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⛄ 内容介绍
针对基本哈里斯鹰算法收敛速度慢和易陷入局部寻优等问题,提出一种集成正态云模型和动态扰动策略的改进哈里斯鹰算法.在全局搜索阶段,利用正态云模型的随机性和模糊性和随机反向学习思想对哈里斯鹰位置进行更新,从而丰富种群多样性和提高算法全局搜索能力.在局部开发阶段,引入动态扰动策略更新不同捕食策略下的哈里斯鹰位置,改善算法局部开发能力.选取不同维度的基准测试函数进行仿真,同时利用Wilcoxon秩和检验,Friedman检验,三杆桁架设计问题对改进哈里斯鹰算法和其它优化算法进行对比分析.实验结果表明:提出的改进哈里斯鹰算法收敛速度更快,寻优精度更高,验证了改进策略的有效性.
哈里斯鹰优化算法（Harris' hawk optimization algorithm）是一种基于鸟群行为的优化算法，其步骤如下：
初始化种群：随机生成一定数量的鹰个体作为初始种群。
计算适应度：根据问题的适应度函数，计算每个个体的适应度值。
选择领导者：根据适应度值选择一定数量的个体作为领导者，可以根据适应度值的大小进行选择。
更新位置：对于非领导者个体，根据领导者个体的位置和速度信息，更新其位置。可以使用正态云分布和动态扰动来生成新的位置。
正态云分布：使用正态分布来生成随机扰动的位置，可以通过随机数生成器和正态分布函数来实现。
动态扰动：根据当前迭代次数和最大迭代次数的比例，调整扰动的大小和方向，使得扰动逐渐减小。
更新速度：根据更新后的位置，计算更新后的速度。
更新领导者：根据新位置的适应度值，更新领导者。
终止条件判断：判断是否满足终止条件，如达到最大迭代次数或找到满意的解。如果满足，则算法结束；否则，返回步骤4。
⛄ 部分代码
% Developed in MATLAB R2013b
% Source codes demo version 1.0
% _____________________________________________________
% Main paper:
% Harris hawks optimization: Algorithm and applications
% Ali Asghar Heidari, Seyedali Mirjalili, Hossam Faris, Ibrahim Aljarah, Majdi Mafarja, Huiling Chen
% Future Generation Computer Systems,
% DOI: https://doi.org/10.1016/j.future.2019.02.028
% https://www.sciencedirect.com/science/article/pii/S0167739X18313530
% _____________________________________________________
% You can run the HHO code online at codeocean.com https://doi.org/10.24433/CO.1455672.v1
% You can find the HHO code at https://github.com/aliasghar68/Harris-hawks-optimization-Algorithm-and-applications-.git
% _____________________________________________________
% Author, inventor and programmer: Ali Asghar Heidari,
% PhD research intern, Department of Computer Science, School of Computing, National University of Singapore, Singapore
% Exceptionally Talented Ph. DC funded by Iran's National Elites Foundation (INEF), University of Tehran
% 03-03-2019
% Researchgate: https://www.researchgate.net/profile/Ali_Asghar_Heidari
% e-Mail: as_heidari@ut.ac.ir, aliasghar68@gmail.com,
% e-Mail (Singapore): aliasgha@comp.nus.edu.sg, t0917038@u.nus.edu
% _____________________________________________________
% Co-author and Advisor: Seyedali Mirjalili
%
% e-Mail: ali.mirjalili@gmail.com
% seyedali.mirjalili@griffithuni.edu.au
%
% Homepage: http://www.alimirjalili.com
% _____________________________________________________
% Co-authors: Hossam Faris, Ibrahim Aljarah, Majdi Mafarja, and Hui-Ling Chen
% Homepage: http://www.evo-ml.com/2019/03/02/hho/
% _____________________________________________________
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Harris's hawk optimizer: In this algorithm, Harris' hawks try to catch the rabbit.
