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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在具有不连续帕累托前沿的多目标优化问题中，在MOEA / D中重置权重向量。

当基于分解的多目标进化算法（MOEA / D）被用于解决具有不连续Pareto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决方案在不连续PF的边界中组装。为克服此限制，本文提出了一种重置MOEA / D的权重向量（RWV）的机制。当触发RWV机制时，经典的数据聚类算法DBSCAN用于将当前解决方案分为几部分。一种称为主成分分析（PCA）的经典统计方法用于确定PF各个部分中理想的解决方案数量。此后，将PCA再次分别用于PF的每个部分，并通过线性插值方法生成虚拟目标解决方案。然后，在Tchebycheff分解框架下，根据最优解和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，提出的MOEA / D-RWV算法对于不连续PF的双目标和三目标优化问题均能取得良好的效果。此外，在最近提出的MaF基准套件上进行的测试表明，MOEA / D-RWV也可以解决其他一些复杂特征的问题。决策空间中的新解决方案通过线性插值方法进行更新。数值实验表明，提出的MOEA / D-RWV算法对于不连续PF的双目标和三目标优化问题均能取得良好的效果。此外，在最近提出的MaF基准套件上进行的测试表明，MOEA / D-RWV也可以解决其他一些复杂特征的问题。决策空间中的新解决方案通过线性插值方法进行更新。数值实验表明，提出的MOEA / D-RWV算法对于不连续PF的双目标和三目标优化问题均能取得良好的效果。此外，在最近提出的MaF基准套件上进行的测试表明，MOEA / D-RWV也可以解决其他一些复杂特征的问题。