Gliding over the Pareto Front with Uniform Designs

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 approximate the entire Pareto front. To address this issue, this paper firstly introduces 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 involved nested min − max − min problem structure. 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 × 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 MOO methods.