Serial multilevel-learned differential evolution with adaptive guidance of exploration and exploitation

Recent years have witnessed a surge in the development of multilevel variants of differential evolution (DE), significantly enhancing the performance of DE algorithms. However, systematically guiding algorithms to strike a balance between exploration and exploitation within a parallel multilevel structure remains a challenge. In response to this challenge, we propose serial multilevel-learned differential evolution (SMLDE) with adaptive guidance for exploration and exploitation. This algorithm establishes a tightly connected multilevel-learned structure and an adaptive current best level. It also incorporates a combination of strategies including single iterative adaption, Cauchy perturbation, and iterative constraint strategy into each of the adapted levels, thus enhancing inter-component connections and dynamically balancing exploration and exploitation. To validate its effectiveness, we conduct ablation experiments and visualized analyses of exploration and exploitation to demonstrate the reliable strength of the multilevel-learned structure. The experimental results comparing SMLDE with 15 state-of-the-art algorithms using the IEEE Conference on Evolutionary Computation (CEC) 2017 benchmark test sets across various dimensions showcase its superior performance. Additionally, its remarkable results on the CEC2011 benchmark test and two real-world engineering optimization problems underscore the robustness and effectiveness of SMLDE.