(x)); end

% F5

function o = F5(x) dim=size(x,2); o=sum(100*(x(2:dim)-(x(1:dim-1).^2)).^2+(x(1:dim-1)-1).^2); end

% F6

function o = F6(x) o=sum(abs((x+.5)).^2); end

% F7

function o = F7(x) dim=size(x,2); o=sum([1:dim].*(x.^4))+rand; end

% F8

function o = F8(x) o=sum(-x.*sin(sqrt(abs(x)))); end

% F9

function o = F9(x) dim=size(x,2); o=sum(x.^2-10*cos(2*pi.*x))+10*dim; end

% F10

function o = F10(x) dim=size(x,2); o=-20*exp(-.2*sqrt(sum(x.^2)/dim))-exp(sum(cos(2*pi.*x))/dim)+20+exp(1); end

% F11

function o = F11(x) dim=size(x,2); o=sum(x.^2)/4000-prod(cos(x./sqrt([1:dim])))+1; end

% F12

% F13

function o = F13(x) dim=size(x,2); o=.1*((sin(3*pi*x(1)))^2+sum((x(1:dim-1)-1).^2.*(1+(sin(3.*pi.*x(2:dim))).^2))+... ((x(dim)-1)^2)*(1+(sin(2*pi*x(dim)))^2))+sum(Ufun(x,5,100,4)); end

% F14

function o = F14(x) aS=[-32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32;,... -32 -32 -32 -32 -32 -16 -16 -16 -16 -16 0 0 0 0 0 16 16 16 16 16 32 32 32 32 32];

for j=1:25 bS(j)=sum((x'-aS(:,j)).^6); end o=(1/500+sum(1./([1:25]+bS))).^(-1); end

% F15

% F16

function o = F16(x) o=4*(x(1)^2)-2.1*(x(1)^4)+(x(1)^6)/3+x(1)*x(2)-4*(x(2)^2)+4*(x(2)^4); end

% F17

function o = F17(x) o=(x(2)-(x(1)^2)*5.1/(4*(pi^2))+5/pi*x(1)-6)^2+10*(1-1/(8*pi))*cos(x(1))+10; end

% F18

function o = F18(x) o=(1+(x(1)+x(2)+1)^2*(19-14*x(1)+3*(x(1)^2)-14*x(2)+6*x(1)*x(2)+3*x(2)^2))*... (30+(2*x(1)-3*x(2))^2*(18-32*x(1)+12*(x(1)^2)+48*x(2)-36*x(1)*x(2)+27*(x(2)^2))); end

% F19

% F20

% F21

function o = F21(x) aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0; for i=1:5 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end

% F22

function o = F22(x) aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0; for i=1:7 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end

% F23

function o = F23(x) aSH=[4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 1 8 1;6 2 6 2;7 3.6 7 3.6]; cSH=[.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

o=0; for i=1:10 o=o-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1); end end

function o=Ufun(x,a,k,m) o=k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a)); end

% This function draws the benchmark functions此函数用于绘制基准函数

function func_plot(func_name)

[lb,ub,dim,fobj]=Get_Functions_details(func_name);

L=length(x); f=[];

surfc(x,y,f,'LineStyle','none');

end

3 运行结果

4 参考文献

[1]赵睿智, and 丁云飞. "基于粒子群优化极限学习机的风功率预测." 上海电机学院学报 22.4(2019):6.

博主简介：擅长智能优化算法、神经网络预测、信号处理、元胞自动机、图像处理、路径规划、无人机等多种领域的Matlab仿真，相关matlab代码问题可私信交流。

部分理论引用网络文献，若有侵权联系博主删除。

% This function draws the benchmark functions此函数用于绘制基准函数

function func_plot(func_name)

[lb,ub,dim,fobj]=Get_Functions_details(func_name);

L=length(x); f=[];

surfc(x,y,f,'LineStyle','none');

end

3 运行结果

4 参考文献

[1]赵睿智, and 丁云飞. "基于粒子群优化极限学习机的风功率预测." 上海电机学院学报 22.4(2019):6.

博主简介：擅长智能优化算法、神经网络预测、信号处理、元胞自动机、图像处理、路径规划、无人机等多种领域的Matlab仿真，相关matlab代码问题可私信交流。

部分理论引用网络文献，若有侵权联系博主删除。

% This function draws the benchmark functions此函数用于绘制基准函数

function func_plot(func_name)

[lb,ub,dim,fobj]=Get_Functions_details(func_name);

L=length(x); f=[];

surfc(x,y,f,'LineStyle','none');

end

3 运行结果

4 参考文献

[1]赵睿智, and 丁云飞. "基于粒子群优化极限学习机的风功率预测." 上海电机学院学报 22.4(2019):6.

博主简介：擅长智能优化算法、神经网络预测、信号处理、元胞自动机、图像处理、路径规划、无人机等多种领域的Matlab仿真，相关matlab代码问题可私信交流。

部分理论引用网络文献，若有侵权联系博主删除。