MOTEA-II: A Collaborative Multi-Objective Transformation Based Evolutionary Algorithm for Bi-Level Optimization

Evolutionary algorithms (EAs) for optimization have received wide attention due to their robustness and practicality. However, the traditional way of asynchronously handling bi-level optimization problems (BLOPs) ignores the benefits brought by effective upper-and lower-level collaboration. To address this issue, this paper proposes a collaborative multi-objective transformation (MOT)-based evolutionary algorithm (MOTEA-II). In MOTEA-II, the BLOP is handled within a decomposition-based multi-objective 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 bi-level optimization possible. In addition, a dynamic decomposition strategy is further proposed to reconstruct the hierarchy relationship in collaborative multi-objective optimization, facilitating the adaptive and flexible importance control of the upper-level objective optimization and lower-level optimality satisfaction for better bi-level 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 bi-level optimization approaches, but using much fewer computational resources.