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：迁移优化通过利用相关源任务的经验先验，能够实现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，因为在严格的评估预算下需要寻找一组折衷解。本文提出了多目标优化中逆向迁移的新概念。逆向迁移的独特之处在于采用概率逆向模型，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，并通过目标空间统一化促进知识迁移。基于这一思想，我们提出了首个逆向迁移多目标进化优化器（invTrEMO）。invTrEMO的一个关键亮点是其能够利用许多应用领域中普遍存在的公共目标函数，即使任务间的决策空间不完全对齐。这使得invTrEMO能够独特而有效地利用异构源任务的信息。此外，invTrEMO还生成了高精度的逆向模型作为重要副产品，能够基于用户偏好按需生成定制化解。在多个多目标和大规模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相比最先进的进化优化和贝叶斯优化算法具有更快的收敛速度和建模精度。invTrEMO的源代码可在https://github.com/LiuJ-2023/invTrEMO获取。