Zhang Chunjiang, Gao Liang, Li Xinyu, Shen Weiming, Zhou Jiajun, Tan Kay Chen
IEEE Trans Cybern. 2022 Sep;52(9):9770-9783. doi: 10.1109/TCYB.2021.3062949. Epub 2022 Aug 18.
When a multiobjective evolutionary algorithm based on decomposition (MOEA/D) is applied to solve problems with discontinuous Pareto front (PF), a set of evenly distributed weight vectors may lead to many solutions assembling in boundaries of the discontinuous PF. To overcome this limitation, this article proposes a mechanism of resetting weight vectors (RWVs) for MOEA/D. When the RWV mechanism is triggered, a classic data clustering algorithm DBSCAN is used to categorize current solutions into several parts. A classic statistical method called principal component analysis (PCA) is used to determine the ideal number of solutions in each part of PF. Thereafter, PCA is used again for each part of PF separately and virtual targeted solutions are generated by linear interpolation methods. Then, the new weight vectors are reset according to the interrelationship between the optimal solutions and the weight vectors under the Tchebycheff decomposition framework. Finally, taking advantage of the current obtained solutions, the new solutions in the decision space are updated via a linear interpolation method. Numerical experiments show that the proposed MOEA/D-RWV can achieve good results for bi-objective and tri-objective optimization problems with discontinuous PF. In addition, the test on a recently proposed MaF benchmark suite demonstrates that MOEA/D-RWV also works for some problems with other complicated characteristics.
当基于分解的多目标进化算法（MOEA/D）用于解决具有不连续帕累托前沿（PF）的问题时，一组均匀分布的权重向量可能会导致许多解聚集在不连续PF的边界处。为克服这一局限性，本文提出了一种用于MOEA/D的权重向量重置（RWV）机制。当触发RWV机制时，使用经典数据聚类算法DBSCAN将当前解分类为几个部分。使用一种称为主成分分析（PCA）的经典统计方法来确定PF各部分中的理想解数量。此后，对PF的每个部分分别再次使用PCA，并通过线性插值方法生成虚拟目标解。然后，根据切比雪夫分解框架下最优解与权重向量之间的相互关系重置新的权重向量。最后，利用当前获得的解，通过线性插值方法更新决策空间中的新解。数值实验表明，所提出的MOEA/D-RWV对于具有不连续PF的双目标和三目标优化问题能够取得良好的结果。此外，在最近提出的MaF基准测试套件上的测试表明，MOEA/D-RWV对于一些具有其他复杂特征的问题也有效。
