Optimal performance design of bat algorithm: An adaptive multi-stage structure

The bat algorithm (BA) is a metaheuristic algorithm for global optimisation that simulates the echolocation behaviour of bats with varying pulse rates of emission and loudness, which can be used to find the globally optimal solutions for various optimisation problems. Knowing the recent criticises of the originality of equations, the principle of BA is concise and easy to implement, and its mathematical structure can be seen as a hybrid particle swarm with simulated annealing. In this research, the authors focus on the performance optimisation of BA as a solver rather than discussing its originality issues. In terms of operation effect, BA has an acceptable convergence speed. However, due to the low proportion of time used to explore the search space, it is easy to converge prematurely and fall into the local optima. The authors propose an adaptive multi-stage bat algorithm (AMSBA). By tuning the algorithm's focus at three different stages of the search process, AMSBA can achieve a better balance between exploration and exploitation and improve its exploration ability by enhancing its performance in escaping local optima as well as maintaining a certain convergence speed. Therefore, AMSBA can achieve solutions with better quality. A convergence analysis was conducted to demonstrate the global convergence of AMSBA. The authors also perform simulation experiments on 30 benchmark functions from IEEE CEC 2017 as the objective functions and compare AMSBA with some original and improved swarm-based algorithms. The results verify the effectiveness and superiority of AMSBA. AMSBA is also compared with eight representative optimisation algorithms on 10 benchmark functions derived from IEEE CEC 2020, while this experiment is carried out on five different dimensions of the objective functions respectively. A balance and diversity analysis was performed on AMSBA to demonstrate its improvement over the original BA in terms of balance. AMSBA was also applied to the multi-threshold image segmentation of Citrus Macular disease, which is a bacterial infection that causes lesions on citrus trees. The segmentation results were analysed by comparing each comparative algorithm's peak signal-to-noise ratio, structural similarity index and feature similarity index. The results show that the proposed BA-based algorithm has apparent advantages, and it can effectively segment the disease spots from citrus leaves when the segmentation threshold is at a low level. Based on a comprehensive study, the authors think the proposed optimiser has mitigated the main drawbacks of the BA, and it can be utilised as an effective optimisation tool.