基于融合黄金正弦和随机游走的哈里斯鹰优化算法(GSHHO)求解单目标优化问题附matlab代码-优快云博客

本文提出了一种融合黄金正弦和随机游走的哈里斯鹰优化算法（GSHHO），旨在解决原算法收敛精度低和易陷入局部最优的问题。通过在探索阶段应用黄金正弦增强全局探索，用非线性能量指数递减策略平衡全局与局部搜索，以及在开发阶段利用高斯随机游走提升局部开发能力，GSHHO算法在23个测试函数上表现出更优的寻优速度和精度。实验结果显示，该算法在优化问题求解中表现出更高的效率和精度。

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⛄ 内容介绍

针对哈里斯鹰优化算法收敛精度低,易陷入局部最优的问题,本文提出了融合黄金正弦和随机游走的哈里斯鹰优化算法.首先,该算法在哈里斯鹰的探索阶段融合黄金正弦优化算法,增强算法的全局探索能力;其次,使用一种非线性能量指数递减策略,平衡算法的全局探索和局部开发能力;然后,在哈里斯鹰的开发阶段引入高斯随机游走策略对猎物进行随机游走,提升算法的局部开发能力;最后,在23个测试函数上进行实验,评估改进后的哈里斯鹰优化算法的寻优性能.实验结果表明,所提算法具有更好的寻优速度和寻优精度.

GSHHO（融合黄金正弦和随机游走的哈里斯鹰优化算法）是一种基于黄金正弦和随机游走的优化算法。它结合了这两种方法的优点，旨在提高优化问题的求解效率和精度。

黄金正弦是一种基于黄金比例（1.618）的算法，它模拟了黄金分割的规律。通过使用正弦函数来生成候选解，可以在搜索空间中尽可能地覆盖更多的区域，从而增加找到全局最优解的概率。

随机游走是一种基于随机性的搜索方法，通过在搜索空间中随机移动来寻找解空间中的最优解。它可以避免陷入局部最优解，并帮助算法跳出局部极值点。

GSHHO算法将黄金正弦和随机游走相结合，通过不断迭代生成新的候选解，并根据一定的策略进行选择和更新。算法会根据目标函数的值来评估候选解的好坏，并根据一定的概率选择是否接受新的解。通过不断迭代优化，GSHHO算法可以找到较好的近似最优解。

需要注意的是，GSHHO算法的具体实现可能会因应用场景和问题而有所差异。该算法的效果和性能也需要根据具体情况进行评估和调整。

⛄ 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 rabbitRabbit_Location=zeros(1,dim);Rabbit_Energy=inf;%Initialize the locations of Harris' hawksX=initialization(N,dim,ub,lb);CNVG=zeros(1,T);t=0; % Loop counterwhile 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)]);%    endendend% ___________________________________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