Impact of Approximating Scalarization Functions on High-dimensional
Multiobjective Optimization: A Fast and Scalable Approach
- Masaya Nakata ,
- Yuma Horaguchi ,
- Kei Nishihara
Abstract
The approximation of objective functions is a major strategy in
surrogate-assisted multi-objective evolutionary algorithms, but it tends
to underperform on high-dimensional problems. We hypothesize that this
is because the above strategy is vulnerable to unreliable approximations
and even a single unreliable approximation model may mislead the entire
search process. Therefore, an alternative strategy is to approximate
each scalarization function, whereby candidate solutions for a
decomposed problem can be evaluated using a single approximation model,
which prevents the negative propagation of unreliable approximations to
the entire search process. Accordingly, this study aims to confirm our
hypothesis by introducing a basic surrogate-assisted algorithm, in which
each approximated scalarization function is independently optimized by a
differential evolution algorithm. Despite its methodological simplicity,
the significant impact of approximating scalarization functions on
high-dimensional problems is revealed for the first time. The presented
algorithm is competitive with state-of-the-art algorithms that are
adapted for high-dimensional problems, while exhibiting a reduced
computational time. This computational efficiency is theoretically
confirmed by our complexity analysis.