Multi-objective (MO) optimization, i.e., the simultaneous optimization of multiple conflicting objectives, is gaining more and more attention in various research areas, such as evolutionary computation, machine learning (e.g., (hyper-)parameter optimization), or logistics (e.g., vehicle routing). Many works in this domain mention the structural problem property of multimodality as a challenge from two classical perspectives: (1) finding all globally optimal solution sets, and (2) avoiding to get trapped in local optima. Interestingly, these streams seem to transfer many traditional concepts of single-objective (SO) optimization into claims, assumptions, or even terminology regarding the MO domain, but mostly neglect the understanding of the structural properties as well as the algorithmic search behavior on a problem’s landscape. However, some recent works counteract this trend, by investigating the fundamentals and characteristics of MO problems using new visualization techniques and gaining surprising insights.

Using these visual insights, this work proposes a step towards a unified terminology to capture multimodality and locality in a broader way than it is usually done. This enables us to investigate current research activities in multimodal continuous MO optimization and to highlight new implications and promising research directions for the design of benchmark suites, the discovery of MO landscape features, the development of new MO (or even SO) optimization algorithms, and performance indicators. For all these topics, we provide a review of ideas and methods but also an outlook on future challenges, research potential and perspectives that result from recent developments.

多目标（MO）优化，即多个冲突目标的同时优化，在进化计算、机器学习（例如（超）参数优化）或物流（例如，车辆路线）。该领域的许多作品都提到了多模态的结构问题属性作为从两个经典角度来看的挑战：（1）找到所有全局最优解集，以及（2）避免陷入局部最优。有趣的是，这些流似乎将许多传统的单目标 (SO) 优化概念转移到关于 MO 领域的声明、假设甚至术语中，但大多忽略了对结构属性的理解以及对问题的算法搜索行为景观。然而，最近的一些工作通过使用新的可视化技术研究 MO 问题的基本原理和特征并获得令人惊讶的见解来抵消这一趋势。

使用这些视觉洞察力，这项工作提出了朝着统一术语迈出的一步，以比通常更广泛的方式捕捉多模态和局部性。这使我们能够调查当前多模态连续 MO 优化的研究活动，并强调基准套件设计、MO 景观特征的发现、新 MO（甚至 SO）优化算法的开发的新含义和有前景的研究方向，以及性能指标。对于所有这些主题，我们提供了对想法和方法的回顾，以及对未来挑战、研究潜力和近期发展带来的前景的展望。