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.

中文翻译：

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重置 MOEA/D 中的权重向量以解决具有不连续帕累托前沿的多目标优化问题


当基于分解的多目标进化算法（MOEA/D）应用于解决不连续帕累托前沿（PF）问题时，一组均匀分布的权向量可能会导致许多解聚集在不连续PF的边界上。为了克服这个限制，本文提出了一种为 MOEA/D 重置权重向量（RWV）的机制。当RWV机制被触发时，使用经典的数据聚类算法DBSCAN将当前的解决方案分为几个部分。一种称为主成分分析 (PCA) 的经典统计方法用于确定 PF 各部分的理想解数。此后，再次对PF的各个部分分别使用PCA，并通过线性插值方法生成虚拟目标解。然后，在Tchebycheff分解框架下根据最优解与权向量之间的相互关系重新设置新的权向量。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，对最近提出的 MaF 基准套件的测试表明，MOEA/D-RWV 也适用于具有其他复杂特征的一些问题。