一种改进ε支配的等度规映射方法

摘要

新型支配机制的研究是进化多目标优化领域中的热点和难点之一,其中,ε支配最具代表性.但是,它的缺点在于对于不同几何形状的Pareto前沿十分敏感.提出了一种改进ε支配机制的等度规映射方法,采用等度规映射把解映射到低维流形空间,发现隐藏于非支配解的几何分布,在低维流形空间进行ε支配的剪枝操作与传统的ε支配相比,该机制不会丢失部分有效解,能够较好地保持解分布的均匀性.另外,为了克服传统ε支配丢失部分极端解的不足,设计了极端解校验算子与NSGAII,SPEA2,NNIA和εMOEA相比,所提出的ε支配和极端解校验算子能够较好地保持解分布的均匀性和宽广性,改进了传统的ε支配.%The study of new types of dominance mechanisms is a key point in current evolutionary multi-objective optimization community and e dominance is a representative among them. However, their ability in diversity maintaining is sensitive to different shapes of Pareto fronts. This paper proposes an improved e dominance mechanism by Isomap, which employs Isomap to embed the original population to low dimensional manifold space. The intrinsic geometric structure of them is discovered and e dominance is adopted to select data in the embedding space. Compared with traditional e dominance, the mechanism does not lose valid solutions and can maintain a set of uniform-distributed solutions. In addition, the extreme solution-check operator is proposed to enhance the ability of holding extreme solutions of e dominance. The detailed experimental comparison with NSGAII, SPEA2, NNIA and sMOEA shows that the two strategies in this study are beneficial to uniformity and spread maintenance, which are in the enhanced version of traditional e dominance.