Sequential transfer optimization (STO), which aims to improve the optimization performance on a task at hand 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 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 variations. The relationships between the optimal solutions of the source and target tasks in these problems are always manually configured, limiting their ability to model different relationships presented in real-world problems. Consequently, the good performance achieved by an algorithm on these problems might be biased and could not be generalized to other problems. In light of the above, in this study, we first introduce four rudimentary concepts for characterizing STO problems (STOPs) 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 propose the general design guidelines and a problem generator with superior scalability. Specifically, the similarity distribution of an STOP 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 STOPs featured by a variety of customized similarity relationships is developed using the proposed generator, which would serve as an arena for STO algorithms and provide more comprehensive evaluation results. The source code of the problem generator is available at https://github.com/XmingHsueh/STOP-G.

翻译：序贯迁移优化旨在通过利用数据库中存储的先前解决的多个优化任务所捕获的知识，来提升当前任务的优化性能，近年来日益受到研究关注。然而，尽管算法设计取得了显著进展，针对序贯迁移优化算法全面比较的系统性基准测试套件的开发却受到较少关注。现有测试问题要么通过简单组合其他基准函数生成，要么从特定实际问题扩展而来且变化有限。这些问题中源任务与目标任务最优解之间的关系始终由人工配置，限制了其模拟现实问题中呈现的不同关系的能力。因此，算法在这些问题上取得的良好性能可能存在偏差，且难以推广至其他问题。鉴于此，本研究首先引入四个用于刻画序贯迁移优化问题的基本概念，并提出一个重要的问题特征——相似性分布，该特征定量描述了源任务与目标任务最优解之间的关系。随后，我们提出了通用设计指南以及一个具有卓越可扩展性的问题生成器。具体而言，序贯迁移优化问题的相似性分布可被轻松定制，从而能够连续谱系化地表征现实问题中多样化的相似性关系。最后，利用所提出的生成器开发了一个包含12个具有各种定制化相似性关系的序贯迁移优化问题的基准测试套件，该套件将作为序贯迁移优化算法的竞技场，并提供更全面的评估结果。问题生成器的源代码可从 https://github.com/XmingHsueh/STOP-G 获取。