中文摘要：

提出了一种采用基于决策树概率模型表示各变量之间条件相关性的分布估算算法：实数编码多目标贝叶斯优化算法（RCMBOA）.通过构建这样的概率模型,继而对模型进行抽样以产生新个体.再对生成的新个体进行变异操作,以提高算法的搜索能力,增加种群的多样性.这种生成新个体的方法结合非劣分层与截断选择机制,可以很好地逼近多目标问题的Pareto前沿.同时,在进行截断选择时,每次只删除一个排挤距离小的个体,之后重新估算个体的排挤距离,以获得分布均匀的非劣解集.对于约束多目标优化问题,算法采用带约束支配关系判别个体的优劣.用该算法对8个较难的测试问题进行了优化计算,获得的非劣解集与NSGA-Ⅱ算法得到的相比,非劣解集的质量更高,分布更为均匀.计算结果说明RCMBOA是一种有效、鲁棒的多目标优化算法.

英文摘要：

This paper proposes an estimation of distribution algorithm with decision-tree-based probabilistic models for multi-objective optimization in continuous domains.This is the Real-Coded Multi-objective Bayesian Optimization Algorithm （RCMBOA）.It uses such probabilistic models to encode conditional dependencies among variables.By building and sampling the probabilistic models,the algorithm reproduces the genetic information of the next generation,Combined such a reproduction mechanism with the nondominated sorting and truncated selection techniques,RCMBOA can approximate the probability density of solutions lying on the Pareto front.In RCMBOA,polynomial mutation operator is incorporated in order to enhance exploration and maintain diversities in the populations.Furthermore,RCMBOA incorporates a proce- dure to eliminate a solution with smaller crowding distance once,so that it can obtain a well distributed set of nondominated solutions.And the constrained-dominance is applied to solve constrained multi-objective optimization problems efficiently.The performance of RCMBOA is evaluated on 8 difficult test problems and metric from literature,The results indicate that the new approach is a general,effective and robust method for multi-objective optimization.