The prior domain knowledge, i.e., the regularity property of continuous multiobjective optimization problems (MOPs), could be learned to guide the search for evolutionary multiobjective optimization. This paper proposes a learning-to-guide strategy (LGS) for assisting the search for multiobjective optimization algorithms in dealing with MOPs. The main idea behind LGS is to capture the regularity via learning techniques to guide the evolutionary search to generate promising offspring solutions. To achieve this, a generative model called the generative topographic mapping (GTM) is adopted to capture the manifold distribution of a population. A set of regular grid points in the latent space are mapped into the decision space within some manifold structures to guide the search for mating with some parents for offspring generation. Following this idea, three alternative LGS-based generation operators are developed and investigated, which combine the local and global information in the offspring generation. To learn the regularity more efficiently in an algorithm, the proposed LGS is embedded in an efficient evolutionary algorithm (called LGSEA). The LGSEA includes an incremental training procedure aimed at reducing the computational cost of GTM training by reusing the built GTM model. The developed algorithm is compared with some newly developed or classical learning-based algorithms on several benchmark problems. The results demonstrate the advantages of LGSEA over other approaches, showcasing its potential for solving complex MOPs.

中文翻译：

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进化多目标搜索的学习规律：基于生成模型的方法


可以学习先验领域知识，即连续多目标优化问题（MOP）的规律性，以指导进化多目标优化的搜索。本文提出了一种学习指导策略（LGS），用于协助搜索处理 MOP 的多目标优化算法。 LGS 背后的主要思想是通过学习技术捕获规律性，以指导进化搜索以生成有希望的后代解决方案。为了实现这一目标，采用称为生成地形图（GTM）的生成模型来捕获种群的流形分布。潜在空间中的一组规则网格点被映射到某些流形结构内的决策空间中，以指导搜索与某些父母的交配以产生后代。遵循这个想法，开发和研究了三种基于 LGS 的替代发电算子，它们结合了后代的本地和全局信息。为了更有效地学习算法中的规律性，所提出的 LGS 被嵌入到高效的进化算法（称为 LGSEA）中。 LGSEA 包括一个增量训练程序，旨在通过重用构建的 GTM 模型来降低 GTM 训练的计算成本。在几个基准问题上，将所开发的算法与一些新开发的或经典的基于学习的算法进行了比较。结果证明了 LGSEA 相对于其他方法的优势，展示了其解决复杂 MOP 的潜力。