面向复杂超多目标优化问题的自适应增强学习进化算法

Adaptive boosting learning evolutionary algorithm for complex many-objective optimization problems

在解决超多目标优化问题中,基于分解的进化算法是一种较为有效的方法.传统的分解方法依赖于一组均匀分布的参考向量,它借助聚合函数将多目标优化问题分解为一组单目标子问题,然后对这些子问题同时进行优化.然而,由于参考向量分布和Pareto前沿形状的不一致性,导致这些预定义的参考向量在解决复杂超多目标优化问题时表现较差.对此,提出一种基于自适应增强学习的超多目标进化算法(MaOEA-ABL).该算法主要分为两个阶段:第1阶段,采用一种自适应增强学习算法对预定义的参考向量进行调整,在学习过程中删除无用向量,增加新的向量;第2阶段,设计一种对Pareto形状无偏好的分解方法.为验证所提出算法的有效性,选取具有复杂Pareto前沿的MaF系列测试函数进行仿真研究,结果显示,MaOEA-ABL算法的IGD(inverted generational distance)均值在67%的测试函数上超过了对比算法,从而表明该算法在复杂超多目标优化问题中表现良好.

The evolutionary algorithm based on decomposition is an effective method in dealing with many-objective optimization problems.The traditional decomposition method relys on a set of uniformly distributed reference vectors,which decomposes the multi-objective optimization problem into a set of single-objective subproblems through aggregation functions,and then optimizes these subproblems simultaneously.However,these predefined reference vectors perform poorly in solving complex many-objective optimization problems because of the inconsistency of the distribution of reference vectors and the shape of the Pareto front.Aiming at the above problems,a many-objective evolutionary algorithm based on adaptive boosting learning(MaOEA-ABL)is proposed.The algorithm can be divided into two stages.In the first stage,an adaptive boosting learning algorithm is used to adjust the predefined reference vectors.In the learning process,useless vectors are deleted and new vectors are added.In the second stage,an unbiased decomposition method of Pareto shape is designed.Simulation has been conducted on the MaF test problems.The experimental results show that the IGD(inverted generational distance)mean value of MaOEA-ABL is better than that of the comparison algorithms in 67%of the test functions,which indicates that the MaOEA-ABL performs well in many-objective optimization problems with complex Pareto front.