  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.
