Abstract:

There are two main aspects of research in multi-objective optimization algorithm, namely, convergence and diversity. While, it is difficult for original algorithms to maintain the diversity of solutions in the high-dimensional objective space. In order to enhance the diversity of algorithms in many-objective optimization problems, a new distance dominance relation is proposed in this paper. Firstly, in order to ensure the convergence of the algorithm, in the same niche, the distance dominance relation calculates the distance from the candidate solution to the ideal point as the fitness value, and selects the candidate solution with good fitness value as the non-dominant solution.Then, in order to enhance the diversity of the algorithm, the distance dominance relation sets each candidate solution to have the same niche and ensures that only one optimal solution is retained in the same niche. Finally, the VaEA algorithm is improved based on the proposed distance dominance relation, and the algorithm is named VaEA-DDR. On the DTLZ and IDTLZ test of 5, 8, 10, 15 dimensional objectives, the improved algorithm is compared with six commonly used algorithms. Experimental results show that the improved algorithm is highly competitive and can significantly enhance the diversity of the algorithm.

Key words: many-objective optimization, distance dominance relation, diversity, VaEA

摘要：

收敛性与多样性是多目标进化算法的两个主要研究方面，随着多目标优化问题目标维度的增加，传统的多目标进化算法很难维持解的多样性。为了增强算法在高维多目标优化问题中的多样性，提出了一种新的距离优势关系。首先，为了保证算法的收敛性，在同一小生境内，基于距离优势关系计算候选解到理想点的距离作为适应度值，选择适应度值好的候选解作为非支配解。然后，为了增强算法的多样性，距离优势关系设定了每个候选解具有相同的小生境，并且保证在同一小生境内只保留一个最优解。最后，基于提出的距离优势关系对VaEA算法进行改进，得到的算法命名为VaEA-DDR。在5、8、10、15维目标的DTLZ及IDTLZ测试问题上将改进的算法与目前六种常用的算法进行实验对比。实验结果表明，改进后的算法具有较强的竞争性，能显著增强算法的多样性。

关键词: 高维多目标优化, 距离优势关系, 多样性, VaEA