Journal of Bionic Engineering (2023) 20:2935–2972 https://doi.org/10.1007/s42235-023-00416-z

Wind Driven Butterfy Optimization Algorithm with Hybrid Mechanism Avoiding Natural Enemies for Global Optimization and PID Controller Design 

Yang He1,4 · Yongquan Zhou1,3,4  · Yuanfei Wei3  · Qifang Luo1,4 · Wu Deng

Yongquan Zhou yongquanzhou@126.com * Qifang Luo l.qf@163.com 

1 College of Artifcial Intelligence, Guangxi University for Nationalities, Nanning 530006, China 

2 College of Electronic Information and Automation, Civil Aviation University of China, Tianjin 300300, China 

3 Faculty of Information Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia 

4 Guangxi Key Laboratories of Hybrid Computation and IC Design Analysis, Nanning 530006, China

Abstract: This paper presents a Butterfy Optimization Algorithm (BOA) with a wind-driven mechanism for avoiding natural enemies known as WDBOA. To further balance the basic BOA algorithm's exploration and exploitation capabilities, the butterfy actions were divided into downwind and upwind states. The algorithm of exploration ability was improved with the wind, while the algorithm of exploitation ability was improved against the wind. Also, a mechanism of avoiding natural enemies based on Lévy fight was introduced for the purpose of enhancing its global searching ability. Aiming at improving the explorative performance at the initial stages and later stages, the fragrance generation method was modifed. To evaluate the efectiveness of the suggested algorithm, a comparative study was done with six classical metaheuristic algorithms and three BOA variant optimization techniques on 18 benchmark functions. Further, the performance of the suggested technique in addressing some complicated problems in various dimensions was evaluated using CEC 2017 and CEC 2020. Finally, the WDBOA algorithm is used proportional-integral-derivative (PID) controller parameter optimization. Experimental results demonstrate that the WDBOA based PID controller has better control performance in comparison with other PID controllers tuned by the Genetic Algorithm (GA), Flower Pollination Algorithm (FPA), Cuckoo Search (CS) and BOA. 

Keywords: Butterfy Optimization Algorithm (BOA) · Wind Driven Optimization (WDO) · Benchmark functions · Global optimization · Proportional integral derivative (PID) · Metaheuristic