【智能优化算法-灰狼算法】基于狩猎 (DLH) 搜索策略的灰狼算法求解单目标优化问题附matlab代码

1 内容介绍

Grey wolf optimization (GWO) algorithm is a new emerging algorithm that is based on the social hierarchy of grey wolves as well as their hunting and cooperation strategies. Introduced in 2014, this algorithm has been used by a large number of researchers and designers, such that the number of citations to the original paper exceeded many other algorithms. In a recent study by Niu et al., one of the main drawbacks of this algorithm for optimizing real﹚orld problems was introduced. In summary, they showed that GWO's performance degrades as the optimal solution of the problem diverges from 0. In this paper, by introducing a straightforward modification to the original GWO algorithm, that is, neglecting its social hierarchy, the authors were able to largely eliminate this defect and open a new perspective for future use of this algorithm. The efficiency of the proposed method was validated by applying it to benchmark and real﹚orld engineering problems.

2 仿真代码

%___________________________________________________________________% % Grey Wolf Optimizer (GWO) source codes version 1.0 % % % % Developed in MATLAB R2011b(7.13) % % % % 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, S. M. Mirjalili, A. Lewis % % Grey Wolf Optimizer, Advances in Engineering % % Software , in press, % % DOI: 10.1016/j.advengsoft.2013.12.007 % % % %___________________________________________________________________%

% This function containts full information and implementations of the benchmark % 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=-100; ub=100; dim=30; case 'F2' fobj = @F2; lb=-10; ub=10; dim=30; case 'F3' fobj = @F3; lb=-100; ub=100; dim=30; case 'F4' fobj = @F4; lb=-100; ub=100; dim=30; case 'F5' fobj = @F5; lb=-30; ub=30; dim=30; case 'F6' fobj = @F6; lb=-100; ub=100; dim=30; case 'F7' fobj = @F7; lb=-1.28; ub=1.28; dim=30; case 'F8' fobj = @F8; lb=-500; ub=500; dim=30; case 'F9' fobj = @F9; lb=-5.12; ub=5.12; dim=30; case 'F10' fobj = @F10; lb=-32; ub=32; dim=30; case 'F11' fobj = @F11; lb=-600; ub=600; dim=30; case 'F12' fobj = @F12; lb=-50; ub=50; dim=30; case 'F13' fobj = @F13; lb=-50; ub=50; dim=30; 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(x) o=sum(x.^2); 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

%This function is used for L-SHADE bound checking
function vi = boundConstraint (vi, pop, lu)

% if the boundary constraint is violated, set the value to be the middle
% of the previous value and the bound
%

[NP, D] = size(pop); % the population size and the problem's dimension

%% check the lower bound
xl = repmat(lu(1, :), NP, 1);
pos = vi < xl;
vi(pos) = (pop(pos) + xl(pos)) / 2;

%% check the upper bound
xu = repmat(lu(2, :), NP, 1);
pos = vi > xu;
vi(pos) = (pop(pos) + xu(pos)) / 2;
end

%___________________________________________________________________% % Grey Wold Optimizer (GWO) source codes version 1.0 % % % % Developed in MATLAB R2011b(7.13) % % %

% This function initialize the first population of search agents function Positions=initialization(SearchAgents_no,dim,ub,lb)

Boundary_no= size(ub,2); % numnber of boundaries

% If the boundaries of all variables are equal and user enter a signle % 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 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

%___________________________________________________________________% % An Improved Grey Wolf Optimizer for Solving Engineering % % Problems (I-GWO) source codes version 1.0 % % % %

% You can simply define your cost in a seperate file and load its handle to fobj % The initial parameters that you need are: %__________________________________________ % fobj = @YourCostFunction % dim = number of your variables % Max_iteration = maximum number of generations % N = number of search agents % lb=[lb1,lb2,...,lbn] where lbn is the lower bound of variable n % ub=[ub1,ub2,...,ubn] where ubn is the upper bound of variable n % If all the variables have equal lower bound you can just % define lb and ub as two single number numbers

% To run I-GWO: [Best_score,Best_pos,GWO_cg_curve]=IGWO(SearchAgents_no,Max_iteration,lb,ub,dim,fobj) %__________________________________________

close all clear clc

Algorithm_Name = 'I-GWO';

N = 30; % Number of search agents Function_name='F2'; % Name of the test function that can be from F1 to F23 (Table 1,2,3 in the paper) Max_iteration = 500; % Maximum numbef of iterations

% Load details of the selected benchmark function [lb,ub,dim,fobj]=Get_Functions_details(Function_name);

[Fbest,Lbest,Convergence_curve]=IGWO(dim,N,Max_iteration,lb,ub,fobj); display(['The best solution obtained by I-GWO is : ', num2str(Lbest)]); display(['The best optimal value of the objective funciton found by I-GWO is : ', num2str(Fbest)]);

figure('Position',[500 500 660 290]) %Draw search space subplot(1,2,1); func_plot(Function_name); title('Parameter space') xlabel('x_1'); ylabel('x_2'); zlabel([Function_name,'( x_1 , x_2 )'])

%Draw objective space subplot(1,2,2); semilogy(Convergence_curve,'Color','r') title('Objective space') xlabel('Iteration'); ylabel('Best score obtained so far');

axis tight grid on box on legend('I-GWO')

% To run I-GWO: [Best_score,Best_pos,GWO_cg_curve]=IGWO(SearchAgents_no,Max_iteration,lb,ub,dim,fobj) %__________________________________________

close all clear clc

Algorithm_Name = 'I-GWO';

N = 30; % Number of search agents Function_name='F2'; % Name of the test function that can be from F1 to F23 (Table 1,2,3 in the paper) Max_iteration = 500; % Maximum numbef of iterations

% Load details of the selected benchmark function [lb,ub,dim,fobj]=Get_Functions_details(Function_name);

figure('Position',[500 500 660 290]) %Draw search space subplot(1,2,1); func_plot(Function_name); title('Parameter space') xlabel('x_1'); ylabel('x_2'); zlabel([Function_name,'( x_1 , x_2 )'])

%Draw objective space subplot(1,2,2); semilogy(Convergence_curve,'Color','r') title('Objective space') xlabel('Iteration'); ylabel('Best score obtained so far');

axis tight grid on box on legend('I-GWO')

3 运行结果

4 参考文献

[1]唐宏伟. 未知环境下基于智能优化算法的多机器人目标搜索研究[D]. 湖南大学.

[2]崔明朗, 杜海文, 魏政磊,等. 多目标灰狼优化算法的改进策略研究[J]. 计算机工程与应用, 2018, 54(5):9.

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