Hierarchical Adaptive Topology Differential Evolution for Multimodal Optimization

Abstract

Multimodal optimization problems (MMOPs) are a class of complex optimization problems that require locating multiple global optima accurately. While evolutionary computation (EC) algorithms are widely used for solving optimization problems, they often struggle to balance exploration and exploitation in solving MMOPs. Most of the existing related studies on EC for MMOPs either directly simulate the collective behavior of specific biological groups or rely on predetermined static interaction structures, while the principles of self-organization and hierarchical topology within groups remain underexplored and insufficiently applied. To address these challenges, we propose a hierarchical adaptive topology differential evolution (HATDE) algorithm, which integrates four key components: (1) a fitness- and diversity-based population division (FDPD) strategy that dynamically partitions individuals into intensive exploitation and extensive exploration subpopulations; (2) a self-organizing layer-based evolution (SLE) strategy that applies distinct evolutionary operators to each subpopulation to effectively generate offspring; (3) an elite learning-based local search (ELLS) strategy for accurate peak optimization; and (4) a nearest-neighbor archiving (NNA) strategy to record explored peaks, effectively guiding the population toward undiscovered regions. Extensive experiments on the CEC2013 MMOP benchmark suite demonstrate that HATDE significantly outperforms 9 state-of-the-art algorithms.