Transfer optimization enables data-efficient optimization of a target task by leveraging experiential priors from related source tasks. This is especially useful in multiobjective optimization settings where a set of trade-off solutions is sought under tight evaluation budgets. In this paper, we introduce a novel concept of \textit{inverse transfer} in multiobjective optimization. Inverse transfer stands out by employing Bayesian inverse Gaussian process models to map performance vectors in the objective space to population search distributions in task-specific decision space, facilitating knowledge transfer through objective space unification. Building upon this idea, we introduce the first Inverse Transfer Evolutionary Multiobjective Optimizer (invTrEMO). A key highlight of invTrEMO is its ability to harness the common objective functions prevalent in many application areas, even when decision spaces do not precisely align between tasks. This allows invTrEMO to uniquely and effectively utilize information from heterogeneous source tasks as well. Furthermore, invTrEMO yields high-precision inverse models as a significant byproduct, enabling the generation of tailored solutions on-demand based on user preferences. Empirical studies on multi- and many-objective benchmark problems, as well as a practical case study, showcase the faster convergence rate and modelling accuracy of the invTrEMO relative to state-of-the-art evolutionary and Bayesian optimization algorithms. The source code of the invTrEMO is made available at https://github.com/LiuJ-2023/invTrEMO.

翻译：迁移优化通过利用相关源任务的经验先验，能够在有限评估预算下实现对目标任务的数据高效优化。这在多目标优化场景中尤为重要，因为此类场景需要在严格评估预算下寻求一组折衷解。本文提出多目标优化中一种新颖的“逆向迁移”概念。该方法的创新之处在于采用贝叶斯逆高斯过程模型，将目标空间中的性能向量映射至任务特定决策空间中的种群搜索分布，通过目标空间统一化实现知识迁移。基于此思想，我们提出了首个逆向迁移进化多目标优化器（invTrEMO）。invTrEMO的核心优势在于能够利用许多应用领域中普遍存在的共同目标函数，即使在任务间决策空间不完全对齐的情况下，也能独特而有效地利用异构源任务的信息。此外，invTrEMO产生的高精度逆模型作为重要副产物，可根据用户偏好按需生成定制化解。在多目标与超多目标基准问题上的实证研究及实际案例表明，相较于最先进的进化算法与贝叶斯优化算法，invTrEMO具有更快的收敛速度与更高的建模精度。invTrEMO源代码已发布于 https://github.com/LiuJ-2023/invTrEMO。