2024年2月15日发(作者：巨长菁)
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 ~exist('ProblemFunction', 'var') ProblemFunction = @Ackley;endif ~exist('DisplayFlag', 'var') DisplayFlag = true;endif ~exist('RandSeed', 'var') RandSeed = round(sum(100*clock));end[OPTIONS, MinCost, AvgCost, InitFunction, CostFunction, FeasibleFunction, ... MaxParValue, MinParValue, Population] = Init(DisplayFlag, ProblemFunction, RandSeed);nEvaluations = e;% % % % % % % % % % % % Initial parameter setting % % % % % % % % % % % %%%%%% Initial parameter settingKeep = 2; % elitism parameter: how many of the best habitats to keep from one generation to the nextmaxStepSize = 1.0; %Max Step sizepartition = ion;numButterfly1 = ceil(partition*e); % NP1 in papernumButterfly2 = e - numButterfly1; % NP2 in paperperiod = 1.2; % 12 months in a yearLand1 = zeros(numButterfly1, );Land2 = zeros(numButterfly2, );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 loopGenIndex = 1;% for GenIndex = 1 : while nEvaluations<
% % % % % % % % % % % % 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 : e 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 : 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 = e; e = numButterfly1; % Make sure each individual is legal. NewPopulation1 = FeasibleFunction(OPTIONS, NewPopulation1); % Calculate cost NewPopulation1 = CostFunction(OPTIONS, NewPopulation1); % the number of fitness evaluations nEvaluations = nEvaluations + e; e = 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*,1,1)); delataX = LevyFlight(StepSzie,); for parnum2 = 1:, 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 = e; e = numButterfly2; % Make sure each individual is legal. NewPopulation2 = FeasibleFunction(OPTIONS, NewPopulation2); % Calculate cost NewPopulation2 = CostFunction(OPTIONS, NewPopulation2); % the number of fitness evaluations nEvaluations = nEvaluations + e; e = 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 generation's elites. n = length(Population); for k3 = 1 : Keep Population(n-k3+1).chrom = chromKeep(k3,:); Population(n-k3+1).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 = GenIndex+1;
end % end for GenIndexConclude2(DisplayFlag, OPTIONS, Population, nLegal, MinCost, AvgCost);toc% % % % % % % % % % End of Monarch Butterfly Optimization implementation %%%% %% %%%function [delataX] = LevyFlight(StepSize, Dim)%Allocate matrix for solutions
2024年2月15日发(作者：巨长菁)
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 ~exist('ProblemFunction', 'var') ProblemFunction = @Ackley;endif ~exist('DisplayFlag', 'var') DisplayFlag = true;endif ~exist('RandSeed', 'var') RandSeed = round(sum(100*clock));end[OPTIONS, MinCost, AvgCost, InitFunction, CostFunction, FeasibleFunction, ... MaxParValue, MinParValue, Population] = Init(DisplayFlag, ProblemFunction, RandSeed);nEvaluations = e;% % % % % % % % % % % % Initial parameter setting % % % % % % % % % % % %%%%%% Initial parameter settingKeep = 2; % elitism parameter: how many of the best habitats to keep from one generation to the nextmaxStepSize = 1.0; %Max Step sizepartition = ion;numButterfly1 = ceil(partition*e); % NP1 in papernumButterfly2 = e - numButterfly1; % NP2 in paperperiod = 1.2; % 12 months in a yearLand1 = zeros(numButterfly1, );Land2 = zeros(numButterfly2, );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 loopGenIndex = 1;% for GenIndex = 1 : while nEvaluations<
% % % % % % % % % % % % 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 : e 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 : 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 = e; e = numButterfly1; % Make sure each individual is legal. NewPopulation1 = FeasibleFunction(OPTIONS, NewPopulation1); % Calculate cost NewPopulation1 = CostFunction(OPTIONS, NewPopulation1); % the number of fitness evaluations nEvaluations = nEvaluations + e; e = 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*,1,1)); delataX = LevyFlight(StepSzie,); for parnum2 = 1:, 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 = e; e = numButterfly2; % Make sure each individual is legal. NewPopulation2 = FeasibleFunction(OPTIONS, NewPopulation2); % Calculate cost NewPopulation2 = CostFunction(OPTIONS, NewPopulation2); % the number of fitness evaluations nEvaluations = nEvaluations + e; e = 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 generation's elites. n = length(Population); for k3 = 1 : Keep Population(n-k3+1).chrom = chromKeep(k3,:); Population(n-k3+1).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 = GenIndex+1;
end % end for GenIndexConclude2(DisplayFlag, OPTIONS, Population, nLegal, MinCost, AvgCost);toc% % % % % % % % % % End of Monarch Butterfly Optimization implementation %%%% %% %%%function [delataX] = LevyFlight(StepSize, Dim)%Allocate matrix for solutions