Sequential transfer optimization (STO), which aims to improve optimization performance by exploiting knowledge captured from previously-solved optimization tasks stored in a database, has been gaining increasing research attention in recent years. However, despite significant advancements in algorithm design, the test problems in STO are not well designed. Oftentimes, they are either randomly assembled by other benchmark functions that have identical optima or are generated from practical problems that exhibit limited variations. The relationships between the optimal solutions of source and target tasks in these problems are manually configured and thus monotonous, limiting their ability to represent the diverse relationships of real-world problems. Consequently, the promising results achieved by many algorithms on these problems are highly biased and difficult to be generalized to other problems. In light of this, we first introduce a few rudimentary concepts for characterizing STO problems (STOPs) and present an important problem feature overlooked in previous studies, namely similarity distribution, which quantitatively delineates the relationship between the optima of source and target tasks. Then, we propose general design guidelines and a problem generator with superior extendibility. Specifically, the similarity distribution of a problem can be systematically customized by modifying a parameterized density function, enabling a broad spectrum of representation for the diverse similarity relationships of real-world problems. Lastly, a benchmark suite with 12 individual STOPs is developed using the proposed generator, which can serve as an arena for comparing different STO algorithms. The source code of the benchmark suite is available at https://github.com/XmingHsueh/STOP.

翻译：连续迁移优化（Sequential Transfer Optimization, STO）旨在通过利用从先前解决的优化任务中捕获并存储在数据库中的知识来提升优化性能。近年来，这一领域的研究关注度日益增长。然而，尽管算法设计取得了显著进展，STO中的测试问题设计仍不完善。这类问题往往要么由具有相同最优值的其他基准函数随机组合而成，要么来源于实际但变化有限的工程问题。这些测试问题中源任务与目标任务最优解之间的关系被人为设定且单调，限制了其表征真实世界问题中多样化关系的能力。因此，许多算法在这些问题上取得的优异结果存在严重偏差，难以推广至其他问题。针对此，我们首先引入描述STO问题（STOPs）的若干基础概念，并揭示先前研究中被忽视的重要问题特征——相似度分布，该特征定量刻画了源任务与目标任务最优解之间的关系。继而提出通用设计准则与一个具有优越可扩展性的问题生成器。具体而言，通过修改参数化密度函数可系统定制问题的相似度分布，从而实现对真实世界问题多样化相似关系的广泛表征。最后，利用所提出的生成器构建了一个包含12个独立STOPs的基准测试套件，可作为不同STO算法比较的竞技场。该基准测试套件的源代码已开源至 https://github.com/XmingHsueh/STOP。