BSO算法介绍及Java实现

头脑风暴过程

头脑风暴法经常被用来解决创新问题。它可以解决很多通常不能由一个人解决的难题。在头脑风暴过程中，一群背景不同的人聚集在一起进行讨论。引导者通常会参与这个过程，但不会直接参与想法的产生。引导者通常应该有足够的引导者经验，但对要解决的问题的了解较少，这样产生的想法就会较少受到来自引导者的认知的影响。头脑风暴的过程是用来产生尽可能多的想法，这样就可以从这些想法中得到解决问题的好办法。

头脑风暴的过程通常包括几轮想法的产生。在每一轮的想法生成中，头脑风暴小组都被要求提出很多想法。在每一轮的想法生成过程结束时，比较好的想法会被挑选出来，作为下一轮创意生成过程中产生想法的线索。在头脑风暴的过程中，还有另外一群人，他们的目的是从每一轮的想法产生过程中挑选出比较好的想法，通过头脑风暴的过程，由人类的集体智慧，往往会产生伟大的解决方案，并且我们的问题通常能够以很高的概率得到解决。

头脑风暴流程建模如下

头脑风暴(BSO)算法简介

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(流程纯Word手打，转载请注明出处！)：

使用Java实现BSO算法

注：为了演示效果，本示例选择Sphere函数作为适应值函数来评价个体。维度设置为2维，且迭代次数仅仅设定20代。

Sphere函数定义如下：

package BSO_Code;import java.util.ArrayList;
import java.util.Random;/*** 头脑风暴智能优化算法实现* @author xudaxia0610*/
public class BSO {//个体数量public int number_of_individuals;//聚类个数public int number_of_clusters;//种群public ArrayList<Cindividual> population;//类簇public ArrayList<ArrayList<Integer>> cluster;//质心集合public ArrayList<Cindividual> meansList;//存放类中心所在下标的集合public ArrayList<Integer> clusterCenterIndex;//新解集合public ArrayList<Cindividual> nSolutions;//最优个体public Cindividual bestIndividual;//下面四个为预先决定的概率public float p_clustering;public float p_generation;public float p_oneCluster;public float p_twoCluster;//下面四个为算法执行过程中生成的比例public float r_clustering;public float r_generation;public float r_oneCluster;public float r_twoCluster;//个体的维数public int dimension;// 迭代次数public int total_evolve_times;// 当前迭代的次数public int current_evolve_times;//随机数生成器public Random random = new Random();//参数k，此k非聚类k的个数，而是新个体产生的公式中变异系数中那个控制斜率的Kpublic int k;//交叉生成新个体时,父母的权重比例public float weight1;public float weight2;//参数初始化public void initParameters() {//解的维数dimension = 2;//个体数量(种群大小)number_of_individuals = 100;//聚类个数number_of_clusters = 5;//初始化各个集合cluster = new ArrayList<>();clusterCenterIndex = new ArrayList<>();nSolutions = new ArrayList<>();meansList = new ArrayList<>();//决定是否需要替换一个类中心的概率p_clustering = 0.2f;//决定新个体产生是由一个还是两个老个体所决定的概率p_generation = 0.8f; //决定由一个类中心还是其它普通个体来生成新个体的概率p_oneCluster = 0.4f;//决定由两个类中心还是其它两个普通个体来生成新个体的概率p_twoCluster = 0.5f;//总迭代次数total_evolve_times = 20;//当前迭代次数current_evolve_times = 0;//初始化k，变异操作控制斜率的参数k = 25;//初始化权重weight1 = 0.5f;weight2 = 0.5f;//初始化最优个体bestIndividual = new Cindividual();bestIndividual.lChromosome = new ArrayList<>();for(int i = 0; i < dimension; i++) {bestIndividual.lChromosome.add(1.0f);}//将初始化的最优个体的Object_value设为最大值，因为object_value越小越好bestIndividual.objectValue = Float.MAX_VALUE;}//种群初始化public void initPopulation() {population = new ArrayList<>();for(int i = 0;i < number_of_individuals;i++) {//生成一个新个体Cindividual t = new Cindividual();t.lChromosome = new ArrayList<>();//随机初始化这个个体initIndividual(t);//根据适应值函数评价该个体evaluate(t);//更新最优个体updateBestIndividual(t);//将该个体的引用置入种群中population.add(t);}}//初始化一个个体public void initIndividual(Cindividual t) {for(int i = 0;i < dimension;i++) {t.lChromosome.add(random.nextFloat() * 200.0f - 100.0f);}}//适应值函数评价个体public void evaluate(Cindividual t) {//此处实现的是最简单的Sphere函数(单峰函数)t.objectValue = 0.0f;float cur = 0.0f;for(int i = 0; i < dimension; i++) {cur = t.lChromosome.get(i);t.objectValue = t.objectValue + cur * cur;}}//更新最优个体public void updateBestIndividual(Cindividual t) {//objectValue值越小越好if (t.objectValue < bestIndividual.objectValue) {bestIndividual.objectValue = t.objectValue;}}//K-Means聚类算法过程public void clustering() {//清空上次聚类的残留结果clusterCenterIndex.clear();cluster.clear();for (int i = 0; i < number_of_clusters; i++){//将类中心数组初始化clusterCenterIndex.add(-1);//生成k个空簇cluster.add(new ArrayList<>());}//随机挑选k个个体作为初始类中心for(int i = 0;i < number_of_clusters;i++) {int centerIndex = -1;while(true) {//flag为标识位，标识挑选的类中心是否距离已经挑选好的类中心距离太近boolean flag = false;//随机挑选一个个体centerIndex = random.nextInt(number_of_individuals);//确保不会出现重复的类中心if (clusterCenterIndex.contains(centerIndex)) {//重复了就重来continue;}//确保随机挑选的类中心之间相距不会太近if (i != 0){for (int j = i - 1; j >= 0; j--){if (getDistance(population.get(centerIndex), population.get(clusterCenterIndex.get(j))) < 