Optimal Transport-Based Distributional Pairing in Transfer Multiobjective Optimization

Jiao Liu, Weiming Liu, Joel Tay Wei En, Caishun Chen, Puay Siew Tan, Yew-Soon Ong

Abstract: As an effective technique in transfer optimization, solution representation alignment aims to transfer high-quality solutions from a source task to a target task by learning mappings between their search spaces. Existing approaches include pairing-based methods, which typically construct explicit source–target pairs by sorting source and target solutions according to their objective function values and then learn mappings to align these pairs, and pairing-free methods, which align distributions or evolutionary trajectories without explicit pairing. In multiobjective optimization, pairing-based strategies face inherent limitations: nondominated solutions lack a well-defined ordering, and even perfectly sorted samples can suffer from chaotic matching, which degrades mapping quality. Pairing-free methods often rely on simplistic assumptions, such as Gaussian population distributions, which fail to capture the complex Pareto set structures. To address these challenges, we propose an optimal transport-based distributional alignment method, termed Optimal Transport Evolutionary Search (OTES). OTES leverages optimal transport theory to align source and target samples in both decision and objective spaces, yielding robust and structurally faithful mappings for transfer multiobjective optimization. Experiments on benchmark and real-world problems show that OTES significantly improves optimization efficiency, accelerating convergence while reducing computational costs. The source code of the proposed RSBench can be found at https://github.com/LiuJ-2023/OTES/tree/main.

External IDs:doi:10.1109/tevc.2025.3624132