Liu Songbai, Lin Qiuzhen, Tan Kay Chen, Gong Maoguo, Coello Coello Carlos A
IEEE Trans Cybern. 2022 May;52(5):3495-3509. doi: 10.1109/TCYB.2020.3008697. Epub 2022 May 19.
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 least similar solutions are extracted as weight vectors to obtain N constrained fuzzy subproblems ( 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 least similar subproblems ( 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.
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）形状的显著影响，因为它们采用的权重向量可能无法很好地拟合PF形状。为避免这种不匹配，一些MOEA将解视为权重向量来指导进化搜索，从而能够自动适应目标MOP的PF。然而，它们的性能仍受用于选择权重向量的相似性度量的影响。为解决此问题，本文提出一种基于模糊分解的MOEA。首先，设计一个模糊预测来估计种群的形状，这有助于准确反映解的相似性。然后，提取N个最不相似的解作为权重向量以获得N个约束模糊子问题（N为种群规模），并据此为所有子问题计算一个共享权重向量以提供稳定的搜索方向。最后，保留m个最不相似子问题（m为目标数量）中每个子问题的角点解以保持多样性，而对于其余子问题，为每个子问题选择在共享权重向量上具有最佳聚合值的一个解以加速收敛。在解决各种测试MOP时，与几种有竞争力的MOEA相比，所提算法在拟合其不同PF形状方面显示出一些优势。