1.0f) {//距离小于2，判定初始类中心相距太近flag = true;break;}}}//如果距离太近，那么就重新生成if (flag) {continue;}//如果类中心既未重复也未距离其他类中心太近，跳出循环break;}clusterCenterIndex.set(i, centerIndex);}//第一次聚类for (int i = 0; i < number_of_individuals; i++) {Cindividual tCindividual = population.get(i);//获取该个体所属簇编号int label = getIndividualOfCluster(tCindividual);//将该个体的下标添加到对应的簇中cluster.get(label).add(i);}float oldVar = -1.0f;float newVar = getVar();//当新旧方差值相差不到1即准则函数值不发生明显变化时，聚类算法终止while(Math.abs(newVar - oldVar) >= 1.0f) {//更新类中心getCenter();//使用质心//getMeans();oldVar = newVar;//清空每个簇for (int i = 0; i < number_of_clusters; i++){cluster.get(i).clear();;}//根据新的聚类中心去获取新的聚类结果for (int i = 0; i < number_of_individuals; i++){//遍历每一个个体Cindividual t = population.get(i);//获取该个体所属簇编号int label = getIndividualOfCluster(t);//将该个体的下标添加到对应的簇中cluster.get(label).add(i);}//计算新的簇内方差值newVar = getVar();}}//获取两个个体之间的欧式距离public float getDistance(Cindividual t1,Cindividual t2) {float res = 0.0f;for(int i = 0;i < dimension;i++) {res += (t1.lChromosome.get(i) - t2.lChromosome.get(i)) * (t1.lChromosome.get(i) - t2.lChromosome.get(i));}return (float) Math.sqrt(res);}//查看当前个体属于哪个类中public int getIndividualOfCluster(Cindividual t) {int label = 0;float minDistance = getDistance(t, population.get(clusterCenterIndex.get(0)));for(int i = 1;i < number_of_clusters;i++) {float anotherDistance = getDistance(t, population.get(clusterCenterIndex.get(i)));if (anotherDistance < minDistance) {minDistance = anotherDistance;label = i;}}return label;}//获得簇集的平方差public float getVar() {float var = 0.0f;for(int i = 0;i < number_of_clusters; i++) {ArrayList<Integer> list = cluster.get(i);for(int j = 0; j < list.size(); j++) {var += getDistance(population.get(clusterCenterIndex.get(i)), population.get(list.get(j)));}}return var;}//将质心作为聚类中心public void getMeans() {//清空上次聚类的质心残留meansList.clear();for(int i = 0;i < number_of_clusters ; i++) {Cindividual cindividual = new Cindividual();cindividual.lChromosome = new ArrayList<>();int clusterSize = cluster.get(i).size();for(int k = 0;k < dimension; k++) {float means = 0.0f;for(int j = 0;j < clusterSize;j++) {means += population.get(cluster.get(i).get(j)).lChromosome.get(k);}means /= clusterSize;cindividual.lChromosome.add(means);}meansList.add(cindividual);}}//确定类中心//下面的实现是基于挑选类中最优个体作为类中心的//如果最终算法收敛效果不好，那么可以尝试一下使用质心作为类中心public void getCenter() {for(int i = 0;i < number_of_clusters;i++) {//定义一个初始的最优值float bestValue = Float.MAX_VALUE;//定义类中心的索引int centerIndex = -1;ArrayList<Integer> list = cluster.get(i);for(int j = 0; j < list.size(); j++) {float curValue = population.get(list.get(j)).objectValue;if (curValue < bestValue) {bestValue = curValue;centerIndex = list.get(j);}}//更新类中心的索引clusterCenterIndex.set(i, centerIndex);}}//新个体生成的过程public void newIndividualGenerate() {//清空新解集合nSolutions.clear();//由单个类生成新个体所需下标参数int clusterIndex = -1, individualIndex = -1;//由两个类生成新个体所需下标参数int clusterIndex1 = -1, clusterIndex2 = -1, individualIndex1 = -1, individualIndex2 = -1;//簇大小int clusterSize1 = -1;int clusterSize2 = -1;//判断是否需要随机挑选出来一个类中心去替换掉//这是一种发散操作r_clustering = random.nextFloat();if (r_clustering < p_clustering) {//随机获取一个类的索引clusterIndex = random.nextInt(number_of_clusters);//随机生成一个新个体Cindividual newObject = new Cindividual();newObject.lChromosome = new ArrayList<>();initIndividual(newObject);//替换刚才选中的那个类中心int replacedObjectIndex = clusterCenterIndex.get(clusterIndex);population.set(replacedObjectIndex, newObject);}//新个体生成的过程for(int i = 0;i < number_of_individuals; i++) {Cindividual newObject = new Cindividual();r_generation = random.nextFloat();//r_generation < p_generation --》 随机挑选一个类去生成新个体     else 随机挑选两个类去生成新个体if (r_generation < p_generation) {r_oneCluster = random.nextFloat();//随机获取一个簇clusterIndex = random.nextInt(number_of_clusters);if (r_oneCluster < p_oneCluster) {//根据刚刚获得的随机类索引，拿到该类的类中心//根据该类中心加入噪声以生成新的个体individualIndex = clusterCenterIndex.get(clusterIndex);Cindividual