# ParetoFlow: Guided Flows in Multi-Objective Optimization Source: [ParetoFlow: Guided Flows in Multi-Objective Optimization]() Collection index: [llms.txt]() Data updated: 2025-10-26T04:09:56.744Z Authors: Ye Yuan, Can Chen, Christopher Pal, Xue Liu Published: 2024-12-04T21:14:18.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Offline Multi-Objective Optimization on RE](): Offline Multi-objective Optimization; RE; Average IGDoffline Rank: 2.92. - [Offline Multi-Objective Optimization on Off-MOO-Bench Sci-Design](): Offline Multi-objective Optimization; Off-MOO-Bench Sci-Design; Average IGDoffline Rank: 3.21. - [Offline Multi-Objective Optimization on Off-MOO-Bench RE](): Offline Multi-objective Optimization; Off-MOO-Bench RE; Average IGDoffline Rank: 5.35. - [Offline Multi-Objective Optimization on Off-MOO-Bench MORL (50th percentile)](): Offline Multi-objective Optimization; Off-MOO-Bench MORL 50th percentile; Average HV Rank: 12.33. - [Offline Multi-Objective Optimization on Off-MOO-Bench MORL](): Offline Multi-objective Optimization; Off-MOO-Bench MORL; Average IGDoffline Rank: 5. - [Offline Multi-Objective Optimization on Synthetic](): Offline Multi-objective Optimization; Synthetic; Average IGDoffline Rank: 8.82. - [Offline Multi-Objective Optimization on Off-MOO-Bench Synthetic](): Offline Multi-objective Optimization; Off-MOO-Bench Synthetic; Average IGDoffline Rank: 8.63. - [Offline Multi-Objective Optimization on Off-MOO-Bench Synthetic (50th percentile)](): Offline Multi-objective Optimization; Off-MOO-Bench Synthetic (50th percentile); Average HV Rank: 9.58. - [Offline Multi-Objective Optimization on Off-MOO-Bench MO-NAS (50th percentile)](): Offline Multi-objective Optimization; Off-MOO-Bench MO-NAS (50th percentile); Average HV Rank: 12.04. - [Offline Multi-Objective Optimization on Off-MOO-Bench Sci-Design (50th percentile)](): Offline Multi-objective Optimization; Off-MOO-Bench Sci-Design (50th percentile); Average HV Rank: 9.88. - [Offline Multi-Objective Optimization on Off-MOO-Bench RE (50th percentile)](): Offline Multi-objective Optimization; Off-MOO-Bench RE (50th percentile); Average HV Rank: 12.21. - [Offline Multi-Objective Optimization on Off-MOO-Bench MO-NAS](): Offline Multi-objective Optimization; Off-MOO-Bench MO-NAS; Average IGDoffline Rank: 9.19. - [Offline Multi-Objective Optimization on Off-MOO-Bench](): Offline Multi-objective Optimization; Off-MOO-Bench; Avg Rank (Overall): 8.15. ## Original sources and implementation [Original paper]() [PDF]()