ParetoFlow: Guided Flows in Multi-Objective Optimization

TL;DR

ParetoFlow tackles offline multi-objective optimization by marrying flow matching with evolutionary priors to approximate the Pareto front ($PF$). It introduces a multi-objective predictor guidance module that uses a uniformly sampled weight vector to form a weighted objective and augments the sampling vector field with gradient information, coupled with a local filtering scheme to handle non-convex PFs. A neighboring evolution module shares knowledge among nearby weight distributions by generating offspring from neighboring flows and selecting the most promising ones, all while maintaining a Pareto set of high-quality samples. Across Off-MOO-Bench tasks, ParetoFlow achieves state-of-the-art hypervolume results and exhibits robust performance under ablations, confirming the effectiveness of both predictor guidance and neighborhood-based sharing for guided flow sampling. The approach enables efficient, scalable design optimization in domains like neural architecture search, molecular design, and engineering applications.

Abstract

In offline multi-objective optimization (MOO), we leverage an offline dataset of designs and their associated labels to simultaneously minimize multiple objectives. This setting more closely mirrors complex real-world problems compared to single-objective optimization. Recent works mainly employ evolutionary algorithms and Bayesian optimization, with limited attention given to the generative modeling capabilities inherent in such data. In this study, we explore generative modeling in offline MOO through flow matching, noted for its effectiveness and efficiency. We introduce ParetoFlow, specifically designed to guide flow sampling to approximate the Pareto front. Traditional predictor (classifier) guidance is inadequate for this purpose because it models only a single objective. In response, we propose a multi-objective predictor guidance module that assigns each sample a weight vector, representing a weighted distribution across multiple objective predictions. A local filtering scheme is introduced to address non-convex Pareto fronts. These weights uniformly cover the entire objective space, effectively directing sample generation towards the Pareto front. Since distributions with similar weights tend to generate similar samples, we introduce a neighboring evolution module to foster knowledge sharing among neighboring distributions. This module generates offspring from these distributions, and selects the most promising one for the next iteration. Our method achieves state-of-the-art performance across various tasks.

Figures (12)

• Figure 1: Motivation of Module 1 in (b) and Module 2 in (c).
• Figure 2: Local filtering: samples outside the hypercone are filtered out as shown in (c).
• Figure 3: Sticks and triangles are rank medians and means.
• Figure 4: Sensitivity to the number of neighbors $K$.
• Figure 5: Sensitivity to the mumber of offspring $O$.