center = population.get(individualIndex);//根据类中心执行变异操作mutation(center,newObject);//评价新个体evaluate(newObject);//更新最优个体updateBestIndividual(newObject);//加入新个体集合nSolutions.add(newObject);}else {//在随机选取的类中我们随机选取一个普通个体，以该个体为根据，加入噪声生成新个体clusterSize1 = cluster.get(clusterIndex).size();//随机选取一个个体individualIndex = cluster.get(clusterIndex).get(random.nextInt(clusterSize1));//避免随机到类中心while(cluster.get(clusterIndex).size() != 1 && individualIndex == clusterCenterIndex.get(clusterIndex)) {individualIndex = cluster.get(clusterIndex).get(random.nextInt(clusterSize1));}Cindividual commonObj = population.get(individualIndex);//根据普通个体执行变异操作mutation(commonObj,newObject);//评价新个体evaluate(newObject);//更新最优个体updateBestIndividual(newObject);//加入新个体集合nSolutions.add(newObject);}}else {r_twoCluster = random.nextFloat();//随机选取两个类clusterIndex1 = random.nextInt(number_of_clusters);clusterIndex2 = random.nextInt(number_of_clusters);while(clusterIndex1 == clusterIndex2) {clusterIndex2 = random.nextInt(number_of_clusters);}//r_twoCluster < p_twoCluster --> 由两个类中心结合，加入噪声去生成新个体//r_twoCluster >= p_twoCluster --> 有两个类中的普通个体交叉，加入噪声去生成新个体if (r_twoCluster < p_twoCluster) {individualIndex1 = clusterCenterIndex.get(clusterIndex1);individualIndex2 = clusterCenterIndex.get(clusterIndex2);//取两个类的类中心作为双亲Cindividual father = population.get(individualIndex1);Cindividual mother = population.get(individualIndex2);//交叉生成crossover(father,mother,newObject);//评价新个体evaluate(newObject);//更新最优个体updateBestIndividual(newObject);//加入新个体集合nSolutions.add(newObject);}else {clusterSize1 = cluster.get(clusterIndex1).size();clusterSize2 = cluster.get(clusterIndex2).size();//去获取两个类中的两个普通个体individualIndex1 = cluster.get(clusterIndex1).get(random.nextInt(clusterSize1));individualIndex2 = cluster.get(clusterIndex2).get(random.nextInt(clusterSize2));//避免随机到类中心while(cluster.get(clusterIndex1).size() != 1 && individualIndex1 == clusterCenterIndex.get(clusterIndex1)) {individualIndex1 = cluster.get(clusterIndex1).get(random.nextInt(clusterSize1));}//避免随机到类中心while(cluster.get(clusterIndex2).size() != 1 && individualIndex2 == clusterCenterIndex.get(clusterIndex2)) {individualIndex2 = cluster.get(clusterIndex2).get(random.nextInt(clusterSize2));}//取两个类中的普通个体作为双亲Cindividual father = population.get(individualIndex1);Cindividual mother = population.get(individualIndex2);//交叉生成crossover(father,mother,newObject);//评价新个体evaluate(newObject);//更新最优个体updateBestIndividual(newObject);//加入新个体集合nSolutions.add(newObject);}}}System.out.println();}//个体变异操作public void mutation(Cindividual center,Cindividual newObj) {//定义传递函数的指数部分float j = (0.5f * total_evolve_times - current_evolve_times) / k;newObj.lChromosome = new ArrayList<>();for(int i = 0;i < dimension; i++) {float r1 = random.nextFloat();float r2 = random.nextFloat();newObj.lChromosome.add((float) (center.lChromosome.get(i) + (r1 * r2)/(1 + Math.exp(-j))));}}//交叉生成public void crossover(Cindividual father,Cindividual mother,Cindividual newObj) {// 定义传递函数的指数部分float j = (0.5f * total_evolve_times - current_evolve_times) / k;newObj.lChromosome = new ArrayList<>();for(int i = 0;i < dimension; i++) {float r1 = random.nextFloat();float r2 = random.nextFloat();newObj.lChromosome.add((float) (weight1*father.lChromosome.get(i) + weight2*mother.lChromosome.get(i) + (r1 * r2)/(1 + Math.exp(-j))));}}//挑选过程，对同一下标的新老个体进行对比，好的留下，坏的淘汰public void selection() {for(int i = 0;i < number_of_individuals;i++) {if (nSolutions.get(i).objectValue < population.get(i).objectValue) {population.set(i, nSolutions.get(i));}}}//进化函数public void evolve() {//参数初始化initParameters();//种群初始化initPopulation();//迭代开始while (current_evolve_times < total_evolve_times) {//先聚类clustering();//生成新个体newIndividualGenerate();//挑选selection();System.out.println("当前迭代次数:"+current_evolve_times + "次，本次最优个体值为:"+bestIndividual.objectValue);current_evolve_times++;}}public static void main(String[] args) {BSO bso = new BSO();bso.evolve();}}

