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 inverse transfer in multiobjective optimization. Inverse transfer stands out by employing probabilistic inverse 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 Multiobjective Evolutionary 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：传递优化通过利用相关源任务的先验经验，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有用，因为该场景需要在有限的评估预算下寻找一组折衷解集。本文提出了多目标优化中反向传递的新概念。反向传递的独特之处在于，它采用概率逆向模型将目标空间中的性能向量映射到任务特定决策空间中的种群搜索分布，从而通过目标空间统一实现知识传递。基于这一思想，我们首次提出了反向传递多目标进化优化器（invTrEMO）。invTrEMO的一个关键亮点在于，即使任务之间的决策空间不完全对齐，它也能利用许多应用领域中普遍存在的共同目标函数。这使得invTrEMO能够独特且有效地利用异构源任务的信息。此外，invTrEMO作为重要副产品生成了高精度逆向模型，能够根据用户偏好按需生成定制化解集。在多目标和超多目标基准问题上的实证研究，以及实际案例研究，展示了invTrEMO相较于最先进的进化算法和贝叶斯优化算法具有更快的收敛速度和建模准确性。invTrEMO的源代码已在https://github.com/LiuJ-2023/invTrEMO 上公开。