摘要
现实中多目标优化问题的Pareto前沿面往往是非规则形式,针对这类问题的进化算法已逐渐成为研究热点。对现有非规则Pareto前沿面多目标优化问题的进化算法进行总结和分类,给出了多目标优化问题的通用数学描述,并给出了支配和非支配解等该研究领域内的相关定义。整理了典型的具有非规则Pareto前沿面的多目标优化测试问题,以及汽车碰撞问题等实际优化问题中的具有非规则Pareto前沿面的多目标优化问题。将现有处理具有非规则Pareto前沿面的多目标优化问题的进化算法分为4个大类:根据种群分布调整参考向量的方法、固定参考向量结合其他辅助方法、参考点的方法、聚类和分区的方法,并分别进行了分析和讨论。研究表明:尽管针对具有非规则Pareto前沿面的多目标优化问题的进化算法已经取得了一定成效,但现有算法一般只在部分非规则Pareto前沿面问题上表现较好,适应所有种类的非规则Pareto前沿面问题的算法还有待开发,决策变量或目标数量高维的、动态的、数据驱动的具有非规则Pareto前沿面的多目标优化问题也是有待解决的研究领域;更加智能的,可以辨别和处理多类型非规则Pareto前沿面的进化算法是未来的研究重点;用多种环境选择方法混合、迁移学习结合进化计算、多任务结合进化计算是可行的解决途径。
In reality,the Pareto fronts of multi-objective optimization problems are often irregular.Evolutionary algorithms for such problems have gradually become a hot topic.This paper provides a survey of the existing evolutionary algorithms for the multi-objective optimization problems with irregular Pareto fronts,gives a general mathematical description of the multi-objective optimization problems,and introduces the relevant definitions in the research field such as dominated and non-dominated solutions.It suggests a taxonomy of the typical multi-objective optimization test problems with irregular Pareto fronts,as well as the actual multi-objective optimization test problems with irregular Pareto fronts such as car crash test problem.The existing evolutionary algorithms for multi-objective optimization problems with irregular Pareto fronts are divided into four categories:the methods of adjusting the reference vectors according to the population distribution,the fixed reference vectors merging other auxiliary methods,the methods of reference points,and the methods of clustering and partitioning.Their strengths and weaknesses are discussed.Although evolutionary algorithms for multi-objective optimization problems with irregular Pareto fronts have achieved certain success,existing algorithms generally perform well only on some irregular Pareto front problems.Algorithms that can work efficiently on all kinds of irregular Pareto front problems are yet to be developed.High dimensional,dynamic and the data-driven multi-objective problems with irregular Pareto fronts remain to be solved.More intelligent evolutionary algorithms that can identify and handle multiple types of multi-objective optimization problems with irregular Pareto fronts are the focus of future research.Hybrid approaches,transfer learning or multi-task learning and optimization combined with evolutionary computation are possible solutions.
作者
华一村
刘奇奇
郝矿荣
金耀初
HUA Yicun;LIU Qiqi;HAO Kuangrong;JIN Yaochu(College of Information Science and Technology, Donghua University, Shanghai 201620, China;Department of Computer Science, University of Surrey, Surrey GU2 7XH, U.K.)
出处
《郑州大学学报（工学版）》
CAS
北大核心
2021年第1期1-8,共8页
Journal of Zhengzhou University（Engineering Science）
基金
国家自然科学基金资助项目(61806051)
上海市自然科学基金资助项目(20ZR1400400)。
