Gliding over the Pareto Front with Uniform Designs

Part of Advances in Neural Information Processing Systems 37 (NeurIPS 2024) Main Conference Track

Authors

Xiaoyuan Zhang, Genghui Li, Xi Lin, Yichi Zhang, Yifan Chen, Qingfu Zhang

Abstract

Multiobjective optimization (MOO) plays a critical role in various real-world domains. A major challenge therein is generating $K$ uniform Pareto-optimal solutions to represent the entire Pareto front. To address this issue, this paper firstly introduces \emph{fill distance} to evaluate the $K$ design points, which provides a quantitative metric for the representativeness of the design. However, directly specifying the optimal design that minimizes the fill distance is nearly intractable due to the nested $\min-\max-\min$ optimization problem. To address this, we propose a surrogate max-packing'' design for the fill distance design, which is easier to optimize and leads to a rate-optimal design with a fill distance at most $4\times$ the minimum value. Extensive experiments on synthetic and real-world benchmarks demonstrate that our proposed paradigm efficiently produces high-quality, representative solutions and outperforms baseline methods.