MOTEA-II: A Collaborative Multiobjective Transformation-Based Evolutionary Algorithm for Bilevel Optimization

Evolutionary algorithms (EAs) for optimization have received wide attention due to their robustness and practicality. However, the traditional way of asynchronously handling bilevel optimization problems (BLOPs) ignores the benefits brought by effective upper- and lower-level collaboration. To address this issue, this article proposes a collaborative multiobjective transformation (MOT)-based EA (MOTEA-II). In MOTEA-II, the BLOP is handled within a decomposition-based multiobjective optimization paradigm using a two-stage collaborative MOT strategy. The stage-1 MOT focuses on multiple lower-level optimizations and collaboration, while stage-2 collaborates the upper-level optimization with lower-level optimization, which makes simultaneously horizontal and vertical optimization information sharing in bilevel optimization possible. In addition, a dynamic decomposition strategy is further proposed to reconstruct the hierarchy relationship in collaborative multiobjective optimization, facilitating the adaptive and flexible importance control of the upper-level objective optimization and lower-level optimality satisfaction for better-bilevel search efficiency. Empirical studies are conducted on two groups of commonly used BLOP benchmark suites and four practical applications. Experimental results show that the proposed collaborative MOTEA-II can achieve performance comparable to that of the previous MOTEA and three other representative EA-based bilevel optimization approaches, but using much fewer computational resources.