Sphere函数的最优解非常直观，就是0，我们来观察一下算法的效果.

当前迭代次数:0次，本次最优个体值为:146.48228
当前迭代次数:1次，本次最优个体值为:21.945087
当前迭代次数:2次，本次最优个体值为:20.831068
当前迭代次数:3次，本次最优个体值为:6.7565203
当前迭代次数:4次，本次最优个体值为:0.6902876
当前迭代次数:5次，本次最优个体值为:0.19008647
当前迭代次数:6次，本次最优个体值为:0.015031425
当前迭代次数:7次，本次最优个体值为:0.010165354
当前迭代次数:8次，本次最优个体值为:0.0011416364
当前迭代次数:9次，本次最优个体值为:0.0011416364
当前迭代次数:10次，本次最优个体值为:0.0011416364
当前迭代次数:11次，本次最优个体值为:0.0011416364
当前迭代次数:12次，本次最优个体值为:3.4804514E-4
当前迭代次数:13次，本次最优个体值为:2.8302986E-4
当前迭代次数:14次，本次最优个体值为:2.8302986E-4
当前迭代次数:15次，本次最优个体值为:2.8302986E-4
当前迭代次数:16次，本次最优个体值为:2.8302986E-4
当前迭代次数:17次，本次最优个体值为:2.8302986E-4
当前迭代次数:18次，本次最优个体值为:1.7496837E-4
当前迭代次数:19次，本次最优个体值为:1.7496837E-4