Evolutionary Preference Sampling for Pareto Set Learning

TL;DR

PSL learns the entire Pareto set by mapping preference vectors to Pareto-optimal solutions, but fixed preference sampling can fail on complex fronts. The authors introduce Evolutionary Preference Sampling (EPS), an adaptive sampling strategy that treats preference vectors as evolving individuals to accelerate PSL training. EPS is integrated into five PSL baselines and evaluated across seven benchmarks and four real-world problems, yielding faster convergence in most cases, especially for non-conv or disconnected fronts, with limited gains for HV-focused methods. The work advances efficient Pareto-front learning and motivates future extensions to constrained or integer multi-objective problems.

Abstract

Recently, Pareto Set Learning (PSL) has been proposed for learning the entire Pareto set using a neural network. PSL employs preference vectors to scalarize multiple objectives, facilitating the learning of mappings from preference vectors to specific Pareto optimal solutions. Previous PSL methods have shown their effectiveness in solving artificial multi-objective optimization problems (MOPs) with uniform preference vector sampling. The quality of the learned Pareto set is influenced by the sampling strategy of the preference vector, and the sampling of the preference vector needs to be decided based on the Pareto front shape. However, a fixed preference sampling strategy cannot simultaneously adapt the Pareto front of multiple MOPs. To address this limitation, this paper proposes an Evolutionary Preference Sampling (EPS) strategy to efficiently sample preference vectors. Inspired by evolutionary algorithms, we consider preference sampling as an evolutionary process to generate preference vectors for neural network training. We integrate the EPS strategy into five advanced PSL methods. Extensive experiments demonstrate that our proposed method has a faster convergence speed than baseline algorithms on 7 testing problems. Our implementation is available at https://github.com/rG223/EPS.

Figures (9)

• Figure 1: The sampling distribution of preference vector. Left figure: uniform distribution. Right figure: sampling preference vector focuses on the location of the Pareto front (PF).
• Figure 2: The process of Pareto set learning.
• Figure 3: Evolutionary preference vector sampling strategies. For every $T$ iterations, we will collect the preference vectors $\Lambda_{i} (i=1,...N-1)$ during the period (0-th to T-th iterations collect uniformly sampled preference vectors). Afterward, subset selection is executed on these preference vectors to select outstanding individuals. Then, the population $P$, which is composed of these individuals, provides preference vectors for the next period through crossover and mutation.
• Figure 4: The process of preference vector sampling by population. This process includes three parts: crossover, mutation, and repair mechanism.
• Figure 5: Convergence comparison of log HV differences on different baselines and test problems over 11 runs. Different colors indicate different algorithms, the solid line indicates that the original algorithm uses uniform sampling in preference vector sampling, and the dotted line indicates that the original algorithm uses the EPS strategy.