@inproceedings{
zhang2024gliding,
title={Gliding over the Pareto Front with Uniform Designs},
author={Xiaoyuan Zhang and Genghui Li and Xi Lin and Yichi Zhang and Yifan Chen and Qingfu Zhang},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=WoEXVQcHFw}
}
Multiobjective optimization (MOO) plays a critical role in various real-world domains. A major challenge therein is generating $K$ uniform Pareto-optimal solutions that represent the entire Pareto front. To address the very challenge, this study first introduces \emph{fill distance} to evaluate the $K$ design points, which provides a quantitative metric for the representativeness of the design. However, the direct specification of the optimal design that minimizes fill distance is almost intractable considering the nested $\min-\max-\min$ optimization problem. We further propose a surrogate to the fill distance, which is easier to optimize and induce a rate-optimal design whose fill distance proves at most $4\times$ the minimum one. Rigorous derivation also shows that asymptotically this induced design will converge to the uniform measure over the Pareto front. Extensive experiments on synthetic and real-world benchmarks demonstrate that our proposed paradigm efficiently produces high-quality, representative solutions and outperforms baseline methods.
Gliding over the Pareto Front with Uniform Designs
Xiaoyuan Zhang Genghui Li Xi Lin Yichi Zhang Yifan Chen Qingfu Zhang