We continue recent work on the definition of multimodality in multiobjective optimization (MO) and the introduction of a test bed for multimodal MO problems. This goes beyond well-known diversity maintenance approaches but instead focuses on the landscape topology induced by the objective functions. More general multimodal MO problems are considered by allowing ellipsoid contours for single-objective subproblems. An experimental analysis compares two MO algorithms, one that explicitly relies on hypervolume gradient approximation, and one that is based on local search, both on a selection of generated example problems. We do not focus on performance but on the interaction induced by the problems and algorithms, which can be described by means of specific characteristics explicitly designed for the multimodal MO setting. Furthermore, we widen the scope of our analysis by additionally applying visualization techniques in the decision space. This strengthens and extends the foundations for Exploratory Landscape Analysis (ELA) in MO.

中文翻译：

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多模态多目标问题的搜索动力学

我们继续最近关于多目标优化 (MO) 中多模态定义的工作，并引入了多模态 MO 问题的测试平台。这超出了众所周知的多样性维护方法，而是侧重于由目标函数引起的景观拓扑。通过允许单目标子问题的椭球轮廓来考虑更一般的多模态 MO 问题。一项实验分析比较了两种 MO 算法，一种明确依赖于超体积梯度近似，另一种基于局部搜索，两者都基于生成的示例问题的选择。我们不关注性能，而是关注由问题和算法引起的交互，这可以通过为多模态 MO 设置明确设计的特定特征来描述。此外，我们通过在决策空间中额外应用可视化技术来扩大我们的分析范围。这加强并扩展了 MO 中探索性景观分析 (ELA) 的基础。