【优化求解】蝴蝶算法MBO matlab源码
摘要：蝴蝶优化算法 （Butterfly optimization algorithm，BOA）是由 Arora于基于蝴蝶BOA觅食过程提出的自然启发式算法。该算法具有较高的收敛精度。
1.算法原理
蝴蝶利用自身的感知器定位食物的来源。该算法中，假设每只蝴蝶产生一定强度的香味，这些香味会传播并被区域内的其它蝴蝶感知。每只蝴蝶释放出的香味与它的适应度有关。这就意味着当一只蝴蝶移动了位置，它的适应度也将随之变化。当蝴蝶感觉到另一只蝴蝶在这个区域散发出更多的香味时，就会去靠近，这个阶段被称为全局搜索。另外一种情况，当蝴蝶不能感知大于它自己的香味时，它会随机移动，这个阶段称为局部搜索阶段。
香味是根据 刺 激 的 物 理 强 度 来 表 述 的。其 计 算 如 式（1）所示：
2.算法流程：
(1) 计算适应度函数f ( x ) , x = ( x 1 , . . . , x d i m ) f(x),x=(x1,...,xdim)f(x),x=(x1,...,xdim)
(2) 给每个蝴蝶生成ｎ ｎｎ个初始解 x i = ( i = 1 , 2 , . . . , n ) x_i=(i=1,2,...,n)xi=(i=1,2,...,n)
(3) 声明变量 c , α , g ∗ , p c,\alpha,g^*,pc,α,g∗,p
(4) while未到终止条件do
(5) for每一个蝴蝶do
(6) 采用式(1)计算其香味函数f ff
(7) end for
(8) 找出最优的香味函数f ff，并赋值给g ∗ g^*g∗
(9) for 每一个蝴蝶do
(10) 采用式(4)计算概率 ｒ
(11) if r
(12) 采用式(2)进行全局搜索
(13) else
(14) 采用式(3)进行局部随机搜索
(15) end if
(16) end for
(17) end while
(18) 输出最优解 ．
3.参考文献：
[1] Arora S, Singh S. Butterfly optimization algorithm: a novel approach for global optimization[C]. soft computing, 2019, 23(3): 715-734.
[2]李田来,刘方爱.带混沌映射的WSN蝴蝶优化定位算法[J].计算机工程与设计,2019,40(06):1729-1733.
[3]刘云涛.基于蝴蝶优化的粒子滤波算法[J].信息技术与网络安全,2018,37(07):37-41.
4.MATLAB代码
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %%
%% 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 generation 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);
% % % % % % % % % % % % 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
for GenIndex = 1 : OPTIONS.Maxgen
% % % % % % % % % % % % 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 butterflies 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);
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);
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 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 %%%%%%%%%% %% %
%%
end % end for GenIndex
Conclude1(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 i=1:Dim
% Cauchy distribution
fx = tan(pi * rand(1,StepSize));
delataX(i) = sum(fx);
end
完整代码或者代写添加QQ1575304183