| Author Name | Affiliation | | Sifeng Zhu | School of Computer and Information Engineering, Tianjin Chengjian University, Tianjin, 300384, China | | Chengrui Yang | School of Computer and Information Engineering, Tianjin Chengjian University, Tianjin, 300384, China | | Jiaming Hu | School of Computer and Information Engineering, Tianjin Chengjian University, Tianjin, 300384, China |
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| Abstract: |
| Balancing the diversity and convergence of the population is challenging in multi-objective optimization. The work proposed a many-objective evolutionary algorithm based on indicator Iε+(MaOEA/I) to solve the above problems. Indicator Iε+(x,y) is used for environmental selection to ensure diversity and convergence of the population. Iε+(x,y) can evaluate the quality of individual x compared with individual y instead of the whole population. If Iε+(x,y) is less than 0, individual x dominates y. If Iε+(x,y) is 0, individuals x and y are the same. If Iε+(x,y) is greater than 0, no dominant relationship exists between individuals x and y. The smaller Iε+(x,y), the closer the two individuals. The dominated individuals should be deleted in environmental selection because they do not contribute to convergence. If there is no dominant individual, the same individuals and similar individuals should be deleted because they do not contribute to diversity. Therefore, the environmental selection of MaOEA/I should consider the two individuals with the smallest Iε+(x,y). If Iε+(x,y) is not greater than 0, delete individual y; if Iε+(x,y) is greater than 0, check the distance between individuals x, y, and the target point and delete the individual with a longer distance. MaOEA/I is compared with 6 algorithms until the population does not exceed the population size. Experimental results demonstrate that MaOEA/I can gain highly competitive performance when solving many-objective optimization problems. |
| Key words: many-objective evolutionary algorithm indicator diversity convergence |
| DOI：10.11916/j.issn.1005-9113.2022085 |
| Clc Number:TP18 |
| Fund: |
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| Descriptions in Chinese: |
| MaOEA/I：一种基于指标的高维多目标进化算法 朱思峰，杨诚瑞，胡家铭 (天津城建大学 计算机与信息工程学院，天津，300384) 摘要：在高维多目标优化问题中，种群收敛性与多样性的平衡相较于多目标优化问题面临更大挑战。本文提出了一种基于指标的高维多目标进化算法用以解决上述问题。指标被应用于环境选择，以指标的二元关系替代非支配关系，保证高维环境下种群收敛性与多样性的平衡。指标更加注重局部信息，仅以解两两之间的关系评估解的质量。当的值小于0时，解支配解；当的值等于0时，解与解相同；当的值大于0时，解与解之间不存在支配关系，但是此时的值越小，两解的距离越近。可以认为，的值越小，这组解对种群的贡献越低，环境选择将依次删除对种群贡献最低的解。本文提出的算法与其他6种算法进行了对比实验，结果证明本文提出的算法能够取得更优的结果。 关键词 高维多目标；进化算法；指标；收敛性；多样性 |
