基于聚类的新型多目标分布估计算法及其应用

为改善常见的多目标分布估计算法在求解多目标优化问题的过程中存在的不足,即:对问题的规则特性考虑不够,对种群中异常解的处理不当,种群多样性容易丢失,过多的计算开销用于构建最优概率模型,提出一种基于聚类的新型多目标分布估计算法(clustering based multi objective estimation of distribution algorithm, CEDA)。CEDA在每一代运用凝聚层次聚类算法发掘种群个体的邻近结构,基于此结构,为每个个体构建一个多元高斯模型逼近种群结构并抽样产生新个体。为了降低建模计算开销,邻近个体共享相同的协方差矩阵建立高斯模型。基于标准测试题的对比实验表明CEDA能够解决复杂的多目标优化问题。基于齿轮减速器优化设计的实际应用表明CEDA同样具有良好的实用性和优越性。

Clustering-based multi-objective estimation of distributionalgorithm and its application

In order to improve the deficiencies, that is, insufficiently considering the regularity property, inappropriately handling abnormal solutions, easily losing populationdiversity, and the excessive computational cost of constructing the optimal probabilistic model, which exist in the process of using common multi-objective estimation ofdistribution algorithms to solve multi-objective optimization problems, this paper proposes a clustering-based multi-objective estimation of distribution algorithm (CEDA). Ateach generation, CEDA adopts an agglomerative hierarchical clustering algorithm to find the neighborhood structure of population, and based on the structure, CEDA builds amultivariate Gaussian model for each solution to approximate population structure and to sample new solutions. In order to reduce the computational cost of modelling,neighboring solutions share the same covariance matrix to construct Gaussian models. The comparison experiments based on benchmark instances indicate that CEDA is able to solvecomplicated multi-objective optimization problems. Practical application based on optimization design of the gear reducer shows CEDA also has favorable practicability andsuperiority.