  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.
