针对离线多目标优化中解集多样性差的问题,提出新方法提升解的质量与分布均匀性。
Diversity-Driven Offline Multi-Objective Optimization via Nested Pareto Set Learning

- 通过累积风险控制缓解训练数据与生成解间的分布外问题
- 设计嵌套帕累托集学习策略,适应不同形状的帕累托前沿
- 引入专用指标IGD_offline,兼顾收敛性与多样性,避免超体积指标偏差
多目标优化(MOO)在处理多目标复杂问题中表现出强大能力。但在实际场景中,函数评估可能不可用或成本过高,需仅基于固定离线数据集进行优化,即离线MOO。其目标是在无法访问真实目标函数的情况下,找到帕累托集。该设置面临分布外(OOD)问题,代理模型对未见设计不准确,导致优化器选择不在真实帕累托前沿上的解,并偏向极端解。为此,本文提出多样性驱动的离线多目标优化(DOMOO),旨在寻找高质量且多样化的解集。首先,引入累积风险控制模块,估计候选解的风险,缓解训练数据与生成解间的OOD问题。其次,提出嵌套帕累托集学习(PSL)策略,联合学习偏好与PSL参数并优化,以适应多样化的帕累托前沿几何结构。为进一步提升解质量,设计了多样性驱动的选择策略,提取具有代表性且分布均匀的最终解集。为此,提出$ ext{IGD}_ ext{offline}$,一种专为离线设置设计的指标,同时考虑多样性与收敛性,避免超体积指标的偏差。在合成与真实世界基准上的大量实验表明,DOMOO在收敛性和多样性上均优于对比方法,平均排名最佳。
原文摘要 · Abstract (English)
Multi-objective optimization (MOO) has emerged as a powerful approach to solving complex optimization problems involving multiple objectives. In many practical scenarios, function evaluations are unavailable or prohibitively expensive, necessitating optimization solely based on a fixed offline dataset. In this setting, known as offline MOO, the goal is to find out the Pareto set without access to the true objective functions. This setting suffers from the out-of-distribution (OOD) issue, where the surrogate model is not accurate for unseen designs. Due to the OOD issue, surrogate errors may cause the optimizer to select solutions that do not lie on the true Pareto front and are biased toward its extremes. To address this, this paper proposes Diversity-driven Offline Multi-Objective Optimization (DOMOO), which aims to find out a diverse and high-quality set of solutions. First, DOMOO incorporates an accumulative risk control module that estimates the potential risk of candidate solutions and alleviates the OOD issue between the training data and the generated solutions. In addition, a nested Pareto set learning (PSL) strategy is proposed to jointly learn preference and PSL parameters, then optimize them, enabling adaptation to diverse Pareto front geometries. To further enhance solution quality, we design a diversity-driven selection strategy that extracts a representative and well-distributed set of final solutions. To achieve this diversity-driven selection strategy, we propose $\text{IGD}_\text{offline}$, a tailored indicator for the offline setting that considers both diversity and convergence, and avoids the bias of hypervolume indicator. Extensive experiments on synthetic and real-world benchmarks show that DOMOO achieves the best average rank across tasks in both convergence and diversity among the compared methods.
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