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