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Impact of Approximating Scalarization Functions on High-dimensional Multiobjective Optimization: A Fast and Scalable Approach
  • Masaya Nakata ,
  • Yuma Horaguchi ,
  • Kei Nishihara
Masaya Nakata
Yokohama National University, Yokohama National University, Yokohama National University

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Yuma Horaguchi
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Kei Nishihara
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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.