【优化算法】头脑风暴优化算法（BSO）【含Matlab源码 497期】

一、获取代码方式

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二、头脑风暴优化算法（BSO）简介

受人类创造性解决问题过程——头脑风暴会议的启发， 2011年史玉回老师在第二次群体智能国际会议 (The Second International Conference on Swarm Intelligence(ICSI11)) 中提出一种新的群智能优化算法——头脑风暴优化算法，算法采用聚类思想搜索局部最优，通过局部最优的比较得到全局最优；采用变异思想增加了算法的多样性，避免算法陷入局部最优，在这聚与散相辅相承的过程中搜索最优解，思想新颖，适合于解决多峰高维函数问题。
算法流程建模如下

算法步骤描述

三、部分源代码

function best_fitness = bso2(fun,n_p,n_d,n_c,rang_l,rang_r,max_iteration)
% fun = fitness_function
% n_p; population size
% n_d; number of dimension
% n_c: number of clusters
% rang_l; left boundary of the dynamic range
% rang_r; right boundary of the dynamic range
prob_one_cluster = 0.8; % probability for select one cluster to form new individual;
stepSize = ones(1,n_d); % effecting the step size of generating new individuals by adding random values
popu = rang_l + (rang_r - rang_l) * rand(n_p,n_d); % initialize the population of individuals
popu_sorted  = rang_l + (rang_r - rang_l) * rand(n_p,n_d); % initialize the  population of individuals sorted according to clusters
n_iteration = 0; % current iteration number
% initialize cluster probability to be zeros
prob = zeros(n_c,1);
best = zeros(n_c,1);  % index of best individual in each cluster
centers = rang_l + (rang_r - rang_l) * rand(n_c,n_d);  % initialize best individual in each cluster
centers_copy = rang_l + (rang_r - rang_l) * rand(n_c,n_d);  % initialize best individual-COPY in each cluster FOR the purpose of introduce random best
best_fitness = 1000000*ones(max_iteration,1);
fitness_popu = 1000000*ones(n_p,1);  % store fitness value for each individual
fitness_popu_sorted = 1000000*ones(n_p,1);  % store  fitness value for each sorted individual
indi_temp = zeros(1,n_d);  % store temperary individual
%**************************************************************************
%**************************************************************************
% calculate fitness for each individual in the initialized population
for idx = 1:n_pfitness_popu(idx,1) = fun(popu(idx,:));
end
while n_iteration < max_iterationcluster = kmeans(popu, n_c,'Distance','cityblock','Start',centers,'EmptyAction','singleton') % k-mean cluster% clustering    fit_values = 100000000000000000000000000.0*ones(n_c,1);  % assign a initial big fitness value  as best fitness for each cluster in minimization problemsnumber_in_cluster = zeros(n_c,1);  % initialize 0 individual in each cluster      for idx = 1:n_pnumber_in_cluster(cluster(idx,1),1)= number_in_cluster(cluster(idx,1),1) + 1;        % find the best individual in each clusterif fit_values(cluster(idx,1),1) > fitness_popu(idx,1)  % minimizationfit_values(cluster(idx,1),1) = fitness_popu(idx,1);best(cluster(idx,1),1) = idx;end            end  best% form population sorted according to clusterscounter_cluster = zeros(n_c,1);  % initialize cluster counter to be 0     acculate_num_cluster = zeros(n_c,1);  % initialize accumulated number of individuals in previous clusters    for idx =2:n_cacculate_num_cluster(idx,1) = acculate_num_cluster((idx-1),1) + number_in_cluster((idx-1),1);end    %start form sorted populationfor idx = 1:n_pcounter_cluster(cluster(idx,1),1) = counter_cluster(cluster(idx,1),1) + 1 ;temIdx = acculate_num_cluster(cluster(idx,1),1) +  counter_cluster(cluster(idx,1),1);popu_sorted(temIdx,:) = popu(idx,:);fitness_popu_sorted(temIdx,1) = fitness_popu(idx,1);end       % record the best individual in each clusterfor idx = 1:n_ccenters(idx,:) = popu(best(idx,1),:);        endcenters_copy = centers  % make a copyif (rand() < 0.2) %  select one cluster center to be replaced by a randomly generated centercenIdx = ceil(rand()*n_c);centers(cenIdx,:) = rang_l + (rang_r - rang_l) * rand(1,n_d);end           % calculate cluster probabilities based on number of individuals in% each clusterfor idx = 1:n_cprob(idx,1) = number_in_cluster(idx,1)/n_p;if idx > 1prob(idx,1) = prob(idx,1) + prob(idx-1,1);endend    % generate n_p new individuals by adding Gaussian random values                   for idx = 1:n_pr_1 = rand();  % probability for select one cluster to form new individualif r_1 < prob_one_cluster % select one clusterr = rand();for idj = 1:n_cif r < prob(idj,1)                      if rand() < 0.4  % use the centerindi_temp(1,:) = centers(idj,:); else % use one randomly selected  clusterindi_1 = acculate_num_cluster(idj,1) + ceil(rand() * number_in_cluster(idj,1));indi_temp(1,:) = popu_sorted(indi_1,:);  endbreakendendelse % select two clusters% pick two clusters cluster_1 = ceil(rand() * n_c);indi_1 = acculate_num_cluster(cluster_1,1) + ceil(rand() * number_in_cluster(cluster_1,1));          cluster_2 = ceil(rand() * n_c);indi_2 = acculate_num_cluster(cluster_2,1) + ceil(rand() * number_in_cluster(cluster_2,1));         tem = rand();if rand() < 0.5 %use centerindi_temp(1,:) = tem * centers(cluster_1,:) + (1-tem) * centers(cluster_2,:); else   % use randomly selected individuals from each cluster            indi_temp(1,:) = tem * popu_sorted(indi_1,:) + (1-tem) * popu_sorted(indi_2,:); endend      %Griewank
function z = griewank(x)
% unimodal optimum 0
[m,n]=size(x);
for j=1:mfor e=1:nf1(e)=x(j,e)^2;f2(e)=cos(x(j,e)/sqrt(e));end

四、运行结果

五、matlab版本及参考文献

1 matlab版本
2014a

2 参考文献
[1] 包子阳,余继周,杨杉.智能优化算法及其MATLAB实例（第2版）[M].电子工业出版社，2016.
[2]张岩,吴水根.MATLAB优化算法源代码[M].清华大学出版社，2017.