Top-K-Aware Set Optimization for Component-Sharing Multiobjective Optimization

Liang Zhao, Peng Wang, Jiangtao Shen, Luziwei Leng, Zhichao Lu, Qingfu Zhang

Abstract: Component-sharing multiobjective optimization (CSMOO) is an emerging research topic that seeks to identify a set of optimal solutions with shared components in the decision space. This task can be modeled as a bi-level structured multiobjective optimization problem (MOP), where the upper level is a single-objective optimization problem, and the lower level is an MOP parameterized by upper-level variables. However, existing methods often generate an unnecessary large set of solutions when solving each lower-level MOP. This not only complicates decision-making, but also leads to significant resource waste when only a small number of top-K solutions are ultimately required. To mitigate this issue, we adopt a concatenated vector to encode the size-K solution set and introduce a new problem formulation that explicitly incorporates the top-K requirement in CSMOO. To efficiently solve the newly formulated problem, we develop a top-K-aware bi-level search (TopK-BLS) algorithm. It leverages similarities among the top-K-aware lower-level MOPs to solve multiple lower-level tasks in a cooperative manner, thereby improving computational efficiency. The effectiveness of our proposed TopK-BLS is demonstrated through experiments on benchmark and real-world problems. Experimental results indicate that the proposed method can not only generate superior top-K solution sets but also significantly reduce the number of function evaluations compared to other state-of-the-art methods.

External IDs:doi:10.1109/tevc.2026.3678952