【智能优化算法】基于融合莱维飞行与黄金正弦的蚁狮算法求解单目标优化问题matlab代码

1 简介

针对蚁狮优化算法较易陷入局部最优停滞、收敛精度低以及收敛速度较慢等问题，将莱维飞行机制和黄金正弦算法融合到蚁狮优化算法中，提出了融合莱维飞行与黄金正弦的蚁狮优化算法( LGSALO) 。该算法利用 Lévy 飞行的变异机制对寻优过程中位置更新方式进行变异操作，可以改善种群多样性，使得算法跳出局部最优，提高全局寻优能力，并在一定程度上避免了算法的过早收敛; 同时引入黄金正弦算法改进精英蚁狮的寻优方式，协调算法的全局探索与局部开发能力。实验仿真结果表明，该改进算法的寻优性能良好，开发能力强。蚁狮优化算法是根据蚁狮幼虫诱捕蚂蚁的捕猎机制原理而提出的一种智能算法。

蚁狮狩猎时实施的五个主要步骤为蚂蚁的随机游走、建造陷阱、诱捕蚂蚁进入陷阱、捕捉猎物以及重新建造陷阱。狩猎方式如下: 蚁狮幼虫会在沙地上挖出不同大小锥形的陷阱坑，在挖出陷阱后，藏在陷阱中心的下方等待蚂蚁被困在坑里，当猎物被抓住时马上就会被拉到土壤里吃掉; 在吃完猎物后，蚁狮会把剩下的食物扔到坑外，然后再去重新构建陷阱，寻找下一个猎物。蚁狮优化算法模仿了蚁狮捕猎蚂蚁的聪明行为。构建模型寻求最优解时，有以下七个假设条件: a) 蚂蚁以不同的随机游走步长在蚁狮的搜索空间中移动，其游走行为受陷阱范围的限制; b) 随机游走适用于蚂蚁的所有维度; c) 蚁狮可以与它们的适应度成正比( 适应性越高，锥形陷阱半径越大，越容易捕获蚂蚁) ; d) 每一个蚂蚁都可以在每一次迭代中被一个精英蚁狮捕获; e) 随机游走的范围可以自适应地减少，以模拟蚂蚁滑向坑底的行为; f) 如果蚂蚁比蚁狮的适应值更高，意味着它被蚁狮捕获; g) 蚁狮在捕猎之后会把自己重新定位到捕获的猎物的位置，并在寻找下一个猎物的过程中建立一个适应值更高的陷阱来改善它的捕猎机制。蚂蚁在寻找食物时的随机游走公式如下:

2 部分代码

%___________________________________________________________________%

%  Ant Lion Optimizer (ALO) source codes demo 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

% SearchAgents_no = 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 ALO: [Best_score,Best_pos,cg_curve]=ALO(SearchAgents_no,Max_iteration,lb,ub,dim,fobj)

function [min_value,Elite_antlion_fitness,Elite_antlion_position,Convergence_curve]=ALO(N,Max_iter,lb,ub,dim,fobj)

% Initialize the positions of antlions and ants

antlion_position=initialization(N,dim,ub,lb);

ant_position=initialization(N,dim,ub,lb);

% Initialize variables to save the position of elite, sorted antlions, 

% convergence curve, antlions fitness, and ants fitness

Sorted_antlions=zeros(N,dim);

Elite_antlion_position=zeros(1,dim);

Elite_antlion_fitness=inf;

Convergence_curve=zeros(1,Max_iter);

antlions_fitness=zeros(1,N);

ants_fitness=zeros(1,N);

% Calculate the fitness of initial antlions and sort them

for i=1:size(antlion_position,1)

    antlions_fitness(1,i)=fobj(antlion_position(i,:)); 

end

[sorted_antlion_fitness,sorted_indexes]=sort(antlions_fitness);

for newindex=1:N

     Sorted_antlions(newindex,:)=antlion_position(sorted_indexes(newindex),:);

end

Elite_antlion_position=Sorted_antlions(1,:);

Elite_antlion_fitness=sorted_antlion_fitness(1);

% Main loop start from the second iteration since the first iteration 

% was dedicated to calculating the fitness of antlions

Current_iter=2; 

while Current_iter<Max_iter+1

    % This for loop simulate random walks

    for i=1:size(ant_position,1)

        % Select ant lions based on their fitness (the better anlion the higher chance of catching ant)

        Rolette_index=RouletteWheelSelection(1./sorted_antlion_fitness);

        if Rolette_index==-1  

            Rolette_index=1;

        end

        % RA is the random walk around the selected antlion by rolette wheel

        RA=Random_walk_around_antlion(dim,Max_iter,lb,ub, Sorted_antlions(Rolette_index,:),Current_iter);

        % RA is the random walk around the elite (best antlion so far)

        [RE]=Random_walk_around_antlion(dim,Max_iter,lb,ub, Elite_antlion_position(1,:),Current_iter);

        ant_position(i,:)= (RA(Current_iter,:)+RE(Current_iter,:))/2; % Equation (2.13) in the paper          

    end

    for i=1:size(ant_position,1)  

        % Boundar checking (bring back the antlions of ants inside search

        % space if they go beyoud the boundaries

        Flag4ub=ant_position(i,:)>ub;

        Flag4lb=ant_position(i,:)<lb;

        ant_position(i,:)=(ant_position(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;  

        ants_fitness(1,i)=fobj(ant_position(i,:));        

    end

    % Update antlion positions and fitnesses based of the ants (if an ant 

    % becomes fitter than an antlion we assume it was cought by the antlion  

    % and the antlion update goes to its position to build the trap)

    double_population=[Sorted_antlions;ant_position];

    double_fitness=[sorted_antlion_fitness ants_fitness];

    [double_fitness_sorted I]=sort(double_fitness);

    double_sorted_population=double_population(I,:);

    antlions_fitness=double_fitness_sorted(1:N);

    Sorted_antlions=double_sorted_population(1:N,:);

    % Update the position of elite if any antlinons becomes fitter than it

    if antlions_fitness(1)<Elite_antlion_fitness 

        Elite_antlion_position=Sorted_antlions(1,:);

        Elite_antlion_fitness=antlions_fitness(1);

    end

    % Keep the elite in the population

    Sorted_antlions(1,:)=Elite_antlion_position;

    antlions_fitness(1)=Elite_antlion_fitness;

    % Update the convergence curve

    Convergence_curve(Current_iter)=Elite_antlion_fitness;

    % Display the iteration and best optimum obtained so far

    if mod(Current_iter,1)==0

        display(['At iteration ', num2str(Current_iter), ' the elite fitness is ', num2str(Elite_antlion_fitness)]);

    end

min_value(Current_iter)=Elite_antlion_fitness;

    Current_iter=Current_iter+1; 

end

3 仿真结果

4 参考文献

[1]于建芳, 刘升, 王俊杰,等. 融合莱维飞行与黄金正弦的蚁狮优化算法[J]. 计算机应用研究, 2020, 37(8):5.

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