1 简介针对蝴蝶优化算法(butterfly optimization algorithm,BOA)中存在的局部开采和全局探索能力不均衡,易陷入局部最优值,收敛精度低等缺陷,提出收敛因子和黄金正弦指引机制的蝴蝶优化算法(convergence factor and gold sinusoidal guidance mechanism of butterfly optimization algorithm,AGSABOA).受到鲸鱼优化算法的启发将收敛因子融入算法的全局位置更新处,提高算法全局搜索的多样性;结合黄金正弦指引机制,弥补BOA算法迭代后期种群多样性下降,易陷入局部最优的不足.选取9个常用的基准测试函数进行的仿真结果表明,AGSABOA算法在寻优精度,收敛速度,鲁棒性方面更优.2 部分代码%% Monarch Butterfly Optimization (MBO) % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %% %% Notes: % Different run may generate different solutions, this is determined by % the the nature of metaheuristic algorithms. %% function [MinCost] MBO(ProblemFunction, DisplayFlag, RandSeed) % Monarch Butterfly Optimization (MBO) software for minimizing a general function % The fixed Function Evaluations (FEs) is considered as termination condition. % INPUTS: ProblemFunction is the handle of the function that returns % the handles of the initialization, cost, and feasibility functions. % DisplayFlag true or false, whether or not to display and plot results. % ProbFlag true or false, whether or not to use probabilities to update emigration rates. % RandSeed random number seed % OUTPUTS: MinCost array of best solution, one element for each generation % Hamming final Hamming distance between solutions % CAVEAT: The ClearDups function that is called below replaces duplicates with randomly-generated % individuals, but it does not then recalculate the cost of the replaced individuals. tic if ~exist(ProblemFunction, var) ProblemFunction Ackley; end if ~exist(DisplayFlag, var) DisplayFlag true; end if ~exist(RandSeed, var) RandSeed round(sum(100*clock)); end [OPTIONS, MinCost, AvgCost, InitFunction, CostFunction, FeasibleFunction, ... MaxParValue, MinParValue, Population] Init(DisplayFlag, ProblemFunction, RandSeed); nEvaluations OPTIONS.popsize; % % % % % % % % % % % % Initial parameter setting % % % % % % % % % % % %%%% %% Initial parameter setting Keep 2; % elitism parameter: how many of the best habitats to keep from one generation to the next maxStepSize 1.0; %Max Step size partition OPTIONS.partition; numButterfly1 ceil(partition*OPTIONS.popsize); % NP1 in paper numButterfly2 OPTIONS.popsize - numButterfly1; % NP2 in paper period 1.2; % 12 months in a year Land1 zeros(numButterfly1, OPTIONS.numVar); Land2 zeros(numButterfly2, OPTIONS.numVar); BAR partition; % you can change the BAR value in order to get much better performance % % % % % % % % % % % % End of Initial parameter setting % % % % % % % % % % % %% %% % % % % % % % % % % % % Begin the optimization loop % % % % % % % % % %%%% % Begin the optimization loop GenIndex 1; % for GenIndex 1 : OPTIONS.Maxgen while nEvaluations OPTIONS.MaxFEs % % % % % % % % % % % % Elitism Strategy % % % % % % % % % % % %%%%% %% Save the best monarch butterflis in a temporary array. for j 1 : Keep chromKeep(j,:) Population(j).chrom; costKeep(j) Population(j).cost; end % % % % % % % % % % % % End of Elitism Strategy % % % % % % % % % % % %%%% %% % % % % % % % % % % % % Divide the whole population into two subpopulations % % % %%% %% Divide the whole population into Population1 (Land1) and Population2 (Land2) % according to their fitness. % The monarch butterflis in Population1 are better than or equal to Population2. % Of course, we can randomly divide the whole population into Population1 and Population2. % We do not test the different performance between two ways. for popindex 1 : OPTIONS.popsize if popindex numButterfly1 Population1(popindex).chrom Population(popindex).chrom; else Population2(popindex-numButterfly1).chrom Population(popindex).chrom; end end % % % % % % % % % % % End of Divide the whole population into two subpopulations % % %%% %% % % % % % % % % % % % %% Migration operator % % % % % % % % % % % %%%% %% Migration operator for k1 1 : numButterfly1 for parnum1 1 : OPTIONS.numVar r1 rand*period; if r1 partition r2 round(numButterfly1 * rand 