Sequential transfer optimization (STO), which aims to improve the optimization performance on a task of interest by exploiting the knowledge captured from several previously-solved optimization tasks stored in a database, has been gaining increasing research attention over the years. However, despite the remarkable advances in algorithm design, the development of a systematic benchmark suite for comprehensive comparisons of STO algorithms received far less attention. Existing test problems are either simply generated by assembling other benchmark functions or extended from specific practical problems with limited scalability. The relationships between the optimal solutions of the source and target tasks in these problems are also often manually configured, limiting their ability to model different similarity relationships presented in real-world problems. Consequently, the good performance achieved by an algorithm on these problems might be biased and hard to be generalized to other problems. In light of the above, in this study, we first introduce four concepts for characterizing STO problems and present an important problem feature, namely similarity distribution, which quantitatively delineates the relationship between the optima of the source and target tasks. Then, we present the general design guidelines of STO problems and a particular STO problem generator with good scalability. Specifically, the similarity distribution of a problem can be easily customized, enabling a continuous spectrum of representation of the diverse similarity relationships of real-world problems. Lastly, a benchmark suite with 12 STO problems featured by a variety of customized similarity relationships is developed using the proposed generator. The source code of the problem generator is available at https://github.com/XmingHsueh/STOP-G.

翻译：序贯迁移优化（Sequential Transfer Optimization, STO）旨在通过利用从数据库中存储的多个先前求解的优化任务中捕获的知识，来提升目标任务上的优化性能，近年来获得了越来越多的研究关注。然而，尽管算法设计取得了显著进展，但为系统比较STO算法而开发的标准化基准测试套件却鲜有研究。现有测试问题要么通过简单组装其他基准函数生成，要么从特定实际问题的有限规模扩展而来。这些问题中源任务与目标任务最优解之间的关联关系也往往通过人工配置，限制了其模拟实际应用中多样化相似关系的能力。因此，算法在这些问题上表现出的良好性能可能存在偏差，难以推广至其他问题。基于上述不足，本研究首先提出描述STO问题的四个概念，并引入一个重要问题特征——相似性分布（similarity distribution），该特征可定量刻画源任务与目标任务最优解之间的关系。随后，我们提出STO问题的通用设计准则，并构建一个具备良好可扩展性的特定STO问题生成器。具体而言，该生成器能够灵活定制问题的相似性分布，从而连续表征实际应用中多样化的相似关系。最后，利用所提出的生成器，我们开发了一个包含12个STO问题的基准测试套件，这些问题具有多样化的定制相似关系。问题生成器的源代码可在 https://github.com/XmingHsueh/STOP-G 获取。