% T: maximum iterations, N: populatoin size, CNVG: Convergence curve
% To run HHO: [Rabbit_Energy,Rabbit_Location,CNVG]=HHO(N,T,lb,ub,dim,fobj)
function [Rabbit_Energy,Rabbit_Location,CNVG]=HHO(N,T,lb,ub,dim,fobj)
% initialize the location and Energy of the rabbit
Rabbit_Location=zeros(1,dim);
Rabbit_Energy=inf;
%Initialize the locations of Harris' hawks
X=initialization(N,dim,ub,lb);
CNVG=zeros(1,T);
t=0; % Loop counter
while t<T
for i=1:size(X,1)
% Check boundries
FU=X(i,:)>ub;FL=X(i,:)<lb;X(i,:)=(X(i,:).*(~(FU+FL)))+ub.*FU+lb.*FL;
% fitness of locations
fitness=fobj(X(i,:));
% Update the location of Rabbit
if fitness<Rabbit_Energy
Rabbit_Energy=fitness;
Rabbit_Location=X(i,:);
end
end
E1=2*(1-(t/T)); % factor to show the decreaing energy of rabbit
% Update the location of Harris' hawks
for i=1:size(X,1)
E0=2*rand()-1; %-1<E0<1
Escaping_Energy=E1*(E0); % escaping energy of rabbit
if abs(Escaping_Energy)>=1
%% Exploration:
% Harris' hawks perch randomly based on 2 strategy:
q=rand();
rand_Hawk_index = floor(N*rand()+1);
X_rand = X(rand_Hawk_index, :);
if q<0.5
% perch based on other family members
X(i,:)=X_rand-rand()*abs(X_rand-2*rand()*X(i,:));
elseif q>=0.5
% perch on a random tall tree (random site inside group's home range)
X(i,:)=(Rabbit_Location(1,:)-mean(X))-rand()*((ub-lb)*rand+lb);
end
elseif abs(Escaping_Energy)<1
%% Exploitation:
% Attacking the rabbit using 4 strategies regarding the behavior of the rabbit
%% phase 1: surprise pounce (seven kills)
% surprise pounce (seven kills): multiple, short rapid dives by different hawks
r=rand(); % probablity of each event
if r>=0.5 && abs(Escaping_Energy)<0.5 % Hard besiege
X(i,:)=(Rabbit_Location)-Escaping_Energy*abs(Rabbit_Location-X(i,:));
end
if r>=0.5 && abs(Escaping_Energy)>=0.5 % Soft besiege
Jump_strength=2*(1-rand()); % random jump strength of the rabbit
X(i,:)=(Rabbit_Location-X(i,:))-Escaping_Energy*abs(Jump_strength*Rabbit_Location-X(i,:));
end
%% phase 2: performing team rapid dives (leapfrog movements)
if r<0.5 && abs(Escaping_Energy)>=0.5, % Soft besiege % rabbit try to escape by many zigzag deceptive motions
Jump_strength=2*(1-rand());
X1=Rabbit_Location-Escaping_Energy*abs(Jump_strength*Rabbit_Location-X(i,:));
if fobj(X1)<fobj(X(i,:)) % improved move?
X(i,:)=X1;
else % hawks perform levy-based short rapid dives around the rabbit
X2=Rabbit_Location-Escaping_Energy*abs(Jump_strength*Rabbit_Location-X(i,:))+rand(1,dim).*Levy(dim);
if (fobj(X2)<fobj(X(i,:))), % improved move?
X(i,:)=X2;
end
end
end
if r<0.5 && abs(Escaping_Energy)<0.5, % Hard besiege % rabbit try to escape by many zigzag deceptive motions
% hawks try to decrease their average location with the rabbit
Jump_strength=2*(1-rand());
X1=Rabbit_Location-Escaping_Energy*abs(Jump_strength*Rabbit_Location-mean(X));
if fobj(X1)<fobj(X(i,:)) % improved move?
X(i,:)=X1;
else % Perform levy-based short rapid dives around the rabbit
X2=Rabbit_Location-Escaping_Energy*abs(Jump_strength*Rabbit_Location-mean(X))+rand(1,dim).*Levy(dim);
if (fobj(X2)<fobj(X(i,:))), % improved move?
X(i,:)=X2;
end
end
end
%%
end
end
t=t+1;
CNVG(t)=Rabbit_Energy;
% Print the progress every 100 iterations
% if mod(t,100)==0
% display(['At iteration ', num2str(t), ' the best fitness is ', num2str(Rabbit_Energy)]);
% end
end
end
% ___________________________________
function o=Levy(d)
beta=1.5;
sigma=(gamma(1+beta)*sin(pi*beta/2)/(gamma((1+beta)/2)*beta*2^((beta-1)/2)))^(1/beta);
u=randn(1,d)*sigma;v=randn(1,d);step=u./abs(v).^(1/beta);
o=step;
end⛄ 运行结果
⛄ 参考文献
[1]张帅,王俊杰,李爱莲,等.集成正态云和动态扰动的哈里斯鹰优化算法[J].[2023-07-23].