Performance of multi/many-objective evolutionary algorithms (MOEAs) based on decomposition is highly impacted by the Pareto front (PF) shapes of multi/many-objective optimization problems (MOPs), as their adopted weight vectors may not properly fit the PF shapes. To avoid this mismatch, some MOEAs treat solutions as weight vectors to guide the evolutionary search, which can adapt to the target MOP’s PF automatically. However, their performance is still affected by the similarity metric used to select weight vectors. To address this issue, this article proposes a fuzzy decomposition-based MOEA. First, a fuzzy prediction is designed to estimate the population’s shape, which helps to exactly reflect the similarities of solutions. Then, N{N} least similar solutions are extracted as weight vectors to obtain N{N} constrained fuzzy subproblems ( N{N} is the population size), and accordingly, a shared weight vector is calculated for all subproblems to provide a stable search direction. Finally, the corner solution for each of m{m} least similar subproblems ( m{m} is the objective number) is preserved to maintain diversity, while one solution having the best aggregated value on the shared weight vector is selected for each of the remaining subproblems to speed up convergence. When compared to several competitive MOEAs in solving a variety of test MOPs, the proposed algorithm shows some advantages at fitting their different PF shapes.

中文翻译：

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一种基于模糊分解的多目标/多目标进化算法


基于分解的多目标进化算法（MOEA）的性能受到多目标优化问题（MOP）的帕累托前沿（PF）形状的高度影响，因为它们采用的权重向量可能无法正确拟合PF形状。为了避免这种不匹配，一些 MOEA 将解决方案视为权重向量来指导进化搜索，从而可以自动适应目标 MOP 的 PF。然而，它们的性能仍然受到用于选择权重向量的相似性度量的影响。为了解决这个问题，本文提出了一种基于模糊分解的 MOEA。首先，设计模糊预测来估计总体形状，这有助于准确反映解的相似性。然后，提取N{N}个最不相似的解作为权向量，得到N{N}个约束模糊子问题（N{N}为种群大小），并相应地为所有子问题计算一个共享的权向量，以提供稳定的模糊子问题。搜索方向。最后，保留 m{m} 个最不相似子问题（m{m} 是目标数）中每一个的角点解以保持多样性，同时为每个子问题选择一个在共享权重向量上具有最佳聚合值的解。剩余的子问题以加速收敛。与解决各种测试 MOP 时的几种竞争性 MOEA 相比，所提出的算法在拟合不同 PF 形状方面显示出一些优势。