An improved TLEA-CMA-ES for Solving Bilevel Optimization Problems

Yutao Lai, Hai-Lin Liu, Fangqing Gu, Jiechang Wen

Abstract: In recent years, bilevel optimization has aroused great interest among researchers. However, due to the lower-level optimization problems’ own high level of complexity, the classical optimization methods of gradient-based algorithms can not solve the bilevel optimization effectively. In another way, despite the fact that the evolutionary algorithm (EA) is a reliable and efficient way to solve bilevel optimization problems. Unfortunately, due to the nested structure, It is necessary to optimize many lower-level optimization processes in parallel, which incurs a high computational cost, while bilevel optimization problems can naturally be employed multi-task learning or transfer learning to accelerate algorithm convergence. However, the positive transfer can accelerate algorithm convergence, while the negative transfer can cause the algorithm’s performance to deteriorate. Hence, we propose two strategies to enhance the positive transfer, including introducing an indicator used to select the most similar tasks to execute knowledge transfer and an adaptive tuning method for adjusting the probability of cross-task knowledge transfer to determine when to transfer. Aiming to confirm the efficacy of our suggested strategy, this paper combines the proposed strategies with a transfer learning-based framework to form a new algorithm called ITLEA-CMA-ES. Compared with four well-established algorithms on two sets of extensively used benchmark problems, The effectiveness and reliability of ITLEA-CMA-ES have been confirmed b y t he experimental results.