A Scalable Test Problem Generator for Sequential Transfer Optimization

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.