Fractional order dung beetle optimizer with reduction factor for global optimization and industrial engineering optimization problems

Abstract

Dung beetle optimizer (DBO) is a novel meta-heuristic algorithm inspired by the behaviors of dung beetles in nature, including ball rolling, dancing, foraging, stealing, and breeding. However, the standard DBO has weaknesses in global optimization, including the imbalance between the ability of exploration and exploitation, low accuracy in function solution, and susceptibility to falling into local optimum. To overcome the weaknesses of DBO, the fractional order dung beetle optimizer with reduction factor (FORDBO) is proposed. Firstly, the good nodes set sequence is employed to replace the randomly initialized population in the algorithm, aiming to enhance the diversity of the population. To enhance the global optimization performance of the algorithm, a reduction factor is designed to balance between the ability of exploration and exploitation. On the other hand, the fractional order calculus strategy is employed to adjust the dynamic boundary of the optimization region. The strategy enables the algorithm to focus on exploiting the potential optimization region. Finally, the repetitive renewal mechanism of the pathfinder dung beetle is proposed to enhance the ability of the algorithm to escape the local optimum. To evaluate the performance of FORDBO, on the one hand, we analyze the complexity of FORDBO and prove its convergence mathematically in this work. On the other hand, this work also compares the FORDBO with 23 similar swarm intelligence technologies through CEC2005, CEC2017, and CEC2022 benchmark functions for global optimization. At the same time, the FORDBO is applied to six industrial engineering optimization problems. The experimental numerical results show that the performance of FORDBO is better than other most swarm intelligence technologies. The source code of FORDBO is publicly available at https://github.com/Huangzhi-Xia/FORDBO.