0.5); Land1(k1,parnum1) Population1(r2).chrom(parnum1); else r3 round(numButterfly2 * rand 0.5); Land1(k1,parnum1) Population2(r3).chrom(parnum1); end end %% for parnum1 NewPopulation1(k1).chrom Land1(k1,:); end %% for k1 % % % % % % % % % % % %%% End of Migration operator % % % % % % % % % % % %%% %% % % % % % % % % % % % % Evaluate NewPopulation1 % % % % % % % % % % % %% %% Evaluate NewPopulation1 SavePopSize OPTIONS.popsize; OPTIONS.popsize numButterfly1; % Make sure each individual is legal. NewPopulation1 FeasibleFunction(OPTIONS, NewPopulation1); % Calculate cost NewPopulation1 CostFunction(OPTIONS, NewPopulation1); % the number of fitness evaluations nEvaluations nEvaluations OPTIONS.popsize; OPTIONS.popsize SavePopSize; % % % % % % % % % % % % End of Evaluate NewPopulation1 % % % % % % % % % % % %% %% % % % % % % % % % % % % Butterfly adjusting operator % % % % % % % % % % % %% %% Butterfly adjusting operator for k2 1 : numButterfly2 scale maxStepSize/(GenIndex^2); %Smaller step for local walk StepSzie ceil(exprnd(2*OPTIONS.Maxgen,1,1)); delataX LevyFlight(StepSzie,OPTIONS.numVar); for parnum2 1:OPTIONS.numVar, if (rand partition) Land2(k2,parnum2) Population(1).chrom(parnum2); else r4 round(numButterfly2*rand 0.5); Land2(k2,parnum2) Population2(r4).chrom(1); if (rand BAR) % Butterfly-Adjusting rate Land2(k2,parnum2) Land2(k2,parnum2) scale*(delataX(parnum2)-0.5); end end end %% for parnum2 NewPopulation2(k2).chrom Land2(k2,:); end %% for k2 % % % % % % % % % % % % End of Butterfly adjusting operator % % % % % % % % % % % % %% % % % % % % % % % % % % Evaluate NewPopulation2 % % % % % % % % % % % %% %% Evaluate NewPopulation2 SavePopSize OPTIONS.popsize; OPTIONS.popsize numButterfly2; % Make sure each individual is legal. NewPopulation2 FeasibleFunction(OPTIONS, NewPopulation2); % Calculate cost NewPopulation2 CostFunction(OPTIONS, NewPopulation2); % the number of fitness evaluations nEvaluations nEvaluations OPTIONS.popsize; OPTIONS.popsize SavePopSize; % % % % % % % % % % % % End of Evaluate NewPopulation2 % % % % % % % % % % % %% %% % % % % % % % Combine two subpopulations into one and rank monarch butterflis % % % % % % %% Combine Population1 with Population2 to generate a new Population Population CombinePopulation(OPTIONS, NewPopulation1, NewPopulation2); % Sort from best to worst Population PopSort(Population); % % % % % % End of Combine two subpopulations into one and rank monarch butterflis % %% % % %% % % % % % % % % % % % % Elitism Strategy % % % % % % % % % % % %%% %% % %% Replace the worst with the previous generations elites. n length(Population); for k3 1 : Keep Population(n-k31).chrom chromKeep(k3,:); Population(n-k31).cost costKeep(k3); end % end for k3 % % % % % % % % % % % % End of Elitism Strategy % % % % % % % % % % % %%% %% % %% % % % % % % % % % % Precess and output the results % % % % % % % % % % % %%% % Sort from best to worst Population PopSort(Population); % Compute the average cost [AverageCost, nLegal] ComputeAveCost(Population); % Display info to screen MinCost [MinCost Population(1).cost]; AvgCost [AvgCost AverageCost]; if DisplayFlag disp([The best and mean of Generation # , num2str(GenIndex), are ,... num2str(MinCost(end)), and , num2str(AvgCost(end))]); end % % % % % % % % % % % End of Precess and output the results %%%%%%%%%% %% % %% %% Update generation number GenIndex GenIndex1; end % end for GenIndex Conclude2(DisplayFlag, OPTIONS, Population, nLegal, MinCost, AvgCost); toc % % % % % % % % % % End of Monarch Butterfly Optimization implementation %%%% %% % %% function [delataX] LevyFlight(StepSize, Dim) %Allocate matrix for solutions delataX zeros(1,Dim); %Loop over each dimension for i1:Dim % Cauchy distribution fx tan(pi * rand(1,StepSize)); delataX(i) sum(fx); end3 仿真结果4 参考文献[1]高文欣、刘升、肖子雅、于建芳. 收敛因子和黄金正弦指引机制的蝴蝶优化算法[J]. 计算机工程与设计, 2020, 41(12):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仿真有科研问题可私信交流。部分理论引用网络文献若有侵权联系博主删除。